A graphical anatomical database of neural connectivity · Agraphicalanatomicaldatabaseofneural...

A graphical anatomical database of neuralconnectivity

William A Press1 Bruno A Olshausen2 and David C Van Essen3

1Department of Psychology Stanford University Stanford CA 94305 USA2Center for Neuroscience (and Department of Psychology) 1544 Newton Court UC Davis Davis CA 95616 USA3Department of Anatomy and NeurobiologyWashington University School of Medicine St Louis MO 63110 USA

We describe a graphical anatomical database program called XANAT (so named because it wasdeveloped under the X window system in UNIX) that allows the results of numerous studies on neuro-anatomical connections to be stored compared and analysed in a standardized format Data are enteredinto the database by drawing injection and label sites from a particular tracer study directly ontocanonical representations of the neuroanatomical structures of interest along with providing descriptivetext information Searches may then be performed on the data by querying the database graphically forexample by specifying a region of interest within the brain for which connectivity information is desiredor via text information such as keywords describing a particular brain region or an author name orreference Analyses may also be performed by accumulating data across multiple studies and displaying acolour-coded map that graphically represents the total evidence for connectivity between regions Thusdata may be studied and compared free of areal boundaries (which often vary from one laboratory to thenext) and instead with respect to standard landmarks such as the position relative to well-known neuro-anatomical substrates or stereotaxic coordinates If desired areal boundaries may also be decentned by theuser to facilitate the interpretation of results We demonstrate the application of the database to theanalysis of pulvinar^cortical connections in the macaque monkey for which the results of over 120 neuro-anatomical experiments were entered into the database We show how these techniques can be used toelucidate connectivity trends and patterns that may otherwise go unnoticed

Keywords graphical database neuroanatomy cortex thalamus inference

1 INTRODUCTION

The application of modern pathway tracing techniquesover the past several decades has revealed a wealth of infor-mation on the connections between brain regions in avariety of diiexclerent species Although our current store ofknowledge could be considered vast most of the data existsscattered through journal articles in the form of photo-graphs or diagrams of tissue cross-sections that have beenmarked (or scoredrsquo) in the locations where labelling wasobserved after a neuroanatomical tracer was injected in aparticular region of the brain Those sites where labellingwas observed provide evidence that a connection existsbetween them and the location where the injection wasmade Currently few methods exist for viewing this wealthof data in a unicented format that accurately summarizes theexisting state of our knowledge As the amount of neuro-anatomical data increases it will become increasingly dicurren-cult to access and assimilate this information usingconventional literature searches and human memory Justas genome and protein databases have proven critical formolecular biologists neuroanatomical databases are nowbecoming an important tool for organizing the increasingamount of information on neural connection pathways Inthis paper we describe our eiexclorts at building a graphical

database of neural connection patterns that preserves asmuch anatomical detail as possible

Among current methods for representing neuralconnectivity information in a unicented or summarizedformat one of the most popular is the schematic wiringdiagram in which boxes that represent diiexclerent brainareas are connected with lines that denote the existence ofconnections between them (eg Felleman amp Van Essen1991) Although such diagrams are helpful in ascertainingglobal trends in connectivity they gloss over a tremen-dous amount of information that is available in the dataon a centner scale For example in some instances a fairlylocalized topographical organization to the connectionpatterns may exist (such as between areas V1 and V2) andin other cases not (such as between V4 and theinferotemporal complex) In addition there may also bediiexclerences in the degree of connectivity Some regionsmay be densely interconnected (showing heavy labelling)whereas others may be sparsely interconnected (showingonly light labelling) This type of information can becaptured to some extent by a connectivity matrix inwhich each element denotes the strength of an inferredconnection (eg Young 1993 Stephan et al 2000b) but stillonly at the macroscopic level Schematic wiring diagramsalso typically do not diiexclerentiate between evidenceagainst a connection versus lack of evidenceoumlie if a linedoes not connect two boxes in the diagram it is not

Phil Trans R Soc Lond B (2001) 356 1147^1157 1147 copy 2001 The Royal Society

doi 101098rstb20010907

Author for correspondence (baolshausenucdavisedu)

immediately obvious whether it is due to there being nolabelling observed in an experiment that would revealsuch a connection or whether the experiment simply hasnot yet been done

