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A 3-D model-based registration approach for the PET, MR and MCG

cardiac data fusion

Timo Makela a b c ∗, Quoc Cuong Pham b, Patrick Clarysse b, Jukka Nenonen a c,Jyrki Lotjonen d, Outi Sipila e, Helena Hanninen f , Kirsi Lauerma e,Juhani Knuuti g, Toivo Katila a c and Isabelle E. Magnin b

aLaboratory of Biomedical Engineering, Helsinki University of Technology,P.O.B. 2200, FIN-02015 HUT, Finland

bCREATIS, INSA, Batiment Blaise Pascal, 69621 Villeurbanne Cedex, France

cBioMag Laboratory, Helsinki University Central Hospital, P.O.B. 503, FIN-00029 HUS, Finland

dVTT Information Technology, P.O.Box 1206, FIN-33101 Tampere, Finland

eDepartment of Radiology, Helsinki University Central Hospital, P.O.B. 340, FIN-00029 HUS, Finland

fDivision of Cardiology, Helsinki University Central Hospital, P.O.B. 340, FIN-00029 HUS, Finland

gTurku PET Centre, c/o Turku University Central Hospital, Box 52, FIN-20521, Finland

In this paper, a new approach is presented for the assessment of a 3-D anatomical and functional model ofthe heart including structural information from magnetic resonance imaging (MRI) and functional informationfrom positron emission tomography (PET) and magnetocardiography (MCG). The method uses model-based co-registration of MR and PET images and marker-based registration for MRI and MCG. Model-based segmentationof MR anatomical images results in an individualized 3-D biventricular model of the heart including functionalparameters from PET and MCG in an easily interpretable 3-D form.

1. Introduction

Ischemic diseases and their dramatic conse-quence, the myocardial infarct, are the leadingcause of mortality in industrial countries. Fromthe physio-pathological point of view, ischemiaresults from a disequilibrium between myocar-dial perfusion, metabolism and contractile func-tion. Following an ischemic event, the questionof myocardial viability arises. Both ischemia di-agnosis and viability estimation rely on the joint

∗This study was partly granted by the Scientific De-partment of the French Embassy in Finland, the RegionRhone Alpes, through the ADeMO project and The Foun-dation of Technology in Finland. This work was per-formed within the framework of the joint incentive action”Beating Heart” of the research groups ISIS, ALP andMSPC of the French National Center for Scientific Re-search (CNRS).

analysis of the perfusion, metabolism, and con-tractile function, each of which being quantifiedwith specific imaging modalities (Fig. 1). Con-sequences onto the electric and magnetic activ-ity of the heart have also been observed. There-fore, computer-based methods are required to au-tomatically perform multi-modal cardiac imageregistration in 3-D. This is the purpose of thiswork.

Anatomical (structural) information of theheart is usually provided by Magnetic ResonanceImaging (MRI) and ultrasound (US). Metabolismcan be analyzed with Positron Emission Tomog-raphy (PET), perfusion with thallium Single Pho-ton Emission Computed Tomography (SPECT),MRI, or PET, and contractile function by usingMRI and US. Fluorodeoxyglucose (FDG) PET

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Figure 1. Variety of imaging modalities requiredfor the cardiac viability assessment.

imaging is considered as the gold standard todetermine viable areas of the heart (Hartialaand Knuuti, 1995). The electrical activity ofthe heart creates both an electric and a mag-netic field and can be measured by using electro-cardiography (ECG) and magnetocardiography(MCG), respectively (Siltanen, 1988). In MCGand ECG inverse problems, a current distribu-tion inside of the heart is estimated from non-invasively measured signals by solving a regular-ized inverse problem (Hamalainen and Nenonen,1999; MacLeod and Brooks, 1998). Thus, multi-channel MCG and ECG studies can be applied inlocating abnormal electrical activity in the heart(Nenonen et al., 2001). The MCG signals aregenerated by the same bioelectric currents as theECG, but the MCG may show ischemia-induceddeviations from the normal direction of depolar-ization and repolarization in a different way thanECG (Hanninen et al., 2001). In the literature,electrical activity and metabolism have usuallybeen studied separately, principally because theacquisition system are quite different and involvedifferent specialists. From the physiopathologicalpoint of view, it is clear that all the activities arerelated one to each other. Therefore, our objec-tive here was to allow for the study of the cor-relation between the electrical (MCG data) andmetabolic (PET imaging) activities which may

