Medical Informatics Group

Morphological Quantification of the Human Cerebral Cortex from MRI using

Deformable Surfaces

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MEDICAL INFORMATICS GROUPDEPARTMENT OF HEALTH SCIENCE AND TECHNOLOGY

AALBORG UNIVERSITY2008

SIMON FRISTED ESKILDSEN

Medical Informatics Group

THE MEDICAL INFORMATICS GROUP IS PART OF THE DEPARTMENT OF HEALTH SCIENCE AND TECHNOLOGY AT AALBORG UNIVERSITY.ITS MAIN RESEARCH AREA, INITIATED AT AALBORG UNIVERSITY IN 1978, IS INFORMATION SYSTEMS USED FOR RECORDING, ANALYZING, REPRE-SENTING AND INTERPRETING CLINICAL INFORMATION. THE AIM OF THE MEDICAL INFORMATICS GROUP IS TO FURTHER DEVELOP METHODOLOGIES AND SYSTEMS WITHIN THREE MAIN AREAS:• METABOLIC MODELING

• IMAGE ANALYSIS

• INFORMATION SYSTEMS

• TELEHEALTH

WITH A CLEAR EMPHASIS ON CLINICAL APPLICABILITY FOR THE BENEFIT OF PATIENTS IN THE HEALTH CARE SYSTEM.

MIMedical Informatics Group

Department of Health Science and TechnologyAalborg University

Fredrik Bajers Vej 7DDK-9220 Aalborg

Denmark

Telephone: +45 9940 8080Telefax: +45 9815 4008

URL: www.mi.hst.aau.dke-mail: contact@hst.aau.dk

ISBN: 978-87-7094-010-8

71914_PhD_Simon_Fristed.indd 1 13/02/09 13:19:33

AUTHOR

Simon FriSted eSkildSen waS born in ÅrhuS, denmark. he received hiS m.Sc. in electrical engineering with Specialization in medical inFormaticS From aalborg univerSity in the Summer oF 2003. From 2003 to 2005 he waS employed aS a reSearch aSSiStant at the department oF health Science and technology. in 2005 he Started hiS ph.d. Study which waS deFended in november 2008 at aalborg univerSity. Since 2008 he haS been emplo-yed aS an aSSiStant proFeSSor at the department oF health Science and technology.

iSbn: 978-87-7094-010-8

71914_PhD_Simon_Fristed.indd 2 13/02/09 13:19:33

Morphologi al Quanti� ation of the Human CerebralCortex from MRI using Deformable Surfa es

PhD thesis bySimon Fristed Eskildsen

Medi al Informati s GroupDepartment of Health S ien e and Te hnologyAalborg University· 2008 ·

This thesis was �nished July 2008 and was su essfully defended November 26th 2008 atAalborg University. The evaluation ommittee onsisted of the following members:Professor, MD, DMS , Elna-Marie LarssonDepartment of Radiology, Aalborg SygehusÅrhus University, DenmarkAsso iate Professor, PhD, Louis CollinsMontreal Neurologi al InstituteM Gill University, CanadaAsso iate Professor, PhD, Stig Kjær Andersen (Chairman)Department of Health S ien e and Te hnologyAalborg University, Denmark

The over image is a rendering of surfa es extra ted from a T1 weighted magneti reso-nan e s an using the methods dis losed in the thesis.ISBN: 978-87-7094-011-5

Abstra tThis Ph.D. thesis investigates morphologi al quanti� ation of the human erebral or-tex from magneti resonan e images (MRI). Morphologi al quanti� ation of the erebral ortex is important for understanding the manifestation and progression of neurodegenera-tive diseases su h as Alzheimer's disease and su h quanti� ation are onsidered importantdisease markers and may aid in early diagnosis. The �rst part of the thesis deals withre onstru tion of the ortex from T1 weighted MRI. The se ond part is on erned withusing the orti al morphologi al measurements from the re onstru tions to ompare dif-ferent orti es, and applying the quanti� ation methods in a study of a neurodegenerativedisease. The thesis is based on �ve papers; three papers overing the �rst part and twopapers on the se ond part.In paper I, the method for re onstru ting the orti al boundaries as parametri sur-fa es is presented. The entire pro ess from s anner images to orti al thi kness results isdes ribed and test of the method on simulated MRI data, several young healthy individ-uals and a single Alzheimer's patient s anned with an interval of six months is presented.The paper presents a novel ombination of a pressure for e with a gradient ve tor �ow ina deformable surfa e model for modeling the outer orti al boundary.In paper II, an improved surfa e deformation pro ess is presented. The energy fun -tional des ribed in the �rst paper is altered to express ve tor for es, and a lo al weightingof for es is introdu ed to better adapt to the highly folded orti al sheet. Test of themethod on simulated MRI is reported and it is shown to be more a urate than ap-proa hes without the lo al weighting strategy. The main ontribution of the paper is adeformation approa h free of sear h spa es and a novel urvature in�uen ed weighting ofthe terms in the energy fun tional.Paper III des ribes the omparison of the developed method with the ortex extra tionmethod used the most in the literature. The omparison is based on phantom MRI images onstru ted from orti al surfa es extra ted from real MRI images. In this way, groundtruth orti al boundaries are reated and the geometri al error of the ortex re onstru -tions an be quanti�ed. The paper reports that the developed method is re onstru ting the orti al surfa es with a subvoxel a ura y and that it performs better than the ompetingmethod in most of the tests while being mu h faster.In paper IV, the problem of omparing di�erent orti es is addressed. A proposed fea-ture driven orti al mapping algorithm is presented together with tests of it and four othermapping algorithms: a feature driven approa h, two spheri al mapping approa hes, anda basi iterative losest point algorithm. The algorithms are evaluated with onstru ted riteria for a good mapping, a landmark test using manually pla ed landmarks and ananalysis of statisti al maps generated by the results of the algorithms. It is demonstratedthat ea h method has its strengths and weaknesses and no single method performs betteron all riteria and for all purposes. However, it is indi ated that a ombination of someof the evaluated algorithms ould be a promising approa h.Paper V reports the results of applying the developed methods to identify orti alstru tural hanges in individuals with a familial variant of frontotemporal dementia. Ninepresymptomati individuals arrying the disease mutation are ompared to seven individ-uals from the same family without the mutation. The study is based on two serial MRIiii

s ans of ea h individual and annualized atrophy rates are al ulated. Both volumetri and thi kness measurements show that the presymptomati mutation arriers degeneratefaster than the healthy ontrols. The thi kness measurements have a higher sensitivitythan the volumetri measurements and they are able to dete t the fo al di�eren es be-tween the two groups. Furthermore, the involved orti al areas are linked to symptomsobserved in lini al frontotemporal dementia patients and support the pathogeni ity ofthe mutation.The work presented in the thesis demonstrate that it is possible to dete t subtle mor-phologi al hanges in the human erebral ortex with MRI, and suggest that the goal ofusing morphologi al disease markers in improving diagnosis of neurodegenerative diseasesis attainable.

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Dansk Resumé (Danish Abstra t)Denne Ph.D. afhandling omhandler morfologisk kvanti� ering af den menneskelige hjerne-bark fra magnetisk resonans skanning (MRS). Morfologisk kvanti� ering af hjernebarkener vigtig for forståelsen af hvordan neurodegenerative sygdomme som Alzheimers syg-dom manifesterer sig og udbredes i hjernen. Det vurderes at sådan kvanti� ering kanidenti� ere sygdomsmarkører og kan bidrage til tidligere diagnose af neurodegenerativesygdomme. Første del af afhandlingen omhandler rekonstruktion af hjernebarken fra T1vægtet MRS. Anden del fokuserer på at anvende rekonstruktionerne af hjernebarken tilat kvanti� ere morfologien og sammenligne forskellige hjernebarker, og kvanti� eringsme-toderne anvendes i et studie af en neurodegenerativ sygdom. Afhandlingen er baseret påfem artikler; tre artikler dækker første del og to omhandler anden del.I artikel I præsenteres metoden til rekonstruktion af hjernebarkens vævsgrænser somparametriske over�ader. Hele pro essen fra skannerbilleder til måling af hjernebarkenstykkelse er beskrevet og metoden testes på simuleret MRS data, unge raske individer ogen enkelt Alzheimers patient skannet med seks måneders mellemrum. Artiklen præsentereren tryk kraft kombineret med en gradient vektor kraft i en deformérbar over�ademodel tilmodellering af hjernebarkens ydre vævsgrænse.I artikel II præsenteres en forbedret deformeringspro es. Energifunktionen beskreveti artikel I er forandret så der udtrykkes vektorkræfter, og en lokal vægtning af kræfterneintrodu eres for bedre tilpasning til hjernebarkens meget foldede struktur. Metoden testespå simulerede MRS og det vises at den er mere nøjagtig end metoder uden lokal vægtningaf kræfterne. Hoved-bidraget i artiklen er en deformeringsmetode uden søgerum og enunik vægtning af termerne i energifunktionen baseret på over�adens krumning.I artikel III sammenlignes den udviklede metode med den i litteraturen mest benyttederekonstruktionsmetode. Sammenligningen er baseret på fantom MRS billeder konstrueretfra over�ader af hjernebarken udtrukket fra rigtige skanninger. På denne måde genereresder data hvor den sande hjernebark er kendt og geometriske fejl i rekonstruktionerne kanmåles. Artiklen viser at den udviklede metode har en nøjagtighed bedre end opløsningenaf billederne, og at metoden er mere nøjagtig og hurtigere end den konkurrerende metode.Artikel IV tager sig af problemet med at sammenligne forskellige hjernebarker. Enmetode til at referere mellem hjernebarker, som er baseret på sammenligning af ge-ometriske features, præsenteres og testes sammen med �re andre referen emetoder; enanden feature baseret algoritme, to algoritmer der refererer til en kugle, og en simple it-erativ nærmeste punkt algoritme. Algoritmerne evalueres med opstillede kriterier for engod referen e, en test med manuelt pla erede �kspunkter, samt en analyse af statistiskeover�adekort genereret på baggrund af algoritmernes resultater. Det demonstreres at hvermetode har sine styrker og svagheder, og at en enkelt metode ikke kan foretrækkes fremfor en anden til alle formål på baggrund af de opstillede kriterier. Det antydes at enkombination af nogle af metoderne synes at være en lovende løsning på problemet.Artikel V rapporterer resultaterne af at anvende de udviklede kvanti� eringsmetodertil at identi� ere strukturelle forandringer i hjernebarken i individer fra en familie meden nedarvet variant af frontotemporal demens. Ni præsymptomatiske bærere af sygdoms-genet er sammenlignet med syv individer uden sygdommen fra samme familie. Studiet erbaseret på to serielle skanninger af hvert individ, og atro�rater kan dermed beregnes. Bådev

volumetriske målinger og målinger af hjernebarkens tykkelse viser at de præsymptomatiskesygdomsbærere degenererer hurtigere end de raske kontrolpersoner. Tykkelsesmålingernehar en højere sensitivitet end de volumetriske målinger, og disse muliggør detektering affokale forskelle de to grupper imellem. De involverede områder i hjernebarken kan henførestil symptomer observeret i kliniske patienter med frontotemporal demens og understøtterdermed patogeni iteten af sygdomsmutationen.Forskningen præsenteret i denne afhandling demonstrerer at det er muligt at detek-tere små morfologiske forandringer i den menneskelige hjernebark fra strukturel MRS, ogsandsynliggør at morfologiske sygdomsmarkører kan benyttes til at forbedre diagnosen afneurodegenerative sygdomme.

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A knowledgmentsI wish to express my gratitude to the following institutions and foundations whi h have�nan ially supported the Ph.D. study:• Novi Innovation A/S• Center for Fun tional and Integrative Neuros ien e, Aarhus University• HEALTHnTECH Resear h Center• Virtual Centre for Health Informati s• Spar Nord Fonden• Det Obelske Familiefond• Otto Mønsteds Fond• The International Do toral S hool of Te hnology and S ien e, Aalborg UniversityDuring my study I had the pleasure of visiting The M Connell Brain Imaging Centre(BIC), Montréal Neurologi al Institute, M Gill University. I am grateful to Professor AlanC. Evans for the invitation, and to the inspiring and helpful people at the BIC. Also, I amgrateful to the BIC for putting data from the International Consortium of Brain Mappingat my disposal during the Ph.D. study.I wish to thank Dr. Peter Johannsen for ollaboration and involving me in the FTD-3 study. Also thanks to Anders B. Rodell and Center for Fun tional and IntegrativeNeuros ien e, Aarhus University for ollaboration and good onstru tive dis ussions andadvi e. Thanks to Andrew Janke and Centre for Magneti Resonan e, The University ofQueensland, Australia for providing hallenging MRI data. Also thanks to the people atthe radiologi al department at Aalborg Hospital for ollaboration and o-supervision ofstudents.Spe ial thanks to Mark Uldahl and Anders Prisak who o-founded the orti al re on-stru tion proje t during our master's thesis.Finally, I wish to thank Camilla S. Grünberger and Mette Den ker for proof reading,all the ni e people at the Medi al Informati s group, and my supervisors Prof. Ole K.Hejlesen and Lasse R. Østergaard for their patien e and support.

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Prefa eThe ontent of this Ph.D. thesis is based on �ve papers written during the period ofJanuary 2005 to June 2008. Four papers were a epted for presentation at the following onferen es:• SPIE Medi al Imaging 2005 - International So iety for Opti al Engineering, Medi alImaging onferen e in San Diego, USA, February 2005. Full papers (12 pages) werea epted on the basis of peer reviewed extended abstra ts (4 pages).• MICCAI 2006 - Medi al Image Computing and Computer-Assisted Intervention on-feren e in Copenhagen, Denmark, O tober 2006. 232 full papers (8 pages) weresele ted from 578 submissions based on peer reviews, a eptan e rate: 40.1%. Pro- eedings are published in Le ture Notes on Computer S ien e.• MICCAI 2007 - Medi al Image Computing and Computer-Assisted Intervention on-feren e in Brisbane, Australia, O tober-November 2007. 237 full papers (8 pages)were sele ted from 637 submissions based on peer reviews, a eptan e rate: 37.2%.Pro eedings are published in Le ture Notes on Computer S ien e.• SIBGRAPI 2008 - The XXI Brazilian Symposium on Computer Graphi s and ImagePro essing in Campo Grande, Mato Grosso do Sul, Brazil, O tober 2008. 38 full pa-pers (8 pages) were sele ted from 107 submissions based on peer reviews, a eptan erate: 35.5%. Pro eedings are published by IEEE CS Press.The last paper has been a epted by the journal NeuroImage and is urrently in press.NeuroImage ommuni ates �important advan es, using imaging and modelling te hniquesto study stru ture-fun tion relationships in the brain.� NeuroImage has an impa t fa torof 5.5 (2007).Ea h paper is inserted into the thesis as a hapter only hanging the layout and remov-ing the abstra t ompared to the publi ation/submission. In addition to the �ve papers,the thesis ontains a general introdu tion and dis ussion of the subje t going into detailsnot overed by the papers. Referen e listings are ontained within ea h hapter.The algorithms developed and presented during the thesis have been implementedusing the freely available software and programmer's interfa e MINC, whi h is availablefrom http://www.bi .mni.m gill. a/software/ Simon Fristed EskildsenAalborg, July 2008

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ContentsList of Figures xivList of Tables xv1 Introdu tion 11.1 Ba kground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Quanti� ation of Corti al Stru tures . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Region Based Approa hes . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Morphometry Based Approa hes . . . . . . . . . . . . . . . . . . . . 51.2.3 Surfa e Based Approa hes . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Aim of the Ph.D. Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4 Outline and Contents of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 12Referen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Extra tion of the Cerebral Corti al Boundaries from MRI for Measure-ment of Corti al Thi kness 232.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.1 Initial Inner Surfa e Generation . . . . . . . . . . . . . . . . . . . . . 242.2.2 Inner Surfa e Deformation . . . . . . . . . . . . . . . . . . . . . . . . 252.2.3 Outer Surfa e Deformation . . . . . . . . . . . . . . . . . . . . . . . 262.2.4 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.4 Con lusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Referen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 A tive Surfa e Approa h for Extra tion of the Human Cerebral Cortexfrom MRI 353.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.1 Deformation Pro ess . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.2 Internal For es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.3 External For es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4 Summary and Con lusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Referen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 Quantitative Comparison of Two Corti al Surfa e Extra tion MethodsUsing MRI Phantoms 434.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.1 FreeSurfer Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.2 Fast A urate Cortex Extra tion Method . . . . . . . . . . . . . . . 44xi

4.2.3 Phantom Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2.4 A ura y Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.4 Dis ussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Referen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Evaluation of Five Algorithms for Mapping Brain Corti al Surfa es 515.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.2 Ba kground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.3 Proposed Mapping Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 525.4 Algorithms Sele ted for Comparison . . . . . . . . . . . . . . . . . . . . . . 535.5 Mapping Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.7 Dis ussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.8 Con lusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Referen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Corti al Volumes and Atrophy Rates in FTD-3 CHMP2B Mutation Car-riers and Related Non- arriers 636.1 Introdu tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.2.1 Subje ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2.2 Image A quisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2.3 Image Pro essing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2.4 Corti al Boundary Extra tion . . . . . . . . . . . . . . . . . . . . . . 666.2.5 Corti al Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2.6 Surfa e Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2.7 Statisti al Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.3.1 Corti al Boundary Extra tion and Compartment Segmentations . . 686.3.2 Cross-se tional Di�eren es . . . . . . . . . . . . . . . . . . . . . . . . 696.3.3 Longitudinal E�e ts . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3.4 Atrophy Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3.5 Volume Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 726.3.6 Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.4 Dis ussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.4.1 Corti al Thi kness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.4.2 Cerebral Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.4.3 Limitations of the Study . . . . . . . . . . . . . . . . . . . . . . . . . 776.4.4 Con lusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Referen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 Dis ussion and Con lusion 837.1 Corti al Re onstru tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.1.1 Deformable Surfa e Algorithm . . . . . . . . . . . . . . . . . . . . . 837.1.2 Automation and Robustness . . . . . . . . . . . . . . . . . . . . . . 857.1.3 Computational Expense . . . . . . . . . . . . . . . . . . . . . . . . . 867.2 Corti al Surfa e Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.3 Appli ation on Neurodegenerative Diseases . . . . . . . . . . . . . . . . . . 877.4 Future Dire tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.5 Con lusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Referen es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90xii

List of Figures2.1 Pipeline of the method. Rounded boxes indi ate pro essing steps. Grayboxes indi ate data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2 Pro ess of generating the initial surfa e. Rounded boxes indi ate pro essingsteps. Gray boxes indi ate data. . . . . . . . . . . . . . . . . . . . . . . . . 252.3 Example of how the in�ation for e enables modeling of narrow sul i withno CSF evident. The gray solid line indi ates the deformable surfa e, whi happroa hes the GM/CSF boundary from the WM/GM boundary. As thedeformable surfa e is pushed in the dire tion of the lo al surfa e normals,it will eventually meet itself inside deep narrow sul i. . . . . . . . . . . . . . 272.4 Example of a GGVF �eld based on an edge map al ulated from the sumof the WM and GM memberships using the �rst order derivative. . . . . . . 282.5 Visualization of the extra ted inner and outer orti al surfa es of an ICBMsubje t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.6 Interse tions of inner and outer surfa es with MRI data of an ICBM subje t.Top row: Inner surfa e. Bottom row: Outer surfa e. A few errors are visiblein the images of se ond olumn, where the surfa es are penetrating bothventri les. These errors originate from the topology orre tion algorithm,that enfor es a losed genus zero surfa e. . . . . . . . . . . . . . . . . . . . . 302.7 Corti al thi kness mapped onto the outer orti al surfa e as gray levels.Dark regions are thin, while bright regions are thi k, ranging from 0 mm to6 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.8 The thi kness pattern of 16 ICBM subje ts seen from the top. . . . . . . . . 312.9 Corti al thi kness at two time points (The olor s ale ranges from 0 mm(bla k) to 6 mm (white)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.1 Illustration of how the pressure for e enables modelling of narrow sul i withno CSF evident. As the deformable surfa e (grey line) is pushed away fromthe WM/GM boundary in the dire tion of the lo al surfa e normals, it willeventually meet itself inside narrow sul i. . . . . . . . . . . . . . . . . . . . 383.2 Outer surfa e deformation pro ess using di�erent external for es at di�erentstages in the pro ess. Left to right: Deformation pro ess at iterations 0,5,15and 30. Top: Only pressure for e is enabled. Middle: Only GGVF for eis enabled. Bottom: Combination of both for es balan ed by the urvatureweighting fun tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3 Example of a generated ortex from ICBM data. Left: Rendering of outersurfa e. Right: Inner (bla k) and outer (white) surfa es superimposed ontoMRI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.1 Flow hart illustration of the omparison method. . . . . . . . . . . . . . . 444.2 Fuzzy membership volumes generated from the extra ted surfa es. Left toright: WM, GM, and CSF. . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3 Phantom produ ed by the MRI simulator (left), and �nal phantom afternormalisation and added original tissue (right). . . . . . . . . . . . . . . . . 46xiii

4.4 Left: Surfa e extra ted from original s an by FACE. Middle: Re onstru -tion from phantom by FreeSurfer. Right: Re onstru tion from phantom byFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.1 From ortex surfa e to sphere. Left: Original orti al surfa e. Middle: In-�ated surfa e with urvature values superimposed. Right: Surfa e mappedto a sphere with urvature values superimposed. . . . . . . . . . . . . . . . 545.2 Average errors of mapping with the �ve tested algorithms between permu-tations of the 10 orti al surfa es (n=90). . . . . . . . . . . . . . . . . . . . 565.3 Average distan es in mm from mapped landmark to manually labeled land-mark of 90 mappings. Landmarks are temporal pole (TP), supramarginalgyrus (SG), uneus (Cun), gyrus re tus (GR), post entral gyrus (PCG),and anterior ingulate gyrus (CG). . . . . . . . . . . . . . . . . . . . . . . . 575.4 ICF ompared vertex by vertex to the other four mapping algorithms vi-sualized on an in�ated referen e surfa e. White areas indi ate signi� antdi�eren e (p<0.05) in the orti al thi knesses mapped to a vertex. . . . . . 576.1 Extra tion of the orti al boundaries. a) Spatially aligned MRI data withinitial (red ontour) and �nal (yellow ontour) brain extra tion ontour su-perimposed. b) Brain tissue lassi�ed as WM, GM, and CSF. ) Ventri lesand sub orti al regions labelled as WM, and WM separated into hemi-spheres by a sagittal ut through orpus allosum. d) Edge map al ulatedfrom the fuzzy lassi� ations. e) WM surfa e superimposed on the MRIdata. f) GM surfa e superimposed on the MRI data. . . . . . . . . . . . . . 666.2 Statisti al parametri map of di�eren es in orti al thi kness showing areaswith p < 0.01 for one-sided t-test testing signi� ant thinner ortex in muta-tion arriers ompared to non- arriers. Map generated from pooled (base-line and follow-up) measurements and blurred with a di�usion smoothingapproximating a Gaussian kernel smoothing with 10 mm FWHM. . . . . . . 696.3 Statisti al parametri map of longitudinal di�eren es in orti al thi knessin mutation arriers showing areas with p < 0.05 for paired t-test testingsigni� ant thinner ortex. Map blurred with a di�usion smoothing approx-imating a Gaussian kernel smoothing with 10 mm FWHM. . . . . . . . . . 716.4 Statisti al parametri map of signi� antly (p<0.01) higher atrophy ratios inmutation arriers. Map blurred with a di�usion smoothing approximatinga Gaussian kernel smoothing with 10 mm FWHM. Surfa e parts have beenremoved for better visualization of regions buried by the lateral �ssures.Labels orrespond to the lusters listed in table 6.5. Cluster sizes mayappear smaller than they are due to visualization on a partially �attenedsurfa e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

xiv

List of Tables2.1 Mean distan e to nearest vertex on referen e surfa e and standard deviations. 294.1 Errors measured by the four metri s on both WM and GM surfa es. Errorsare deviation from the referen e surfa es. For ea h metri the performan eon both FreeSurfer and FACE phantoms is ompared for the two methods(two-tailed paired t-test). Signi� ant smaller errors are marked by bold font. 475.1 Average di�eren e in mean orti al thi kness after mapping. . . . . . . . . . 565.2 Per ent verti es of referen e surfa e where the MWW test reje ts thehypothesis that the orti al thi knesses ome from the same population(α = 0.05) for the di�erent mapping algorithms, whi h means that themappings in�uen e the on lusion. . . . . . . . . . . . . . . . . . . . . . . . 586.1 Subje t demographi information. . . . . . . . . . . . . . . . . . . . . . . . 656.2 Corti al thi kness measurements (mm) averaged within main lobes at base-line and follow-up for mutation arriers (MC) and non- arriers (NC). Longi-tudinal di�eren es evaluated by two-tailed paired t-test. Group di�eren esevaluated by one-sided t-test with assumption of unequal varian e on pooledmeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.3 Anatomi al regions with signi� antly (p < 0.01) thinner ortex in mutation arriers ompared to non- arriers after smoothing. Only regions with aninvolved area of more than 1 m2 of either the left (LH) or right (RH)hemisphere are reported. The signi� ant areas are visualized in �gure 6.2. . 716.4 Annualized atrophy rates as per ent de line of baseline thi kness for muta-tion arriers (MC) and non- arriers (NC). Di�eren e between groups eval-uated as one-sided t-test with assumption of unequal varian e. . . . . . . . 736.5 Clusters of statisti ally signi� ant higher atrophy ratios in mutation arriers ompared with non- arriers. Clusters with signi� ant ontiguous areas >20mm2 are reported. Clusters are visualized in �gure 6.4. . . . . . . . . . . . 746.6 Compartment volumes (ml) orre ted by eTIV for mutation arriers (MC)and non- arriers (NC) at baseline and follow-up. Longitudinal di�eren eswere adjusted for inter-s an interval and evaluated by two-tailed paired t-test. Group di�eren es were evaluated by two-tailed t-test with assumptionof unequal varian e on pooled group measurements. . . . . . . . . . . . . . 74

xv

xvi

Chapter 1Introdu tion1.1 Ba kgroundMagneti resonan e imaging (MRI) emerged in the seventies [68, 80℄ and in the eightiesthe te hnology was introdu ed for lini al purposes [33℄. Today, MRI is widely used forstru tural and fun tional imaging as well as for spe tros opy. Unlike other te hnologiesbased on x-rays or ultra-sound, MRI has the ability to distinguish soft tissues based onmagneti properties of atomi nu lei and this has revolutionized the �eld of stru turalmedi al imaging of the inner organs. Continuing improvement of MRI regarding imageresolution and ontrast has pushed the level of detail for visualization of the anatomy andimages with sub-millimeter resolution are now ommon. Espe ially within the �eld of neu-rology, MRI has brought important new perspe tives into understanding and diagnosingvarious diseases and disorders of the entral nervous system as detailed visualization ofthe brain tissues is possible. Many neurologi al diseases and disorders are manifested inMRI visible pathologies of the erebral anatomy.Sin e the introdu tion of stru tural MRI in the �eld of neurology, in reasing e�orthas been put into quanti� ation of the imaged anatomi al stru tures. In addition tophysi ians' qualitative and subje tive assessments in lini al pra ti e, resear h has pushedthe need for standardized quantitative data to ompare brain images a ross patients andimaging equipment, understand disease e�e ts and progression and formalize diagnosti riteria based on the imaging data. One way to quantify an anatomi al stru ture is bydelineation of its boundaries. Proto ols for manual delineations of anatomi al stru tureboundaries are widely used [101, 116℄ and sin e the early nineties spe i� attention hasbeen given to omputerization and automation of stru tural quanti� ation for onsisten yand pre ision improvement and human workload minimization.Pathologi al onditions of both the erebral gray matter (GM) and the erebral whitematter (WM) have been intensively investigated. The GM is primarily omposed of neu-rons and holds fun tional areas ontrary to the erebral WM whi h is omposed of signaltransmitting myelinated axons. Many neurologi al disorders are linked to degenerationof the neurons, while others are due to hroni damage to the brain tissues. Important hroni neurologi al disorders a�e ting the erebral tissues in lude epilepsy and mentaldisorders su h as s hizophrenia. Some neurodegenerative diseases su h as multiple s le-rosis primarily a�e t the WM while most neurodegenerative diseases primarily a�e t theGM. An important lass of neurodegenerative diseases a�e ting the GM is dementias su has Alzheimer's disease (AD) whi h is re ognized as one of the major health hallengesof this entury be ause of the growing elderly population [11℄. Pathologi al GM regionsare mainly found in the erebral ortex, the largest part of the human brain. Regions ofextensive resear h are the hippo ampal formation and neo orti al regions.Hippo ampus is part of the limbi system and primarily involves memory formations.It is a�e ted in diseases su h as s hizophrenia, temporal lobe epilepsy (TLE) and various1

Chapter 1: Introdu tion 2neurodegenerative diseases. In TLE, the hippo ampal size and shape play riti al rolesin the diagnosis and assessment of need for surgi al intervention and for these reasonsmeasurement of the hippo ampus is used in lini al pra ti e. Be ause of the stru tural ompa tness and limited size of the hippo ampus, it is possible to quantify the stru tureby manual delineation of the boundaries dire tly on the images. Various neurodegenera-tive diseases su h as AD, vas ular dementia, and Parkinson's disease ause hippo ampalatrophy [12, 65, 67℄. However, hippo ampal volume estimates are not used in the lini- al diagnosis of these patients despite existing eviden e that hippo ampal volume is animportant lini al marker in these diseases and may aid in earlier diagnosis omparedto diagnosti riteria only based on neuropsy hologi al tests [18℄. A reason for this isthat, ontrary to TLE, hanges in the hippo ampal stru ture are not spe i� for theseneurodegenerative diseases as more information is needed to di�erentiate between the di-agnoses. Studies indi ate that a ombination of hanges found in the hippo ampus andthe neo ortex may provide better di�erentiation [18℄. Despite the small and on�ned sizeof the hippo ampus, no globally a epted onsensus on the manual delineation yet ex-ists [78℄. Even if operators follow the same segmentation proto ol, signi� ant inter- andintra-operator variability in the resulting hippo ampal volume is observed [55℄. This makeshippo ampal measurements di� ult to ompare a ross studies and ompli ates statisti sbased on su h measurements.The neo ortex is a tightly folded sheet of tissue overing the erebral hemispheres.Neo ortex is relatively thin (2-3 mm) ompared to its area (2000-2500 m2) and holds themajority of the brain's fun tional areas su h as visual, sensory and auditory pro essingand interpretation, motor ontrol and ognition [44℄. In some diseases, e.g. frontotemporaldementia, the primary stru tural hanges are found in the neo ortex, thus rendering thisanatomi al stru ture an important lini al marker [96℄. The asso iation neo ortex is alsoinvolved in early AD and this involvement of neo ortex di�erentiates AD from normalaging a ording to histopathologi al studies [18℄. However, as with the hippo ampus,neo orti al stru tural hanges are rarely used in the diagnosis of neurodegenerative diseasesand MRI s ans are usually only a quired to rule out di�erential diagnoses su h as tumorsor other brain damage when diagnosing a suspe ted dementia [100℄.Many of the neurodegenerative diseases a�e ting the erebral ortex are di� ult todiagnose be ause of their overlapping symptoms and insidious onset. This is the aseespe ially for dementias and as only symptomati and disease stalling treatment an beo�ered, early and orre t diagnosis is riti al [45℄. Corti al atrophy is seen as one pos-sible marker in early dementia [93℄. Widespread orti al atrophy an be observed fromMRI images, often manifested in enlarged ventri les, but it is not learly present in theearly stages of neurodegenerative diseases. The subtle fo al hanges related to the earlystages of neurodegenerative diseases, as revealed by detailed stru tural MRI, have beenextensively resear hed for the purpose of early dete tion, thus aiding in early diagno-sis [3, 7, 12, 15, 16, 18, 37, 46, 56�58, 65, 67, 92, 96, 100, 117℄. Dete tion of su h fo al orti al hanges o urring in larger orti al areas seems highly impra ti al in the lini using on-ventional manual delineations when onsidering the limited lini al use of hippo ampalquanti� ation. Therefore, robust, automati delineations or segmentations of the erebral ortex may be the only way to integrate knowledge of subtle stru tural hanges in theearly diagnosis of neurodegenerative diseases.In addition to aiding in patient diagnosis, automati methods for quantifying erebralstru tures bring the possibility of performing large s ale ohort studies when investigat-ing the stru tural manifestations of various brain diseases. Furthermore, standardizedquanti� ations may aid in validating pharma euti als targeted to stop or redu e erebralatrophy and may even speed up the pro ess of lini al trials. In re ognition of these impor-tant perspe tives, numerous automati or semi-automati methods have been developedfor quantifying the stru tures of the human erebral ortex.