For the investigator braving a foray into the literature inorder to learn the specicentcs of certain connection patternsthere is yet another problem lurking namely diiexclerentauthors often use diiexclerent nomenclatures to describe thesame brain region (eg Brodmann 1909 Felleman amp VanEssen 1991) The pulvinar nucleus of the thalamus is anexcellent example of where there is wide disagreementamong authors as to the placement of borders delineatingvarious subnuclei What constitutes the lateral pulvinar toone author may be the medial pulvinar to another Otherregions such as inferior pulvinar are constantly under-going further subdivision (Cusick et al 1993 Gary et al1999) Thus one cannot simply trust a verbal report in apaper claiming to have found `evidence for connectionsbetween V1 and lateral pulvinarrsquo One must examine thescored cross-sections and compare the actual label siteswith onersquos own `mental databasersquo of these various regionsAlthough such work is routine for a skilled neuroanato-mist it cannot reasonably be expected of the wider class ofinvestigators that need access to detailed informationabout neural connectivity Thus there is a need for toolsthat allow for the objective analysis and comparison ofcentne-scale neuroanatomical data

Our eiexclort to build a neuroanatomical database wasinitially stimulated by an interest in the patterns ofconnectivity between the pulvinar and visual cortex inthe macaque monkey The dicurrenculties encountered inintegrating information across multiple studies due to themultiplicity of partitioning schemes used for both cortexand the pulvinar motivated our development of agraphically orientated database The idea behind agraphical database as opposed to a conventional textorientated database is that data are represented within acanonical neuroanatomical atlas irrespective of parti-tioning schemes Our database program called XANATallows injection and label sites from multiple experimentsand across diiexclerent laboratories to be entered onto asingle consistent graphical representation of the anato-mical structures of interest The connectivity trendswithin the entire set of data may then be revealed usinganalysis routines which display the cumulative evidencefor connectivity between user-specicented regions of interestin a colour-coded `heatmaprsquo that is superimposed on theneuroanatomical atlas In this way one can summarizethe evidence for connectivity between any arbitrarilychosen locations in the brain accumulated from all datawithin the database without relying upon (thoughpossibly guided by) previous area-partitioning schemes

Graphical representations of data have found success ina number of anatomical applications including volu-metric atlases (Toga 1989 Jones 2000) and volumetricreconstruction of data collected from a series of slices(Schwaber et al 1991 Funka-Lea amp Schwaber 1994) Inaddition graphical representations at the macroscopiclevel have been shown to allow for the translation of oneparcelization scheme to another (Stephan et al 2000a)Perhaps most closely paralleling our own eiexclorts is theprogram NeuARt (Dashti et al 1997) which allows sitesof various types of anatomical labelling (not necessarily

connectivity related) to be scored within a canonicalatlas The implementation of graphical search capabilityfor this program is still in progress

Another capability that we have attempted to buildinto our database is the ability to represent and combinedata probabilistically This capability is importantbecause there are uncertainties inherent in the data dueto both the probabilistic nature of dye transport and theprocess of registering injection and labelling sites withinthe canonical atlas Thus rather than simply super-imposing multiple datasets one would actually like toobtain a measure of the probability that a connectionpathway exists between one area and another given allthe data available XANATdoes this by using the rules ofBayesian inference to combine evidence from multipledatasets thus taking into account both the structure andvariability inherent in the data in a principled manner(Grenander amp Miller 1993) Such a probabilistic approachhas recently been employed successfully for combininginformation about areal boundaries in the cortex fromdiiexclerent animals (Van Essen et al 2001)

In this paper we describe the structure of XANATandthe tools we have built for analysing data on neuroanato-mical connectivity (see frac12 2) We then demonstrate its usein inferring patterns of connectivity between the cortexand pulvinar of the macaque monkey (see frac12 3) Finally wediscuss the lessons learned from this eiexclort and somefuture directions for improving the methods of data entryand data representation

2 METHODS

(a) The graphical representationInjection and tracer data are represented in XANAT by

their coordinates within a canonical brain atlas This represen-tation comprises three separate levels the atlas correspondingsupplementary images and explicit area-partitioning schemes