reveal new aspects of hearts complex patholog-ical processes. To our knowledge, this kind ofcomparison has not been done before. The pre-sented 3-D method gives good possibilities es-pecially for visual comparison of data from dif-ferent imaging modalities. Whereas PET imag-ing is used to study the cardiac metabolism, themultichannel ECG and MCG mappings allow acomprehensive study of the electromagnetic fieldsof the heart. These mapping techniques giveunique additional information on the electromag-netic manifestations of myocardial ischemia andviability. At present, the nuclear imaging modal-ities are mainly used in elective manner, appliedonly rarely in clinical decisions concerning car-diac care unit patients, whereas ECG monitoringis widely used in emergency care units. In the fu-ture, technical development will hopefully allowthe MCG mapping function as clinical tool with-out need for shielding. Multichannel ECG andMCG studies, used with standard torso models(to obtain individual torso model one needs usu-ally MR images), could then give estimation of is-chemia (and viability). The 3-D model based ap-proaches could be first used with functional datafrom ECG and/or MCG, and then be extendedduring the clinical studies with other modalities,such as MR and nuclear medicine studies. In thispaper, we will use MRI for obtaining the heart’sanatomy. Myocardial functional data are issuedfrom FDG-PET for the metabolism and MCGdata for the heart’s electrical activity.

In viability studies, mental registration of theinformation from different imaging modalities isroutinely performed by clinicians. Automatic reg-istration, based on computer programs, is how-ever expected to offer better accuracy, repeata-bility, and to save time. Registration of cardiacimages is a more complex problem than brain im-age registration because of the mixed motions ofthe heart and the thorax structures. Moreover,as compared to the registration of brain images,the heart exhibits much fewer accurate anatom-ical landmarks and the images are usually ac-quired with lower resolution. A review of car-diac image registration approaches can be foundin (Makela et al., 2002a). These methods are usu-ally based on manual intervention (Behloul et al.,

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2001; Waiter et al., 2000), automatic registrationof thorax surfaces (Pallotta et al., 1995; Gilardiet al., 1998; Yu et al., 1995; Tai et al., 1997; Caiet al., 1999; Makela et al., 2001a) or heart surfaces(Faber et al., 1991; Sinha et al., 1995; Anders-son et al., 1995; Declerck et al., 1997; Thirion,1995, 2001; Nekolla et al., 2000). Another cat-egory of methods relies on the matching of im-age intensities (Hoh et al., 1993; Bettinardi et al.,1993; Slomka et al., 1995; Eberl et al., 1996; Deyet al., 1999; Carrillo et al., 2001; Lotjonen andMakela, 2001). In (Behloul et al., 2001), max-imal myocardial deformation from tagged MRIand FDG-PET metabolism were combined usingneuro-fuzzy rules to generate polar maps repre-senting the viability. The registration was per-formed manually with the help of the long axisangles defined in the MRI protocol. In the “Mu-nichHeart” software, endocardial and epicardialcontours were manually delineated in Short Axis(SA) MR images and registered with the samecontours extracted from PET or SPECT usingthe maximum count detection algorithm (Nekollaet al., 1998, 2000).

In this work, we propose a method for extract-ing an individualized 3-D anatomical heart modelwhich combines myocardial metabolic data fromPET and electrical measurements from MCG. Afirst approach of the method was presented inMakela et al. (2001b). Here, it is improved byadding functional MCG results to the model. Themethod provides a 3-D geometric representationof the heart onto which functional informationcan be displayed. The data are presented in sec-tion 2. An overview of the approach is given insection 3, and the different steps are describedin section 4. The extraction of an individual-ized heart model is explained in section 5. Theconstruction of functional cartographies are de-scribed in section 6. Results are presented in sec-tion 7 and discussed in section 8.

2. Cardiac imaging protocol

The cardiac data were composed of MR andPET images and MCG data of ten patients (iden-tified by P1 to P10) suffering from three vesselscoronary artery disease, diagnosed with coronary

angiography and regional dyskinesia in cinean-giograms (Lauerma et al., 2000). The mean agewas 69 (8 men, 2 women). All patients un-derwent MR and fluorine-18-deoxyglucose (FDG)PET imaging within 10 days. MCG measure-ments were also acquired.

• MR images

The MR data were acquired with a1.5 T Siemens Magnetom Vision imager(Siemens, Erlangen, Germany) at the De-partment of Radiology in Helsinki Univer-sity Central Hospital (HUCH). A series of39 ECG-gated contiguous transaxial imageswas acquired during free respiration using aTurboFLASH sequence (Fig. 2a). The pixelsize and the slice thickness were 1.95 x 1.95mm and 10 mm, respectively. Five ECG-gated breath-hold cine SA sections werealso acquired (Fig. 2b). The pixel size forSA slices was 1.25 x 1.25 mm and the slicethickness 7 mm with a gap of 15 mm be-tween slices. About 15 time points weretaken for each section with a repetition timeof 40 msec.