3 1.2 Quanti� ation of Corti al Stru tures1.2 Quanti� ation of Corti al Stru turesTraditionally, stru tural brain imaging has been applied to dete t pathologies readily vis-ible in the images. Pathologi al onditions su h as tumors, hemorrhages and is haemiaare usually dis overed by a single MR s an while tissue in the pro ess of neurodegen-eration may not be dete table from a single s an. Be ause of the large variability ofthe normal brain, the subtle hanges o urring in the early stages of neurodegenerativediseases require serial s ans to follow the progression and dete t the pathologi al tissue.However, with the in reasing knowledge of the alterations to the brain tissues aused byvarious neurodegenerative diseases, disease spe i� atrophy patterns or signatures may berevealed in the future whi h enables dete tion of early atrophy from a single s an [118℄.Therefore, resear hers are working toward a goal of di�erentiating between di�erent neu-rodegenerative diseases by orti al atrophy patterns and identifying lini al markers to aidin early diagnosis. Rea hing this goal involves a urately measuring subtle morphologi al hanges, identifying similar patterns of atrophy in population groups, and �nally applyingthe quanti� ation methods in lini al studies.To e�e tively measure subtle morphologi al hanges and di�eren es in the erebral ortex, 3D T1 weighted high resolution images are needed [4℄ and are usually a quired bygradient e ho sequen es. Voxel sizes around one ubi millimeter are ommon and imageswith high tissue ontrast are generated with at least 1.5 Tesla s anners. 3 Tesla s annersare in reasingly be oming available in hospitals [90℄.Even though MRI an apture the erebral anatomy in high detail and with ex el-lent ontrast, the morphologi al quanti� ation is ompli ated by fa tors related to noise,distortion and other artifa ts found in MRI [119℄. Corti al morphologi al quanti� ationis further ompli ated by the omplex stru ture and proximate obje ts with overlappingimage intensities su h as the dura mater and larger veins.A proliferation of methods to quantify di�eren es and hanges in the erebral ortexhas been seen during the last twenty years. The methods apply a variety of te hniquesand a taxonomy of the methods an be onstru ted based on these te hniques [107℄. Herethe fo us is on three main ategories in whi h most work on orti al quanti� ation fall:1) methods that perform segmentation of the ortex by labeling the image voxels (regionbased), 2) methods that quantify hanges in intensity between s ans (morphometry based)and 3) methods that integrate knowledge of the underlying anatomy to re onstru t thetissue boundaries (surfa e based).1.2.1 Region Based Approa hesA lassi al way of quantifying stru tures in images is segmentation of the obje t of inter-est. Region based approa hes operate in the image domain analyzing the intensity valuesand perform dis rete morphologi al operations to identify stru tures. Segmentation isperformed by labeling ea h pixel or voxel in the image as belonging to di�erent lasses(di�erent obje ts of interest). Stru tural quanti� ations are usually based on voxel ounts(volumetri measurements).Conventional image segmentation te hniques in lude thresholding, region growing and lustering algorithms. However, when analyzing biologi al images su h simple approa hesare rarely su� ient. Within the �eld of neuro imaging, more omplex segmentation so-lutions have therefore been proposed. Here three ategories of segmentation approa hesare overed: region of interest segmentation, atlas based methods and segmentation ap-proa hes based on tissue lassi� ation.Region of InterestRegion of interest (ROI) methods ompute an overall size for ea h brain stru ture basedon segmentations. Conventional segmentations involve manual delineations of tissueboundaries in onse utive sli es of an MRI s an [56�58℄. Su h delineations of tissue

Chapter 1: Introdu tion 4boundaries are laborious and subje t to inter-operator variability [30℄. However, semi-automated [92,125℄ and fully automated [51�53,89℄ methods have been proposed, but theseare not widely used [3℄. Other ROI methods use stereology to quantify the stru ture [26℄.Volume estimates from ROI analysis an provide valuable insight into neurodegenerativediseases, but in the early stages of neurodegenerative diseases, hanges in overall volumeare minimal [4℄ and the subtle hanges in subregions of the ROI may be overlooked. ROIanalysis is mainly applied in quanti� ation of relatively small on�ned stru tures su h asthe hippo ampus, the audate nu leus and the entorhinal ortex as these are of a manage-able size but still re ognized as important surrogate markers for several neurodegenerativediseases [92℄.Apart from human intera tion related problems of manual or semi-automated methods,the fo us on a single stru ture ignores hanges in other stru tures and may forestall newinsight into the pathology of neurodegenerative diseases [3℄.Atlas BasedAtlas based approa hes o-register the subje t image with a template ontaining prede-�ned target regions of interest (atlas) so that segmentation of the target regions an beobtained by mapping atlas regions to the subje t image. Su h an approa h is depen-dent on the registration te hnique used, the template sele ted and the atlas applied forthe segmentation. Numerous registration methods exist [77, 128℄, as image registration isintensively resear hed and driven by a wide range of appli ation areas.Usually a brain template is the average of a large sample of spatially aligned images.Su h an average has well-de�ned image edges of morphologi ally invariant stru tures whilestru tures with greater variation, su h as the orti al regions, are usually blurred in thetemplate image. Morphologi al variations an be redu ed by generating templates basedon high dimensional non-linear registrations, thus resulting in averages with more well-de�ned image edges. However, removing morphologi al variations may lead to alignmentswhere the images no longer are anatomi ally onsistent. Several groups have developedand re�ned MRI brain templates and atlases [32, 34, 39℄.Choi e of template is important for the subsequent segmentation [95℄. If the subje tsunder study are homogeneous with respe t to fa tors su h as age and disease stage, itmay be preferred to use an image from the target population as template instead of anaverage template from a broader population [16℄. In su h ases, manual intervention isneeded to de�ne the regions of interest in the template. Problems with artifa ts and poorsignal-to-noise of a single image an be solved by repeated imaging and averaging of thesame subje t [54℄.Atlas based approa hes are well-suited for quanti� ation of regions with little mor-phologi al variation. However, in the ase of the erebral ortex it is di� ult, if notin on eivable, to reate a template representative of the great variation in orti al foldingpatterns.Tissue Classi� ationTissue lassi� ation of the orti al GM provides means for measuring the orti al volume.Usually, a lassi� ation into WM, GM, and erebrospinal �uid (CSF) is performed. Inorder to a omplish su h lassi� ation, non- erebral tissues are usually removed prior to lassi� ation. A variety of lassi� ation methods have been proposed based on Bayesiananalysis [81℄, lustering [86℄, fuzzy lassi� ation [112℄, neural networks [114℄, deterministi annealing [40℄, Markov Random Fields [98℄ and ombinations [8℄.Other methods for orti al GM lassi� ation have been proposed. Bazin and Phamproposed a method that enfor es a given topology on the target stru ture whi h preventsholes and handles from o urring in the segmentation [10℄. Su h topologi al in onsisten iesare often seen in onventional lassi� ation methods due to image noise. Angelini et al.used a deformable model to segment the brain into WM, GM and CSF [2℄. As des ribed

5 1.2 Quanti� ation of Corti al Stru tureslater on, deformable models are often used to re onstru t the orti al surfa e; however,this approa h uses a level set frame work solely for voxel lassi� ation.Tissue lassi� ation of voxels in the image is limited by the image resolution so partialvolume e�e ts in�uen e the segmentation. Furthermore, lassi� ation of the orti al GMonly provides global measures of di�eren es in the orti al volume. For measuring fo ale�e ts regional subdivisions are needed. This involves manual delineations or ombinationwith an atlas te hnique.Dis ussion of Region Based Approa hesRegion based approa hes for quanti� ation of the erebral ortex all have problems at-ta hed: ROI analysis requires human intera tion whi h is laborious and prone to errorsand variability. Model and atlas based approa hes have di� ulties apturing the wide mor-phologi al variety of the human ortex. Tissue lassi� ation only provides global measuresof orti al volume di�eren es.Generally, methods resulting in voxel based segmentation su�er a number of problemsregardingmorphologi al quanti� ation. Firstly, the segmentations are limited by the imageresolution so only stru tural hanges of voxel size proportions an be dete ted. Se ondly,morphologi al hara teristi s su h as urvature and thi kness are di� ult to apture fromsimple onne ted segmentations. This is even more ompli ated for the orti al stru turebe ause of its tightly folded appearan e. Corti al thi kness estimates have been proposedusing a segmentation method propagating out distan e values from the WM omponentuntil the GM/CSF interfa e is rea hed [73℄. However, partial volume e�e ts ompli atethe dete tion of GM/CSF image edges and often subvoxel a ura y is needed to identifysubtle tissue di�eren es.1.2.2 Morphometry Based Approa hesMorphometry based approa hes analyze the intensity di�eren e between serial images orbetween an image and a template. Su h approa hes rely on registration te hniques tospatially align images. Three types of intensity di�eren e based methods have been devel-oped for quanti� ation of erebral stru tures. Two approa hes dire tly measure di�eren esin intensity while one analyzes the deformation �eld involved in the spatial alignment ofimages.Intensity Shift Approa hesIntensity shift approa hes ompute brain volume hange by quantifying the di�eren e inimage intensity between spatially aligned serial MRI s ans in longitudinal studies. Usuallyonly whole brain volume hange is measured automati ally; regional atrophy is determinedby manually de�ned regions. Two intensity shift methods are popular, namely the bound-ary shift integral (BSI) [38℄ and stru tural image evaluation using normalization of atrophy(SIENA) [103℄.BSI uses a rigid transformation in the alignment and intensities are normalized to ompare follow-up s ans with the baseline s an. The method quanti�es the shift in tissueboundaries by integrating over the di�eren e in image intensities.SIENA orre ts for skull size in the registration pro edure whi h results in a full a�netransformation and resamples both baseline and follow-up s ans to obtain images withsimilar interpolation-related blurring. SIENA identi�es edge points in both images andestimates the motion of ea h point perpendi ularly to the lo al edge. This redu es thesensitivity to intensity normalization.Both BSI and SIENA have been shown to provide reasonably a urate measures ofbrain atrophy [14℄ and to be apable of separating AD patients from healthy ontrols[46℄. However, whole brain measures are insu� ient for determining subtle hanges in theearly stages of neurodegenerative diseases and regional measures using these methods are

Chapter 1: Introdu tion 6dependent on manual intervention. Furthermore, these methods are dependent on serials ans whi h indu e diagnosis delay [4℄.Intensity shift approa hes are highly dependent on the registration and normaliza-tion of intensities whi h is ompli ated by ommon intensity non-uniformities aused byinhomogeneities in the radio frequen y �eld oil [127℄ and other artifa ts [119℄.Voxel Based MorphometryVoxel based morphometry (VBM) performs voxel-wise omparisons between spatiallyaligned MRI s ans of subje t groups enabling identi� ation of in reased or de reasedGM density throughout the entire brain [5, 120℄. The spatial alignment involves lassi�- ation of GM, WM and CSF. The GM map is non-linearly registered to a template andgroup averages are al ulated and spatially smoothed with a �lter. Group di�eren es and orrelations with lini al parameters are estimated by �tting a statisti al model at ea hvoxel [3℄.The a ura y of VBM depends on the registration te hnique used and anatomi aldi�eren es may be inferred by systemati registration errors or by systemati shifts inuna�e ted regions aused by hanges in a�e ted regions [13,110℄. To address these issues,information of the deformations (expansions or ontra tions) involved in the registrationis en oded in the aligned GM map [43℄. This approa h is alled optimized VBM.A similar approa h, alled regional analysis of volumes examined in normalized spa e(RAVENS), has been proposed [29,30,42℄. RAVENS use a high-dimensional elasti trans-formation driven by point orresponden es in the spatial normalization pro ess while opti-mized VBM relies on relatively smoother parametri transformations [4,30℄. The informa-tion of the deformation �eld is en oded in the aligned map thus preserving tissue volumesof the original image similar to optimized VBM [30℄.VBM analysis has been applied in numerous studies of erebral disorders [62, 117℄,normal brain development and aging [104℄ and other non-pathologi al investigations [25,82, 88℄.VBM te hniques are riti ized for being too reliant on a perfe t registration and doubt-ful assumptions in the statisti al model [110℄. Another issue is that VBM does not a ountfor the orti al folds whi h means that small e�e ts of opposing sul al walls may give riseto an a umulated signi� ant e�e t when averaging the GM maps [3, 36℄.Tensor Based MorphometryTensor based morphometry (TBM) analyzes the deformation �eld involved in high-dimensional non-linear mapping of serial intra-subje t images [6, 19℄. Using the determi-nant of the Ja obian matrix asso iated with the deformation �eld, lo al tissue expansionand shrinkage an be identi�ed and the Ja obian maps an be used to quantify intra-subje t longitudinal e�e ts and di�eren es between subje t groups. Expressing the tissueexpansion and shrinkage by the Ja obian maps removes dire tional information of atrophywhi h may be non-isotropi . New methods use the full dimensionality of the deformationtensors and an better dete t and visualize fo al areas of atrophy [3℄.TBM has been used in di�erent areas su h as studying the developing human brain [21℄,visualizing the atrophy pattern in patients with AIDS [19℄ and measuring degeneration inAlzheimer's disease [37℄ and fronto-temporal lobar degeneration [7, 15, 105℄.The a ura y of TBM depends on the applied registration method and orti al foldingpatterns are not a ounted for.Dis ussion of Morphometry Based Approa hesMorphometry based approa hes address the problem of the limited resolution as sub-voxel hanges of the stru tures an be seen as hanges in voxel intensity. However, su h

7 1.2 Quanti� ation of Corti al Stru turesapproa hes have other problems atta hed regarding the morphologi al quanti� ation. In-tensity shift analysis measures whole brain hanges whi h is insensitive to subtle orti al hanges found in the early stages of many neurodegenerative diseases. Furthermore, thesemethods are very reliant on intensity normalization and registration performan e whi hmay introdu e un ertainties in the measurements. Also VBM and TBM are relying on thequality of image registration and they further la k the ability to distinguish e�e ts fromopposing walls of tight sul i.1.2.3 Surfa e Based Approa hesSurfa e based approa hes model the orti al sheet with 2D manifold surfa es embeddedin 3D, thus aiming at modeling the underlying anatomy. This relaxes the restri tions im-posed by the limited image resolution and enables in orporation of anatomi al knowledge.Furthermore, surfa e based approa hes are potentially independent of image registrationand intensity normalization. Finally, su h approa hes allow for distinguishing opposingwalls of sul i due to the expli it re onstru tion of the orti al sheet.Apart from morphologi al quanti� ation purposes, surfa e based re onstru tion of the erebral ortex has appli ation within fun tional brain imaging for mapping a tivity ontothe orti al surfa e [109℄ and within neuro-surgery for preoperative planning, postoperativeevaluation and surgery simulation. Also, visualizations of the buried orti al regions arepossible by orti al unfolding [36℄, as well as assignment of anatomi al labels to the orti alGM [99℄. In addition to visualization purposes, surfa e re onstru tions provide the meansfor reating surfa e based atlases where anatomi al and fun tional regions an be de�nedin a anoni al spa e, thus omplementing the widely a epted volumetri oordinate spa esand atlases [36℄.As the human erebral ortex is a omplex, highly onvolved sheet-like stru ture, themodeling of the stru ture using surfa es is hallenging. In MRI, the orti al boundariesare often obs ured or partly missing be ause of noise, inhomogeneity artifa ts and partialvolume e�e ts originating from the a quisition [119℄. Opposite banks of tight sul i on theouter boundary may meet inside the sul al folds and appear as onne ted in MRI. Surfa emodeling an ompensate for obs ured and in omplete image edges. However, in MRI,information on the outer orti al boundary may be ompletely missing in several tightsul i and at the top of gyri the boundary may be obs ured by meninges and dura mater lose to the ortex. Furthermore, issues on erning the topology of the orti al sheet areunavoidable be ause of the inherent noise in MR images.The ideal surfa e modeling of the erebral ortex must align with the true underly-ing anatomi al boundaries of the ortex and respe t the true orti al topology whi h isspheri al if losed at the brain stem [48℄. To a hieve these properties, a proliferation ofmethods for modeling the erebral ortex with surfa es has been proposed during the lastde ade. One way of re onstru ting the ortex is using deformable models where a on-tour or surfa e is manipulated to �t target image boundaries. Usually, approa hes basedon deformable models implement either a variant of the lassi al a tive ontours [23, 61℄;parametri deformable models or a variant based on geometri deformable models [87,97℄.Other approa hes for orti al re onstru tion by surfa es usually apply voxel based te h-niques in ombination with iso-surfa e algorithms su h as Mar hing Cubes [74℄.A ommon trait of deformable models is that an initial ontour or surfa e is evolvedtoward target boundaries. In parametri deformable models, the initial ontour or surfa ekeeps the same topology during deformation. This is espe ially useful when the targetstru ture has a known topology. Geometri deformable models have the ability to hangetopology and adapt to the topology of the target stru ture. This is advantageous in manysegmentation problems, however, when the target stru ture has a known topology it is adistin t disadvantage not having a �xed topology during surfa e evolution. This drawba kis espe ially pronoun ed when geometri deformable models are applied to noisy imagesas found in MRI.

Chapter 1: Introdu tion 8Usually the ontour or surfa e is initialized ompletely inside or ompletely outside thetarget boundary and uses in�ation or ontra tion to approa h the target boundary in aniterative manner. The main di� ulty in orti al re onstru tion lies in orre tly modelingthe tightly folded sul i. Methods initializing a surfa e outside the ortex have problemspenetrating the sul i and rea hing their fundi. The GM/WM boundary is easier to dis ernin MRI be ause these image edges, ontrary to the GM/CSF boundary, are una�e ted bythe tight folds and proximate dura mater. Therefore, several methods utilize information ofthe GM/WM boundary to dete t the GM/CSF boundary as the ortex an be onsideredas a ontinuous laminar stru ture with smoothly varying thi kness.Methods for surfa e re onstru tion of the erebral ortex have been developed sin ethe early nineties and many resear h groups have ontributed to the �eld. The followingdes ribe a sele tion of these ontributions using parametri and geometri deformablemodels as well as other surfa e based approa hes for re onstru ting or quantifying the erebral ortex.Parametri Deformable ModelsParametri deformable models are originating from the so- alled snake formulation by Kasset al. [61℄. The basi method des ribes a parametri 2D ontour in�uen ed by internalspline for es and external image and onstraint for es. A fun tional expressing the energyof the snake was iteratively minimized to obtain the lo ation of the ontour with the lowestenergy, thus resulting in a segmentation of the image. Cohen and Cohen introdu ed anin�ation for e to the a tive ontour [22℄ and extended it to 3D and so named it a balloonmodel [23℄.Davatzikos and Prin e proposed to model the orti al sheet by a ribbon model where a2D ontour was �tted to the enter of the orti al sheet using the homogeneity of intensitylevels within the GM [31℄. Davatzikos and Bryan extended the ribbon model to 3D withinitialization outside the brain [28℄. Vaillant and Davatzikos further re�ned the methodand obtained parametrizations of the sul al folds using separate a tive ontours for ea hfold [113℄. This approa h relies on lose initialization of the ontour and manual intera tionin order to model the sul al folds. Furthermore, the use of separate a tive ontours tomodel the sul i alters the topology of the re onstru tion.M Inerney and Terzopoulos added a reparametrization step to the a tive ontour byde�ning a grid of nodes as either inside or outside the ontour [83, 85℄. This way, the ontour an dynami ally hange the topology and easily grow from a small initialization ontour. These so- alled T-snakes were extended to 3D (T-surfa es), and it was demon-strated that a T-surfa e an be �tted to the GM/CSF boundary by initializing it outsidethe ortex [84℄. This strategy, however, fails to grow into the sul i.Ma Donald et al. used a sphere as the initial surfa e and deformed it to the GM/WMboundary in a multis ale fashion. Subsequently, a oupled surfa e approa h was applied.In this approa h, two surfa es simultaneously are deformed under proximity onstraintsmaintaining a prede�ned minimum and maximum distan e between the GM/WM andGM/CSF boundary [75℄. This way the GM/CSF surfa e is dragged towards the fundi ofsul i and spheri al topology is enfor ed due to the spheri al initial surfa e. The proximity onstraints prevent the oupled surfa es model from a urately delineating orti al areaswith a thi kness outside the prede�ned distan e interval. Furthermore, su h an approa his more omputational expensive as the model be omes more omplex by the surfa e oupling.An approa h by Dale et al. identi�es the GM/WM boundary using voxel lassi� ations,iso-surfa e extra tion and a deformable model. This surfa e is subsequently expandedtowards the GM/CSF boundary [27℄. This has the advantage that all sul i are present inthe initial state and enables the preservation of the sul i during deformation even thougheviden e of the GM/CSF boundary may be missing in the MRI data. The tight sul al foldsare modeled by preventing self-interse tions in the deforming surfa e, thus the delineationof the folds are pla ed equidistantly from the sul al walls of the GM/WM boundary.

9 1.2 Quanti� ation of Corti al Stru turesClearly, the dire tion of in�ation is important to the resulting outer surfa e. Dale et al.used the dire tions of the surfa e normals. This single surfa e approa h is faster thanthe oupled surfa e approa h by Ma Donald et al. and it aptures all the tight sul i.However, the expansion of the surfa e towards the outer boundary is sensitive to smallerrors or irregularities in the initial surfa e whi h may lead to modeling of non-existentfolds.Xu et al. also used a GM/WM surfa e as the initialization of a deformable model [121℄.They used a gradient ve tor �ow (GVF) to de�ne dire tions toward the entral layer ofthe ortex. This solution provides a fast and onsistent onvergen e of the surfa e, buttight sul i with no eviden e of the outer boundary are not aptured by this method. Theirapproa h does not impose self-interse tion onstraints whi h is ne essary when segmentingthe outer boundary and the approa h requires manual intera tion.Another approa h using a WM/GM boundary representation for subsequent GM/CSFdelineation was proposed by Kriegeskorte and Goebel [66℄. They extra t the WM voxelsin ea h hemisphere of the erebrum using a ombination of atlas masking, intensity inho-mogeneity orre tion, anisotropi �ltering and region growing. The hemispheri WM om-ponents are modi�ed to obtain spheri al topology and are tessellated to polygon meshes.Verti es of the polygon meshes are shifted along surfa e normals to delineate the GM/WMboundary and the GM/CSF boundary. Unfortunately, it is not lear from the do umen-tation how the boundaries are dete ted during the deformation pro ess.Kim et al. [64℄ proposed a method where the WM surfa e is obtained by deforminga spheri al polygon model to the GM/WM boundary as done by Ma Donald et al. [75℄.The GM/CSF boundary is found by expanding the WM surfa e along a Lapla ian �eldgenerated between the WM surfa e and a skeletonized CSF image while preventing self-interse tions. While a hieving relatively robust and onsistent onvergen e, this method ishighly dependent on lassi� ation of CSF and the assumption that CSF is at least partlyvisible between all sul al folds.Xu et al. initialized an ellipsoidal mesh outside the ortex and used a GVF �eld ombined with an inward pressure for e to deform the mesh to the orti al boundaries[122℄. They used a reprodu ing kernel parti le method as the deformation model whi hprovides e� ient reparametrization pro edures and self-interse tions are avoided by usingfast mar hing methods. Though this approa h is novel in the way the deformations areimplemented, the shrink-wrapping strategy still su�ers from inability to rea h deep intotight sul al folds.Geometri Deformable ModelsGeometri deformable models are variants of the propagating fronts methods [17,20,87,97℄,where the surfa e is impli itly represented as the zero isovalue of a level set fun tion. Be- ause of the impli it representation, no self-interse tions an o ur in geometri deformablemodels. After propagation of the level set fun tion, a parametri surfa e an be obtainedby omputing an iso-surfa e at the zero isovalue of the level set fun tion. Level set methodsare numeri ally stable and faster than algorithms deforming parametri models [50℄.Zeng et al. used a oupled surfa es approa h in a level set framework [126℄. Goldenberget al. adopted the oupled surfa es approa h and formulated the segmentation as a mini-mization problem [41℄. Coupled surfa es approa hes enable modeling of tight sul al foldsbe ause of an inter-surfa e distan e onstraint. However, these methods su�er the sameproblems as the approa h by Ma Donald et al. [75℄. Furthermore, in both approa hes theresulting surfa es have arbitrary topologies due to the level set evolution te hnique.Han et al. proposed a topology preserving geometri deformable model (TGDM) wherethe evolving surfa e is kept homeomorphi to the boundary of a digital obje t delineatedby the level set fun tion on an underlying grid [47, 50℄. The surfa e is only allowed to hange sign at simple points of the underlying grid, thus preserving the topology of thedigital obje t and the surfa e. A GM/WM surfa e is obtained by WM lassi� ationfollowed by a TGDM with a regularizing for e and a signed pressure for e based on fuzzy

Chapter 1: Introdu tion 10tissue lassi� ations. The entral orti al layer are delineated by evolving the GM/WMsurfa e using a TGDM with a GVF for e similar to the parametri approa h by Xu etal. [121℄. Finally, the GM/CSF boundary is obtained by propagating the entral orti alsurfa e using a TGDM with ombined pressure and GVF for es. This approa h over omesa number of the problems related to orti al surfa e re onstru tion by enfor ing orre ttopology while maintaining fast and onsistent onvergen e. However, manual intera tionis required in the prepro essing steps of the method.Xue et al. used the framework of Han et al. [47℄ to re onstru t the orti al surfa es ofneonates [124℄. Corti al re onstru tion of neonate brains is parti ularly di� ult be auseof inverted GM/WM ontrast in MRI images ompared to adults, lower ontrast-to-noiseratio, the maturation pro ess whi h ontinuously hanges the GM/WM ontrast and thedi�erent folding patterns at di�erent stages of the developing brain. Therefore, the maindi�eren es between the methods by Xue et al. and Han et al. are the tissue lassi� ationpro ess and a relaxation of the spheri al topology onstraint as the topology of neonate orti es are not well-established. In ontrast to the method by Han et al., the re on-stru tion of neonatal orti es is fully automati , suggesting that re onstru tions of adult orti es also ould be done fully automati .Li et al. proposed a very fast method based on dual front a tive ontours [71℄. Dualfront a tive ontours iteratively �nd the global minimum within an a tive region basedon minimal path te hniques [24℄ where the a tive region is de�ned on both sides of the ontour, typi ally by simple dilations with a stru turing element. For the purpose of ortex segmentation, Li et al. used histogram analysis to de�ne the a tive region insteadof simple dilations. The approa h requires manual adjustment of histogram parameters.Furthermore, in pathologi al brains tissue intensities may not have distin t peaks in thehistogram whi h ompli ates the estimation of a proper threshold. Finally, the topologyproblem was not addressed in the proposed method.Other Surfa e Re onstru tionsThough most approa hes to orti al re onstru tion are variants of parametri or geometri deformable models, other te hniques have also been suggested. In addition to low levelmethods su h as edge dete tion [63℄ and region growing [123℄, a variety of algorithms havebeen proposed. For example Mangin et al. used a 3D skeletonization of the GM/CSFinterfa e to generate a surfa e and extra t sul al patterns [79℄. Van Essen et al. useda ombination of Gaussian intensity transformations, gradient information and manualguidan e with subsequent iso-surfa e extra tion and topology orre tion to obtain a surfa erepresentation of the enter of the ortex [115℄. Shattu k and Leahy segmented the WM ofea h hemisphere, modi�ed the WM omponent to obtain spheri al topology, and extra tedthe GM/WM boundary using an iso-surfa e algorithm [102℄. A similar approa h with aBayesian segmentation was used by Joshi et al. on digitized ryose tions of ma aquemonkey brains [60℄. However, su h methods are not well suited for generating a urateand topologi ally orre t representations of the outer orti al boundary whi h is whydeformable models have gained popularity within the �eld over the re ent years.Some methods quantify the orti al morphology by ombining a surfa e representationwith analysis of the image intensity. Barta et al. used a sto hasti model of the intensitydistan e histogram relative to the GM/WM surfa e to measure the orti al thi kness [9℄.Others al ulate the orti al thi kness using voxel segmentation and only use the or-ti al surfa e for proje tion of the thi kness, thus enabling visualization and mapping ofthe orti al thi kness [111℄. It is argued that voxel based orti al thi kness estimations,though less a urate, are more robust than approa hes expli itly modeling the outer or-ti al boundary [9, 111℄. Su h hybrid methods may be useful. However, to quantify themorphology of the orti al sheet to its full extent, omplete surfa e re onstru tions stillseem to be the best solution.