The atlas comprises a set of images onto which all data aredrawn providing a canonical representation for combiningresults across experiments and studies Ideally these images arelike those of a conventional atlas they show the structuralgeography and cytoarchitectural organization and do not relyupon explicit segmentation The atlas used in our exemplar ofcorticopulvinar connectivity includes two types of images(centgure 1ab) a poundat map of Macaca mulatta cerebral cortexgeography (gyri and sulci) and eight coronal Nissl-stainedsections through the Macaca fuscata pulvinar and associatedsubcortical regions (posterior to anterior displayed from left toright by row) The Macaca fuscata pulvinar atlas was usedinstead of one for Macaca mulatta because it was the highestquality atlas available at the time of development The corticalpoundat map was scanned directly from Felleman amp Van Essen(1991) using a Microtek poundat-bed scanner The pulvinar imageswere digitized directly from Kusama amp Mabuchi (1970) using a512 pound512 pixel charge-coupled device (CCD) camera and thusinclude Kusama amp Mabuchirsquos designated thalamic nucleusboundaries and labels These images also included stereotaxiccoordinates which were then translated into pixels in the atlas

The supplementary images used in XANAT are in registerwith the atlas images and can be toggled to be displayed intheir stead These supplementary images contain additionalinformation that aids data entry and analysis For example ourpoundat map of cortical geography (centgure 1b) has a corresponding

1148 W A Press and others A graphical anatomical database of neural connectivity

PhilTrans R Soc Lond B (2001)

supplementary image of the Felleman amp Van Essen (1991) area-partitioning scheme (centgure 1c) We did not include supplement-ary images for the pulvinar sections because our atlas imagesalready happened to include nucleus boundaries Supplementaryimages for the pulvinar sections can easily be added though ifone wished to use an alternate partitioning scheme such asCusick et al (1993) Gary et al (1999) Other possible supple-mentary images include myelin- or antibody-stained slices thatcorrespond to Nissl-stained slices in the atlas

To facilitate the interpretation of analyses performed inXANAT it is useful to have an explicit segmentation of the atlasinto its constituent subdivisions not just an image of the parti-tioning scheme This segmentation is achieved by drawingborders explicitly as polygons onto either the atlas or thecorresponding supplementary images using an accompanyingapplication tool Although multiple partitioning schemes may berepresented simultaneously we limit our corticopulvinarexample to just Felleman amp Van Essenrsquos (1991) partition scheme(corresponding to the supplementary image centgure 1c) Thesearea-decentning polygons are not displayed during normalXANAT use However overlap between these polygons andentered data are reported with every injection and label sitedrawn into the atlas and can be used to guide data searches andinterpret the results of analyses

Images are typically limited to representing one hemispherehowever the entire graphical representation (the atlas supple-mentary images and area segmentations) can be poundipped abouttheir vertical axis This facilitates the entry of data collectedfrom either hemisphere

(b) Entering dataEach data record in XANATcontains both text and graphical

information that correspond to a single neuroanatomical experi-ment showing a single injection site multiple injection sites or alesion as well as the resulting pattern of labelling (or degenera-tion in a lesion study)These data drawn as polygons and ellipsesare transferred manually from either illustrations or sectionedslices onto the atlas andor supplementary images Label strengthand injection halos are encoded by stipple density and in amultiple-injection study diiexclerent injections and labelling aredistinguished from one another by colour (up to centve diiexclerentinjections are supported in the current version of XANAT)

In addition to these graphical data every record containstext information These include the reference tracer typeinjection and labelling distribution by area (if areas are decentnedsee frac12 2a) comments and concentdence in the data The concentdenceallows the investigator that enters the data to evaluate subjec-tively its accuracy and assign a quantitative (0^100) measure

A graphical anatomical database of neural connectivity W A Press and others 1149

Phil Trans R Soc Lond B (2001)

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Figure 1 The atlas comprises images of the anatomical structures of interest In this example it consists of eight coronalNissl-stained sections of the pulvinar and a poundat map of macaque cortical geography (a) The most caudal pulvinar section isshown on the top left with increasingly rostral slices proceeding left to right and then down (b) Atlas image of cortical geographytaken from Felleman amp Van Essen (1991) (c) Supplementary image for the cortical poundat map showing area-partitioning scheme