• PET images

The static cardiac PET data were ac-quired with a Siemens ECAT 931/08-12(Siemens/CTI, Knoxville, USA) PET scan-ner at the Turku PET Centre (Turku, Fin-land). A series of 16 contiguous trans-mission and emission images were acquired(Fig. 2c, 2d). Transmission images wereused for attenuation correction of emissionimages and also provided structural infor-mation that was utilized for registrationpurposes. The emission image, which canbe assumed to be in good registration withthe transmission image (Kim et al., 1991),gives absolute quantification of glucosis up-take. For both transmission and emissionimages, the pixel size and the slice thick-ness were 2.41 mm x 2.41 mm and 6.75 mm,respectively.

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(a) (b)

(c) (d)

Figure 2. (a) Transaxial and (b) SA MR images,(c) transmission and (d) emission PET images.

• MCG data

The MCG measurements were performed atrest and after stress with the 67-channelcardiomagnetometer (4-D NeuroImaging,Helsinki, Finland) at the BioMag Labora-tory (Montonen et al., 2000) at HUCH.Acute ischemia was induced by exercisetesting with a non-magnetic stress ergome-ter (Hanninen et al., 2001), pedaled insupine position.

The ST-segment difference signals of aver-aged post-stress and rest recordings wereused in computing current density estimates(CDE) (Nenonen et al., 2001). In thiswork, the depolarization (QRS complex)data at rest was utilized. Patient-specificboundary-element torso models were ac-quired from magnetic resonance images, in-cluding the triangulated thorax and LV sur-faces (Lotjonen et al., 1999; Pham et al.,2001). The torso was assigned a constantelectrical conductivity of 0.2 S/m. DiscreteCDE values were computed on the LV atmidwall locations. The ill-posed inverse

problem was regularized with three differ-ent methods (Tikhonov regularization withan identity or a surface Laplacian opera-tor, and a maximum a posteriori estima-tor, MAP; for details, see Nenonen et al.(2001)). In the present study, we selectedMCG results obtained with the MAP esti-mator.

3. Method Overview

The aim of the overall approach is to extract a3-D anatomical model of the heart from patientMR images and to incorporate functional data,such as FDG uptake, information of the magneto-electric properties of the heart and other clinicallyrelevant parameters to the model. The process issummarized in Fig. 3.

First, MR transaxial images were co-registered(rigid transformation) with the PET transmissionimage (Makela et al., 2001a). The obtained regis-tration parameters were used to register transax-ial MR images and the PET emission image. PETslices that correspond to SA MR images were cal-culated by using MR header information. Then,a 3-D biventricular deformable model was initial-ized in the SA MR images to segment the my-ocardium. The deformed model was transformedinto the registered SA PET image to obtain FDGuptake values. The model was also transformedto the transaxial MR image and MCG values werecalculated for the LV midwall locations. Themain steps of the method are described in thefollowing sections.

4. Registration

4.1. PET-MRI registration

The rigid registration method for cardiac PETand MR images was fully described in (Makelaet al., 2001a). The registration method is basedon the matching of the thorax and lungs surfaceswhich are visible in both PET transmission andMR transaxial images. The registration proto-col first matches PET transmission and transax-ial MR images by using a surface-based registra-tion algorithm and then computes the SA PETslices corresponding to the SA MR slices. The

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Figure 3. Extraction of the 3-D anatomical and functional model of the heart including PET-FDG uptakeand MCG values: main steps of the process.

emission and transmission PET and transaxialMR images were first interpolated to the sameisotropic voxel dimensions using tri-linear inter-polation. Then, the PET transmission and emis-sion images, which had smaller physical dimen-sions than MR image, was set to the geometriccenter of the MR image space. The thorax andlung surfaces were segmented from PET trans-mission image using the deformable model basedsegmentation method proposed in Lotjonen et al.(1999). Segmentation of the thorax structures(thorax and lungs surfaces) was based on the elas-tic deformation of a topologic and geometric priormodel using a multiresolution approach. A tho-rax model including a full triangulated thorax

and the lungs surfaces was used with MR images(Fig. 4a) while with the PET transmission im-ages, the model was truncated (Fig. 4b). Theinitialization of the models can be made in threeways in our software: 1) manually, 2) matchingbounding boxes set around the model and bina-rized (thresholded) volume or 3) making rigid reg-istration with the model and binarized volume.In this work, the initialization was done manu-ally. However, we have also used successfully thesecond approach in more than 50 cases as the tho-rax is segmented from MR images. Although thebounding boxes do not allow any rotation cor-rection, it has performed well because subjectsare always lying on the bed in an approximately

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same orientation. The segmentation algorithmcan cope initialization errors up to a few degreesand several centimeters as demonstrated also inthe original article (Lotjonen et al., 1999).

(a) (b)

Figure 4. Geometric and topologic prior modelof the thorax for the (a) MR and (b) PET trans-mission image segmentation.