11 1.2 Quanti� ation of Corti al Stru turesDis ussion of Surfa e Based Approa hesSurfa e based approa hes applying deformable models have problems atta hed to surfa einitialization, topology of target stru ture and robust dete tion of image boundaries duringsurfa e evolution. As des ribed above several solutions to over ome these problems havebeen proposed.Several resear hers suggest the use of oupled surfa es [41, 75, 126℄. Coupled surfa esapproa hes have the advantage of expli itly using information of both orti al boundariesto dete t the outer boundary. This enables the GM/CSF surfa e to model the deep, narrowsul i. The oupling is a hieved by spe ifying a minimum and a maximum distan e betweenthe surfa es. Su h onstraints, however, pre lude the modeling of anatomy deviating fromthe norm as de�ned by the distan e limits. When modeling abnormal anatomy found inneurodegenerative diseases and other neurologi al disorders or normal neonatal anatomy,restri tions on the orti al thi kness render su h approa hes inapt to a urately quantifythe true morphology [124℄. Furthermore, even in normal adult orti es, a bias betweenthe hosen prede�ned distan e and a measured orti al thi kness may be inferred by therestri tions [75℄.Re ent methods seem to develop in similar dire tions. The most promising meth-ods, whether based on parametri or geometri deformable models, for re onstru ting theGM/CSF boundary use a GM/WM boundary representation to �t the surfa e to the outer orti al boundary. These methods follow roughly the steps of 1) erebrum WM lassi� a-tion, 2) topology orre tion, 3) WM tessellation and 4) expansion of WM surfa e towardsthe GM/CSF boundary [27, 47, 64, 66℄, where step 2 and 3 may be omitted if a spheri alsurfa e is deformed to the WM/GM boundary [64℄. The methods proposed by Dale etal. [27℄, Xu et al. [121℄, Han et al. [47℄, and Kim et al. [64℄ all use similar strategies forexpanding the WM surfa e towards the entral/GM surfa e; all four methods use a ve tor�eld for guiding the surfa e towards the target boundary. Dale et al. use surfa e normals,Xu et al. and Han et al. use a GVF �eld, and Kim et al. use a Lapla ian �eld. Su hve tor �elds provide better and more onsistent onvergen e than using variants of thebasi image gradient.Developers expanding the WM surfa e to the entral orti al layer instead of the outer orti al boundary argue that this representation of the ortex provides better geometri information than both the inner and outer boundaries [72, 121℄. However, expli it rep-resentations of the tissue boundaries better support measurements of orti al thi kness.Furthermore, altered morphology aused by pathologies may be easier dete table at thetissue boundaries than at the enter-line of the stru ture.The di�erent image for es proposed for evolving the deformable models towards the or-ti al boundaries an all be applied in both parametri and geometri frameworks. Choi eof framework seems to be dependent on what property the individual developer �nds mostimportant. One property that is emphasized repeatedly is the ability to onstrain topologyof the �nal ontour. With the lassi al deformable models this ould only be a hieved byparametri models. However, with the development of topology preserving level sets [49℄,the use of geometri models for orti al re onstru tion have be ome more popular. Re- ently, Ségonne developed a level set method where the topology an be ontrolled withoutloosing the ability of ontours to merge, split and vanish during evolution whi h usuallyadvo ates a strong advantage over parametri deformable models [108℄. Others are alsoworking on variants of topology preserving level sets [1, 69, 94, 106℄.Hybrid methods ombining surfa e re onstru tion with voxel based analysis are po-tentially very robust. However, full orti al surfa e re onstru tions provide information ofthe morphology whi h annot be quanti�ed by hybrid methods. So far, the most promis-ing methods to obtain omplete orti al re onstru tions rely on deformable models. Eventhough problems related to deformable models, su h as robustness, are evident in today'ssurfa e solutions, the goal is still a urate re onstru tions of the erebral ortex for thedete tion of subtle, fo al morphologi al hanges as found in neurodegenerative diseases.

Chapter 1: Introdu tion 121.3 Aim of the Ph.D. StudyA main goal within the �eld of stru tural brain imaging and brain morphometry is todi�erentiate between di�erent neurodegenerative diseases by orti al atrophy patterns.This thesis addresses the initial steps toward this goal. The aim is to develop methodsfor quantifying stru tural hanges in the human erebral ortex from MRI images. Toa omplish this, a method based on deformable models is developed to automati allydelineate the orti al boundaries. Spe i� ally, parametri deformable surfa es are used todelineate the GM/WM and GM/CSF boundaries of the ortex. From surfa es representingthe orti al boundaries several measures des ribing the orti al stru ture an be obtained.The orti al thi kness is an important measure, but quantities su h as the orti al areaand urvature may also be involved in des ribing the hanging ortex as well as orti alvolume for omparison purposes with volumetri methods.Measuring the orti al thi kness from surfa es of the orti al boundaries is not a sim-ple matter due to the omplex morphology. Several methods for measuring the thi knessfrom orti al re onstru tions have been proposed [35,59,70,76℄. Also morphologi al quan-ti� ation by other measures exists [91℄, but it is outside the s ope of this Ph.D. study todevelop new methods for su h quanti� ation.The ability to quantify the orti al stru ture from MRI provides a mean for quantifying hanges over time or di�eren es between subje ts for the entire orti al stru ture. However,su h global quantities are not sensitive to small orti al hanges and this raises a need forquantifying fo al hanges and di�eren es. This an be a omplished by subdividing the orti al sheet by means of an atlas whi h may be based on anatomi al, fun tional or othertypes of regions. However, applying �xed orti al regions wherein the measurements areaveraged, also limits the sensitivity of the quanti� ation as fo al hanges may be presenta ross regions. Therefore, a point orresponden e between orti al surfa es is needed tofully bene�t from the measurements orti al surfa es provide and part of the study is on erned with the sear h for a suitable method for obtaining su h a orti al mapping.Finally, the Ph.D. study investigates the appli ation of the methods developed duringthe study within the �eld of neurodegenerative diseases. This is done by applying themethods to quantify orti al stru tural hanges in individuals from a large Danish familywith an inherited variant of frontotemporal dementia.1.4 Outline and Contents of ThesisThe thesis is based on �ve papers. Two papers des ribe the fundamental method forextra ting the orti al boundaries from MRI using deformable surfa es. The third pa-per ompares the developed method with a well-known and widely used method. Thefourth paper deals with the mapping between di�erent orti al surfa es to ompare sim-ilar anatomi al regions over groups of subje ts. Finally, in the last paper, the methodsdeveloped during the Ph.D. study are applied in a study of pre lini al individuals with afamilial neurodegenerative disease.Paper I: Extra tion of the Cerebral Corti al Boundaries from MRIfor Measurement of Corti al Thi kness (Chapter 2)In this paper the fundamental idea of extra ting the orti al boundaries is presented. Theentire pro ess from s anner images to orti al thi kness results is des ribed and test of themethod on simulated MRI data, several young healthy individuals and a single AD patients anned with an interval of six months is presented. The surfa e deformation pro essdes ribed in the paper is based on a parametri deformable model and uses a dis retesear h spa e to minimize an energy fun tional. The method is related to the approa h byM Inerney and Terzopoulos [84℄ in the sense that reparametrizations are performed during

13 1.4 Outline and Contents of Thesissurfa e evolution. The main ontribution of the paper is the ombination of a pressurefor e with a gradient ve tor �ow in the deformation of the outer orti al boundary.Paper II: A tive Surfa e Approa h for Extra tion of the HumanCerebral Cortex from MRI (Chapter 3)In this paper an improved surfa e deformation pro ess is presented. Instead of minimizingan energy fun tional in a dis rete sear h spa e, the optimal deformation dire tions areexpressed as ve tors leading to a for e balan ing s heme. The energy fun tional des ribedin the �rst paper is altered to express ve tor for es and a lo al weighting of for es isintrodu ed to better adapt to the highly folded orti al sheet. Test of the method onsimulated MRI is reported and the resulting orti al surfa es are shown to better modelthe folded stru ture than surfa es obtained by a pressure for e or a gradient ve tor �owfor e alone. The main ontribution of the paper is a deformation approa h free of sear hspa es and a novel weighting of the terms in the energy fun tional in�uen ed by surfa e urvature.Paper III: Quantitative Comparison of Two Corti al Surfa e Ex-tra tion Methods Using MRI Phantoms (Chapter 4)This paper des ribes the omparison of the developed method with the ortex extra tionmethod used the most in the literature, namely FreeSurfer, whi h is developed at Harvardand based on the method by Dale et al. [27℄. The omparison is based on phantomMRI images onstru ted from orti al surfa es extra ted from real MRI images. In thisway, ground truth orti al boundaries are reated and the geometri al error of the ortexre onstru tions an be quanti�ed. The paper's on lusion is that the developed method isre onstru ting the orti al surfa es with a subvoxel a ura y and that it performs betterthan FreeSurfer in most of the tests as well as being mu h faster.Paper IV: Evaluation of Five Algorithms for Mapping Brain Cor-ti al Surfa es (Chapter 5)In this paper �ve di�erent algorithms for mapping between surfa es of the erebral ortexare evaluated. The fo us is on algorithms for mapping between verti es of dis rete surfa eswhi h is ompli ated by the possibly arbitrary vertex ount of the orti al surfa es. Aproposed feature driven mapping algorithm is presented together with tests of it and fourother mapping algorithms onsisting of a feature driven approa h, two spheri al mappingapproa hes and a basi iterative losest point algorithm. The algorithms are evaluatedwith onstru ted riteria for a good mapping, a landmark test using manually pla edlandmarks and an analysis of onstru ted statisti al maps. The paper on ludes that noalgorithm an be singled out as the best hoi e of mapping between orti al surfa es; ea hmethod has its strengths and weaknesses. However, it is indi ated that a ombination ofa spheri al warp approa h with an iterative feature based algorithm ould be a promising hoi e.Paper V: Corti al Volumes and Atrophy Rates in FTD-3 CHMP2BMutation Carriers and Related Non- arriers (Chapter 6)This paper reports the results of applying the developed methods to identify orti alstru tural hanges in individuals with a familial variant of frontotemporal dementia. Ninepresymptomati individuals arrying the disease mutation are ompared to seven individ-uals from the same family without the mutation. The study is based on two serial MRIs ans of ea h individual and annualized atrophy rates are al ulated. Both volumetri and thi kness measurements show that the presymptomati mutation arriers degenerate

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Chapter 2Extra tion of the CerebralCorti al Boundaries from MRIfor Measurement of Corti alThi knessAdapted from: S. F. Eskildsen, M. Uldahl and L. R. Østergaard: Extra tion of the Cere-bral Corti al Boundaries from MRI for Measurement of Corti al Thi kness, Progress inBiomedi al Opti s and Imaging, vol. 5747, issue II, 2005, p. 1400-10.2.1 Introdu tionSeveral diseases degenerate the human erebral ortex. One of the most ommon and fastdeveloping neurodegenerative diseases is Alzheimer's disease (AD). Subtle, spatially lo al-ized atrophy may o ur before the �rst lini al signs [2℄. Knowledge on the earliest signsof atrophy and its initiating site in AD patients may a ompany earlier and more a uratediagnosis of AD. Atrophy of the erebral ortex may be quanti�ed in vivo by measuringthe volume or thi kness of the ortex from a magneti resonan e imaging (MRI) s an, ontaining a series of ross-se tional images. Knowledge of orti al volume may indi ateatrophy, but annot reveal the exa t site of atrophy as lo al thi kness measurements an.Measurements of orti al thi kness from a series of MRI images is ompli ated as it re-quires the images to be orthogonal onto the measured stru ture in order to avoid under- orover-estimates. In addition to this, the relatively low resolution and partial volume e�e ts(PVE) may ompli ate an a urate de�nition of the orti al boundaries. Manual measure-ment of the orti al thi kness is a tedious and time onsuming pro ess, and the manualmeasurements are likely to be biased to the operator due to the di� ulty of de�ning the orti al boundaries. Hen e, there is a need for fully automati and obje tive methods.Automati measurements of the ortex requires an automati delineation of the orti alboundaries. The erebral ortex is a thin sheet of gray matter (GM), surrounding the erebrum white matter (WM), and surrounded by erebrospinal �uid (CSF). In this paperthe WM/GM and GM/CSF rossings are referred to as the inner and outer boundary ofthe ortex respe tively. The ortex is isomorph to a sphere, if losed at the brain stem [1℄.Thus, advantageously, the boundaries may be represented as simple surfa es, isomorph toa sphere.Segmentation algorithms based on deformable surfa es rely on a ombination of high-and low-level information, whi h enables delineation of the boundary in areas where imageedges are obs ured or missing. Opposite banks of tight sul i may meet inside the sul al23

Chapter 2: Extra tion of the Cerebral Corti al Boundaries from MRI for Measurementof Corti al Thi kness 24folds and appear as onne ted in MRI due to undersampling and artifa ts. The maindi� ulty in orti al segmentation lies in orre tly penetrating su h sul i and rea hingtheir fundi, as the true orti al thi kness otherwise will be overestimated. Ma Donald etal. [9℄ addressed this problem by deforming the inner and outer surfa e simultaneouslyunder in�uen e of interse tion onstraints and an inter-surfa e distan e onstraint, whi hdrags the outer surfa e towards the fundi of sul i. However, a bias between the hosenprede�ned distan e and the measured orti al thi kness may exist [9℄.A di�erent approa h to modeling the ortex without a distan e onstraint is taken byDale et al. [5℄ In this approa h, Dale et al. �t a surfa e to the inner boundary of the ortex, and in�ates it towards the outer boundary of the ortex. The approa h ausesthe surfa e to settle at approximately the midpoints of tight sul i when no CSF is evi-dent between the sul al banks, and onstraints prevent the surfa e from self-interse ting.Clearly, the dire tion of in�ation is important to the resulting outer surfa e. Dale et al.use the dire tions of the surfa e normals. However, su h an approa h requires the use ofex essive smoothing to avoid the formation of non-existent folds, in the presen e of small on avities, or noise in the in�ating surfa e. Xu et al. [16℄ introdu ed an alternative tothe dire tion of the surfa e normals with a generalized gradient ve tor �ow (GGVF) for e,whi h provides ve tors pointing towards the nearest image boundary. Xu et al. used thisfor e for extending the inner surfa e towards the entral layer of the ortex. Xu et al.noted that their approa h ould be tailored to segmenting the GM/CSF boundary insteadof the entral layer. However, their approa h does not impose self-interse tion onstraints,whi h is ne essary when segmenting the outer boundary, nor is it fully automati .This paper presents a new method inspired by the work of Dale et al. [5℄ and Xu etal. [16℄ The method is apable of fully automati ally extra ting measurements of orti althi kness, volume and area from a T1-weighted MRI s an. The details of the method isdes ribed in the following se tion, and preliminary test results are presented in se tion2.3.2.2 MethodsThe data used as input to the method are T1-weighted MRI s ans en ompassing theentire erebrum. Tissue inhomogeneity artifa ts in the MRI volumes are redu ed usinga method by Sled et al. [12℄, and the volumes are registered into a ommon referen espa e using a method by Collins et al. [4℄ The steps in the ortex extra tion method isillustrated in �gure 2.1. An initial surfa e is extra ted from the T1-weighted MRI s an,and deformed to �t the inner orti al boundary. The resulting surfa e is then deformedto �t the outer orti al boundary. From these surfa e representations of the inner andouter orti al boundary, anatomi al properties of the ortex, su h as the thi kness, an beobtained.Generation

Initial Inner SurfaceDeformation

Inner SurfaceDeformation

Outer SurfaceCortex ModelMRI Volume MeasurementsFigure 2.1: Pipeline of the method. Rounded boxes indi ate pro essing steps. Gray boxesindi ate data.2.2.1 Initial Inner Surfa e GenerationA surfa e of the inner boundary of the erebral ortex is generated by extra ting the WM omponent of the erebrum, and then performing a tessellation of this omponent. Thesteps are illustrated in �gure 2.2.The brain is extra ted from the MRI volume using a brain extra tion tool [13℄. Theresult after applying the brain extra tion tool is a volume onsisting of the erebrum,

25 2.2 MethodsBrain Extraction

Cerebrum WMIsolation of

Cerebrum WM Segmentation Surface Generation

TessellationCorrectionTopology Initial Inner

SurfaceFuzzy SegmentationMRI VolumeFigure 2.2: Pro ess of generating the initial surfa e. Rounded boxes indi ate pro essingsteps. Gray boxes indi ate data.the erebellum and the brain stem. To identify the WM voxels in the volume, the fuzzy -means algorithm is applied [14℄. The volume is divided into WM, GM, CSF and ba k-ground, and the output of the algorithm is a membership volume for ea h lass. TheWM membership volume is used in the further pro edure of generating the initial sur-fa e. To �nd the WM inside the erebrum, the erebrum is automati ally separated fromthe erebellum and brain stem, using morphologi al operations on the WM membershipvolume.A tessellation of the erebrumWM is performed using a simple iso-surfa ing algorithm.The tessellation of the erebrum WM may in lude handles or holes. To ensure that thetessellated surfa e is isomorph to a sphere, a topology orre tion algorithm by Han etal. [6℄ is applied to the tessellated surfa e of the erebrum WM.2.2.2 Inner Surfa e DeformationThe initial estimate of the inner boundary of the erebral ortex is a surfa e lose tothe true WM/GM boundary. The purpose of the surfa e deformation is to smoothenthe surfa e and adjust it to the orre t tissue boundary. An a tive ontour frameworkoriginally des ribed by Kass et al. [8℄ is used to deform the surfa e. The deformation ismade by iteratively moving the verti es to the positions, in a spheri al sear h spa e, whi hresult in the lowest energy level expressed by an energy fun tion. The energy fun tion mustensure that the energy minimum is situated where the surfa e �ts the orre t WM/GMboundary.Internal and external energies are used to ontrol the behavior of the deformable sur-fa e. The internal energies are applied to a hieve a smooth hara teristi of the surfa eand help keeping the verti es uniformly distributed on the surfa e. For this purpose atension term and a �exural term are used. The tension term is an approximation of theLapla ian [10℄:

ELaplacian = ‖~L(~v)‖, where ~L(~v) =1

n

n∑

i=0

~vi − ~v , (2.1)where ~v is a vertex in the surfa e, ~vi is the ith neighbor to ~v, and n is the number ofneighboring verti es to ~v. The �exural term is an approximation to the squared Lapla ian[10℄:Esquared Laplacian =

∥

∥

∥

∥

∥

1

n

n∑

i=0

~L(~v) − ~L(~vi)

∥

∥

∥

∥

∥

(2.2)External energies are used to guide the surfa e towards the WM/GM boundary. Threedi�erent external energies are used, namely gradient, in�ation and initial energy.The gradient energy attra ts the deforming surfa e to the WM/GM boundary when lose to image edges of this boundary:Egradient = −‖~∇I(~v)‖ , (2.3)where ~∇I is the �rst derivative of the intensities in the MRI volume. The magnitude of

Chapter 2: Extra tion of the Cerebral Corti al Boundaries from MRI for Measurementof Corti al Thi kness 26the gradient is used, as the energy fun tion must return an energy level at a given position,not a ve tor.The fuzzy membership values and the dire tions of the surfa e normals are used todispla e the surfa e towards the orre t tissue boundary. If a vertex in the surfa e ispla ed in WM, the vertex is displa ed in the dire tion of the surfa e normal. Contrary,if the vertex is pla ed outside WM, the vertex is displa ed in the opposite dire tion ofthe surfa e normal. The WM membership is assumed to equal or to be lose to theGM membership when exa tly on the GM/WM boundary, but to di�er signi� antly fromthe GM membership when far from the boundary. The in�ation energy has no in�uen ewhenever the di�eren e between the WM and GM memberships is between the thresholds−T and T :

Einflation =

−(~n(~v) · ~D), if µWM (~v) − µGM (~v) > T (In WM)−(−~n(~v) · ~D), if µWM (~v) − µGM (~v) < −T (In GM)0, otherwise (Border region),where ~n(~v) is the unit surfa e normal at vertex ~v, ~D des ribes the dire tion of the move-ment of ~v, and µ is the membership values from the fuzzy segmentation. The expressionis negated to yield a low energy whenever the inner produ t between ±~n and ~D is high.The initial surfa e is generally a good estimate of the WM/GM boundary. Therefore,an energy penalizing large deviations from the initial surfa e is introdu ed:

Einitial = g(|~vinitial − ~vdeforming|), (2.4)where ~vinitial is a vertex in the initial surfa e and ~vdeforming is the orresponding vertexin the deforming surfa e. g is a weighting fun tion ontrolling the extent of a range Rwhere the energy has no in�uen e. This range is ne essary as the initial surfa e is only anapproximation. g is de�ned as:g(x) =

{

|x − R|2 , if x > R0 , otherwise (2.5)The omplete energy fun tion used for the deformation of the inner surfa e is:

Einner = c1ELaplacian + c2Esquared Laplacian

+c3Egradient + c4Einflation + c5Einitial,(2.6)where c1...c5 are weights. This fun tion is an expression of the energy level of a singleposition in the sear h spa e of a vertex. The greedy algorithm by Williams et al. [15℄is used to �nd the minimum energy position in the sear h spa e of ea h vertex. Theverti es are moved in this way until the number of verti es moved during an iteration isbelow a given threshold, where equilibrium is assumed. The used sear h spa e is spheri al ontaining 26 di�erent positions.Two hard onstraints are applied to the surfa e during deformation; one that ensures a ertain minimum distan e between neighboring verti es, and one that prevents the surfa efrom self-interse ting.2.2.3 Outer Surfa e DeformationThe inner surfa e is used as the initial estimate of the outer orti al boundary. As men-tioned in the introdu tion, the image edges of the outer boundary in tight sul al folds annot always be observed in MRI s ans. As the ortex has approximately the same on-vexity and on avity as the WM, tight sul al folds an be modeled by displa ing the innersurfa e in the dire tion of the surfa e normals. This is done using an in�ation energysimilar to the one used in the inner surfa e deformation. If a vertex is lo ated in WM orGM, the vertex is displa ed in the dire tion of the surfa e normal, otherwise it is displa ed

27 2.2 Methodsin the opposite dire tion:Einflation =

{

−(~n(~v) · ~D), if µGM (~v) + µWM (~v) ≥ µCSF (In WM or GM)−(−~n(~v) · ~D), otherwise (In CSF)A hard onstraint prevents the surfa e from self-interse ting in sul i where no CSF isevident in-between the sul al banks. This auses the in�ation energy to ollapse walls oftight sul al folds at a position approximately equidistant to the inner surfa e, when noCSF is evident (see �gure 2.3). However, the in�ation energy may erroneously ollapse

(a) Initial (b) Deforming ( ) FinalFigure 2.3: Example of how the in�ation for e enables modeling of narrow sul i with noCSF evident. The gray solid line indi ates the deformable surfa e, whi h approa hes theGM/CSF boundary from the WM/GM boundary. As the deformable surfa e is pushed inthe dire tion of the lo al surfa e normals, it will eventually meet itself inside deep narrowsul i.the surfa e in small on avities, and for example model non-existent folds on top of gyri.In reasing the in�uen e of the internal energies resolves these problems, but also impairsthe ability of the surfa e to onform to urved regions on the outer boundary. To over omethis tradeo�, an energy displa ing the surfa e dire tly towards the GM/CSF image edge isin luded in the energy fun tion. This energy has the e�e t of unfolding on avities on thedeforming surfa e when no outer surfa e on avities is evident in the image data, and thusavoids forming non-existent folds in the surfa e. A proper weighting between this energyand the in�ation energy auses tight sul al folds to ollapse and small on avities to beunfolded, while apturing the GM/CSF image edge. The energy uses a GGVF �eld by Xuet al. [16℄ The omponents of the GGVF �eld point towards edges in a given edge map. Inorder to ensure that the GGVF �eld points towards the outer boundary, the edge map is al ulated by taking the �rst derivative of the sum of the WM and GM fuzzy memberships(see �gure 2.4). The GGVF energy is the inner produ t between the normalized GGVF�eld ve tor ~G and the normalized dire tion ve tor ~D:EGGV F = −~G(~v) · ~D (2.7)When lose to the edge de�ned by the edge map, the GGVF energy is swit hed to agradient energy al ulated from the MRI data. This swit h is made when the di�eren ebetween the CSF and GM membership value goes below a given threshold ρ:

EGGV F =

{

−~G(~v) · ~D , if |µCSF − µGM | ≥ ρ

−‖~∇I(~v)‖ , otherwise (2.8)The same internal energies is used for the deformation of the outer surfa e as thoseused for the inner surfa e. The omplete energy fun tion used for the deformation of theouter surfa e is:Eouter = c6ELaplacian + c7Esquared Laplacian + c8Einflation + c9EGGV F , (2.9)

Chapter 2: Extra tion of the Cerebral Corti al Boundaries from MRI for Measurementof Corti al Thi kness 28

Figure 2.4: Example of a GGVF �eld based on an edge map al ulated from the sum ofthe WM and GM memberships using the �rst order derivative.where c6...c9 are weights.2.2.4 MeasurementsHaving the inner and outer boundary of the ortex represented as losed surfa es, it ispossible to obtain a variety of measurements, su h as volume, area and thi kness. However,in this paper the fo us is on the orti al thi kness. The thi kness is measured as theshortest distan e from a given vertex on the outer surfa e to the fa e of the inner surfa e(not ne essarily being a vertex). A thi kness measurement is obtained at ea h vertex ofthe outer surfa e.2.3 ResultsThe generated surfa es ontain approximately 200.000 verti es ea h. The entire extra tionof the orti al boundaries requires less than one hour on a 2.8GHz Pentium 4 pro essor,although the deformation pro ess alone is done in less than 10 minutes.The method was tested on six simulated MRI s ans of a brain phantom [3℄ with respe -tively 0%, 1%, 3%, 5%, 7% and 9% of noise added, and an isotropi voxel size of 1.00mm.Surfa es representing the GM/CSF tissue boundary were extra ted for all datasets, andthe surfa e of the dataset without noise was used as a referen e in order to fa ilitate a omparison. The omparison was made by al ulating the distan e to the nearest vertexon the referen e surfa e for all verti es on ea h of the remaining surfa es. The mean dis-tan es and standard deviations are reported in table 2.1. Only a small in rease in error,measured as mean distan e, is the result when the noise level is in reased from 1% to 9%.

29 2.3 Results1% 3% 5% 7% 9%0.27mm (0.22) 0.31mm (0.26) 0.34mm (0.27) 0.37mm (0.30) 0.41mm (0.33)Table 2.1: Mean distan e to nearest vertex on referen e surfa e and standard deviations.To assess the robustness of the method, thi kness measurements of the same subje t,s anned at two di�erent sessions on the same s anner were ompared. First session voxelsize was 0.89x0.89x2.00mm, and the se ond session voxel size was 0.86x0.86x2.00mm. Thedi�eren e in mean orti al thi kness between the �rst and se ond s an was 0.01mm. To in-vestigate these subtle deviations, a vertex to vertex omparison of the orti al thi kness forthe two s ans was done by al ulating the deviation in orti al thi kness for orrespondingverti es (using nearest point orresponden e) on the GM/CSF surfa es of the two s ans.The mean deviation was found to 0.33mm with a standard deviation of 0.27mm.