This takes into account at least three factors concentdence in theoriginal data concentdence in data entry and concentdence in tracertransport reliability Because these assessments are subjective itis not straightforward to develop a precise quantitative relation-ship for combining them into a single concentdence valueCurrently we simply combine these factors mentally to come upwith a single concentdence score

(c) AnalysesIn addition to selecting each record separately for display and

editing XANATcontains analysis tools for combining data acrossinjections and studies There are two main types of analysis toolslist-generating analyses (searches and stacks) and graphicalanalyses that depict their results graphically (but also generate lists)

(i) Searches and stacksThe simplest analysis tools are searches and stacks which

reduce the original dataset by generating a subset list of recordsThe process by which these lists are created is dependent uponwhich method is used

Searches select records that have certain keywords in the refer-ence or comments centeld as well as those that have projections toor from a particular area or areas Search criteria can becombined using simple logical operators For example one canselect a set of records that were published by a particular authoror a set that had connections with visual areaV4 as well as somekeyword of interest in the comments centeld eg anterogradersquo

Searching for records on the basis of area informationrequires an explicit segmentation of the atlas according to somearea-partitioning scheme (discussed above) The search yields alist of records that show projections to or from the designatedlocations The direction of projections in which one is interesteddetermines whether injection or label is used to select a givenrecord For example a search for inputs to area V4 will includethose records that have either anterograde-tracer labelling orretrograde-tracer injections that lie in V4 because in either casethe location of the injection or label respectively indicates thesource of these projections Conversely records containingretrograde-tracer labelling or anterograde-tracer injections inV4 would not be included in the search results as they provideno information about projections to V4

The stack list is set entirely by the user by selecting recordsindividually Items are pushed onto or popped from the stackusing a LIFO (last in centrst out) ordering The stack primarilyserves as a temporary store that facilitates the direct comparisonof two or more otherwise unrelated entries Also the results ofgraphical analyses described in the next section can be pushedonto the stack allowing one to compare various analyses withone another or with raw data

(ii) First- order graphical analysesGraphical analyses provide a way to extract and visualize

information from multiple studies The user specicentes a region ofinterest within the atlas and a graphical representation ofconnection strengths from that location to that location orboth is generated as a colour-coded `heatmaprsquo Specifying thesearch area can be done either graphically or textuallyGraphical search areas can be selected by drawing ellipses orpolygons on any or all of the available images One may alsoclick on an existing polygon specicented by an area-partitioningscheme Areas having a corresponding text label can be selectedby performing a text-based search and then using the results ofthe search for the analysis

XANATsupports two primary methods of graphical analysissuperposition and probabilistic Both yield a colour-codedheatmap where colour represents a measure of the total strength(number of studies) or probability of connections respectively

A superposition analysis is generated using a weighted sum ofthe connectivity across the dataset The relative weight eachrecord contributes is determined by the product of three factorsthe fraction of the search area that overlaps the recordrsquos relevantdata (whether it be injection or label or both) the fraction ofthe recordrsquos relevant data that overlaps the search area and theconcentdence weighting given the data at the time of data entry or

record weight ˆ confidence poundsize of (search data)2

size of (search) pound size of (data)

(21)

where size of (X) is the number of pixels in region X Theheatmap colour spectrum that results from this analysis rangesfrom least weight (blue) to greatest weight (red)

Although the superposition analysis oiexclers a simple methodfor combining data across diiexclerent studies it suiexclers from thefact that it does not distinguish between a lack of evidenceversus evidence against there being a connection In additionthe heatmap value assigned does not properly repoundect the totalevidence for a connection because it will be heavily biased bythe number of studies that happen to have been done for a parti-cular region The solution to these problems is to combine thedata probabilistically

In a probabilistic analysis the resulting heatmap repoundects theactual probability that each pixel in the atlas is connected withthe identicented search area ranging from 0 (blue) to 1 (red)with a value of 05 indicating complete ignorance (green)Specicentcally we calculate the posterior probability P(c(x y)jD)where c(x y) is a binary-valued function that represents thepresence or absence of a connection between the search area xand some point y in the atlas and D is the set of relevant experi-mental data that speak to this connection Dˆfd1 (x y) d2(x y) dn (x y)g Each di(x y) is a binary variable that repre-sents whether or not a connection is indicated by the ith studyin the database (presence or absence of label) The posteriorprobability is given from Bayesrsquo rule