The free-form based deformation algorithmadapts the prior model to locally fit the salientedges in the image within a minimization process.The energy to be minimized is

Etotal = Eimage + γEmodel, (1)

where Eimage represents the matching error be-tween the prior model and the partial edges inthe data volume. Emodel tends to preserve themodel’s shape by restricting the deformation ofthe prior model. It describes the deviation of themodel’s surface normals from their original orien-tation. The image energy results from a distancemap (Borgefors, 1988) built upon edges extractedeither by a Canny-Deriche method (Canny, 1986)or image thresholding (Fig. 5). In order to se-lect edges corresponding to the model, orienteddistance maps (Lotjonen et al., 1999) were com-puted. The parameter γ sets the contribution ofthe two energy components. A multiresolutionprocess speeds up the minimization process andimproves the convergence. Fig. 6a and Fig. 6bshow segmentation results for the thorax struc-tures in MR and PET transmission images.

Figure 5. MR distance maps. The registrationalgorithm minimizes the distance of the thoraxsurface points in PET relatively to this distancemap.

(a) (b)

Figure 6. Segmented (a) MR and (b) PET trans-mission images.

The parameters of the rigid transformation pa-rameters (3 translations, 3 rotations) between thetwo image sets are derived from the minimiza-tion of the distance between the point set fromsegmented PET transmission image surfaces anda distance map (Borgefors, 1988) built upon thesegmented transaxial MR surfaces (Fig. 5). Theuniformly distributed nodes of the deformablemodel were used as point set from PET transmis-sion image surface. PET transmission and MRtransaxial images are acquired in a similar geome-try; the model is therefore initialized in a positionclose to the registration solution. The minimiza-tion algorithm is more detailed in (Makela et al.,2001a).

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PET emission image was registered withtransaxial MR image using the computed regis-tration parameters. The PET transmission imagewas thus used as a linking mediator to registerPET emission image to MR image coordinates.

After registration of the PET emission im-age with the transaxial MR image, the SA PETslices that corresponded to the SA MR imageswere computed using MR header information oftransaxial and SA MR images (Fig. 7). Note that,as PET acquisition was not gated in this study,the PET images were registered with the SA MRdata at end-diastole. This cardiac instant bestcorresponds to the average PET image.

4.2. MCG-MRI registration

MCG measurements were registered with MRIdata by using external markers. The position ofthe MCG recording system with respect to thepatient is determined by attaching three markercoils (magnetic dipoles) to the skin. The mag-netic fields produced by the coils are then usedto compute the sensor locations relatively to themarker coils (Montonen et al., 2000). The threemarker coils were also used to define the MCGsensor coordinates with respect to the MCGmarkers, a set of nine external marker positionswhich were selected for registering the MCG sen-sor system to MR images (Fig. 8).

The locations of the MCG markers were de-fined by attaching a cross-shaped object consist-ing of two silicone strips of rubber on the skin ofthe thorax. The separation between neighboringMCG markers was 5 cm in the head-feet directionand 10 cm in the left-right direction. The loca-tions of the MCG markers and the small markercoils were defined with a 3-D digitization system(3SPACE ISOTRAK II, Polhemus Inc., Colch-ester, VT, USA). The digitized MCG marker po-sitions were stamped with non-toxic ink, visibleonly in ultraviolet light. Prior to MR imaging, thenine MRI markers were placed on the stampedpositions on the skin. The MRI markers were con-structed from two perpendicular tubes filled with1 mmol/l MnCl2 fluid, inserted inside a piece ofplastic of 4.0 × 4.0 × 0.7 cm. The cross-shapedfigure of a marker was well visible in the MRimages. The MRI markers were located manu-

Figure 8. Placements of the nine MCG markersand three marker coils on the chest in a typical pa-tient study. The round pieces of plastic in two sil-icone strips of rubber denote the MCG marker lo-cations. Their centerpoints are digitized, and thepieces are removed from the strips before stamp-ing the locations with ink visible in UV light. Thethree marker coils are used to define the MCGsensor coordinates in respect to the MCG mark-ers.

ally from MR images, using a dedicated software.The nine marker coordinate sets (x, y, z) in theMCG and MRI coordinate systems, respectively,were registered using a non-iterative least-squaresmethod (Arun et al., 1987). Only rigid trans-formations including global rotations and trans-lations were considered. MCG-MRI registrationprotocol has been applied to more than 50 patientstudies (Pesola et al., 2000). With our patientstudies we have obtained the root mean square(RMS) error of the nine registered markers to beabout 6 mm. The registration error includes var-ious error sources such as the effect of breath-ing, reattachment of the markers between MCGand MR measurements, localization of the mark-ers from MR images and shape changes in thoraxbetween the measurements because of the flexibil-ity of the shoulders and the skin (Makela et al.,2002b). One of the reasons why the RMS errorvalues are relatively low in our measurements isthat the markers in our protocol were attached inpositions which were not very sensitive to differ-ent alignment errors.