(a) Rendering of the outer orti al surfa e. (b) Interse tions of inner and outer orti alsurfa es with MRI data.Figure 2.5: Visualization of the extra ted inner and outer orti al surfa es of an ICBMsubje t.The method was applied to 38 T1-weighted MRI s ans of healthy subje ts a quiredfrom the ICBM database [7℄. These data have an isotropi voxel size of 1.00mm. A visualinspe tion of surfa e/data interse tions for all 38 datasets revealed few visible errors (see�gures 2.5 and 2.6). The mean orti al thi kness for the 38 subje ts was measured to2.59mm (0.15mm). This is within the range of what was measured in a post-mortem studyby Pakkenberg et al. [11℄, where the mean thi kness in the four main lobes were measuredto be in the range 2.16mm to 2.88mm. The orti al thi kness of the 38 subje ts was olormapped onto the outer orti al surfa e. An example of this, onverted to grays ale, isshown in �gure 2.7. As it an be observed from the �gure, the ortex is measured to bethi kest in the frontal and temporal regions, and thinnest in the o ipital and parietalregions. This was the ase of all 38 subje ts, and is onsistent with normal anatomi al�ndings. Even though the pattern of thi k frontal and temporal lobes, and thin parietaland o ipital lobes an be re ognized in all subje ts, inter-subje t variations exist in the orti al thi kness. Figure 2.8 illustrates this by the thi kness map of 16 healthy subje tsseen from the top.To evaluate the method on a brain with an abnormal morphology, orti al thi knessmeasurements were obtained from two MRI s ans of an Alzheimer's patient with severeatrophy a quired six months apart. These data have an isotropi voxels size of 0.9 mm,however, the ontrast is lower than the ICBM data. The method su eeded in apturingthe inner and outer orti al surfa es of the brain with abnormal morphology, and thethi kness measurements indi ated a small de rease in mean orti al thi kness from 2.02

Chapter 2: Extra tion of the Cerebral Corti al Boundaries from MRI for Measurementof Corti al Thi kness 30

Figure 2.6: Interse tions of inner and outer surfa es with MRI data of an ICBM subje t.Top row: Inner surfa e. Bottom row: Outer surfa e. A few errors are visible in theimages of se ond olumn, where the surfa es are penetrating both ventri les. These errorsoriginate from the topology orre tion algorithm, that enfor es a losed genus zero surfa e.

(a) Top view (b) Left viewFigure 2.7: Corti al thi kness mapped onto the outer orti al surfa e as gray levels. Darkregions are thin, while bright regions are thi k, ranging from 0 mm to 6 mm.mm to 1.89 mm. Figure 2.9 shows the orti al thi kness measurements extra ted fromthe two s ans, mapped onto the outer orti al surfa es as gray levels. The small de reasein orti al thi kness an be observed from the surfa es by a faintly darker texture on these ond surfa e.

31 2.3 Results

Figure 2.8: The thi kness pattern of 16 ICBM subje ts seen from the top.

Chapter 2: Extra tion of the Cerebral Corti al Boundaries from MRI for Measurementof Corti al Thi kness 32

(a) Time point 1 (b) Time point 2Figure 2.9: Corti al thi kness at two time points (The olor s ale ranges from 0 mm(bla k) to 6 mm (white)).2.4 Con lusionThis paper presented a new fully automati method for segmenting the inner and outerboundaries of the human erebral ortex from MRI data. The method is based on adeformable surfa e framework, and in orporates a new ombination of energies in theenergy fun tion. The a urate initial surfa e speeds up the overall extra tion pro ess, asfewer iterations are ne essary in the deformation pro ess, and in reases the probability oflo ating the orre t minimum of the energy fun tion.The tests ondu ted on a simulated brain phantom with various degrees of noise added,showed that in reased image noise only in�uen es the sub-voxel a ura y of the method.This, along with the test/retest experiment, suggests that the method is robust to hangesin image noise and other image artifa ts.Preliminary tests have been ondu ted on neuroanatomi al data of normal brains andbrains with severe atrophy at di�erent time points. Results of these tests show that themethod is fast, robust and a urate for segmenting the orti al boundaries. The thi knessmeasurements ondu ted on normal subje ts are lose to post-mortem measurements, andthe relative thi kness between the major lobes are in a ordan e with the known anatomyof the brain. The inter-subje t variability in the orti al thi kness patterns, found amongthe normal subje ts (illustrated in �gure 2.8), indi ates that knowledge of this variabilitymust be obtained in order to dis ern normal and abnormal anatomy. The results obtainedfrom the Alzheimer's subje t indi ate that the method is apable of tra king progressionof atrophy in Alzheimer's patients.In the near future, we intend to apply the method on a large olle tion of MRI s ansof Alzheimer's patients, and a olle tion of longitudinal data from Alzheimer's patients.This data material give us the opportunity to investigate the possibility of tra king theprogression of orti al atrophy. Furthermore, we intend to reate statisti al models ofboth Alzheimer's and normal brains based on the data material. With this, we hopeto get indi ations of whi h anatomi al markers ould be relevant in the identi� ation ofAlzheimer's patients.A knowledgementsThe data material of normal healthy subje ts was provided with ourtesy of the Inter-national Consortium of Brain Mapping. The data material of the Alzheimer's subje twas provided with ourtesy of Centre for Magneti Resonan e, University of Queensland,

33 REFERENCESAustralia. The brain phantom used in the robustness test was provided with ourtesy ofM Connell Brain Imaging Centre, Montréal Neurologi al Institute, M Gill University. Theauthors thank these institutions for their ontribution. The authors also thank Center forFun tionally Integrative Neuros ien e, Aarhus University, Denmark, for their ooperationand funding.Referen es[1℄ L. Abrams, D. E. Fishkind, and C. E. Priebe. A proof of the spheri al homeomorphism onje ture for surfa es. IEEE Transa tions on Medi al Imaging, 21(12):1564�1566,2002.[2℄ G. Chetelat and J.-C. Baron. Early diagnosis of alzheimer's disease: ontribution ofstru tural neuroimaging. NeuroImage, 18:525�541, 2003.[3℄ D. Collins, A. Zijdenbos, V. Kollokian, J. Sled, N. Kabani, C. Holmes, and A. Evans.Design and onstru tion of a realisti digital brain phantom. IEEE Transa tions onMedi al Imaging, 17(3):463�468, June 1998.[4℄ D. L. Collins, A. P. Zijdenbos, T. Paus, and A. C. Evans. Use of registration for ohortstudies. Te hni al report, Montreal Neurologi al Institute, M Gill University, 2000.[5℄ A. M. Dale, B. Fis hl, and M. I. Sereno. Corti al surfa e-based analysis i: Segmentationand surfa e re onstru tion. NeuroImage, 9:179�194, 1999.[6℄ X. Han, C. Xu, U. Braga-Neto, and J. L. Prin e. Topology orre tion in brain or-tex segmentation using a multis ale, graph-based algorithm. IEEE Transa tions onMedi al Imaging, 21(2):109�121, 2002.[7℄ ICBM. International Consortium for Brain Mapping.http://www.loni.u la.edu/ICBM/, 2002.[8℄ M. Kass, A. Witkin, and D. Terzopoulos. Snakes: A tive ontour models. InternationalJournal of Computer Vision, 1988.[9℄ D. Ma Donald, N. Kabani, D. Avis, and A. C. Evans. Automated 3-D extra tion ofinner and outer sura es of erebral ortex from mri. NeuroImage, 12:340�356, 2000.[10℄ T. M Inerney and D. Terzopoulos. Topology adaptive deformable surfa es for medi alimage volume segmentation. IEEE Transa tions on Medi al Imaging, 18(10):840�850,1999.[11℄ B. Pakkenberg and H. J. G. Gundersen. Neo orti al neuron number in humans: E�e tof sex and age. Journal of Comparative Neurology, (384):312�320, 1997.[12℄ J. G. Sled, A. P. Zijdenbos, and A. C. Evans. A non-parametri method for automati orre tion of intensity non-uniformity in mri data. IEEE Transa tions on Medi alImaging, 17(1):87�97, 1998.[13℄ S. M. Smith. Fast robust automated brain extra tion. Human Brain Mapping,17(3):143�155, 2002.[14℄ J. S. Suri, S. Singh, and L. Reden. Computer vision and pattern re ognition te hniquesfor 2-D and 3-D MR erebral orti al segmentation(part I): A state-of-the-art review.Pattern Analysis and Aplli ations, 5:46�76, 2002.[15℄ D. J. Williams and M. Shah. A fast algorithm for a tive ontours. In Third Interna-tional Conferen e on Computer Vision, 1990.[16℄ C. Xu, D. L. Pham, M. E. Rettmann, D. N. Yu, and J. L. Pri e. Re onstru tion ofthe human erebral ortex from magneti resonan e images. IEEE Transa tions onMedi al Imaging, 18(6):467�480, 1999.

REFERENCES 34

Chapter 3A tive Surfa e Approa h forExtra tion of the HumanCerebral Cortex from MRIAdapted from: Simon F. Eskildsen and Lasse R. Østergaard: A tive Surfa e Approa hfor Extra tion of the Human Cerebral Cortex from MRI, MICCAI 2006, Le ture Notes inComputer S ien e, 4191, pp. 823-830, O tober, 2006.3.1 Introdu tionDuring the last de ade, several methods for extra ting the boundaries of the human ere-bral ortex from magneti resonan e imaging (MRI) have been proposed [1,3,5�8,10,11℄.The segmentation of the erebral ortex may fa ilitate extra tion of important anatomi alfeatures, su h as the orti al thi kness, whi h may be utilised in studying the progress ofa long list of neurodegenerative diseases, and in turn may aid in diagnosing these diseases.Furthermore, anatomi al models of the ortex may be useful in onne tion with surgerysimulation, preoperative planning, and postoperative evaluation.The human erebral ortex is a omplex, highly onvolved sheet-like stru ture. InMRI the orti al boundaries are often obs ured or partly missing be ause of poor on-trast, noise, inhomogeneity artifa ts and partial volume averaging originating from thea quisition. Opposite banks of tight sul i on the outer boundary may meet inside the sul- al folds and appear as onne ted in MRI. A tive surfa es have the ability to ompensatefor obs ured and in omplete image edges. However, in brain MRI, information of the outer orti al boundary may be ompletely missing in several tight sul i. The most promisingmethods for delineating the outer boundary use information of the white matter/greymatter (WM/GM) boundary to �t the surfa e to the outer orti al boundary. Ma Donaldet al. used a oupled surfa e approa h, where the inner and outer surfa e simultaneouslywere deformed under proximity onstraints maintaining a prede�ned minimum and maxi-mum distan e between the inner and outer boundary [7℄. Zeng et al. also used the oupledsurfa es approa h in a level set framework [11℄. The oupled surfa es approa h has theadvantage of expli itly using information of both orti al boundaries to dete t the outerboundary. This solves the problem of penetrating the deep narrow sul i. The drawba ksare the omputational expense, and the onstraints of a prede�ned distan e, whi h mayprevent the dete tion of abnormal thin or thi k areas of the ortex. Kim et al. proposed amodi� ation to the method by Ma Donald et al. whi h does not ontain a oupled surfa e onstraint [6℄. This method has shown promising results.Another approa h by Dale et al. identi�ed the inner orti al boundary, and expandedthis surfa e towards the outer boundary [3℄. This has the advantage that all sul i are35

Chapter 3: A tive Surfa e Approa h for Extra tion of the Human Cerebral Cortex fromMRI 36present in the initial state, and enables the preservation of the sul i during deformation,even though the eviden e of the outer boundary may be missing in the MRI data. Thetight sul al folds are modelled by preventing self-interse tions in the deforming surfa e,thus the delineation of the folds is pla ed equidistant from the sul al walls of the innerboundary. This single surfa e approa h is fast and aptures all the tight sul i. However,the expansion of the surfa e towards the outer boundary is sensitive to small errors orirregularities in the initial surfa e, whi h may lead to modelling of non-existent sul i. Xuet al. used a Generalised Gradient Ve tor Flow (GGVF) to de�ne a dire tion toward the entral layer of the ortex [10℄. This solution provided a fast and onsistently onvergen eof the surfa e, but tight sul i with no eviden e of the outer boundary were not apturedby this method. Re ent work by Han et al. expands the surfa e from the entral layertoward the outer boundary using a topology-preserving geometri deformable model [5℄.In this approa h the GGVF is only in luded in the model when re onstru ting the entral orti al layer.This paper presents an a tive surfa e approa h for ortex extra tion hara terised bythe in lusion of a GGVF in the extra tion of the outer orti al boundary and the use ofa lo al weighting strategy based on the intrinsi properties of the deforming surfa e.3.2 MethodsThe strategy for re onstru ting the erebral ortex is to �rst extra t the inner boundary,and then displa e this surfa e towards the outer boundary under the in�uen e of internaland external for es. The inner boundary is extra ted using the method dis losed in ourearlier work [4℄ ensuring a surfa e topology of a sphere. The following explains the defor-mation that �ts a surfa e to the outer orti al boundary using a surfa e estimating theinner boundary.3.2.1 Deformation Pro essThe a tive surfa e is a non-parametri triangular mesh. The surfa e is deformed by it-eratively updating ea h vertex with a ve tor de�ned as the sum of deformation for es.This deformation s heme has the advantage of being fast (O(n)) and eliminates problemsregarding granularity, whi h is found in dis rete methods. Even though onvergen e maybe fast, absolute equilibrium is never rea hed, due to the iterative nature of the algorithm.Therefore, a threshold for the update ve tor is given that de�nes whether or not a vertexhas moved during an iteration. The stop riterion is met when a su� iently small numberverti es are displa ed during an iteration.During surfa e deformation the surfa e is remeshed at prespe i�ed intervals using asimple mesh adaption algorithm. The remeshing is based on the vertex density of thesurfa e. This is done to avoid lustering of verti es and allowing the surfa e to expandwhere ne essary, i.e. the distribution of verti es are kept uniform throughout the surfa e.The surfa e remeshing algorithm does not hange the topology of the surfa e, but is allowedto alter the surfa e geometry. Finally, the surfa e is prevented from self-interse ting duringdeformation using the same prin iple as des ribed in [3℄.3.2.2 Internal For esInternal for es are applied to keep the verti es well-distributed and a hieve a smooth hara teristi of the surfa e. The internal for es used in this paper are similar to onven-tional smoothing for es [1, 8℄ in form of a tensile and a �exural for e. The tensile for e is al ulated by an approximation of the Lapla ian [8℄:~L(i) =

1

m

∑

j∈N(i)

~x(j) − ~x(i) , (3.1)

37 3.2 Methodswhere ~x(i) is the position of vertex i, N(i) are the neighbour verti es to i, ~x(j) is theposition of i's neighbour j, and m is the number of verti es in N(i). The �exural for e is al ulated by an approximation of the squared Lapla ian [8℄:~L2(i) =

1

m

∑

j∈N(i)

~L(~x(j)) − ~L(~x(i)) (3.2)Both ~L and ~L2 are de omposed into a tangential and a normal omponent of the for eve tor as in the method of Dale et al. [3℄. This enables adjustment of the ontra tive e�e tof the internal for es by weighting ea h omponent.The internal for es have the e�e t of smoothing and �attening the surfa e, however,as the target boundary is highly onvolved with both peaked and �at areas, the internalfor es should be relaxed in ertain areas of the surfa e and in reased in others. Thedeforming surfa e is used as a referen e for the urvature of the target boundary to obtainlo al urvature weighting of the internal for es. To enable the surfa e to ompensate forerrors in the initial surfa e, and fa ilitate some degree of surfa e urvature alteration, the urvature values are re al ulated at prespe i�ed intervals during the deformation pro ess.The urvature is estimated at ea h vertex of the deforming surfa e using the expression:ρ(i) =

{

σ(i) , if ~w(i) · ~n(i) ≤ 0−σ(i) , otherwise

(3.3)σ(i) =

1

m

∑

j∈Ng(i)

π − 2cos−1

(

~x(j) − ~x(i)

|~x(j) − ~x(i)|· ~w(i)

)

, (3.4)where Ng(i) is a geodesi neighbourhood around vertex i, ~w(i) is a unit ve tor pointingfrom i towards the entre of gravity of Ng(i), ~n(i) is the unit ve tor normal at i, and m isthe number of verti es in Ng(i). Curvature values of zero are found in �at areas, positivevalues in onvex areas and negative values in on ave areas. Note that the size of Nghas great in�uen e on the urvature values and should be hosen arefully. The urvaturevalues are Gaussian �ltered (σ = 1), normalised, and in this form used to weight theinternal for es:~̂uint(i) = f(ρ(i))~uint(i), (3.5)where f is a weighting fun tion de�ned as

f(x) = 1 −1

2tan(|x|), x ∈ [−1; 1] (3.6)3.2.3 External For esThe outer boundary of the erebral ortex follows approximately the same onvexities and on avities as the inner orti al boundary. Hen e, a surfa e delineating the inner orti alboundary is used as an initial estimate of the outer orti al boundary. This inner surfa eis displa ed in the dire tion of the lo al surfa e normals until the surfa e meets itself (see�gure 3.1), and thereby model sul i, even though only little or no image information isavailable. For this purpose a pressure for e [1℄ is used. The for e is similar to the externalfor e used in [3, 8℄, but based on fuzzy memberships of the tissue lasses as des ribedin [10℄. The fuzzy memberships are al ulated using the fuzzy -means algorithm [9℄. Thepressure for e is expressed as:

~p(i) = ∆µ(i)~n(i)∆µ(i) = µWM (i) + µGM (i) − µCSF (i),

(3.7)where µ is the membership values (trilinearly interpolated) and ~n(i) is the unit ve tornormal at vertex i. A weighting fun tion is applied to the membership di�eren e to

Chapter 3: A tive Surfa e Approa h for Extra tion of the Human Cerebral Cortex fromMRI 38(a) Initial (b) Deforming ( ) FinalFigure 3.1: Illustration of how the pressure for e enables modelling of narrow sul i withno CSF evident. As the deformable surfa e (grey line) is pushed away from the WM/GMboundary in the dire tion of the lo al surfa e normals, it will eventually meet itself insidenarrow sul i.ensure a degree of freedom at membership di�eren es lose to zero:

~̂p(i) = c1g(∆µ(i))~n(i), (3.8)where c1 is a weighting onstant andg(x) = x(2 − 2cos(x)), x ∈ [−1 : 1] (3.9)Surfa e normals, approximated from a dis rete mesh, may be misleading, as they anbe perturbed by noise in the surfa e. This may erroneously ause modelling of non-existingfeatures, when the surfa e is displa ed over larger distan es. In reasing the in�uen e ofthe internal for es resolves this problem, but also prevents the surfa e from rea hing small on avities, whi h are truly evident in the MRI. To solve the problem, the pressure for eis ombined with a GGVF for e similar to the one used by Xu et al. [10℄, but with anedge map of the outer orti al boundary instead of the entral orti al layer. This edgemap is the �rst order derivative of the sum of the WM and GM fuzzy memberships.The GGVF for e performs best at the gyri where information of the GM/CSF boundaryis evident in the MRI, thus the normal ve tor is ombined with the GGVF ve tor so theGGVF ve tor dominates the normal ve tor at the rown and ridges of gyri, and the normalve tor dominates the GGVF ve tor along the fundi, and walls of sul i. The lo al surfa e urvature, al ulated in a geodesi neighbourhood, is used for balan ing the in�uen e ofthe GGVF ve tor and the normal ve tor:

~uext(i) = c2

(

~̂p(i)1 − ρ(i)

2+ ~g(i)

1 + ρ(i)

2

)

, (3.10)where ~̂p(i) is the pressure for e ve tor at vertex i, ~g(i) is the GGVF ve tor at vertex i,ρ(i) is the urvature value at i given in (3.3), and c2 is a onstant.Gradient information is used to s ale the update ve tor ~u, so the magnitude of theupdate ve tor is redu ed when the magnitude of the gradient in reases. This is done bymapping the normalised gradient magnitudes with the fun tion:

h(x) = cos(π

2x), x ∈ [0 : 1] (3.11)and s aling the update ve tor ~u by the result. The update ve tor is un hanged whenthere is no gradient and greatly shortened when a strong gradient is present at the givenvertex position. Information of the gradient is used only when lose to the GM/CSFboundary and suppressed when far from the boundary. The weighted membership di�er-en e g(∆µ(i)) in (3.8), that provides an estimate for the spatial position of the GM/CSF

39 3.3 Resultsboundary, is therefore utilised to weight the in�uen e of the gradient. The resulting up-date ve tor is given as a weighted sum of a gradient weighted term and a non-gradientweighted term:~u(i) = ((1 − τ)cos

(

π2 |

~∇(i)|)

+ τ)(~̂uint(i) + ~uext(i)),

τ = |g(∆µ(i))|,(3.12)where ~∇(i) is the image gradient trilinearly interpolated at vertex i, ~̂uint(i) is the weightedsum of the internal for es given in (3.5), and ∆µ(i) is given in (3.7).3.3 ResultsSimulated MRI s ans of a brain phantom1 [2℄ and 36 T1 weighted MRI datasets of youngnormal subje ts from the International Consortium for Brain Mapping (ICBM) databasewere used for testing the general behaviour of the deformation. The same weighting onstants were used in all test ases. Initial surfa es isomorph to a sphere were generatedand �tted to the inner orti al boundary. The initial surfa es onsisted of approximately

1.5 · 105 verti es. During deformation this number was in reased to approximately 2.0 ·105. The deformation pro ess onverged after 30-40 iterations with the stop riterion of(#moved verti es) < (1% of total verti es). The deformation of the outer surfa e requiredapproximately 20 minutes on a 3 GHz Pentium 4 pro essor. The self-interse tion testsperformed throughout the deformation of the inner and outer surfa e were responsible forthe majority of the pro essing time.Figure 3.2 shows three di�erent modes of the deformation pro ess in a sele ted partof the simulated MRI. The three modes di�er in their external for es, the internal for esare the same for all three modes. In the �rst mode, only the pressure for e is enabled,simulating the method by Dale et al. [3℄. This learly shows that the use of the pressurefor e alone result in irregularities in the surfa e. This is espe ially evident at top of gyri.In the se ond mode, only the GGVF for e is enabled, simulating the method by Xu etal. [10℄. In this ase the surfa e does not rea h the fundus of sul i without eviden e ofCSF. There is also an undesirable behaviour in some of the sul i, be ause the surfa e isattra ted to the nearest visible GM/CSF image edge. The last mode shows deformationwith both the pressure for e and the GGVF for e enabled, balan ed using the urvatureweighting fun tion. Now the tight sul i are being modelled orre tly while avoiding surfa eirregularities on top of gyri.All 36 orti es from the ICBM database were automati ally re onstru ted and quali-tatively assessed by visual inspe tion. An example of an extra ted outer surfa e is shownin �gure 3.3. As it an be seen from the �gure, the extra ted surfa e appears smooth,realisti and major gyri and sul i are easily re ognised. The qualitative assessment of thea ura y of the extra ted surfa es was made by superimposing the surfa es onto the MRIand visually inspe ting the ontours (�gure 3.3, right). As it an be observed from the�gure the outer orti al boundary is a urately delineated. Tight sul i are modelled evenwhen the rowns of adja ent gyri are not separated in the image data, and the surfa etend to be pla ed at a position equidistant to the WM walls when no CSF is evident insul i. This indi ates that the method follows the intended behaviour.3.4 Summary and Con lusionThis paper presented a new method for extra ting the outer boundary of the human ere-bral ortex from MRI. The a tive surfa e approa h ombines a onventional pressure for ewith fuzzy tissue lassi� ations, and a generalised gradient ve tor �ow for e, while lo ally1The brain phantom was provided by the M Connel Brain Imaging Centre at the Montreal Neurologi alInstitute, http://www.bi .mni.m gill. a

Chapter 3: A tive Surfa e Approa h for Extra tion of the Human Cerebral Cortex fromMRI 40

Figure 3.2: Outer surfa e deformation pro ess using di�erent external for es at di�erentstages in the pro ess. Left to right: Deformation pro ess at iterations 0,5,15 and 30.Top: Only pressure for e is enabled. Middle: Only GGVF for e is enabled. Bottom:Combination of both for es balan ed by the urvature weighting fun tion.

Figure 3.3: Example of a generated ortex from ICBM data. Left: Rendering of outersurfa e. Right: Inner (bla k) and outer (white) surfa es superimposed onto MRI.weighting the for es based on the surfa e urvature. Preliminary tests were ondu tedon both simulated data and real data of young normal subje ts. The primary results of

41 REFERENCESthese tests indi ate that the method is fast, robust and a urate for segmenting the or-ti al boundary in both simulated and real neuroanatomi al data. Still, the method needsfurther validation, as it must be able to perform on data with varying quality and froma varying population, if it is going to be appli able in everyday lini al use. Future workin lude a large s ale validation on both healthy subje ts and subje ts with altered orti almorphology.A knowledgementsTest data were provided ourtesy of the International Consortium of Brain Mapping andM Connell Brain Imaging Centre, Montreal Neurologi al Institute, M Gill University.Referen es[1℄ L. D. Cohen and I. Cohen. Finite-element methods for a tive ontour models and bal-loons for 2D and 3D images. IEEE Trans. Pattern Analysis and Ma hine Intelligen e,1993.[2℄ D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. Sled, N. Kabani, C. Holmes, andA. Evans. Design and onstru tion of a realisti digital brain phantom. IEEE Trans-a tions on Medi al Imaging, 17(3):463�468, June 1998.[3℄ A. M. Dale, B. Fis hl, and M. I. Sereno. Corti al surfa e-based analysis i: Segmentationand surfa e re onstru tion. NeuroImage, 9:179�194, 1999.[4℄ S. F. Eskildsen, M. Uldahl, and L. R. Østergaard. Extra tion of the erebral orti alboundaries from mri for measurement of orti al thi kness. Progress in Biomedi alOpti s and Imaging - Pro eedings of SPIE, 5747(2):1400�1410, 2005.[5℄ X. Han, D. Pham, D. Tosun, M. Rettmann, C. Xu, and J. Prin e. Cruise: Corti alre onstru tion using impli it surfa e evolution. NeuroImage, 23(3):997�1012, 2004.[6℄ J. S. Kim, V. Singh, J. K. Lee, J. Ler h, Y. Ad-Dab'bagh, D. Ma Donald, J. M. Lee,S. I. Kim, and A. C. Evans. Automated 3-d extra tion and evaluation of the inner andouter orti al surfa es using a lapla ian map and partial volume e�e t lassi� ation.NeuroImage, 27(1):210�221, 2005.[7℄ D. Ma Donald, N. Kabani, D. Avis, and A. C. Evans. Automated 3-D extra tion ofinner and outer sura es of erebral ortex from mri. NeuroImage, 12:340�356, 2000.[8℄ T. M Inerney and D. Terzopoulos. Topology adaptive deformable surfa es for medi alimage volume segmentation. IEEE Trans. Medi al Imaging, 18(10):840�850, 1999.[9℄ D. Pham and J. Prin e. Adaptive fuzzy segmentation of magneti resonan e images.IEEE Transa tions on Medi al Imaging, 18(9):737�752, September 1999.[10℄ C. Xu, D. L. Pham, M. E. Rettmann, D. N. Yu, and J. L. Prin e. Re onstru tionof the human erebral ortex from magneti resonan e images. IEEE Trans. Medi alImaging, 18(6):467�480, 1999.[11℄ X. Zeng, L. H. Staib, R. T. S hultz, and J. S. Dun an. Segmentation and measurementof the ortex from 3-d mr images using oupled-surfa es propagation. IEEE Trans.Medi al Imaging, 18(10):100�111, O tober 1999.

REFERENCES 42

Chapter 4Quantitative Comparison of TwoCorti al Surfa e Extra tionMethods Using MRI PhantomsAdapted from: Simon F. Eskildsen and Lasse R. Østergaard: Quantitative Comparison ofTwo Corti al Surfa e Extra tion Methods Using MRI Phantoms, MICCAI 2007, Le tureNotes in Computer S ien e, 4791, pp. 409-416, O tober, 2007.4.1 Introdu tionRe onstru tion of the human erebral ortex from magneti resonan e (MR) images fa- ilitates morphometri studies and brain mapping, and provides intuitive visualisation ofthe human brain for the use in e.g. surgi al planning. Sin e the nineties a number ofalgorithms has been developed for extra ting the boundaries of the ortex from MR im-ages [2, 4, 8, 9, 12, 13, 15℄. FreeSurfer has been around for more than seven years, and has,due to the fa t that it is freely available, be ome widespread in the s ienti� ommunity.We have re ently published a method (hen eforth designated Fast A urate Cortex Extra -tion (FACE)), whi h resembles FreeSurfer in many aspe ts, but is signi� antly improvedin terms of omputational speed [5, 6℄.When performing morphometri studies the a ura y of the ortex re onstru tions isvery important. Therefore, it is of interest to investigate how well FACE performs interms of a ura y ompared to FreeSurfer. Quanti� ation of the a ura y is di� ult asthe ground truth is rarely available. A means to measure the a ura y is using phantomsresembling real neuroanatomi al data. Lee et al. [11℄ ompared FreeSurfer [4℄, CLASP[9℄ and BrainVISA [12℄ using generated phantoms. They found that CLASP was morea urate than BrainVISA and FreeSurfer. However, CLASP is not publi ly available,while the two other methods are. FreeSurfer performed se ond best in the study. In thisstudy we ompare our method, FACE, to FreeSurfer using realisti phantoms generatedfrom real MR s ans.4.2 MethodsTo evaluate the two ortex extra tion methods, eight healthy young subje ts (age: 32±7.4)and eight healthy middle-aged subje ts (age: 54.3±6.0) were sele ted , and a omparisonmethod similar to the method des ribed by Lee et al. was used [11℄. For ea h subje tboth methods were used to extra t the orti al boundaries. The surfa es extra ted byea h method were used as referen e for the generation of simulated MR s ans as des ribed43

Chapter 4: Quantitative Comparison of Two Corti al Surfa e Extra tion Methods UsingMRI Phantoms 44below. The ortex of these ustomised phantoms were extra ted by ea h method and theresulting surfa es were ompared to the referen e surfa es (see �gure 4.1).

Figure 4.1: Flow hart illustration of the omparison method.The following brie�y des ribes the two ortex extra tion methods, the generation ofthe test phantoms, and how the error between the referen e surfa es and the test surfa eswas quanti�ed.4.2.1 FreeSurfer MethodFreeSurfer [4, 7℄ �rst registers the input MR volume to Talaira h spa e [3℄. Non-uniformities originating from inhomogeneities in the magneti �eld are orre ted, andthe intensities are normalised. The resulting volume is skull stripped using an approa hsimilar to BET [14℄. The WM voxels inside the skull stripped volume is labelled using atwo-step segmentation algorithm based on intensities and prior knowledge of the GM/WMinterfa e. The ventri les and sub orti al matter inside the WM omponent is �lled, andthe WM is separated into the two hemispheres by a sagittal ut through the orpus al-losum and an axial ut through the pons. A onne ted omponent algorithm is used toisolate the main body of WM voxels, i.e. the erebrum WM voxels.From the WM voxels a surfa e mesh is onstru ted by generating onne ted triangleson the fa es of the voxels. The resulting surfa e for ea h hemisphere is topology orre tedto be isomorph to a sphere, and a deformation pro ess smoothes the surfa e while main-taining it at the WM/GM interfa e. The pial, or GM surfa e is found by displa ing theWM surfa e toward the GM/CSF interfa e using the lo al surfa e normals and intensitygradients.4.2.2 Fast A urate Cortex Extra tion MethodFACE performs similar prepro essing steps as FreeSurfer. The registered, intensity or-re ted, and skull stripped volume is segmented into WM, GM, and CSF using a fuzzy lustering algorithm solely based on the intensities, and a WM labelling is performed bymaximum membership lassi� ation. Cerebellum and the brain stem is removed usingatlas information, and the hemispheres are separated by a sagittal ut through the orpus allosum. After a onne ted omponent analysis spheri al topology of ea h hemisphere

45 4.2 Methodsis obtained using a topology orre tion algorithm [1℄, and the WM hemispheres an betessellated by an iso-surfa e algorithm yielding surfa es with Euler hara teristi s of asphere (genus=0).The iso-surfa e generated from the WM erebrum voxels are deformed to �t theWM/GM interfa e under the in�uen e of smoothing for es and for es derived from thesurfa e normals, the fuzzy voxel lassi� ation, and gradient information of the originalimage.The GM surfa e is found using the method des ribed in [6℄. The WM surfa e isdispla ed towards the GM/CSF interfa e using a ombination of the lo al surfa e normalsand a gradient ve tor �eld al ulated from an edge map of the voxel segmentation. Thein�uen e of the two ve tor for e �elds on ea h vertex in the surfa e is weighted by the urvature of the surfa e, whi h enables di�erent deformation behaviour a ording theposition on the surfa e (sul us or gyrus). The deformation is not minimising an obje tivefun tion, whi h means that the omplexity is low ompared to the deformation pro ess inFreeSurfer.4.2.3 Phantom GenerationMembership volumes of WM, GM, and CSF were generated dire tly from the extra tedsurfa es. This was a omplished by labelling ea h voxel ompletely inside the WM surfa eas WM, and al ulating the inside fra tion of ea h voxel interse ted by the surfa e. Thiswas also done for the GM surfa e, and the memberships for the three tissue lasses were al ulated from the fuzzy labelled volumes (see �gure 4.2). The three membership volumes

Figure 4.2: Fuzzy membership volumes generated from the extra ted surfa es. Left toright: WM, GM, and CSF.were used as input to an MRI simulator [10℄ with the same a quisition parameters as theoriginal MR s ans (TR=18ms, TE=10ms, 1mm sli es). The intensities of the resultingvolume were normalised to the range of the original s an. Finally, sub ortex, ventri les, erebellum, brain stem, and extra- erebral tissue were added from the original s an bysuperimposing the simulated brain s an onto the original (�gure 4.3).4.2.4 A ura y AssessmentTo test the a ura y of ea h method, re onstru tions of the orti al boundaries weregenerated from the 32 phantoms. The re onstru tions were then ompared to the re on-stru tions of the original MR s ans. Both methods ensures orre t topology by volume-or surfa e- orre tion. Thus the omparison was based solely on geometri al fa tors. Fourfa tors were onsidered, namely volume di�eren e, surfa e area di�eren e, over/under seg-

Chapter 4: Quantitative Comparison of Two Corti al Surfa e Extra tion Methods UsingMRI Phantoms 46

Figure 4.3: Phantom produ ed by the MRI simulator (left), and �nal phantom afternormalisation and added original tissue (right).mentation ratio, and the expli it geometri al error. Also the vertex density was takinginto onsideration in the omparison.• Volume Di�eren e: The en losing volume of the surfa es was al ulated and thedi�eren e (in per ent) from the referen e surfa es was measured.• Surfa e Area Di�eren e: Surfa e areas were al ulated and the di�eren e (inper ent) from the referen e surfa es was measured.• Over/under segmentation ratio: Tissue membership volumes of WM, GM andCSF were reated from the test surfa es similar to the pro edure used in the phantomgeneration. The resulting fuzzy maps were ompared to the maps generated fromthe referen e surfa es, and the per entages of voxels respe tively missing inside (falsenegatives) and added outside (false positives) the referen e map were al ulated.• Expli it Geometri al Error: The Eu lidean distan e from ea h vertex in thereferen e surfa e to the losest fa e on the test surfa e was measured. The rootmean square error of these distan es was al ulated for both the WM surfa e andthe GM surfa e. Similarly, the distan e was measured from the test surfa e to thereferen e surfa e. The latter was done to avoid that simply adding verti es to thesurfa e did not ne essarily redu e the error.4.3 ResultsThe orti al extra tions were performed on an AMD Opteron 2.6 GHz pro essor with 12GB memory. The average extra tion time from native s an to �nal surfa es for FreeSurferwas 20.1 hours, while it was 0.8 hours for FACE. The following presents the results onhow well the methods re onstru ted the original surfa es from the generated phantoms.When omparing the re onstru ted surfa es visually, only small di�eren es an bedis erned. Figure 4.4 shows the original GM surfa e along with the re onstru tions bythe two methods. The number of verti es in the surfa es generated by the two methods

47 4.4 Dis ussion

Figure 4.4: Left: Surfa e extra ted from original s an by FACE. Middle: Re onstru tionfrom phantom by FreeSurfer. Right: Re onstru tion from phantom by FACE.FreeSurfer Phantom FACE PhantomMetri FreeSurfer FACE P-value FreeSurfer FACE P-valueWM ∆vol (%) 1.2±1.1 5.4±2.6 0.00 1.7±1.9 4.9±2.3 0.00WM ∆area (%) 7.6±1.9 3.1±1.5 0.00 15.4±3.4 9.4±1.9 0.00Brain ∆vol (%) 4.4±1.2 4.0±1.0 0.36 5.5±2.0 3.7±0.8 0.01GM ∆area (%) 5.4±1.4 5.0±3.1 0.54 2.5±2.4 1.6±1.5 0.22WM FN (%) 8.5±1.3 4.2±0.6 0.00 10.0±2.1 3.2±0.6 0.00WM FP (%) 7.8±0.8 9.1±2.3 0.01 8.7±0.8 7.4±1.8 0.00GM FN (%) 23.4±1.3 21.9±2.0 0.01 26.4±3.7 19.9±1.9 0.00GM FP (%) 15.7±1.4 7.3±1.4 0.00 17.6±3.1 6.9±1.3 0.00WM ref2test (mm) 0.95±0.64 1.14±0.11 0.20 1.47±0.90 0.63±0.07 0.00WM test2ref (mm) 0.75±0.14 0.84±0.17 0.13 1.28±0.17 0.46±0.05 0.00GM ref2test (mm) 0.86±0.50 1.07±0.11 0.08 1.26±0.92 0.64±0.08 0.02GM test2ref (mm) 0.83±0.14 0.63±0.13 0.00 1.39±0.19 0.59±0.06 0.00Table 4.1: Errors measured by the four metri s on both WM and GM surfa es. Errors aredeviation from the referen e surfa es. For ea h metri the performan e on both FreeSurferand FACE phantoms is ompared for the two methods (two-tailed paired t-test). Signi�- ant smaller errors are marked by bold font.vary. FreeSurfer generates surfa es with almost twi e the number of verti es ompared toFACE (310,415±18,628 vs. 169,218±9,755).Table 4.1 lists the results for ea h error metri averaged for the 16 subje ts. The errorsof the two methods for ea h metri was ompared and tested by two-tailed paired t-test(the p-values are listed in the right hand olumn of ea h phantom). Signi� ant smallererrors are marked by bold font. The volume and area errors are absolute per ent hange ompared the to referen e surfa es. The under/over segmentation error is measured byper ent outside referen e surfa e volume (false positives (FP)) and per ent missing insidereferen e surfa e (false negatives (FN)). The expli it geometri al di�eren e is measuredby the RMS error in mm.4.4 Dis ussionFrom table 4.1 it an be observed that FACE has signi� antly fewer WM false negativesand GM false positives when testing on both groups of phantoms. The two metri s are

REFERENCES 48related in that missing WM voxels most likely are lassi�ed as GM voxels. Generally,both methods seem to over-expand the surfa es when ompared to the phantoms. Thisespe ially in reases the GM false negatives per entage, as the GM tissue lass is smallerthan the WM tissue lass.The geometri al error rates show that the average distan e between the test and ref-eren e surfa es is at subvoxel level when testing the a ura y of FACE. Reprodu ibilityerrors of FACE are onsistently around half a voxel size, while FreeSurfer reprodu ibilityerrors are between 0.75 - 0.95 voxel size. For purposes of omparison the di�eren e for thereferen e surfa es of the two methods was measured to 1.48±0.31 mm (average for bothWM and GM surfa es).When looking at the volume and area errors for the GM surfa es, i.e. erebrum vol-ume and area, there is little di�eren e between the two methods, and the error is fairlysmall (1.6% - 5.5%). Also, the WM volume errors are low. However, higher error ratesare found in the WM area. Looking at the area hange per subje t, it was found thatall re onstru ted WM surfa es had a smaller area than the referen e, while the volumeremained more or less the same. This ould point to the fa t that the WM voxels inthe phantoms do not exa tly resemble the original MR WM voxels leading to less deepsul i. Improvements of the phantoms ould solve this bias. Also, visual inspe tion of thesurfa es revealed signi� ant di�eren es in the surfa es at the base of the brain due to thedi�erent brain stem utting strategies in the two methods. The inspe tion also revealedthat FreeSurfer in a few surfa es missed part of the o ipital lobe. This ould be ausedby registration errors whi h again ould be aused by tissue voxels not resembling realMR data.Generally, the tests show that the a ura y of FACE is omparable to Free-Surfer.In most ases FACE has a signi� antly better a ura y. FACE is on average more than25 times faster than FreeSurfer. The longer extra tion time in FreeSurfer an partly beexplained by the high number of verti es in the surfa es. FreeSurfer generates surfa eswith almost twi e the number of verti es ompared to FACE. Another reason for the speeddi�eren e is a very fast onvergen e of the deformation in FACE due to refraining fromminimising an obje tive fun tion.Even though FACE in the omparison proved to be more a urate, results from some ofthe error metri s and visual inspe tions suggested that the phantoms ould be improved toresemble real anatomi al MR data. However, the results indi ate that FACE is omparableto FreeSurfer in terms of a ura y.The subje ts used in this study were healthy without altered orti al morphology.Further studies must examine the a ura y of the two methods when analysing subje tswith altered morphology (e.g. Alzheimer's patients), whi h is often the ase in lini altrials.A knowledgementsTest data were provided ourtesy of Dr. Peter Johannsen, Rigshospitalet, under grantnumber 22-04-0458 Danish Medi al Resear h Counsil, and the International Consortiumof Brain Mapping, M Connell Brain Imaging Centre, Montreal Neurologi al Institute,M Gill University.Referen es[1℄ L. Chen and G. Wagenkne ht. Automated topology orre tion for human brain seg-mentation. Le ture Notes in Computer S ien e, 4191(LNCS):316�323, 2006.[2℄ L. D. Cohen and I. Cohen. Finite-element methods for a tive ontour models and bal-loons for 2D and 3D images. IEEE Trans. Pattern Analysis and Ma hine Intelligen e,1993.

49 REFERENCES[3℄ D. L. Collins, P. Neelin, T. M. Peters, and A. Evans. Automati 3d intersubje tregistration of mr volumetri data in standardized talaira h spa e. Journal of ComputerAssisted Tomography, 18(2):192�205, Mar h-April 1994.[4℄ A. M. Dale, B. Fis hl, and M. I. Sereno. Corti al surfa e-based analysis I: Segmentationand surfa e re onstru tion. NeuroImage, 9(2):179�194, 1999.[5℄ S. F. Eskildsen, M. Uldahl, and L. R. Østergaard. Extra tion of the erebral orti alboundaries from mri for measurement of orti al thi kness. Progress in Biomedi alOpti s and Imaging - Pro eedings of SPIE, 5747(2):1400�1410, 2005.[6℄ S. F. Eskildsen and L. R. Østergaard. A tive surfa e approa h for extra tion of thehuman erebral ortex from mri. Le ture Notes in Computer S ien e, 4191(LNCS):823�830, 2006.[7℄ B. Fis hl, M. I. Sereno, and A. M. Dale. Corti al surfa e-based analysis ii: In�ation,�attening, and surfa e-based oordinate system. NeuroImage, 9(2):195�207, 1999.[8℄ X. Han, D. Pham, D. Tosun, M. Rettmann, C. Xu, and J. Prin e. CRUISE: Corti alre onstru tion using impli it surfa e evolution. NeuroImage, 23(3):997�1012, 2004.[9℄ J. S. Kim, V. Singh, J. K. Lee, J. Ler h, Y. Ad-Dab'bagh, D. Ma Donald, J. M. Lee,S. I. Kim, and A. C. Evans. Automated 3-d extra tion and evaluation of the inner andouter orti al surfa es using a lapla ian map and partial volume e�e t lassi� ation.NeuroImage, 27(1):210�221, 2005.[10℄ R.-S. Kwan, A. Evans, and G. Pike. MRI simulation-based evaluation of image-pro essing and lassi� ation methods. IEEE Transa tions on Medi al Imaging,18(11):1085�97, 1999.[11℄ J. Lee, J.-M. Lee, J. S. Kim, I. Y. Kim, A. C. Evans, and S. I. Kim. A novel quanti-tative ross-validation of di�erent orti al surfa e re onstru tion algorithms using mriphantom. NeuroImage, 31:572�584, 2006.[12℄ J.-F. Mangin, V. Frouin, I. Blo h, J. Régis, and J. López-Krahe. From 3d magneti resonan e images to stru tural representations of the ortex topography using topologypreserving deformations. Journal of Mathemati al Imaging and Vision, 5(4):297�318,De ember 1995.[13℄ T. M Inerney and D. Terzopoulos. Topology adaptive deformable surfa es for medi alimage volume segmentation. IEEE Trans. Medi al Imaging, 18(10):840�850, 1999.[14℄ S. M. Smith. Fast robust automated brain extra tion. Human Brain Mapping,17(3):143�155, 2002.[15℄ X. Zeng, L. H. Staib, R. T. S hultz, and J. S. Dun an. Segmentation and measurementof the ortex from 3-d mr images using oupled-surfa es propagation. IEEE Trans.Medi al Imaging, 18(10):100�111, O tober 1999.

REFERENCES 50

Chapter 5Evaluation of Five Algorithms forMapping Brain Corti al Surfa esAdapted from: S. F. Eskildsen and L. R. Østergaard: Evaluation of Five Algorithms forMapping Brain Corti al Surfa es, SIBGRAPI, pp. 137-144, 2008 XXI Brazilian Sympo-sium on Computer Graphi s and Image Pro essing, 20085.1 Introdu tionMorphologi al analysis of the human erebral ortex from in-vivo medi al images plays animportant role in the investigation of various neurologi al disorders, su h as s hizophreniaand dementia [6, 18℄. In reasing e�ort is being put into measuring orti al morphologi- al hanges over time and di�eren es between populations. Magneti resonan e imaging(MRI) provides ex ellent stru tural information of the erebral tissues, and surfa e re on-stru tions of the ortex from MRI have grown popular for studying morphologi al features,su h as orti al thi kness, area, and patterns of the orti al folds. During the last de adeseveral surfa e re onstru tion algorithms have been proposed [7,9,14,17,21,34℄, and severalways to obtain orti al thi kness measurements and other features from orti al surfa eshave been developed [24, 28℄. Usually the orti al surfa es are approximated by dis retepolygonal meshes, and orti al features are al ulated at ea h vertex provided a reasonablyuniform distribution of verti es a ross the surfa e. To measure morphologi al di�eren esbetween subje ts one an average the measurements over the entire ortex or within spe -i�ed regions, but to exploit the detailed map of measurements provided by high resolutionsurfa es and be able to dete t fo al di�eren es a point orresponden e between orti alsurfa es is required. Su h a mapping must preserve anatomi al landmarks a ross subje tsin order to reliably ompare measurements, i.e. it does not make sense to ompare thetop of a fold (gyrus) on one surfa e with the bottom of a fold (sul us) on another surfa e.Be ause of the high diversity of folding patterns a ross individual orti es, su h a mappingis far from trivial.5.2 Ba kgroundSeveral methods to solve the orti al mapping problem have been proposed. A popularapproa h is to parameterize the orti al surfa e by mapping the surfa e into a anoni alspa e and solve the orresponden e problem in this spa e. Often the unit sphere is used,as it is topologi ally equivalent to the orti al surfa e and provides an attra tive oor-dinate system for easy parameterization [13℄. Utilizing the Riemann mapping theoremon manifold surfa es [1℄ several approa hes have been proposed to onformally map the orti al surfa e to a sphere [16, 19, 23, 25, 26, 31℄. Also other anoni al spa es have been51

Chapter 5: Evaluation of Five Algorithms for Mapping Brain Corti al Surfa es 52used for parameterization, su h as an ellipsoid and the 2D plane [33℄. The latter, so- alled�at maps, require uts in the losed surfa e to be able to map the surfa e to the plane.Consistent uts are hard to automate, thus requiring manual intervention.After parameterization of orti al surfa es the orresponden e between verti es anbe obtained by registration of the surfa es in the anoni al spa e using the preservedgeometri al features as similarity measure. This registration is usually a non-linear warpbe ause of the highly irregular folding patterns [12, 35℄.The mapping onto a anoni al spa e introdu es geometri al distortion in the surfa e,and even though work has been fo used on minimizing the distortion in the onformalmapping [23℄ it remains a problem for the subsequent parameterization and registration.Creating �at maps introdu es more geometri al distortion than the spheri al approa hand alters the topology thus partly destroying geodesi relations between verti es [12℄.Several methods onstrain the mapping using landmark urves [16, 25, 29, 33℄. These areoften manually de�ned, but methods have been proposed to automate identi� ation oflandmark urves [15, 22, 28℄, though it is hard to do onsistently [4℄.Another group of methods try to solve the orresponden e problem without the in-termediate step of mapping to a anoni al spa e. One family of su h methods is derivedfrom the iterative losest point method (ICP) [2,5℄. Apart from variations over the simple losest point method, several methods ombine ICP with point feature registration [10,27℄.Others approa h the problem by �nding a dire t mapping using partial di�erential equa-tions (PDE) [29℄ or di�eomorphisms [32℄.Common for the mapping approa hes des ribed above is the preservation of intrinsi vertex on�guration, ex ept from the uts introdu ed when reating �at maps. This mayseem important, as these geometri properties re�e t the underlying ytoar hite ture ofthe ortex. However, when mapping between orti es with very di�erent orti al foldingpatterns, this onstraint an be relaxed to better mat h morphologi al features. A featurebased method disregarding the intrinsi vertex on�gurations was proposed by Spjuth etal. [30℄. They used a similarity fun tional based on mean urvature, surfa e normals,and Eu lidean distan e to �nd orresponding verti es between surfa es after an initial,global, a�ne registration. The method allows several verti es to map to the same targetvertex while other verti es are left without mapping. Thereby information is lost. Toretain information, the optimal solution is a bije tion between the surfa es only mappingbetween similar anatomi al points. When a vertex to vertex orresponden e is needed themapping annot be a bije tion if the two ortex surfa es have di�erent number of verti es.However, one an try to approximate a bije tion by having unique proje tions for as manyverti es as possible.As des ribed above a variety of algorithms for solving the orti al mapping problemhave been proposed. However, to the best of our knowledge, omparisons of the di�erentapproa hes have not been arried out. In this paper we propose a new algorithm for theproblem of �nding vertex orresponden e between surfa es with di�erent vertex ountsand evaluate the performan e of the proposed algorithm along with a sele tion of othermapping algorithms.5.3 Proposed Mapping AlgorithmThe proposed algorithm for mapping a sour e surfa e to a target surfa e is inspired bySpjuth et al. [30℄, and it uses the same similarity features, but seeks to optimize thenumber of unique mappings, thereby approximating a bije tion as lose as possible. Thealgorithm initially aligns the two surfa es with a rigid transformation found by enter ofmass normalization followed by ICP optimization [5℄. The method for �nding a vertex tovertex orresponden e from sour e to target surfa e uses a ost fun tional J . The ost ofmapping between sour e vertex i and target vertex j is given byJ(i, j) = αec(i,j) + βen(i,j) + γed(i,j) (5.1)

53 5.4 Algorithms Sele ted for Comparisonwhere c is the absolute di�eren e in normalized mean urvature at the verti es, n isthe normalized angle between the vertex normals, d is the normalized Eu lidean distan ebetween the verti es, and α, β and γ are weights. This ost fun tional is sought minimizedper sour e vertex by the following algorithm:De�nitions:Vs is the set of sour e verti es.Vt is the set of target verti es.tc is the ost threshold any mapping must be below.tm is the maximum number of mappings allowed to the same target vertex.Ns is the set of sour e verti es without a mapping.Nt is the set of target verti es with number of mappings < tm.Initial onditions : Ns = Vs, Nt = Vt, and tm = 1.1. For ea h vertex in Ns �nd the vertex in Nt with the lowest mapping ost de�ned by

J .2. For ea h vertex in Vt where number of mappings > tm remove highest ost mappingsuntil number of mappings = tm. Update Ns and Nt.3. Repeat from 1 until no mappings are found with a ost < tc, or either Ns or Nt isempty.4. If Ns is non-empty, set Nt = Vt, tm = tm + 1 and repeat from 1.We designate the algorithm iterative losest feature (ICF), be ause of its use of pointfeatures and iterative behavior. The weights in the ost fun tional were found by repeatedtrials of mapping between two simple phantom surfa es where the true mapping wasknown. The found weights were α = 3.7, β = 1.1, and γ = 2.7.5.4 Algorithms Sele ted for ComparisonApart from the proposed mapping algorithm we wanted to evaluate a handful of typi alalgorithms to �nd their strengths and weaknesses. The following algorithms were in ludedin the evaluation:• Iterative losest point (ICP). The basi ICP algorithm [5℄ to ompare with a simpleand �naive� approa h.• Feature. The method by Spjuth et al. [30℄ was in luded as this method is similarto the proposed algorithm but without the iterative behavior.• Iterative losest feature (ICF). The proposed method as des ribed in se tion 5.3.• Spheri alWarp. This is the method used in FreeSurfer to register a orti al surfa eto a � anoni al� surfa e [12, 13℄. Sour e and target surfa es are mapped to the unitsphere (�gure 5.1) and the folding patterns are aligned using a warp minimizing themean squared di�eren e between the average onvexity [13℄. This method is in ludedas the algorithm is freely available and the spheri al mapping introdu es less metri distortion than other mapping methods [20℄. To obtain a vertex orresponden emap, the geodesi losest points are used between two surfa es registered to the anoni al surfa e provided by FreeSurfer.• Spheri al. A method where sour e and target surfa es are mapped to a sphereand orresponding points are found by rotations of the sour e surfa e optimizing urvature orrelation. The method is similar to the approa h des ribed by Fis hl etal. [12℄, but instead of the �nal non-linear warp a rigid optimization is performediteratively in a multi-s ale manner. The spheri al mapping was done using FreeSurfer

Chapter 5: Evaluation of Five Algorithms for Mapping Brain Corti al Surfa es 54

Figure 5.1: From ortex surfa e to sphere. Left: Original orti al surfa e. Middle: In�atedsurfa e with urvature values superimposed. Right: Surfa e mapped to a sphere with urvature values superimposed.[7℄, while the subsequent optimization was implemented lo ally. As in the warpapproa h des ribed above, a vertex orresponden e map is obtained by the geodesi losest points between the two surfa es after optimization.The following se tion des ribes how the �ve mapping algorithms were evaluated.5.5 Mapping EvaluationPerforman e of the algorithms was tested using 10 orti al surfa es extra ted bythe FreeSurfer software [7℄ from T1 weighted MRI s ans (1.5 Tesla, 30◦�ip angle,TR/TE=18/10 ms, isotropi 1 mm voxels) from young healthy subje ts. FreeSurfer pro-du es surfa es of the inner and outer boundary of the ortex for ea h hemisphere sepa-rately. Surfa es of the outer orti al boundary of left hemispheres only were used in theevaluation, as brain symmetri properties suggest that either hemisphere is representativefor the orti al variation, and the mapping algorithms are expe ted to perform equallywell on both hemispheri surfa es. Surfa es generated by FreeSurfer are triangular mesheswith spheri al topology and have arbitrary number of verti es, thus they are well-suitedfor testing the algorithms des ribed here. The 10 extra ted left orti al surfa es had onaverage 148k±8k verti es. The distribution of verti es were assumed similar for the gen-erated surfa es. All 10 orti al surfa es were in turn used as target for mapping the othernine surfa es, thus resulting in 90 mappings in total used in the evaluation.The optimal orresponding target vertex for any given sour e vertex an be sought eventhough this means that two distin t verti es may map to the same vertex on the targetsurfa e. It is desirable to map to as many verti es on the target surfa e as possible to retaininformation, i.e. the image of the mapping must over as mu h of the target surfa e aspossible. The higher overage of the target surfa e the better approximation of a bije tionbetween the surfa es. Therefore, one riterion for a good mapping is the per entage ofverti es on the target surfa e that are used as orresponden e points for verti es on thesour e surfa e, i.e. the overage of the target surfa e. If the sour e surfa e has less verti esthan the target surfa e full overage is not possible. Therefore the overage error, C, isde�ned as:C = 1 −

|Mt|

min(|Vs|, |Vt|), (5.2)where Mt is the set of target verti es with a mapping, and Vs and Vt are the same as inse tion 5.3. Thus a full overage results in C = 0 while mappings with less overage havehigher values with a theoreti al upper limit of C = 1.In reasing the vertex ount of the sour e surfa e provides better onditions for a good overage. However, a sour e surfa e with twi e as many verti es as the target surfa e may

55 5.5 Mapping Evaluationprovide full overage of the target surfa e without being onsidered a good mapping iffor instan e a large portion of sour e verti es map to the same target vertex. Therefore,another riterion for a good mapping is the mean square number of mappings per targetvertex normalized by the squared sour e/target vertex ount ratio. The multiple mappingerror, M , is de�ned as:M =

1|Vt|

∑

j∈Vt

m2j

( |Vs||Vt|

)2− 1 =

|Vt|∑

j∈Vt

m2j

|Vs|2− 1 (5.3)where mj is the number of mappings to vertex j of the target surfa e. If M = 0 themapping is optimal with regard to the riterion, while higher values of M signal worsemappings with a theoreti al upper limit of M = |Vt| − 1.When mapping between surfa es we expe t that pat hes of the sour e surfa e aremapped to pat hes of similar size on the target surfa e. We introdu e a third riterionaiming at evaluating this property. For ea h vertex i on the sour e surfa e we determinethe geodesi distan es to the neighbors along the target surfa e after applying the map,where the geodesi distan e is al ulated as the minimum edge length between verti es(Dijkstra's algorithm [8℄). Optimally, this distan e should be the same as on the sour esurfa e when surfa es have equally distributed verti es. We al ulate the geodesi errorat vertex i as:

φ(i) =1

|N(i)|

∑

j∈N(i)

|g(m(i), m(j)) − g(i, j)| (5.4)where N(i) is the set of neighboring verti es to vertex i on the sour e surfa e, g(i, j) isthe geodesi distan e between i and neighbor j, while g(m(i), m(j)) the geodesi distan ebetween these verti es after the mapping. The density evaluation riteria, D, is de�nedas the average of the geodesi errors:D =

1

|Vs|

∑

i∈Vs

φ(i) (5.5)A mapping with good preservation of sour e surfa e pat hes has a small D with a theoret-i al minimum of D = 0 for the perfe t preservation. This metri is a�e ted if the vertexdistributions of the two surfa es are highly irregular. For this reason, similar distributionsof the surfa es are assumed.Finally, we wanted to evaluate if verti es are mapped between similar topographi alareas. To quantify this we de�ne a topography riterion, T , as the average di�eren e inmean urvature before and after mapping to the target surfa e:T =

1

|Vs|

∑

i∈Vs

|ρ(i) − ρ(m(i))| (5.6)where ρ(i) is the mean urvature at vertex i and m(i) is the mapping of vertex i (the targetvertex). Curvature values are normalized to the interval [−1 : 1], thus the topography riterion has values in [0 : 2] with theoreti al extrema.The four riteria des ribed above are all quantitative approa hes to evaluating themapping between orti al surfa es. To add a more qualitative approa h we performed alandmark test to evaluate the algorithms' performan e in mapping to the same anatomi allandmarks between di�erent orti al surfa es. Six landmarks were identi�ed manually onall 10 orti al surfa es of the left hemisphere. Landmarks were pla ed by labeling verti esspanning areas of 1-5 mm2. The sele ted anatomi al landmarks were the temporal pole(TP) at the anterior end of the superior temporal gyrus, the supramarginal gyrus (SG) atthe posterior end of the lateral sul us, the uneus (Cun) where the parieto-o ipital sul usmeets the al arine sul us, the posterior part of gyrus re tus (GR), the most superior

Chapter 5: Evaluation of Five Algorithms for Mapping Brain Corti al Surfa es 56Avg. di�eren e (mm) Paired t-test (p-val)ICP -0.10±0.05 <0.01Feature 0.02±0.03 0.11ICF -0.01±0.02 0.06Spheri al 0.00±0.03 0.64Warp 0.01±0.01 0.13Table 5.1: Average di�eren e in mean orti al thi kness after mapping.part of the post entral gyrus (PCG), and the ingulate gyrus (CG) at the anterior end ofthe ingulate sul us. These anatomi al lo ations were used as they are relatively easy tore ognize on the orti al surfa e, but are still subje t of morphologi al variation. For ea hmapping the geodesi distan es between the mapped landmarks and the manually labeledlandmarks were measured and averages over all 90 mappings were al ulated.Finally, we wanted to evaluate the e�e t of di�erent mapping algorithms on statisti- al maps, whi h are often used when measuring orti al thi kness. We wanted to test if hoi e of mapping algorithm would hange the on lusions drawn from orti al thi knessstatisti s. The orti al thi knesses of the 10 subje ts were therefore mapped to a ran-dom target surfa e and the non-parametri Kruskal-Wallis test [3℄ was performed at ea hvertex to test for equality among the mapped values. Furthermore, at ea h vertex the algo-rithms were tested against ea h other using the non-parametri Mann-Whitney-Wil oxon(MWW) test [3℄ to evaluate di�eren es between them.5.6 ResultsThe four quantitative evaluation riteria as de�ned in se tion 5.5 were al ulated for all90 mappings. Figure 5.2 shows the average errors al ulated for ea h algorithm by theevaluation riteria. The results from the landmark test are shown in �gure 5.3. Table 5.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Err

or

Coverage Error

0

1

2

3

4

5

6

7

8

9

Err

or

Multiple Mapping Error

0

1

2

3

4

5

6

7

8

9

Err

or

Density Error

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Err

or

Topography Error

ICP Feature ICF Spherical WarpFigure 5.2: Average errors of mapping with the �ve tested algorithms between permuta-tions of the 10 orti al surfa es (n=90).shows the average di�eren e in mean orti al thi kness before and after mapping the nine orti es to the randomly sele ted referen e surfa e. The Kruskal-Wallis test showed that31% of the verti es were dependent on the mapping algorithm, and the subsequent MWWtest revealed that the feature and ICF algorithms were providing similar statisti al results,while spe i� ally the spheri al rigid approa h had areas with on lusions di�erent fromthe other algorithms (table 5.2). Figure 5.4 shows the statisti al maps when omparingthe ICF algorithm with ea h of the other four mapping algorithms using the MWW test.