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Figure 7. A stack of registered end-diastolic SA MR (top) and PET emission (bottom) image slices forthe P1 case. In the middle row, the images were overlaid in block format to visualize registration results.

5. Capturing the heart anatomy

MR images provide relevant information on thecardiac anatomy. In this section, we presenta method for extracting a 3-D individualizedanatomical model of the heart from MR shortaxis images, based on an Elastic Active RegionModel (ARM) which is an extension of our pre-vious work (Pham et al., 2001). Several groupshave proposed superficial deformable models tosegment the cardiac chambers in three dimen-sions (McInerney and Terzopoulos, 1996). Morerecently, Montagnat and Delingette (2000) intro-duced simplex meshes for segmenting the LV sur-faces from 4-D cardiac sequences in MR, SPECTand ultrasound imaging. The reader can find in(Frangi et al., 2001) a good review of 3-D heartmodeling approaches used for the purpose of seg-mentation. Contrary to superficial models, theARM relies on a volumetric deformation of a ge-ometric heart model. It allows to simultaneouslyextract the LV and RV endocardial surfaces, aswell as the epicardium, while enforcing regular-ity between these surfaces. In addition, it is for-mulated in the mechanical framework of elasticbodies that is often used in the context of mo-tion estimation (Papademetris et al., 2001). TheARM is also closely related to the work of Ser-mesant et al. (2001) who introduced an electro-mechanical model of the heart. In this model, the

contraction is controlled by simulating the propa-gation of electrical waves and taking into accountthe interaction with ultrasound images. Never-theless, in this work, the objective is not to pro-vide a complete biomechanical model of the heart,but to accurately segment MR cardiac images bymeans of a simple but natural description of theheart. The segmentation process can be dividedin two main steps. First, the template is spa-tially positioned by registering it with the imageto be segmented. Then, starting from this initialconfiguration, it is elastically deformed to fit thecardiac structures. Each step will be described inthe following.

5.1. The 3-D biventricular template

A priori information on the shape of the ob-ject of interest strongly constrains the segmenta-tion. We thus developed a 3-D geometric accuraterepresentation of the heart ventricles. This volu-metric template was created from a MR referencedataset. The heart of a healthy volunteer wasimaged using a cine-MR protocol and the end-diastolic time frame was selected, as we only focuson the images corresponding to the end-diastole.A medical expert interactively delineated the epi-and endocardial contours of the two ventricles oneach of the 2-D short axis slices. The correspond-ing surfaces were then reconstructed and the in-terior meshed with tetrahedra using the GHS3D

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software (INRIA, Gamma Project, France). The3-D biventricular template is shown in Fig. 9.

(a)

(b)

Figure 9. (a) 3-D prior biventricular model(19524 nodes, 94402 tetrahedral elements), (b)model immersed in the MR data.

5.2. Interpolating 3-D MR volumes

In order to take advantage of a fully three-dimensional interaction between the model andthe short axis images of the heart, 3-D isotropicvolumes were interpolated from stacks of 2-Dshort axis slices. SA images present a good spa-tial resolution in the acquisition plane, but a poorone in the transversal direction. For the studiedcases, the inter-slice distance was 15 mm, whereasthe pixel size was less than 1.5 mm. In suchconditions, we experimentally observed that theshape based interpolation technique (Grevera andUdupa, 1996) gave better results than polynomialinterpolations on our data.

5.3. The model initialization as a registra-

tion step

The model is rigidly positioned with respect tothe image to be as close as possible to the car-diac structures to be segmented. This is done bysearching for the 6 parameters of the rigid spatialtransformation T (3 translations, 3 rotations) ap-plied to the model, that minimizes the followingenergy :

Eini(T ) = E∂Ω(T ) EW (T ) (2)

Like in (Pluim et al., 2000), the energy to beminimized is a product of an energy based on anintensity criterion and an energy deriving fromthe image gradient. Here, E∂Ω(T ), computed onthe boundary of the template, represents a dis-tance from the model to detected contours in theimage. In practice, we take the mean squareEuclidean distance from the boundary nodes tothe image edges. The region energy EW (T ) isa similarity measure between the image intensi-ties. It is estimated in a floating meshed domainW surrounding the template (Ω ⊂ W ) and caneither be the sum of the square intensity differ-ences (SSD) sampled on the nodes of W , or themutual information (MI) between the two graylevel distributions. In most of the cases, good re-sults are obtained with the SSD criterion whichis known to be efficient in the monomodal case(Fitzpatrick et al., 2000). The total initializationenergy is minimized using the Powell’s optimiza-tion method (Press et al., 1988) which does notrequire the computation of the function’s gradi-ent. Fig. 10 shows initialization results for twopatients.