57 5.7 Dis ussion

ICP Feature ICF Spherical Warp0

10

20

30

40

50

Err

or

(mm

)

TPSGCunGRPCGCG

Figure 5.3: Average distan es in mm from mapped landmark to manually labeled landmarkof 90 mappings. Landmarks are temporal pole (TP), supramarginal gyrus (SG), uneus(Cun), gyrus re tus (GR), post entral gyrus (PCG), and anterior ingulate gyrus (CG).Spherical

ICP

Warp

Feature

(a) Lateral viewsSpherical

ICP

Warp

Feature

(b) Medial viewsFigure 5.4: ICF ompared vertex by vertex to the other four mapping algorithms visualizedon an in�ated referen e surfa e. White areas indi ate signi� ant di�eren e (p<0.05) inthe orti al thi knesses mapped to a vertex.5.7 Dis ussionEvaluation Metri sThe four evaluation riteria in se tion 5.5 were designed to evaluate the behavior of theexamined mapping algorithms. Even though the riteria should optimally result in as low

Chapter 5: Evaluation of Five Algorithms for Mapping Brain Corti al Surfa es 58Feature ICF Spheri al WarpICP 6% 3% 24% 14%Feature - 0% 22% 6%ICF - - 22% 6%Spheri al - - - 22%Table 5.2: Per ent verti es of referen e surfa e where the MWW test reje ts the hypothesisthat the orti al thi knesses ome from the same population (α = 0.05) for the di�erentmapping algorithms, whi h means that the mappings in�uen e the on lusion.values as possible, all riteria annot be expe ted to be low be ause of the highly diversefolding patterns in the surfa es. For example, a low density error, i.e. a good preservationof the intrinsi vertex on�gurations, will inevitably result in a high topography error, assome verti es are mapped from onvexities to on avities and vi e versa. Nevertheless,the four riteria are useful for evaluating the algorithms' strengths and weaknesses.From �gure 5.2 it an be seen that the algorithms behave more or less as expe ted.The ICP algorithm not surprisingly has relatively high overage, multiple mapping, andtopography errors, while the density error is kept low. This is to be expe ted as no onstraints on multiple mappings or topography preservation are applied, and verti es arekept very ompa t as only the Eu lidean distan e is optimized. The feature algorithmas proposed by Spjuth et al. [30℄ has almost as bad a overage as the ICP algorithm,but performs better in both the multiple mapping and topography riteria. As expe tedthe density error for the feature algorithm is high, as neighboring verti es are allowedto jump between gyri resulting in long geodesi distan es between the mapped verti es.The proposed ICF algorithm behaves approximately similar to the feature algorithm withregard to the density and topography riteria. However, when evaluating the overage andmultiple mapping, it an be seen that this algorithm has the lowest errors among the �veevaluated algorithms. This was expe ted as onstraints are enfor ed to prevent multiplemappings and optimize the overage.The two mapping approa hes that use an intermediate step in form of mapping toa sphere have a similar behavior. As expe ted these algorithms have the lowest densityerrors among the algorithms, and the multiple mapping errors are also relatively low.This is be ause the intrinsi vertex on�gurations are retained during the spheri al �ttingpro ess. However, the overage errors are relatively high, and the topography errors arehighest among the evaluated algorithms for the rigid spheri al approa h, while a littlelower for the warp approa h. This is interesting as the �tting pro ess should minimize thetopographi al di�eren es between the surfa es. This is a tangible sign of the high diversityof the folding patterns, and that maintaining the intrinsi vertex on�gurations result inmapping between di�erent topographies. The spheri al warp approa h whi h non-linearlyshould ompensate for the highly diverse folding patterns still has high topography errors.This may be explained by the fa t that the non-linear �tting is done to an average modelinstead of the a tual target surfa e. It seems that a ombination of the ICF and thespheri al approa h may provide a ni e trade-o� between the four mapping riteria.Landmark TestFigure 5.3 reveals that the mapping algorithms are far from perfe t when evaluating howwell they map between manually labeled landmarks. The error is measured as the geodesi distan e to the manually labeled landmark, whi h means that mapping to a gyrus or sul usadja ent to the orre t results in a large error. From the �gure it an be seen that somelandmarks are generally more a urately mapped than others no matter the hoi e ofalgorithm. The ingulate gyrus are in most ases mapped with a pre ision of less than 1 m, and gyrus re tus is also in most ases mapped more a urately than the remainingfour landmarks. These two landmarks are both lo ated medially lose to the midbrain

59 5.7 Dis ussionwhere orti al variations are less pronoun ed. The supramarginal gyrus, whi h is lo atedin an area of deep sul i and great orti al variability, generally has high errors in all �vealgorithms. This emphasize the fa t that highly onvoluted and variable areas are harderto map than less folded areas. The ICP, feature, and ICF algorithms all have similarpatterns of landmark errors not signi� antly (0.21<p<0.40) di�erent from ea h other,whi h may be due to the similar nature of these algorithms. The spheri al approa h withthe rigid optimization seems to have a more uniform distribution of errors, ex ept for the ingulate gyrus. This an be explained by the rigid optimization. The spheri al approa hwith the non-linear optimization is able to ompensate for the high orti al variability, andit results in errors similar to landmarks in areas without great orti al variability, su has the ingulate gyrus and gyrus re tus. Be ause of the high standard deviations in thelandmark errors, it is hard to on�dently determine the best mapping algorithm, however,when averaging all landmark errors within ea h algorithm the spheri al warp approa hperforms signi� antly (p<0.001) better than the other algorithms with an average errorof 9.5±9.0 mm, while the spheri al rigid approa h performs signi� antly (p<0.001) worsewith an average error of 19.0±23.4 mm. Further tests should in lude more subje ts andlandmarks in on ave regions in addition to the onvexly lo ated landmarks used here toget a more representative quanti� ation of mapping a ura y.Statisti al MapsThe averaged orti al thi kness after mapping to the random referen e surfa e did not hange signi� antly ex ept when using the ICP algorithm (see table 5.1). However, thegenerated statisti al maps revealed that almost one third of the verti es on the referen esurfa e are dependent on whi h mapping algorithm is used to map the orti al thi kness tothe referen e. Testing ea h algorithm against the others revealed that the spheri al rigidapproa h is the algorithm with the largest areas (22% - 24%) of deviating on lusionsbased on the MWW test (see �gure 5.4 and table 5.2). Almost no di�eren e is seenbetween the ICF and feature algorithms while smaller di�eren es is seen between ICF andICP (3%) and ICF and the spheri al warp (6%). As it an be seen from �gure 5.4, 3% isa noti eable portion of a ortex, and may lead to wrong on lusions. This suggests thatthe impa t of the mapping algorithm on the statisti al maps is high, and it must be takeninto onsideration when drawing on lusions from the statisti al maps.Proposed AlgorithmThe ICF algorithm extends the simple feature based approa h by iteratively approximat-ing a bije tion. This is re�e ted in the quantitative measures of overage and multiplemapping, where ICF has the lowest errors. However, the algorithm is not more a uratewhen measuring the distan e to the manually pla ed landmarks, and the statisti al mapsshow no di�eren e between the simple feature based method and the ICF. Though pre-serving more information, the ICF algorithm does not seem to improve a ura y or hangethe produ ed statisti al maps.Both approa hes use mean urvature, normal dire tion, and Eu ledian distan e format hing verti es. These features do not distinguish between large onvex areas, su has the sylvian �ssure, and the smaller onvexities, su h as most of the sul i. Additionalfeatures ould be in luded in the ost fun tional to better map areas of similar sized onvexity, e.g. the average onvexity as used by FreeSurfer ould be used [11, 12℄. Also,a term punishing large geodesi distan es between vertex neighbors after mapping ouldbe in luded to ompensate for the high density errors. Furthermore, the weights in the ost fun tional were optimized by a simple phantom surfa e, and better a ura y may bea hieved by optimizing using realisti orti al surfa es.

REFERENCES 605.8 Con lusionThis paper presented a new algorithm for solving the orti al mapping problem and testedit along with four other algorithms. The tests of the �ve mapping algorithms leave amixed result, where no algorithm an be singled out as the best. The four evaluation riteria showed that the algorithms generally behave expe tedly, while the landmark testindi ated that the spheri al warp approa h is more a urate than the rest of the testedalgorithms. Choi e of algorithm should depend on the study. Dependent on whetherthe preservation of intrinsi vertex on�guration or the omparison of similar topographi areas is important, either the spheri al warp or the ICF algorithm should be hosen, asthese are respe tively more a urate and preserve the most information. A ombinationof these algorithms ould be a promising mapping method and should be investigated inthe future. We showed that hoi e of mapping algorithm impa ts the results drawn fromstatisti al maps. However, onsidering the small number of subje ts used here furthertesting should be arried out to on�rm this. Finally, the number of di�erent types ofmapping algorithms tested is limited. Other types of mapping methods, su h as methodsbased on di�eomorphi mapping, should also be ompared in a future evaluation.Referen es[1℄ L. Ahlfors. Complex Analysis. M Graw-Hill S ien e/Engineering/Math, 3rd edition,1979.[2℄ A. Almhdie, C. Léger, M. Deri he, and R. Lédée. 3d registration using a new imple-mentation of the i p algorithm based on a omprehensive lookup matrix: Appli ationto medi al imaging. Pattern Re ognition Letters, 28(12):1523�1533, 2007.[3℄ D. R. Anderson, D. J. Sweeney, and T. A. Williams. Statisti s for business and e o-nomi s. South-Western College Publ., 8th edition, 2002.[4℄ M. A. Audette, F. P. Ferrie, and T. M. Peters. An algorithmi overview of surfa eregistration te hniques for medi al imaging. Medi al Image Analysis, 4(3):201�217,2000.[5℄ P. J. Besl and N. D. M Kay. A method for registration of 3-d shapes. IEEE Transa -tions on Pattern Analysis and Ma hine Intelligen e, 14(2):239�256, 1992.[6℄ G. Chetelat and J. . Baron. Early diagnosis of alzheimer's disease: Contribution ofstru tural neuroimaging. NeuroImage, 18(2):525�541, 2003.[7℄ A. M. Dale, B. Fis hl, and M. I. Sereno. Corti al surfa e-based analysis: I. segmenta-tion and surfa e re onstru tion. NeuroImage, 9(2):179�194, 1999.[8℄ E. W. Dijkstra. A note on two problems in onnexion with graphs. Numeris heMathematik, 1:269�271, 1959.[9℄ S. F. Eskildsen and L. R. Østergaard. A tive surfa e approa h for extra tion of thehuman erebral ortex from mri. Le ture notes in Computer S ien e, 4191 LNCS -II:823�830, 2006.[10℄ J. Feldmar and N. Aya he. Rigid, a�ne and lo ally a�ne registration of free-formsurfa es. International Journal of Computer Vision, 18(2):99�119, 1996.[11℄ B. Fis hl and A. M. Dale. Measuring the thi kness of the human erebral ortex frommagneti resonan e images. Pro eedings of the National A ademy of S ien es of theUnited States of Ameri a, 97(20):11050�11055, 2000.[12℄ B. Fis hl, M. I. Sereno, and A. M. Dale. Corti al surfa e-based analysis: II. In�ation,�attening, and a surfa e-based oordinate system. NeuroImage, 9(2):195�207, 1999.[13℄ B. Fis hl, M. I. Sereno, R. B. H. Tootell, and A. M. Dale. High-resolution intersubje taveraging and a oordinate system for the orti al surfa e. Human Brain Mapping,8(4):272�284, 1999.

61 REFERENCES[14℄ R. Goldenberg, R. Kimmel, E. Rivlin, and M. Rudzky. Cortex segmentation: A fastvariational geometri approa h. IEEE Transa tions on Medi al Imaging, 21(12):1544�1551, 2002.[15℄ G. L. Goualher, E. Pro yk, D. Louis Collins, R. Venugopal, C. Barillot, and A. C.Evans. Automated extra tion and variability analysis of sul al neuroanatomy. IEEETransa tions on Medi al Imaging, 18(3):206�217, 1999.[16℄ X. Gu, Y. Wang, T. F. Chan, P. M. Thompson, and S. . Yau. Genus zero surfa e onformal mapping and its appli ation to brain surfa e mapping. IEEE Transa tionson Medi al Imaging, 23(8):949�958, 2004.[17℄ X. Han, D. L. Pham, D. Tosun, M. E. Rettmann, C. Xu, and J. L. Prin e. Cruise:Corti al re onstru tion using impli it surfa e evolution. NeuroImage, 23(3):997�1012,2004.[18℄ P. J. Harrison. The neuropathology of s hizophrenia. a riti al review of the data andtheir interpretation. Brain, 122(4):593�624, 1999.[19℄ M. K. Hurdal and K. Stephenson. Corti al artography using the dis rete onformalapproa h of ir le pa kings. NeuroImage, 23(SUPPL. 1), 2004.[20℄ L. Ju, M. K. Hurdal, J. Stern, K. Rehm, K. S haper, and D. Rottenberg. Quantitativeevaluation of three orti al surfa e �attening methods. NeuroImage, 28(4):869�880,2005.[21℄ S. K. June, V. Singh, K. L. Jun, J. Ler h, Y. Ad-Dab'bagh, D. Ma Donald, M. L.Jong, S. I. Kim, and A. C. Evans. Automated 3-d extra tion and evaluation of theinner and outer orti al surfa es using a lapla ian map and partial volume e�e t las-si� ation. NeuroImage, 27(1):210�221, 2005.[22℄ C. . Kao, M. Hofer, G. Sapiro, J. Stern, K. Rehm, and D. A. Rottenberg. A geomet-ri method for automati extra tion of sul al fundi. IEEE Transa tions on Medi alImaging, 26(4):530�540, 2007.[23℄ F. Kruggel. Robust parametrization of brain surfa e meshes. Medi al Image Analysis,12(3):291�299, 2008.[24℄ J. P. Ler h and A. C. Evans. Corti al thi kness analysis examined through poweranalysis and a population simulation. NeuroImage, 24(1):163�173, 2005.[25℄ L. M. Lui, Y. Wang, T. F. Chan, and P. Thompson. Landmark onstrained genuszero surfa e onformal mapping and its appli ation to brain mapping resear h. AppliedNumeri al Mathemati s, 57(5-7 SPEC. ISS.):847�858, 2007.[26℄ J. Nie, T. Liu, G. Li, G. Young, A. Tarokh, L. Guo, and S. T. C. Wong. Least-square onformal brain mapping with spring energy. Computerized Medi al Imagingand Graphi s, 31(8):656�664, 2007.[27℄ A. Rangarajan, H. Chui, E. Mjolsness, S. Pappu, L. Dava hi, P. Goldman-Raki , andJ. Dun an. A robust point-mat hing algorithm for autoradiograph alignment. Medi alImage Analysis, 1(4):379�398, 1997. Cited By (sin e 1996): 45.[28℄ M. E. Rettmann, X. Han, C. Xu, and J. L. Prin e. Automated sul al segmentationusing watersheds on the orti al surfa e. NeuroImage, 15(2):329�344, 2002.[29℄ Y. Shi, P. M. Thompson, I. Dinov, S. Osher, and A. W. Toga. Dire t orti al mappingvia solving partial di�erential equations on impli it surfa es. Medi al Image Analysis,11(3):207�223, 2007.[30℄ M. Spjuth, F. Gravesen, S. F. Eskildsen, and L. R. Østergaard. Early dete tion ofad using orti al thi kness measurements. Progress in Biomedi al Opti s and Imaging- Pro eedings of SPIE, 6512, 2007.[31℄ D. Tosun, M. E. Rettmann, and J. L. Prin e. Mapping te hniques for aligning sul ia ross multiple brains. Medi al Image Analysis, 8(3):295�309, 2004.

REFERENCES 62[32℄ M. Vaillant, A. Qiu, J. Glaunès, and M. I. Miller. Di�eomorphi metri surfa emapping in subregion of the superior temporal gyrus. NeuroImage, 34(3):1149�1159,2007.[33℄ D. C. Van Essen, H. A. Drury, S. Joshi, and M. I. Miller. Fun tional and stru turalmapping of human erebral ortex: Solutions are in the surfa es. Pro eedings of theNational A ademy of S ien es of the United States of Ameri a, 95(3):788�795, 1998.[34℄ H. Xue, L. Srinivasan, S. Jiang, M. Rutherford, A. D. Edwards, D. Rue kert, andJ. V. Hajnal. Automati segmentation and re onstru tion of the ortex from neonatalmri. NeuroImage, 38(3):461�477, 2007.[35℄ G. Zou, J. Hua, and O. Muzik. Non-rigid surfa e registration using spheri al thin-platesplines, volume 4791 LNCS. 2007.

Chapter 6Corti al Volumes and AtrophyRates in FTD-3 CHMP2BMutation Carriers and RelatedNon- arriersAdapted from: Simon F. Eskildsen, Lasse R. Østergaard, Anders B. Rodell, Leif Øster-gaard, Jørgen E. Nielsen, Adrian M. Isaa s, and Peter Johannsen: Corti al Volumes andAtrophy Rates in FTD-3 CHMP2B Mutation Carriers and Related Non- arriers, Neu-roImage, In press6.1 Introdu tionFrontotemporal dementia (FTD) is a syndromi lini al variant of frontotemporal lobardegeneration (FTLD) whi h onstitutes the third most prevalent group of neurodegenera-tive diseases with ognitive impairment [28,43℄. Within re ent years the lini al, mole ulargeneti and pathologi al lassi� ations of FTD have evolved [8, 16℄. Up to 40% of FTD ases are onsidered autosomal dominantly inherited. One of the rarer auses of famil-ial FTD is CHMP2B -mutation related FTD with a pathogeni G-to-C transition in thea eptor spli e site of CHMP2B exon 6 ( .532-1G>C) on hromosome 3 (FTD-3) [47℄.The CHMP2B protein is a part of the Es ort-3 omplex involved in tra� king proteinsdestined for degradation in the Golgi apparatus. The mole ular disease me hanism is notyet fully known. The disease was primarily des ribed in a large Danish family [26, 36℄,but a novel nonsense mutation in the CHMP2B gene was re ently identi�ed in a Belgianfamilial FTD patient further supporting the gene to be involved in FTD [53℄.The Danish FTD-3 family is very large with 33 identi�ed patients and another 250at risk for developing the disease within the next 60 years. The average FTD-3 lini alonset is 57 years with a broad range from 43 to 65. As the symptom onset is insidious theexa t time of onset an be di� ult to determine. Patients present with primarily a lin-i al syndrome of frontotemporal dementia with behavioural hanges, apathy, sometimesaggression and/or hanged eating behaviour. During the early ourse they rarely havelanguage disturban es, but when neuropsy hologi ally tested they often have impairmentof more posteriorly orti ally lo ated fun tions su h as memory and visuospatial problems.Urinary in ontinen e and gait disturban es are normally late features although they some-times an be seen during the early years of the disease. Disease duration from diagnosisto death ranges from 2 to over 20 years.In FTD orti al stru tural hanges are per se primarily found in the frontal and tem-63

Chapter 6: Corti al Volumes and Atrophy Rates in FTD-3 CHMP2B Mutation Carriersand Related Non- arriers 64poral lobes [7℄. However, studies have also reported hanges in the parietal lobes [4,25,55℄.The aim of the present study is to assess orti al stru tural hanges in pre lini al FTD-3CHMP2B mutation positive ases ompared to mutation negative family members, andfurthermore to assess a possible progression of orti al hanges. A se ondary aim has beento try to identify possible pre lini al fo al orti al abnormalities.In vivo investigation of brain orti al stru tural hanges using magneti resonan eimaging (MRI) has primarily employed manual or semi-automati tra ing of tissue bound-aries to quantify anatomi al stru tures [29,42℄. Su h approa hes are time onsuming andsubje t to inter-rater variability. Therefore, automati unbiased omputational approa heshave gained popularity when studying ohorts of subje ts.A variety of studies [54℄ have used voxel-based morphometry (VBM) to dete t brain hanges in diseases with FTLD and di�eren es between disease FTLD sub-types andhealthy ontrols sin e the introdu tion of the method [2, 60℄. VBM performs voxel-wise omparisons between spatially aligned MRI s ans of subje t groups enabling identi� ationof tissue growth and tissue loss throughout the entire brain. A related method is tensor-based morphometry (TBM) [3℄, analyzing the deformation �eld involved in non-linearmapping of images, su h as mapping of intra-subje t serial s ans and mapping of subje tto group average. This way, lo al expansions and ontra tions an be identi�ed, and thetensor maps an be used to quantify longitudinal e�e ts and di�eren es between subje tsand groups. TBM has been used in di�erent areas, su h as studying the developing humanbrain [12℄ and measuring degeneration in Alzheimer's disease [23℄. TBM has been usedless extensively than VBM within the �eld of FTLD, but re ently more studies using TBMhave been reported [4, 9, 52℄.A third type of method for measuring orti al hanges is the expli it segmentationof the erebral ortex for measurements of orti al thi kness using parametri or geo-metri deformable models [15, 21, 27, 31�33, 62, 64℄. The ortex is expli itly or impli itlyrepresented as surfa es of the white matter/gray matter boundary and the gray mat-ter/ erebrospinal �uid boundary �tted to the images with subvoxel pre ision. This en-ables measurements of orti al thi kness throughout the entire ortex with the advantageof standardized thi kness measures, whi h is unavailable through VBM or TBM. In addi-tion, VBM does not onsider the orti al geometry, and annot di�erentiate the orti althi kness of opposing walls in sul i. The drawba k of surfa e based methods is the la k ofquanti� ation of sub orti al regions, su h as the thalamus, and basal ganglia. However,in studies where orti al stru tures are the obje tive and sub orti al stru tures are lessrelevant, surfa e based methods are preferable. Surfa e based methods have been usedto quantify hanges in a variety of diseases, su h as s hizophrenia [34, 40, 63℄, obsessive- ompulsive disorder [46℄, and Alzheimer's disease [35℄. In diseases with FTLD surfa ebased methods are apt, as degeneration is expe ted in the orti al lobes.In this study we applied a surfa e based orti al segmentation method to serial MRIs ans of pre lini al individuals with CHMP2B -mutation related FTD and individuals with-out the mutation from the same family. Global volume measurements and lo al orti althi knesses were determined from the orti al surfa es. Longitudinal and ross-se tionaldi�eren es in orti al thi kness were evaluated by lobe averages and by onstru tion ofstatisti al parametri maps.6.2 Materials and MethodsThe study adhered to the Helsinki II de laration, and was approved by The County Ethi sCommittees in the Counties of Aarhus, Viborg-Nordjylland and Copenhagen, Denmark.Subje ts were re ruited via a family onta t group that distributes information within theDanish FTD-3 family. All parti ipants signed the ethi s approved informed onsent form.All subje ts had previously parti ipated in geneti studies where they had been geneti allytested for the CHMP2B mutation. The parti ipating individuals and lini ians involvedin s anning or with any dire t onta t to the parti ipants have been and still are blinded

65 6.2 Materials and MethodsMutation arriers Non- arriersN 9 7Male:female ratio 7:2 4:3Age at baseline (years, mean±SD) 55.8±5.6 54.3±6.0Inter-s an interval (years, mean±SD) 1.3±0.2 1.3±0.1Table 6.1: Subje t demographi information.to the geneti status of the subje ts.6.2.1 Subje tsNine individuals arrying the CHMP2B mutation and seven age-mat hed 1.-degree rela-tives without the mutation (non- arriers) from the third and fourth generation of the largeDanish FTD-3 family were in luded in the study. All individuals were pre-symptomati at the follow-up s an without any subje tive omplaints and working full time or re entlyretired due to age. Subje ts and lose relatives (usually the spouse) were interviewed ina semi-stru tured manner by an experien ed lini ian, used to assess FTD patients ingeneral and the FTD-3 patients spe i� ally. For all parti ipants, neither the subje t northe informant des ribed any hanges in behaviour or personality. Some of the parti i-pants had previously agreed to neuropsy hologi al s reening where no abnormalities werefound. There were no omorbidities a�e ting erebral stru ture. S reening with standardinstruments, su h as the MMSE, is not valid for the present disease, as MMSE is knownto be normal even though the patients have gross behavioural and personality hanges.None of the parti ipants showed any sign of insidious symptoms on neither the lini alinterview nor the behavioural observation. Table 6.1 lists the demographi information ofthe subje ts. The age range at baseline s an was from 45 to 65 years of age.6.2.2 Image A quisitionT1 MRI data were obtained on a 3T GE Signa Ex ite using a 3D inversion re overyfast spoiled gradient re alled sequen e with TR/TE/TI = 6.3/2.9/750 ms, 14◦ �ip angle,0.94×0.94 mm2 in-plane resolution (256×256 pixels), and a sli e thi kness of 1.2 mm. Fullhead images were a quired with 126 - 148 axial sli es using a standard head oil. Stan-dard non-volumetri T2 weighted (22 axial sli es, TR/TE=4000/102 ms) images were alsoa quired. All images were he ked for obvious a quisition artefa ts su h as motion andsus eptibility artefa ts whi h an a�e t the image pro essing and subsequent quanti� a-tion.6.2.3 Image Pro essingThe MRI data were linearly and nonlinearly registered to a ommon model using theICBM152 [38℄ as target spa e. This was done using an automati iterative multiresolu-tion approa h similar to Collins et al. [14℄ and Janke et al. [30℄. The ommon model wasbased on 85 subje ts non-linearly registered, whi h resulted in an average with more well-de�ned image gradients than averages based on a�ne registrations, thus enabling morea urate registration of the target MRI data. Intensity non-uniformities originating frominhomogeneities in the magneti �eld were orre ted by the N3 algorithm [48℄. A brainmask was reated by iteratively �tting a deformable surfa e to the brain meninges usingan algorithm similar to the brain extra tion tool (BET) by Smith [50℄ (�gure 6.1.a). Thevoxels inside the brain mask were lassi�ed into white matter (WM), gray matter (GM),and erebrospinal �uid (CSF) using a fuzzy lustering algorithm (�gure 6.1.b). Stereo-taxi masks of the brain stem and erebellum were applied to isolate the erebral WM withan axial ut of separation approximately at lamina te ti. The ventri les and sub orti al