5.4. The deformation model

The second step of the segmentation process isseen as the deformation of an elastic body submit-ted to an external force field. The myocardiumis modeled as a linear elastic continuous medium.Under the small deformation assumption, the lin-earized form of the Green-Lagrange strain tensoris used:

[ε] =1

2(∇u + ∇ut) (3)

where u denotes the displacement vector. Thestress is related to the strain by the constitutive

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(a) (b) (c) (d)

Figure 10. Initialization step. (a) : patient P1, before registration, (b) : patient P1, after registration,(c) : patient P2, before registration, (d) : patient P2, after registration. First row : basal cross-section,second row : mid-ventricular level.

law of the material. For a homogeneous isotropicmaterial, it takes the form:

σ = Rε = RSu (4)

where σ = (σ11, σ22, σ33, σ12, σ23, σ31)t and

ε = (ε11, ε22, ε33, ε12, ε23, ε31)t are respectively

the stress and the strain vectors, R the elasticitymatrix depending on two mechanical parame-ters (either the Lame coefficients λ and µ, orthe Young modulus E and the Poisson ratio ν),and S a differential operator. If we note Ω theconsidered domain, ∂Ω its boundary, and t thesuperficial external forces applied on the bound-ary, the equilibrium state corresponds to theminimum of the following potential energy :

Eglob(u) =1

2

∫

Ω

σε dx

︸ ︷︷ ︸

Eelast(u)

−α

∫

∂Ω

t(I + u) · u ds

︸ ︷︷ ︸

Edata(u)

(5)

The first term Eelast(u) is an elastic energy whichregularizes the deformations imposed by the ex-ternal energy Edata(u), evaluated in the deformed

configuration (if we assume that the displace-ments are small). In the case of large dis-placements, the geometric non-linearity should betaken into account by updating the elastic energyduring the deformation process. The externalforce field deriving from the image is chosen suchthat it tends to attract the model’s boundary to-wards salient features existing in the image. Oneway to compute a 3-D force field is to calculatethe gradient of a potential image t(x) = −∇P (x)which can be, for example, either the norm ofthe image gradient, an edge map extracted witha Canny-Deriche operator and smoothed with agaussian filter, or a distance map (chamfer orEuclidean distance). The Gradient Vector Flow(GVF), proposed by Xu and Prince (1998), di-rectly provides a force field which allows a betterconvergence, especially in the case of concavities.In our experiments, the GVF computed from thenorm of the image gradient was used in most ofthe cases.

Eq. (5) is discretized using the Finite Ele-ment Method (FEM) with linear basis functions

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(Zienkiewicz and Taylor, 1987). The energy to beminimized thus becomes :

Eglob(U) =1

2UtKU + αF · U (6)

with U being the global displacement vector, F

the global force vector and K the stiffness matrix.A minimum is reached for :

KU = F (7)

As F is a function of the displacement, Eq. (7)is solved iteratively using a semi-implicit Eu-ler scheme. Final segmentation results after themodel deformation are shown in Fig. 11 for thetwo same cases.

(a) (b)

Figure 11. Segmentation results. (a) patientP1, (b) patient P2. First row : basal slice,second row : mid-ventricular level.

6. Functional model of the heart

6.1. FDG-PET cartography

After the registration and segmentation steps,functional data was attributed to the elements

and nodes of the 3-D biventricular model. Alsosome parameters with clinical interest was de-rived from MR imaging. First, the model was la-beled so that it was possible to separate the rightand left ventricles and obtain internal and exter-nal surfaces. Moreover, cavity volumes, myocar-dial mass and local wall thickness were computed.In order to enrich the model with metabolic in-formation, the model was transformed into theregistered PET-FDG emission image. A LV me-dial surface was automatically calculated betweenLV endo- and epicardial surfaces (Fig. 12).

Figure 12. Calculation of the medial surface us-ing the segmented epicardial and endocardial sur-faces.

The medial surface nodes were calculated by,first computing the 3-D normal to each node ofthe endocardial surface and, secondly, calculatingthe middle point of the segment normal to theendocardial surface and its intersection with theepicardial surface (Fig. 13a). Surfaces were trans-formed to registered PET emission image and aFDG uptake mean value was computed at eachnode of the medial surface (Fig. 13b, middle con-tour) in a 5 x 5 x 5 neighborhood, which corre-sponds to 6.25 mm x 6.25 mm x 6.25 mm physicaldimensions (Fig. 13c).

6.2. Magneto-electric cartography

MCG inverse current-density estimates werecalculated for the nodepoints of the medial sur-face. To this aim, the medial surface was trans-formed from MR SA plane to transaxial MR co-

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(a) (b) (c)

Figure 13. (a) Intersection of endocardial (innercontour), epicardial (outermost contour) and cal-culated medial (middle contour) surfaces with aMR SA slice, (b) the same contours are shownin the corresponding registered PET SA image(medial contour in the middle) and (c) the meanvalue of the FDG-uptake was computed at themedial surface nodes in a small neighborhood.

ordinate system by using MR header information.The MCG measurements were regularized with aMAP estimator.