Chapter 6: Corti al Volumes and Atrophy Rates in FTD-3 CHMP2B Mutation Carriersand Related Non- arriers 66

Figure 6.1: Extra tion of the orti al boundaries. a) Spatially aligned MRI data withinitial (red ontour) and �nal (yellow ontour) brain extra tion ontour superimposed. b)Brain tissue lassi�ed as WM, GM, and CSF. ) Ventri les and sub orti al regions labelledas WM, and WM separated into hemispheres by a sagittal ut through orpus allosum.d) Edge map al ulated from the fuzzy lassi� ations. e) WM surfa e superimposed onthe MRI data. f) GM surfa e superimposed on the MRI data.regions were labelled WM to obtain a solid WM omponent for the following surfa e gener-ation and orti al segmentation. The erebrum WM was separated into two hemispheresby a mid-sagittal ut, and spheri al topology of ea h hemisphere was obtained using atopology orre tion algorithm [11℄ (�gure 6.1. ). An edge map of the GM/CSF interfa ewas reated using the membership volumes obtained by the previous fuzzy lassi� ation(�gure 6.1.d). The edge map was used in the orti al boundary extra tion as explainedbelow. All pro essing steps were fully automati .6.2.4 Corti al Boundary Extra tionCorti al boundaries were identi�ed using deformable surfa es and a for e balan ing s heme[39℄. Ea h hemisphere was pro essed separately. An initial surfa e was obtained by apply-ing an iso-surfa e algorithm on the topologi al orre t WM omponent reating a losedtriangulated surfa e [37℄. The initial surfa e was deformed iteratively to the WM/GMboundary under in�uen e of for es derived from the fuzzy lassi� ations and the gradientimage (6.1.e) [17℄. The GM/CSF boundary was found by expanding the initial surfa eunder in�uen e of deformation for es derived from the surfa e normals, a gradient ve tor�eld [61℄, and the GM/CSF edge map shown in �gure 6.1.d [18, 19℄. The resulting sur-fa es a urately delineated the erebral ortex rea hing into the deep narrow sul i (�gure6.1.f). The ortex extra tion method has been validated on healthy subje ts and phantom

67 6.2 Materials and Methodsdata [17�19℄, but has not yet been validated on neuropathologi al data. Therefore, orti- al surfa es were visually inspe ted for segmentation errors, both using a 3D visualizationtool and by superimposing the surfa es onto the original MR images.6.2.5 Corti al MeasurementsThe surfa es generated for ea h hemisphere were triangular meshes ea h onsisting ofapproximately 9×104 verti es uniformly distributed over the ortex. The orti al thi knesswas measured at ea h vertex as the distan e between the WM and GM surfa e orthogonalto the GM surfa e using a ombination of the surfa e normals and the nearest point(Eu lidian) on the opposite surfa e. The nearest point distan es between the surfa eswere used to restrain how far along the surfa e normals to sear h for interse tions of theopposite surfa e, thus preventing gross overestimation of the thi kness where the linesde�ned by the GM surfa e normals do not interse t the WM surfa e within the same lo altopography. To in rease the signal-to-noise ratio (SNR), orti al thi kness measurementswere blurred with a surfa e-based di�usion smoothing approximating a Gaussian kernelsmoothing with 10 mm full-width half maximum (FWHM) [13℄. Ea h hemisphere wasdivided into the main lobes based on an atlas in stereotaxi spa e that a ompany theMRI ro software pa kage [44℄, thus enabling regional based analysis. The atlas is de�nedas a labelled 3D image in stereotaxi spa e, and the subdivision of the surfa es was doneby assigning a label to ea h vertex with the losest image label measured by Eu lidiandistan e.Tissue ompartment volumes were estimated by utilizing the volumes en losed by theGM and WM surfa es. The surfa es en lose the ventri les and sub orti al regions fromthe lamina te ti and rostrally. Therefore, erebrum volume was estimated by the volumeen losed by the GM surfa e minus the volume of the ventri les and sub orti al regions,whi h were al ulated from non-linearly aligned masks. WM volume was al ulated simi-larly using the WM surfa e. Corti al volume was al ulated as the di�eren e between the erebrum and WM volume. Compartment volumes were normalized by estimated totalintra ranial volume (eTIV) obtained from an intra ranial mask non-linearly �tted to theimages.The a quired T2 images were visually he ked for hanges in WM lesions in order toensure that WM lesions ould not be an explanation for the results. We did not �nd any hanges in the number of WM lesions over the ourse of the study. Only one subje t hadminor age- onsistent WM-lesions. Thus there was not a lini ally relevant di�eren e inthe number of WM-lesions between the two groups.6.2.6 Surfa e MappingSurfa e mapping was applied to obtain vertex to vertex orresponden e between intra-subje t surfa es at baseline and follow-up, thus enabling point-wise di�eren es in orti althi kness. After an initial rigid alignment of the surfa es using the ICP algorithm [5℄,vertex orresponden e was al ulated by minimizing a ost fun tion expressing di�eren esin mean urvature, orientation, and spatial position of the surfa e verti es [20, 51℄. Tofa ilitate the onstru tion of statisti al parametri maps of orti al di�eren es between thegroups, baseline surfa es were mapped to a referen e surfa e hosen among the subje ts.Surfa es at baseline were geometri ally smoothed using a Lapla e operator and mappedto the referen e surfa e using the mapping method [20,51℄. The smoothing was performedto redu e geometri al distortion and obtain more well-de�ned sul al patterns.6.2.7 Statisti al AnalysisDistributions of orti al thi kness a ross subje ts were assumed to follow normal distribu-tions, both with regard to regional averages and single point measurements. Di�eren es

Chapter 6: Corti al Volumes and Atrophy Rates in FTD-3 CHMP2B Mutation Carriersand Related Non- arriers 68a ross groups were evaluated using t-tests with assumptions of unequal varian e. Longi-tudinal di�eren es within ea h group were evaluated using paired t-tests.Statisti al parametri maps were onstru ted to identify point-wise di�eren es overtime and between the groups. The maps were onstru ted by performing hypothesistesting at ea h vertex (approximately 105 verti es) of the referen e surfa e testing hangein orti al thi kness or di�eren es in orti al thi kness between the groups. Problemswith false positives related to multiple omparisons were addressed by al ulating FalseDis overy Rate (FDR) orre ted signi� an e thresholds [24℄. The statisti al maps wereblurred in the same way as the orti al thi kness measurements to in rease SNR andenhan e fo al e�e ts. The blurring, whi h approximated a Gaussian kernel smoothing with10 mm FWHM, had the e�e t of removing areas with s attered signi� an e (di�use e�e ts)leaving only fo al e�e ts ( lusters of signi� an e). Fo al e�e ts were determined wheresigni� ant di�erent ontiguous areas ( lusters) ex eeded an area of 20 mm2 al ulatedas the surfa e area spanned by lusters of onne ted verti es with p-values below thesigni� an e threshold. Anatomi al labels were assigned to the fo al di�eren es in thestatisti al parametri map by mapping labels from the stereotaxi atlas onto the referen esurfa e as des ribed above [44℄. The area of the signi� ant ontiguous areas was summedwithin ea h region to report regional involvement.To limit the intra-subje t variability and in rease statisti al power to the group om-parison, di�eren es in orti al thi kness and volume between groups were determined by omparing pooled data from mutation arriers (baseline and follow-up) with pooled datafrom non- arriers. This was done as subje ts at a given time (baseline or follow-up) notne essarily are homogeneous, e.g. the disease stage in a mutation arrier at baseline may orrespond to the disease stage in another mutation arrier at follow-up.Annualized orti al atrophy rates in ea h lobe were al ulated as per ent de line ofbaseline lobe average thi kness. To avoid magnifying noise in orti al thi kness the atrophyrate per vertex was al ulated as a ratio (r) asri =

m2,i − m1,i

∆t(m2,i + m1,i)(6.1)where m1,i and m2,i are measurements at vertex i at respe tively baseline and follow-up, and ∆t is the subje t s an interval. By normalizing with the summed thi kness forbaseline and follow-up unrealisti ally high atrophy rates, aused by baseline measurements lose to zero, were avoided.Asymmetry was evaluated by the left to right ratio between thi kness measurementsand atrophy rates averaged within the hemispheres and within the main lobes.6.3 Results6.3.1 Corti al Boundary Extra tion and Compartment Segmen-tationsAll generated orti al surfa es were found to be free of obvious segmentation errors byvisually he king 3D rendered images as well as images of the original MR data withthe surfa e ontours superimposed. The masks �tted to the intra- ranial avity, the ven-tri les, and sub orti al regions were visually examined by superimposing them onto theoriginal MR data. Intra ranial and sub orti al masks were found to a urately �t theimages. However, examining the ventri ular masks revealed problems of �tting to the pos-terior part of the lateral ventri les in two subje ts of both groups. In these subje ts theventri ular volume is underestimated. The ina urate ventri ular segmentations lead tooverestimations of the WM and erebrum volume while the orti al volume is una�e tedby the ventri ular segmentation. The segmentation a ura y was visually estimated to besimilar for baseline and follow-up why it was assumed that longitudinal di�eren es in WMand erebrum volumes are una�e ted by the segmentation errors.

69 6.3 Results

Figure 6.2: Statisti al parametri map of di�eren es in orti al thi kness showing areaswith p < 0.01 for one-sided t-test testing signi� ant thinner ortex in mutation arriers ompared to non- arriers. Map generated from pooled (baseline and follow-up) measure-ments and blurred with a di�usion smoothing approximating a Gaussian kernel smoothingwith 10 mm FWHM.6.3.2 Cross-se tional Di�eren esAll lobes were signi� antly thinner in mutation arriers ompared to non- arriers (table6.2). For an FDR of 5% the statisti al parametri maps implied an appropriate thresholdof signi� an e at αFDR = 0.011 for the left and αFDR = 0.010 for the right hemisphere.We hose a threshold of αFDR = 0.01 for both hemispheres. Figure 6.2 shows the blurredstatisti al parametri map of group di�eren es in orti al thi kness. Blurring the statis-ti al map removed 85% of the signi� ant points leaving highly signi� ant lusters. Table6.3 lists the anatomi al regions that in lude the largest areas of signi� ant di�eren e. Sig-ni� antly di�erent regions were primarily found in the parietal lobes (24.8 m2) and theright temporal lobe (10.9 m2). O ipital lobes displayed less di�eren e (6.2 m2), whileonly small signi� ant di�eren es were found in the left frontal lobe (2.4 m2). No part ofthe ortex was signi� antly thinner in non- arriers ompared to the mutation group.6.3.3 Longitudinal E�e tsAnalysis of group lobe averages revealed that in mutation arriers all lobes ex ept theparietal lobes and the right temporal lobe were signi� antly thinner at follow-up omparedto baseline (table 6.2). In non- arriers only the left o ipital lobe was signi� antly thinnerat follow-up.None of the p-values in the statisti al parametri maps of the longitudinal di�eren esof orti al thi kness was below α/N (α = 0.05, N = 105), whi h resulted in no validFDR adjusted signi� an e threshold. Setting the threshold to α = 0.01 showed no fo aldi�eren es for either mutation arriers or non- arriers. Analyses of the unblurred statisti almaps revealed s attered areas of signi� an e in both frontal and temporal lobes in mutation arriers with more signi� an e in the left lobes. Also, s attered areas of signi� an e werefound in the left o ipital and left medial frontal lobes. In non- arriers s attered areas ofsigni� an e were observed in the left o ipital lobe. Lowering the signi� an e thresholdto α = 0.05 revealed signi� ant ontiguous areas (1.4 m2) in the left temporal lobe ofmutation arriers (see �gure 6.3).6.3.4 Atrophy RatesTable 6.4 lists the annualized orti al atrophy rates within the main lobes for both groups.The orti al atrophy rate was signi� antly higher in the left frontal and left temporal lobein mutation arriers ompared to non- arriers. FDR analysis of the statisti al parametri map of group di�eren es in annualized orti al atrophy ratios ( al ulated by Eq. 6.1)provided no valid signi� an e threshold for the same reason as des ribed above. Setting

Chapter6:Corti alVolumes

andAtrophyRatesinFTD-3

CHMP2BMutationCarrier

sandRelatedN

on- arriers70

Frontal lobe Temporal lobe Parietal lobe O ipital lobeLeft Right Left Right Left Right Left RightMC Baseline (mean±SD) 2.24±0.26 2.20±0.23 2.62±0.24 2.52±0.21 1.57±0.25 1.56±0.25 1.90±0.17 1.88±0.17Follow-up (mean±SD) 2.13±0.31 2.11±0.28 2.50±0.28 2.48±0.27 1.54±0.26 1.50±0.25 1.75±0.14 1.79±0.17Longitudinal di�eren e 0.005 0.015 0.007 0.335 0.440 0.193 0.002 0.003(p-value)NC Baseline (mean±SD) 2.48±0.17 2.44±0.18 2.84±0.08 2.80±0.13 1.94±0.12 1.88±0.16 2.15±0.20 2.10±0.21Follow-up (mean±SD) 2.46±0.12 2.40±0.16 2.78±0.05 2.81±0.06 1.92±0.06 1.84±0.09 2.00±0.13 2.07±0.18Longitudinal di�eren e 0.629 0.312 0.112 0.736 0.614 0.348 0.030 0.496(p-value)Pooled group di�eren e 0.011 0.012 0.010 0.002 0.001 0.002 0.003 0.008(p-value)Table 6.2: Corti al thi kness measurements (mm) averaged within main lobes at baseline and follow-up for mutation arriers (MC) and non- arriers(NC). Longitudinal di�eren es evaluated by two-tailed paired t-test. Group di�eren es evaluated by one-sided t-test with assumption of unequalvarian e on pooled measurements.

71 6.3 ResultsAnatomi al region Involved area, LH Involved area, RHAngular gyrus 655 mm2 456 mm2Supramarginal gyrus 479 mm2 463 mm2Middle temporal gyrus 221 mm2 987 mm2Middle o ipital gyrus 251 mm2 221 mm2Superior temporal gyrus 158 mm2 76 mm2Inferior parietal gyrus 226 mm2 22 mm2Superior parietal gyrus 106 mm2 No e�e tTable 6.3: Anatomi al regions with signi� antly (p < 0.01) thinner ortex in mutation arriers ompared to non- arriers after smoothing. Only regions with an involved areaof more than 1 m2 of either the left (LH) or right (RH) hemisphere are reported. Thesigni� ant areas are visualized in �gure 6.2.

Figure 6.3: Statisti al parametri map of longitudinal di�eren es in orti al thi knessin mutation arriers showing areas with p < 0.05 for paired t-test testing signi� antthinner ortex. Map blurred with a di�usion smoothing approximating a Gaussian kernelsmoothing with 10 mm FWHM.

Chapter 6: Corti al Volumes and Atrophy Rates in FTD-3 CHMP2B Mutation Carriersand Related Non- arriers 72

Figure 6.4: Statisti al parametri map of signi� antly (p<0.01) higher atrophy ratios inmutation arriers. Map blurred with a di�usion smoothing approximating a Gaussiankernel smoothing with 10 mm FWHM. Surfa e parts have been removed for better visu-alization of regions buried by the lateral �ssures. Labels orrespond to the lusters listedin table 6.5. Cluster sizes may appear smaller than they are due to visualization on apartially �attened surfa e.the signi� an e threshold to α = 0.01 on the blurred map revealed several fo al e�e ts(�gure 6.4). Blurring the statisti al map removed 78% of the statisti ally signi� ant pointsleaving only highly fo al e�e ts. Clusters of signi� antly higher atrophy ratios with anarea >20 mm2 are listed in table 6.3 along with the involved anatomi al regions. Higheratrophy ratios were found in both left and right frontal and temporal lobes. Espe iallythe left insular ortex had a higher atrophy ratio in the mutation group (1.61 m2), butalso the right inferio-temporal region (0.58 m2) and the right superior frontal gyrus (0.42 m2) showed fo al di�eren es.6.3.5 Volume MeasurementsTable 6.6 lists the measured erebrum, WM, and orti al volumes, p-values for longi-tudinal di�eren es within ea h group, and p-values for di�eren es between the groups.Mutation arriers had signi� antly smaller orti al volume at follow-up ompared to base-line (p=0.007). The orti al volume of non- arriers de reased, but the volume loss wasnot signi� ant (p=0.142). Cerebrum and WM volumes were not signi� antly di�erent atfollow-up in either group. All erebral volumes were signi� antly smaller in mutation ar-riers ompared to non- arriers. The annualized per entage volume loss orre ted for eTIVwas 0.3 ± 1.4% erebrum, -1.4 ± 2.2% WM, and 2.6 ± 2.2% ortex for mutation arriers.Annualized volume loss for non- arriers was 0.1 ± 1.4% erebrum, -0.9 ± 2.0% WM, and1.1 ± 1.8% ortex. Rates of volume loss were not signi� antly di�erent between groups,however there was a trend for higher orti al volume loss in mutation arriers (p=0.17).

736.3Results

Frontal lobe Temporal lobe Parietal lobe O ipital lobeLeft Right Left Right Left Right Left RightMC (mean±SD) 4.18±3.73 3.42±3.51 3.74±3.16 1.37±3.75 1.52±5.30 3.14±6.87 6.15±4.03 3.91±2.97NC (mean±SD) 0.50±3.51 1.15±2.86 1.44±1.96 0.48±2.86 0.81±4.57 1.59±4.89 4.77±5.53 0.84±3.78Di�eren e (p-value) 0.032 0.088 0.048 0.141 0.388 0.303 0.295 0.052Table 6.4: Annualized atrophy rates as per ent de line of baseline thi kness for mutation arriers (MC) and non- arriers (NC). Di�eren e betweengroups evaluated as one-sided t-test with assumption of unequal varian e.

Chapter 6: Corti al Volumes and Atrophy Rates in FTD-3 CHMP2B Mutation Carriersand Related Non- arriers 74Cluster Area (mm2) Lobe Main involved anatomi al regionsL1 120.4 Left frontal Insula (109.5 mm2)L2 119.2 Left frontal Rolandi oper ulum (74.8 mm2)Insula (41.8 mm2)L3 22.4 Left temporal Inferior temporal gyrus (22.4 mm2)R1 53.4 Right temporal Fusiform gyrus (29.7 mm2)Inferior temporal gyrus (23.7 mm2)R2 46.5 Right temporal Transverse temporal gyrus (44.3 mm2)R3 35.3 Right frontal Superior frontal gyrus (31.8 mm2)R4 22.6 Right temporal Middle temporal gyrus (21.0 mm2)Table 6.5: Clusters of statisti ally signi� ant higher atrophy ratios in mutation arriers ompared with non- arriers. Clusters with signi� ant ontiguous areas >20 mm2 arereported. Clusters are visualized in �gure 6.4.

Cerebrum White matter CortexMC Baseline (mean±SD) 980±52 570±31 409±42Follow-up (mean±SD) 969±48 575±30 394±49Longitudinal di� (p-value) 0.161 0.348 0.005NC Baseline (mean±SD) 1048±42 585±32 463±35Follow-up (mean±SD) 1041±26 589±27 453±30Longitudinal di� (p-value) 0.420 0.501 0.086Group di�eren es (p-value) 0.002 0.175 0.005Table 6.6: Compartment volumes (ml) orre ted by eTIV for mutation arriers (MC)and non- arriers (NC) at baseline and follow-up. Longitudinal di�eren es were adjustedfor inter-s an interval and evaluated by two-tailed paired t-test. Group di�eren es wereevaluated by two-tailed t-test with assumption of unequal varian e on pooled group mea-surements.

75 6.4 Dis ussion6.3.6 AsymmetryAsymmetry ratios between hemispheres revealed a trend towards a thinner ortex in theright hemisphere in both mutation arriers (p=0.121) and non- arriers (p=0.061). Byevaluating the averaged orti al thi knesses within lobes signi� ant asymmetry was foundin the frontal lobes (MC: p=0.046, NC: p=0.013) and parietal lobes (MC: p=0.033, NC:p=0.007) with right lobes being thinner in both groups. No asymmetry was found inthe o ipital lobes in either group, while mutation arriers had signi� antly thinner righttemporal lobes (p=0.002). Evaluating the orti al atrophy rates, no asymmetry betweenhemispheres was found in either group.6.4 Dis ussion6.4.1 Corti al Thi knessAfter a 16 month follow-up, presymptomati CHMP2B mutation arriers showed a signif-i antly thinner ortex in the o ipital and frontal lobes and the left temporal lobe. Thisis onsistent with �ndings of other longitudinal studies of other types of symptomati FTD patients [4, 10℄; however, to our knowledge this is the �rst study des ribing orti althinning in premanifest FTD disease.Even though the statisti al parametri maps with FDR adjusted signi� an e thresholddid not show signi� ant fo al atrophy in either group, the unblurred maps revealed s at-tered areas of atrophy in the same lobes, whi h were signi� antly thinner when averagingwithin the lobar measurements. Lowering the signi� an e threshold to α = 0.05 showedfo al e�e ts in the left middle temporal gyrus (�gure 6.3)When omparing the two groups (with and without the CHMP2B mutation) the overalllobe averages were signi� antly thinner in mutation arriers, whereas the statisti al para-metri maps revealed more fo al di�eren es (�gure 6.2). Fo al di�eren es were mainlyfound in the parietal and temporal gyri, while almost no di�eren es were found in thefrontal lobes. However, due to the small number of subje ts in both groups and pre lin-i al stage of mutation arriers these di�eren es may simply re�e t normal variations in orti al thi kness; and not ne essarily a pathologi al e�e t. This is supported by the fo aldi�eren es in atrophy ratio, whi h displayed a di�erent pattern (�gure 6.4). We onsider hange in orti al thi kness a statisti ally stronger metri than the absolute orti al thi k-ness when dealing with su h small number of subje ts. When examining the statisti alparametri map of fo al di�eren es of the atrophy ratio, the right frontal lobe was alsoinvolved, while the o ipital lobes had no fo al e�e ts. The atrophy ratio map reportedmore symmetri ally distributed fo al di�eren es than the dire t orti al thi kness ross-se tional omparison. Spe i� ally, the insular ortex (primarily left), the inferio-temporalregions, and the superior frontal gyri were those with the most pronoun ed fo al e�e ts(�gure 6.4).The anterior insula have been reported to be involved in several types of FTLD, mostlybilateral [6, 45, 58℄, but also in some ases in the left anterior insula [25, 59℄ and asso i-ated with progressive non-�uent aphasia [41℄. Earlier examinations of patients with theCHMP2B mutation have shown varying degree of aphasia [26℄, though it is not a primarysymptom of the disease. Hyperorality and hanged eating behaviour has been observedin FTD-3 patients [26℄, and the atrophy patterns involving the insula areas found hereshare overlapping patterns with those found in FTLD types with abnormal eating be-haviour [58℄. Thus several of the symptoms observed in patients an be related to thepre lini al stru tural hanges found in this study. The two distin t patterns expressed bythe group thi kness di�eren es and the group atrophy di�eren es indi ate that patterns of orti al thi kness may not alone reveal the a�e ted anatomi al regions. Thus using onlyone MRI s an to establish a � lini al� FTD-3 diagnosis in a single CHMP2B mutationpositive subje t seems impossible at the pre lini al stage studied here. A follow-up s an

Chapter 6: Corti al Volumes and Atrophy Rates in FTD-3 CHMP2B Mutation Carriersand Related Non- arriers 76is ne essary to assess the atrophy pattern.Results of orti al thi kness based on the present method may not be dire tly om-parable with results obtained by VBM analyses. VBM reports statisti ally signi� ant lusters of GM hange without onsidering the sul al geometry. Small lusters in oppos-ing parts of a sul us may be insigni� ant when measuring orti al thi kness be ause ofthe relatively large geodesi distan e between the lusters, while in VBM they ould on-verge into one large signi� ant luster be ause of the relatively small Eu lidian distan ebetween the lusters. Thus it is important to onsider sul al geometry when measuringfo al e�e ts [22℄. Therefore, we in luded volumetri measurements to better ompare our�ndings with results from previous studies, whi h used volumetri or VBM measurements,and to evaluate the sensitivity of volumetri measurements ompared to orti al thi kness.6.4.2 Cerebral VolumesThe mutation arriers showed on average an annualized hange in volume of approximatelytwi e the magnitude of the non- arriers. Studies have reported annualized GM volume lossin healthy middle-aged and elderly persons of approximately 0.2% without WM loss [1,49℄.Our measurements of average orti al volume loss (1.1%), though not signi� ant (p=0.14),are in the high end ompared to previous �ndings in healthy subje ts. The small numberof subje ts (n=7) and signi� ant normal variation may explain the di�eren e. Unlikemutation arriers, both in rease and de rease of orti al volume was measured in non- arriers, but rates of orti al volume loss were not signi� antly (p=0.17) higher in mutation arriers.The averaged annualized erebrum volume loss of 0.3% in mutation arriers was in-signi� ant and suggested no hange in whole-brain volume. Re ent �ndings in ubiquitinpositive FTLD reported whole-brain volume loss of 1.7%/year [56, 57℄. These studies in-volved lini ally diagnosed FTD patients above age 55 (average ages of 72/73 years) in ontrast to the asymptomati subje ts in the present study. The whole-brain volume lossfound by Whitwell et al. indi ates an a elerated atrophy rate ompared to the youngerasymptomati mutation arriers studied here, where the loss of tissue seems too subtleto be dete ted by whole-brain measures. However, orti al volume de reased signi� antlywith 2.6% per year on average while a trend (p=0.08) for in reased WM volume wasobserved (1.4%).The in rease of WM volume in both mutation arriers (1.4%) and non- arriers (0.9%),though not signi� ant (p=0.08, p=0.26), was unexpe ted. Other studies have shown noWM volume hange in aged healthy subje ts [49℄ and only a slight in rease in WM volumein non-aged healthy subje ts [1℄. The WM volume was al ulated as the volume en losedby the WM surfa e minus an estimated volume of the ventri les and sub orti al regions.Ventri ular and sub orti al volumes were estimated using atlas masks non-linearly alignedto the images. Examining the a ura y of these masks revealed problems of �tting to theposterior part of the lateral ventri les in some subje ts, why the ventri ular volumes may beregarded as rude estimates a�e ting the a ura y of the al ulatedWM volume. Similarly,ina urate ventri ular volumes also a�e t the erebrum volume estimates. To improvethe WM and erebrum volume estimates the ventri les ould be expli itly segmented,e.g. by the use of deformable surfa es, whi h would also provide measures of ventri ularenlargement.The study did not show signi� ant di�eren es between mutation arriers and non- arriers when testing for global volumetri longitudinal e�e ts. Nevertheless, using orti althi kness measurements we were able to determine higher atrophy rates in lobes, and evenidenti�ed fo al di�eren es between the groups. This indi ates that regional and fo al orti al thi kness measurements are more sensitive than global brain volume or tissue ompartment measurements when quantifying orti al stru tural hanges.

77 6.4 Dis ussion6.4.3 Limitations of the StudyThe main limitation of the study is the low number of subje ts examined. This a�e tsthe statisti al power of the measured di�eren es and ompli ates the assessment of howmeasurements are distributed. The assumption of normally distributed measurements,whi h was made on the grounds of biologi al variations tend to be normally distributed,may therefore be in orre t. It was not possible to re ruit more subje ts, as they had tobe 1.-degree relatives of the same family.The results may be a�e ted by the within subje t variability between the two s ans.A third serial s an would provide more on�dent longitudinal measurements. An addi-tional sour e of error ould arise from the surfa e mapping used a ross subje ts. Spe i� anatomi al lo ations may be ina urate, as a point on a orti al surfa e may be assigned adi�erent anatomi al label before mapping to the referen e surfa e, if it was to be labelledby an expert anatomist. However, the mapping method used ensures that gyral pointsare mapped to a referen e gyrus and sul al points are mapped to a referen e sul us, thus orti al thi kness omparisons are kept within the same orti al topography. Addition-ally, surfa e based registration has been shown to be more a urate a ross subje ts thantraditional image registrations [22℄.Controlling the rate of falsely reje ting the null hypothesis in multiple omparison asused to onstru t the statisti al parametri maps was attempted with the FDR method[24℄. However, only the map al ulated for the di�eren es in absolute orti al thi knessof pooled group data provided FDR orre ted signi� an e thresholds. Other statisti almaps had no p-values less than α/N (α = 0.05, N = 105) thus the FDR method removedall signi� an e. This is an e�e t of the low number of subje ts used in the study. Still, toenable interpretations of the results, it was de ided to report the statisti al maps withoutthe FDR orre ted thresholds. The blurring of the statisti al maps removed between 78%and 100% of the statisti ally signi� ant points (p<0.01), leaving lusters of signi� an e inthe map. Thus it an be argued that su h blurring removes most of the false positives inthe statisti al parametri maps. Furthermore, most of the found fo al e�e ts are bilateral,whi h seems unlikely if they were aused by spurious results.The atlas used for assigning anatomi al labels to the surfa es is de�ned as a 3D image,and the pro edure of assigning labels by Eu lidian distan e may lead to un ertainties inthe exa t anatomi al designation of the signi� ant pathologi al e�e ts. However, as theanatomi al regions used in the study are relatively large, un ertainties are limited to e�e tsin the border regions and are onsidered not to a�e t the interpretation.Finally, the rude estimates of ventri ular volume a�e t the measures of WM and erebrum volume. Therefore, the reported volumetri hanges and di�eren es of these ompartments should be taken lightly. However, the volume measurements of the or-tex are onsidered a urate, as these measurements are not in�uen ed by the ventri ularvolume estimations.6.4.4 Con lusionWe have shown that global and fo al orti al hanges an be measured in asymptomati FTD-3 CHMP2B mutation positive subje ts by using automati orti al delineation.Global orti al volumetri hanges were statisti ally signi� ant, but whole-brain hangeswere of a lower rate than rates previously reported in other types of lini ally manifestFTD patients. Fo al orti al hanges were identi�ed by orti al thi kness measurements,and the results indi ated that su h lo al measures have higher sensitivity for dete tingsmall hanges than global volumetri measures. Be ause of normal variations in orti althi kness and the low number of subje ts studied annualized atrophy rates were onsid-ered the most reliant features des ribing di�eren es between mutation arriers and non- arriers. Symptoms previously reported from patients with the CHMP2B mutation ouldbe asso iated with the a�e ted anatomi al regions and our results further support thepathogeni ity of the CHMP2B .532-1G>C mutation. Comparing presymptomati FTD-

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Chapter 7Dis ussion and Con lusionThis thesis ontributes to the �eld of morphometry of the human erebral ortex fromMRI. The obje tive is to develop methods for quantifying orti al stru tural hangesas found in neurodegenerative diseases and to investigate the ability of su h methods tomeasure hanges in pre lini al individuals. A main goal is to di�erentiate between di�erentneurodegenerative diseases by orti al atrophy patterns and identify lini al markers to aidin early diagnosis. The �rst step to this goal is to a urately measure the size and shapeof the erebral ortex. In this thesis, it is proposed to re onstru t the orti al stru tureby manifold surfa es. The next step towards the goal is to measure atrophy and identifysimilar patterns of atrophy in population groups. For this purpose, orti al mapping isproposed and mapping te hniques are investigated. The last steps toward the goal ofdi�erentiating between neurodegenerative diseases by atrophy patterns involve applyingthe quanti� ation methods in lini al studies. A �rst step is taken in that dire tion byapplying the developed methods to individuals from a family with an inherited variantof frontotemporal dementia. The following dis usses the orti al re onstru tion, orti almapping and appli ation of quanti� ation methods presented in this thesis.7.1 Corti al Re onstru tionSu essful orti al re onstru tions use a ombination of voxel based methods and de-formable models. Voxel based methods are typi ally applied as prepro essing steps priorto a deformable model for the purpose of enhan ing information of tissue boundaries andredu ing manual intera tion. The main fo us of the thesis is on deformable models whileprepro essing steps ne essary for automati ortex re onstru tion has been implementedby use of existing methodologies. The following dis usses the deformable surfa e algorithmas proposed during the thesis, followed by a dis ussion of the steps ne essary for auto-mati and robust orti al re onstru tion and �nally re�e tions on omputational expenseis presented.7.1.1 Deformable Surfa e AlgorithmAs stated in the introdu tion, two riteria are important for surfa e re onstru tions of the erebral ortex. First, the surfa es must a urately model the underlying true anatomi alboundaries. Se ond, the topology of the ortex must be preserved. To meet these riteria,a solution based on parametri deformable surfa es is suggested. By using parametri models, the topology riterion an be met if the initial surfa e has the orre t topologyand self-interse tions are avoided during deformation. Methods for orre ting surfa etopology [5,25℄ and methods to avoid self-interse tions of parametri surfa es [21,39℄ havebeen proposed. By sele ting proper algorithms to solve these problems, the fo us of thestudy is to obtain as a urate orti al re onstru tions as possible using deformable models.83

Chapter 7: Dis ussion and Con lusion 84In Paper I [12℄, it is demonstrated that a parametri deformable surfa e based on the lassi balloon model [7℄ ombined with a gradient ve tor �ow for e [53℄ is able to delineateeven the tight sul al folds. The deformation is based on a greedy algorithm [49℄ whi his fast but prone to be trapped in lo al minima. However, by initializing the deformablesurfa e lose to the target boundaries, the probability of lo al minima is redu ed and fast onvergen e is enabled. It is demonstrated that the proposed method is robust to imagenoise; in reasing the noise level in the image to 9% only results in average errors less thanhalf a voxel size ompared to surfa es extra ted from noiseless data. Finally, the paperreports that thi kness measurements obtained from the re onstru ted orti al surfa es arerealisti ompared to measurements found in post mortem studies.The algorithm proposed in Paper I [12℄ has a few drawba ks. The surfa e positionwith lowest energy is sear hed for in a dis rete sear h spa e, thus limiting the a ura y ofthe solution even if multis ale te hniques are used. Furthermore, the method for enfor ingspheri al topology on the initial surfa e may produ e anatomi al in onsisten ies in thesurfa e. The initial surfa e is a tessellation of the WM of both erebral hemispheres on-ne ted by orpus allosum. A tessellation of an unmodi�ed WM voxel omponent usuallyresults in a surfa e with several handles, where larger handles an be aused by addi-tional inter-hemispheri onne tions su h as the ommissures. In addition, lassi� ationof sub orti al regions often results in a mixture of WM and GM voxels whi h give rise tonumerous topologi al errors. Therefore, the applied topology orre tion algorithm basedon graph utting [25℄ has di� ulties produ ing surfa es with anatomi ally onsistent ap-pearan e. In fa t, in �gure 2.6 on page 30 su h anatomi al in onsisten ies an be observedas bridges a ross the ventri les.In Paper II [13℄, the granularity problem is addressed by altering the deformation ap-proa h to al ulate displa ement ve tors dire tly by the sum of for e ve tors. Furthermore,a lo al weighting strategy of the deformation for es is implemented to improve the a u-ra y and onvergen e of surfa es. Exploiting the lose initial surfa e, normalized surfa e urvature is used to relax regularizing for es in urved regions and balan e the use of thetwo external image for es for optimal modeling of tight sul i. The paper demonstratesthat su h a ombination and weighting of for es is superior to approa hes using only apressure for e [10℄ or only a gradient ve tor �ow for e [52℄.In Paper III [14℄, the topology orre tion method is hanged to a more robust and onsistent approa h [5℄. The hemispheres are separated and ventri les and sub orti alregions �lled and thereby further optimizing the possibility for topologi ally orre t and onsistent surfa es of the neo ortex. The paper demonstrates that the proposed algo-rithm is geometri ally more a urate and faster than the widely used and freely availablere onstru tion algorithm FreeSurfer [10℄.A Note on NoveltyThe �eld of orti al morphometry is rapidly expanding and the progression is fast. At thetime of publi ation of Paper I, several of the surfa e re onstru tion methods referen ed inthe introdu tion of this thesis were not published. Several resear hers around the worldwork on orti al surfa e re onstru tion from MRI and this is re�e ted in the amount ofliterature on the subje t. As noted in the introdu tion, re ent methods seem to onformto the same strategy of re onstru ting the outer orti al boundary by in�ating a surfa e ofthe inner orti al boundary. This is indeed the same strategy adopted in this thesis. Themain di�eren e is how this deformation is performed. The ombination of external imagefor es and weighting strategy presented in the papers of this thesis is onsidered unique.However, re ent studies have pointed in similar dire tions as proposed here.In a re ent omparative study of eight deformable ontour methods, it is on luded thatnew methods ould ombine features from existing methods to handle spe i� segmentationproblems [30℄. Spe i� ally, a ombination of a balloon model with a gradient ve tor�ow (GVF) is given as an example. This ombination is similar to what is presentedin this thesis for the re onstru tion of the outer orti al boundary. Another re ent paper

85 7.1 Corti al Re onstru tionpropose a method for re onstru ting the entral layer of the ortex by ombining a pressurefor e with a GVF for e in the deformation pro ess [37℄. Again, this is similar to theapproa h des ribed in this thesis with the di�eren e that the target here is the outer orti al boundary. These studies on�rm the novelty and performan e of the orti alre onstru tion approa h suggested in this thesis.7.1.2 Automation and RobustnessLarge s ale ohort studies all for automati pro edures to limit tedious and laboriousmanual intera tion and to optimize onsisten y. A goal for the orti al re onstru tionalgorithm developed during the Ph.D. study is full automation. However, when dealingwith biologi al images and omplex target stru tures, this is not an easy task when robust-ness to image and obje t variation is also prioritized. Apart from the deformable surfa ealgorithm, several other pro essing steps are involved in an automati re onstru tion pro- edure. These steps are performed to ful�ll the pre onditions and improve the a ura yof the deformable surfa e algorithm. The main pre ondition of the used deformable sur-fa e approa h is initialization lose to the target boundary. This is a hieved by a good lassi� ation of the erebral WM.The steps taken to perform lassi� ation of the erebrum WM in lude intensity non-uniformity orre tion, image registration to a stereotaxi spa e, brain extra tion, intensitybased lassi� ation into WM, GM and CSF and �nally removal of brain stem and erebel-lum as outlined in Paper I [12℄. Su h prepro essing steps are ommon for several orti alre onstru tion algorithms [10,24,33,35℄. The performan e, robustness and automation of orti al re onstru tions depend on hoi es of algorithms to perform ea h step. For the or-ti al re onstru tion presented in this thesis, these hoi es have remained more or less thesame throughout the ourse of the Ph.D. study and are in the following brie�y dis ussedin onne tion with automation and robustness.Corre tion of intensity non-uniformities aused by inhomogeneities in the radio fre-quen y �eld is usually needed for improving intensity based lassi� ations. The inhomo-geneity in reases with �eld strength and is very pronoun ed at 3 Tesla. Various algorithmsto orre t the intensity non-uniformities in the images have been proposed and a numberof these are publi ly available [31℄. In this thesis, the freely available N3 algorithm isused [43℄. This algorithm is automati and performs well on images generated by both 1.5and 3 Tesla s anners [3℄.Automati image registration to a stereotaxi spa e is a ru ial step involved in almostall stru tural studies as well as many fun tional studies. For this reason, enormous ef-fort has been put into developing robust registration and freely available, well-performingmethods exists [9, 11, 18, 34, 51℄ 1. In this thesis, registration is done using an automati pro edure [8, 9℄ whi h is found to perform well for the purposes of the orti al re on-stru tion. The registration pro edure need not be highly a urate, as the purpose forthe orti al re onstru tion is gross lo alization of the major anatomi al parts. Thus, theregistration is used for the removal of brain stem and erebellum. A registration workingfor the wide variability of brain anatomy is usually not su� iently a urate to be used forbrain extra tion as well.Brain extra tion is ne essary as several tissues in the human head have overlappingT1 intensities whi h impairs the tissue lassi� ation. Su h an algorithm must be able torobustly extra t the brain tissues without removing parts of the brain and optimally with-out in luding proximate tissues su h as dura mater, exterior veins and artilage. Severalbrain extra tion methods have been proposed [40℄. None of the freely available meth-ods [10, 41, 44, 47℄ are found suitable for purposes of robust and automati orti al re on-stru tion. Therefore, in this Ph.D. study, a brain extra tion algorithm has been developedsimilar in spirit to the brain extra tion tool by Smith [44℄. Even though this algorithmworks well for most data, brain extra tion of elderly subje ts has proved di� ult to perform1For a list of available software tools see http://www. ma.mgh.harvard.edu/iatr/

Chapter 7: Dis ussion and Con lusion 86robustly and a urately. The main problem is the in lusion of dura mater and superiorsagittal sinus whi h may have intensities similar to WM, thus ompli ating the erebrumWM lassi� ation. The problem is probably related to hange in MRI signal intensitywhi h is an e�e t of age [32℄.Classi� ation of the erebral tissues into WM, GM and CSF an be performed usingseveral of the lassi� ation approa hes des ribed in the introdu tion. Parti ularly, in thisthesis a fuzzy lustering approa h is used [23℄. This lassi� ation algorithm generally per-forms well; however, no formal omparisons with other algorithms were arried out duringthe Ph.D. study. The algorithm in�uen es the surfa e onvergen e and re onstru tiona ura y as the fuzzy membership images produ ed are used in the deformation pro ess.In Papers I and III the a ura y of the re onstru ted surfa es is shown to be around halfa voxel size, whi h is why the a ura y of the tissue lassi� ation is deemed a eptable.Generally, the orti al re onstru tion pro edure runs fully automati on most MRIs ans. However, a small fra tion of s ans of elderly individuals need manual intera tion toremove parts of the dura mater prior to tissue lassi� ation. This is aused by insu� ientbrain extra tion. It is my experien e that brain extra tion remains the main obsta le toa fully automati and robust orti al surfa e re onstru tion method.7.1.3 Computational ExpenseThe time it takes to generate a urate orti al re onstru tions may be relevant in somes enarios. If orti al re onstru tions are to be used in diagnosti s or preoperative planning,the omputational delay may be a nuisan e at best and riti al at worst. However, in most ases the re onstru tion time is not important though a fast re onstru tion signi� antlyredu es the time needed to obtain results in large s ale studies. Espe ially when repeatedtrials are ne essary to tune parameters, high throughput is desirable. In any ase, opti-mization of omputational expense should be prioritized after a ura y, robustness andautomation.Traditionally, optimization of parametri deformable surfa es is very slow if onver-gen e to a global minimum must be guaranteed. Global minimum solutions an be ob-tained by various minimization algorithms [2, 45℄. The deformation methods applied topropagate the deformable surfa es in this thesis do not guarantee onvergen e to a globalminimum. This enables faster onvergen e and be ause of the lose initialization, themodels are less vulnerable to problems of lo al minima. Applying a global minimizationalgorithm does not ne essarily improve the a ura y as the global minimum may not bethe most a urate delineation of the orti al boundaries due to noise and artefa tual ir-regularities found in MRI. Global minimum algorithms are suited for problems where theinitial guess is far from the solution. However, in orti al re onstru tions, the initial guess an be determined lose to the solution as robust lassi� ation of the erebrum WM anbe a hieved. Therefore, the need for onvergen e of surfa es initialized far from the targetboundary seems arti� ial and omputational expensive optimization algorithms guaran-teeing a global minimum appear super�uous for the purpose of orti al re onstru tion.Geometri deformable models have be ome popular solutions to the orti al re onstru -tion problem sin e the introdu tion of topology preservation to the level set method bythe use of digital topology [26℄. An argument for these models are the low omputationalexpense ompared to parametri models. Authors laim that self-interse tion preventionis very omputational intensive in parametri deformable surfa e models [24, 27℄. The so-lution to orti al re onstru tions with self-interse tion avoidan e presented in this thesisis reasonably fast. Deformation of the GM/CSF surfa e is done in approximately 5 min.per hemisphere on a 2.8 GHz Opteron CPU. But ompared to new level set methods,where the deformation pro ess is measured in se onds [42℄, the parametri high resolutionmodels are outperformed. However, seen in the perspe tive of the entire pro ess neededfor orti al re onstru tion, the deformation pro ess is only a fra tion of the omputationaltime used. Intensity orre tion and lassi� ation algorithms often demand similar ompu-

87 7.2 Corti al Surfa e Mappingtational resour es and if high-dimensional non-linear registration methods are used, theprepro essing steps may be a fa tor ten more time onsuming than the parametri de-formable models. Thus, in pra ti al ortex re onstru tion, the deformation algorithm isnot the omputational bottle ne k if a suitable minimization method is hosen.7.2 Corti al Surfa e MappingThe orti al re onstru tions enable detailed morphologi al quanti� ations of the entireneo ortex. To fully utilize these high resolution measurements and identify di�eren es overtime and between subje ts, point orresponden e between orti al surfa es is ne essary. Inthis thesis the subje t of orti al surfa e mapping for the purpose of point orresponden eis brie�y investigated in paper IV [15℄.The main problem when omparing di�erent orti al surfa es is the great variationin folding patterns. Usually omparison is enabled by mapping the manifold surfa es toea h other or to a template. If the manifold properties of the surfa es are maintainedby a mapping, it is hard, if not impossible, to mat h the orti al folding patterns andthereby mat hing gyri to sul i is unavoidable without loosing information. As the ortexgenerally is thi ker at the top of gyri than at the bottom of sul i, su h mat hing may leadto unreliable measurements of di�eren e in orti al thi kness. By relaxing the manifoldproperties in the mapping, it is possible to only mat h areas of the surfa es with similartopography. A mapping method with this purpose is proposed in paper IV and evaluatedalong with methods that maintain the manifold properties when mapping. The evaluation on�rmed that if the manifold properties are maintained, high topographi al errors o ur.The methods a hieving low topographi al errors due to manifold relaxation result in neigh-boring verti es jumping between gyri and sul i leading to large geodesi distan es. This isalso undesirable as neighboring measurements are not independent and su h large geodesi distan es imposed by a mapping may render the measurements unreliable. Though theproposed algorithm maintains the most information (high overage) of the �ve evaluatedmethods, large geodesi errors are not a eptable.A solution to maintain manifold properties and limit the topographi errors ould beto develop di�erent brain templates ea h re�e ting a �type of brain� ategorized on thebasis of the orti al folding patterns. This way a subje t ortex ould be mat hed to thebest template representing the type of orti al folding of the subje t. How many di�erenttemplates would be needed and to what detail the ategorization an be performed remainsto be investigated. Su h an approa h would be feasible only if the number of di�erent lasses is limited.Another observation supporting the ategorization of brains a ording to the orti alfolding pattern is the large errors and large standard deviations in the landmark testperformed in the paper. All mapping methods resulted in large average geodesi distan esto the manually pla ed landmarks. However, it was observed that in some ases themapping was very lose to the landmarks while in others the geodesi errors were large asthe high standard deviations also suggest. This indi ates that some orti es are generallybetter mat hes whi h further support the ategorization of the brains for the purposeof brain mapping. By spe ializing the brain templates for spe i� orti al patterns, thegeodesi landmark errors ould be redu ed.7.3 Appli ation on Neurodegenerative DiseasesDemonstrating the use of the ortex re onstru tion method on data from individuals witha neurodegenerative disease is ru ial, as methods behaving well on simulated data anddata from non-pathologi al brains may fail on pathologi al brains. In this thesis, the orti al re onstru tion is applied to individuals from a family with an inherited variant offrontotemporal dementia where a pathogeni mutation has been identi�ed on hromosome

Chapter 7: Dis ussion and Con lusion 883 (FTD-3). Nine individuals with the mutation and seven without the mutation arein luded in the study.The study whi h is do umented in Paper V [16℄ revealed that omparison of groupsusing absolute orti al thi kness need more subje ts than the 16 used in order to ompen-sate for the signi� ant normal variation in orti al thi kness. However, when in ludingthe temporal dimension, atrophy rates an be estimated whi h are statisti ally strongerwhen omparing pathologi al e�e ts. This is re�e ted in the di�erent statisti al mapsgenerated by respe tively absolute orti al thi kness and annualized atrophy ratios. Theatrophy ratio statisti al map seems more plausible as it shows bilateral e�e ts ontraryto the statisti al map of di�eren es in absolute orti al thi kness. In the spe i� vari-ant of frontotemporal dementia, bilateral e�e ts are expe ted although the degenerativemanifestations of the disease remain to be fully mapped.The orti al re onstru tion provides means for measuring the erebral volumes. This isdone by al ulating the interior volume of the losed surfa es of the WM and GM. Corti alvolume is determined by the di�eren e in volume between the surfa es. In the FTD-3study, only the orti al volume in mutation arriers de reased signi� antly while trend forin reased WM volume was observed. By only modeling the neo ortex, estimations of WMvolume annot be dire tly obtained why volumes were adjusted by masks of ventri les andsub orti al stru tures. Ventri ular enlargements are expe ted over time and the in reasedWM volume may be due to inability of the masks to �t to the altered ventri les. Ventri ularvolume an be measured more elegantly by modeling the ventri les expli itly by use ofdeformable or shape models.Cerebral volumes should generally be normalized as great inter-subje t variability ex-ists and the volume of the healthy mature brain is presumed to be orrelated with thevolume of the ranium avity [29, 50℄. In the study, the measurements were normalizedwith estimated total intra- ranial volume obtained by a �tted stereotaxi mask. The a u-ra y of su h an approa h is highly dependent on the registration method and intra- ranialvolume estimations al ulated without registration ould improve the a ura y and removeregistration bias.The rate of hange in erebral volumes was not signi� antly higher in mutation arriers ompared to non- arriers while atrophy rates based on orti al thi kness both averagedwithin the lobes and fo ally by the statisti al maps showed signi� ant di�eren e betweenthe groups. This indi ates that orti al thi kness is more sensitive than volume mea-sures. A formal study evaluating the sensitivity of the measures should be arried out todetermine the di�eren e between the measures.The statisti al maps used in the study were reated by hypothesis testing at ea h vertexof a referen e surfa e. In hypothesis testing, there is a probability for in orre tly reje tingthe null hypothesis; the false positive rate. When performing thousands of tests as inthe generation of the statisti al maps, there is bound to be in orre t test out omes, thusleading to false positives. In the study, this problem is addressed by al ulating orre tedsigni� an e thresholds based on ontrolling the false dis overy rate (FDR) [20℄. However,the FDR method eliminated all signi� ant fo al e�e ts in some of the statisti al maps.Controversy exists whether to apply methods for ontrolling the false positive rate at therisk of not reporting important �ndings [19, 38℄. In the FTD-3 study, large smoothingkernels were applied to the maps so only lusters of verti es where the null hypothesis arereje ted remain. The probability that a single test is wrong is at the level of determination;however, the probability that several verti es in the same neighborhood all have wrongout omes is signi� antly redu ed. Therefore, it is argued that problems with multiple omparisons are insigni� ant after smoothing the maps. Even though these argumentsseem to hold, the arguments should be supported by studies investigating the impa t ofthe di�erent parameters involved in reating orti al statisti al maps, e.g. the e�e t ofspatial inter-dependen y of the measurements on the statisti al model. Su h investigationsmay lead to a theoreti al foundation of the statisti al maps generated for orti al features.

89 7.4 Future Dire tions7.4 Future Dire tionsThe subje ts overed in this thesis lead to a range of questions and re ognition of problemsstill unresolved in quanti� ation of erebral orti al stru tures by use of surfa e models.These questions and problems should be addressed in future studies.Firstly, the a ura y of the proposed parametri deformable model must be furtherinvestigated and omparisons with geometri deformable models should be arried out asthese models have be ome popular during re ent years. The a ura y of the re onstru tedsurfa es have been evaluated on the basis of young healthy subje ts and phantom MRIs ans. Studies of the performan e on old and pathologi al brains should be ondu ted. Re- ent initiatives of olle ting data from neurodegenerative diseases, su h as the Alzheimer'sDisease Neuroimaging Initiative2, provide means for evaluations on old and pathologi albrains. Validation by omparison to manual delineations, histologi al measures and ani-mal studies are also possible dire tions for determining the a ura y and reliability of the orti al re onstru tion.Se ondly, for the purpose of high throughput in large s ale studies, automation androbustness is essential. For the orti al re onstru tion method presented here, the brainextra tion step is identi�ed as the weakest link. Future e�ort should be put into improvingthis step with the purpose of developing methods robust to the altered MRI signal intensitydue to age. Robust brain extra tion is ontinuously being resear hed by other groups[1,4,17,28℄ and progress in the �eld may advantageously be in orporated into the orti alre onstru tion pipeline.Thirdly, the investigation of di�erent orti al mapping algorithms revealed a need forimprovements within the �eld whi h was mainly aused by the high variations of orti alfolding patterns between individuals. Future studies should look into the possibility of ategorizing orti es on the basis of folding patterns and the onstru tion of spe ialized orti al templates.Fourthly, evaluations of the measures al ulated from the orti al surfa es have notbeen the subje t of this thesis and work within this �eld ould improve the reliability ofthe results obtained. Others have evaluated di�erent measures of orti al thi kness [36℄ andit should be investigated whether the on lusions drawn by this study apply to the surfa esgenerated by the orti al re onstru tion method presented in the present thesis. Apartfrom orti al thi kness, volume estimates are also derived from the surfa es. When usingthe orti al surfa es to al ulate volume measurements of the erebral tissues two problemsarise: 1) absolute volumes must be normalized by an invariant fa tor orrelated to themaximum matured brain size and 2) WM volume estimates are orrupted by enlargementsof the ventri les as the WM surfa e en ompasses these avities. As done in the FTD-3study, normalization an be performed by estimation of the intra- ranial volume as thismeasure is presumed to re�e t the maximummatured brain volume and to remain onstantover time [50℄. Often the intra- ranial volume is estimated by a brain mask generated toremove the s alp [22, 48, 54℄; however, su h masks may not re�e t the true intra- ranialvolume. Therefore, work spe i� ally dire ted toward estimating the intra- ranial volumeshould be arried out. The problem of enlarged ventri les in the WM volume estimations an be addressed by expli itly modeling the ventri les. Several methods for ventri lesmodeling exist [6℄ and future improvement of the orti al re onstru tion pipeline ouldin orporate a suitable method for modeling the ventri les. In orporation of measures ofventri le size and shape may provide additional information of atrophy progression [46℄.Fifthly, the sensitivity of the orti al thi kness ompared to traditional volume mea-sures should be investigated. The FTD-3 study [16℄ indi ated that the orti al thi knessmeasurements are superior to volume estimates when dete ting subtle orti al hanges.Further work should on�rm this observation and evaluate the sensitivity of the measures.This ould be done using the realisti brain phantoms generated from orti al surfa es asdes ribed in Paper III [14℄.2For more information see http://www.loni.u la.edu/ADNI/

REFERENCES 90Finally, further work on statisti al parametri maps of morphologi al features, su has the orti al thi kness, should be arried out. Studies examining the reliability of theeviden e produ ed by statisti al maps are important for the general a eptan e of resultsfound by orti al surfa e re onstru tions and subsequent mapping. In addition, the statis-ti al method for generating the maps should be evaluated and it should be investigated ifin lusion of the spatial inter-dependen y of the measurements ould improve the statisti almodel.7.5 Con lusionThis thesis has demonstrated that the human erebral ortex an be re onstru ted frombrain MRI by means of parametri deformable surfa es. The resulting high resolutionsurfa es provide means for detailed measurements of the orti al morphology. The a u-ra y of the developed method has been shown to be at subvoxel level and the method isgeometri ally more a urate than a widely used ompeting re onstru tion method. Thetopologi ally orre t orti al surfa es are generated automati ally and robustly by in or-porating a series of prepro essing steps based on existing voxel based methods. Comparedto other parametri re onstru tion methods, the developed algorithm is fast; ompletere onstru tions are generated in less than one hour from native s anner images.The problem of orti al mapping has been addressed and strengths and weaknesses ofdi�erent methods for solving the mapping problem have been un overed in a omparativestudy. The study indi ates that more work needs to be done in this �eld to address thewide morphologi al variability of human orti es.Finally, the developed methods have been applied in a study of pre lini al subje ts withan inherited neurodegenerative disease. It was demonstrated that atrophy is dete tableat this pre lini al stage of the disease and that orti al thi kness based measurements aremore sensitive than volume measures.The work presented in this thesis is part of ongoing e�orts toward the goal of diagnos-ing and di�erentiating between neurodegenerative diseases by means of orti al atrophypatterns. Future dire tions of te hnologi al improvements rendering this goal probablehave been pointed out. If these issues are addressed, the quanti� ation methods are readyto be deployed in large s ale studies toward the goal of diagnosing and di�erentiatingbetween neurodegenerative diseases.Referen es[1℄ J. A osta-Cabronero, G. B. Williams, J. M. S. Pereira, G. Pengas, and P. J. Nestor.The impa t of skull-stripping and radio-frequen y bias orre tion on grey-matter seg-mentation for voxel-based morphometry. NeuroImage, 39(4):1654�1665, 2008.[2℄ A. A. Amini, T. E. Weymouth, and R. C. Jain. Using dynami programming forsolving variational problems in vision. IEEE Transa tions on Pattern Analysis andMa hine Intelligen e, 12(9):855�867, 1990.[3℄ J. B. Arnold, J. . Liow, K. A. S haper, J. J. Stern, J. G. Sled, D. W. Shattu k, A. J.Worth, M. S. Cohen, R. M. Leahy, J. C. Mazziotta, and D. A. Rottenberg. Qualitativeand quantitative evaluation of six algorithms for orre ting intensity nonuniformitye�e ts. NeuroImage, 13(5):931�943, 2001.[4℄ M. Battaglini, S. M. Smith, S. Brogi, and N. De Stefano. Enhan ed brain extra tionimproves the a ura y of brain atrophy estimation. NeuroImage, 40(2), 2008.[5℄ L. Chen and G. Wagenkne ht. Automated topology orre tion for human brain seg-mentation. Le ture Notes in Computer S ien e, 4191(LNCS):316�323, 2006.[6℄ Y. Y. Chou, N. Leporé, G. I. de Zubi aray, O. T. Carmi hael, J. T. Be ker, A. W. Toga,and P. M. Thompson. Automated ventri ular mapping with multi-atlas �uid image

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