7. Results

7.1. FDG-PET cartography

Fig. 14(left) and Fig. 15(left) illustrate theFDG metabolic activity over the LV medial sur-face for 2 cases. Right ventricular and epi-cardial surfaces are shown in transparency. InFig. 14(right) and Fig. 15(right), the correspond-ing PET bull’s eye (polarmap) presentations areshown for a qualitative evaluation of the 3-Ddisplays (Siemens software, Turku PET Centre).Bull’s eye images are commonly used method fordisplaying functional information of the heart.The center corresponds to the apex and the out-ermost ring represents the basal slice. In suchpolarmaps, metabolic activity is estimated at left-ventricular mid-wall.

The corresponding low LV FDG uptake areascan clearly be seen in both the bull’s eye images(dark green in Fig. 14-15(right)) and in the 3-Dmodel displays (arrows in Fig. 14-15(left)). Visu-alizations of the 3-D model were performed usingthe VTK software library2.

2The visualization Toolkit (VTK), www.kitware.com.

7.2. Magneto-electric cartography

MCG results are presented on the medial sur-face for P1 in Fig. 16 and P2 in Fig. 17. Forboth cases, the 3-D visualization is presented onthe left and the corresponding bull’s eye represen-tation computed from the extracted 3-D medialsurface on the right. The MCG results were com-puted from the resting state data at a single timeinstant in the middle of the QRS complex. Theresults have to be regarded illustrative in thatsense that the electrical activity in the right ven-tricle was neglected in the inverse calculations.

8. Discussion and Conclusion

In this paper, we presented a new approachfor the combination of anatomical and functionaldata from various cardiac imaging modalities.It relies on the registration of thorax structures(thorax surfaces) which are extracted from MRanatomical and PET transmission images. In or-der to provide 3-D displays of the heart that areeasily interpretable by the physician, an individu-alized 3-D biventricular heart model is extractedfrom the SA MR images. The various geomet-rical and functional parameters can therefore berepresented onto this model through the LV me-dial surface (Fig. 14-17). Following our previ-ous efforts, we show in this paper the ability ofthe method to integrate information about themagneto-electric activity of the heart from MCG.The fusion of metabolic data from PET andmagneto-electrical potential onto the same indi-vidualized 3-D heart model from MRI has been il-lustrated on two pathological cases. With such anapproach, the localization of metabolic and con-duction defects is straightforward since the biven-tricular model allows for the unambiguous iden-tification of myocardial territories. Within thesame framework, it is natural to envisage the in-clusion of other complementary functional datasuch as information related to the myocardial de-formation or perfusion (Behloul et al., 2001).

The reliability of the method mainly dependson the accuracy of the rigid PET-MRI registra-tion. The registration results of 10 cases werevisually inspected by a medical expert. Nine overthe 10 available cases were considered to provide

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Figure 14. 3-D representation of the FDG PET uptake values on the biventricular heart model (left) forpatient P1. Interactively made bull’s eye representation (Siemens software) of the corresponding PETimage is presented on the right. The polarmap shows PET values at mid-wall location. Scar area can beseen in red at the basal level of the 3-D display (arrows).

satisfactory correspondence results. In the re-maining bad case, unexpected artifacts were ob-served in FDG-PET data. In a previous paper(Makela et al., 2001a), we proposed a quantifi-cation of the registration accuracy based on thecalculation of a distance between segmented sur-faces in PET and MRI. The mean distance was3 mm with a maximum of 4 mm. This is onlyan indication of the performance of the registra-tion algorithm since it highly depends upon thesegmentation of the thorax structures. It alsoprovides a simple mean to detect possible reg-istration failure. A more systematic and accuratevalidation of the registration method is currentlyconducted through image simulations. Also in-tensity based methods, like mutual information,are potential alternative to determine registrationparameters in this kind of registration methodswhere the PET transmission image is used as alinking mediator to register PET emission imageto MR image coordinates. In some cases, inten-sity based methods can even allow to register theemission image directly with the anatomical im-age.

PET imaging devices have typically 4 - 10 mmspatial resolution (Hartiala and Knuuti, 1995).In general, the ability of our 3-D model basedmethod to detect functional abnormalities is lim-

ited by the spatial resolution of the PET imag-ing device. In MCG, accuracies of 5 to 25 mmhave been reported by comparing the MCG local-ization results to: i) cardiac surgery, ii) catheterablation, iii) the results of invasive electrophysio-logical studies, iv) ECG localization results, andv) physiological knowledge (X-ray or MRI). Be-sides patient studies, the ability of the MCG tolocate artificial current dipoles has been testedwith physical thorax phantoms. A non-magneticpacing catheter in a realistically shaped thoraxphantom resulted in equal accuracies of 5 - 10 mmbetween MCG and ECG mapping data (Feniciet al., 1998). On the other hand, the samecatheter in 15 patients showed significantly bet-ter localization accuracy with MCG data (7 mm)than with simultaneously recorded ECG mappingdata (25 mm) (Pesola et al., 1999).

The MCG results in this work were evaluatedon the median LV surface during the cardiac de-polarization. The resting-state MCG data in thepeak of the QRS contains contributions from bothventricles, while the LV contribution dominates.In this study the RV was not included in the in-verse MCG computations. The main motivationto use only the LV surface came from our previousstudy where we investigated the MCG data afterphysical exercise test in the same patient popu-

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Figure 15. Left : 3-D representation of the FDG PET uptake values on the biventricular heart model forpatient P2. Right : corresponding bull’s eye representation (Siemens software) with values estimated atmid-wall location.

lation (Nenonen et al., 2001). In that study theST segment was analyzed and difference signalswere computed (post-exercise minus rest). Thisdifference was associated with exercise-induced is-chemia which was known to arise in the left ven-tricle on the basis of PET and MRI (Lauermaet al., 2000). While the whole MCG (and ECG)source imaging methodology is still under rapiddevelopment (Hamalainen and Nenonen, 1999)the results show that MCG, due to a millisecondtime resolution, may be able to provide new valu-able information on cardiac function, especiallywhen constrained with accurate anatomy fromMRI and combined with other medical imagingdata.

The temporal correspondence of the PET andMR images has been overcome by assuming thecorrespondence between the MR transaxial, end-diastolic SA images, and the PET acquisitions,as it is usually admitted in clinical practice. Infact, transaxial MR images were obtained with asnapshot technique during free respiration whilePET measurements were accumulated during arelatively long period of time (about 10 minutes).This might generate differences in the thorax andlungs shape and, consequently, cause registrationerrors. ECG-gated PET with non-rigid registra-tion could certainly help to better handle the tem-poral correspondence problem.

The results of the automatic extraction of thebiventricular model using the ARM were quitesatisfactory for the two processed cases as shownin Fig. 11. This step, which is independent ofthe others, is important since i) it extracts anindividualized anatomical model from which vol-umes, masses, wall thickness can be derived, ii)it provides the region of interest where the func-tional parameters from PET and MCG are es-timated. We are currently quantifying the per-formance of the ARM in terms of accuracy (ascompared to manual tracing) and robustness, es-pecially as a function of model initialization. Inaddition, acquisition sequences such as stimulatedecho sequences (e.g TrueFISP, bFFE, Fiesta) pro-vide better resolution and contrast and may im-prove the reliability and the accuracy of the seg-mentation results.

The medial surface seems to us the moststraightforward way to obtain functional car-tographies preventing from border effects thatcould occur from slight mis-registration. In thiswork, we implemented a simple geometrical ap-proach to compute this surface. Other methodssuch as the centersurface (Bolson et al., 1995)could also be applied. In order to keep the volu-metric property of the model, the next step willconsist in the anatomical re-parameterization ofthe heart’s geometry so that the functional pa-

15

Figure 16. Left : 3-D representation of the MCG values on the biventricular heart model for patientP1. Right : interactively made corresponding bull’s eye representation calculated from the 3-D medialsurface. Scar area can be seen in red at the basal level of the presentations (arrows).

rameters can be easily depicted on the myocardialborders as well as inside the wall by interactivelypeeling the model, for instance.

In conclusion, we have presented a model-based approach for the combination onto patient-specific heart model of both anatomical and di-verse functional data from multimodality car-diac imaging. In this work, one of the mainpurposes was to automatically register metabolicPET and electromagnetic measurements fromMCG. Similar approach could also be used tocombine other modalities such as SPECT andmultichannel ECG studies. We believe that thepresented approach can help the radiologist orcardiologist to rapidly apprehend the functionalstate of the myocardium through 3-D intuitivecartographies. It is therefore possible to accu-rately compare the different imaged functions(metabolism, magneto-electric activity) in thecontext of physio-pathological studies on the is-chemic diseases, for instance, which consequenceson the cardiac muscle are complex and not yetfully understood. In order to enrich the model,other parameters related to the heart motion andperfusion will be integrated in the near future.

Acknowledgments

This study was partly granted by the ScientificDepartment of the French Embassy in Finland,the Region Rhone Alpes, through the ADeMOproject and The Foundation of Technology in Fin-land. This work was performed within the frame-work of the joint incentive action ”Beating Heart”of the research groups ISIS, ALP and MSPC ofthe French National Center for Scientific Research(CNRS).

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