P(c(x y)jD) P(c(x y))P(Djc(x y)) (22)

which states that the probability of there being a connectionc(x y) given the data D is proportional to the a priori probabilityof there being a connection P(c(x y)) times the probability thatthe data accurately repoundect the true state of connectivity whichfor independent data is given by the factorial distribution

P(Djc(x y)) ˆn

iˆ1

P(di(x y)jc(x y)) (23)

The values P(di(x y)jc(x y)) repoundect the sensitivity and false-positive rate of the data and in our particular implementationthey are directly related to the user-assigned concentdence in thedata (see Appendix A)

Although the probabilistic approach does not obviate theneed to make subjective judgements about the data it doesincorporate these subjective notions into quantitative reasoningin a consistent manner We do not yet have a general solution forsetting the sensitivity and false-positive rates P(di(x y)jc(x y))and in fact the prescription we use here is rather crude andshould be viewed merely as a starting point Our main emphasisin this paper is on formulating a framework for combining these



uncertainties across multiple neuroanatomical studies assumingthey may be reasonably estimated

(iii) Second- order graphical analysesThe results of the above centrst-order analyses may be accumu-

lated compared or contrasted by combining them together invarious ways These second-order analyses can use any graphicalanalyses as their substrate and come in three forms additivemultiplicative and subtractive

The additive analysis allows one to superimpose two analyseson top of one another facilitating their comparison The datafrom single records may also be added to a heatmap allowingfor direct comparisons between an analysis result and the datathat generated it

The multiplicative analysis provides a means of visualizingdirectly the amount of overlap between two analysis results Thegeometric mean of the two operand analyses is taken on a pixel-by-pixel basis and the colour-scale remains unchanged In this wayanalyses with little overlap will result in sparse non-zero values andmultiplying an analysis with itself will leave it unchanged

The subtractive second-order analysis illustrates the relativelocations of two non-overlapping analyses This is done bytaking the pixel-by-pixel diiexclerence of two heatmaps andrescaling the colour-bar to accommodate the entire range withzero in the middle

3 RESULTS

(a) Entering dataFigure 2 shows the results of a retrograde-tracer

injection in areas LIP (lateral intraparietal cortex) andVIP (ventral intraparietal cortex) from a study of Baizer

et al (1993) and its corresponding entry in theneuroanatomical atlas The location of the cortical injec-tion is represented by three separate polygons (red)within the cortical poundat map The zones where labellingwas observed in the pulvinar denoted by triangles in thecentgure are represented by a series of polygons (purple) ineach cross-sectional image with some interpolationrequired in registering the cross-sections of the studywith those in the atlas To date we have entered theresults of 127 injection and lesion experiments in this wayfrom 20 published studies Our rough estimate of theaccuracy with which tracer injection and labelling sitesare typically represented is about 1^2 mm on average

(b) AnalysesWe used the database and the above-described analysis

routines to investigate the overall trends in connectivitybetween visual cortex and the pulvinar Figure 3a showsthe results of analysing connections between cortical areaV4 and the pulvinar using the superposition algorithm(the large image shows in more detail the centfth mostcaudal section of the pulvinar) This was done by selectingthe V4 area-decentning polygons (V4d and V4v) in thecortical atlas (or by typing `V4rsquo into the search window)The result of this analysis accumulated over 21 relevantstudies that contain injection or labelling within V4reveals that most of these connections are with theinferior and lateral pulvinar nuclei at the dorsolateralzone of their shared border

As mentioned in frac12 2 the superposition method providesa simple means of collapsing data across multiple experi-ments but it does not properly represent evidence for or



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Figure 2 Data entry is performed by manually drawing sites of injection and observed labelling directly onto the neuroanato-mical atlas The entry of a cortical injection and resulting pulvinar label from a study by Baizer et al (1993) is shown here Atlasimages not used in the original study are indicated by triangles in their upper-left corner

against connectivity in terms of probability Thus it isalso useful to analyse the data probabilistically as shownin centgure 3b Here the heatmap represents the posteriorprobability of a connection with the search region in thiscase a small subregion of V4 The green coloration visiblein some of the pulvinar images now indicates that littleinformation is actually available regarding visual corticalconnections to the most rostral slices of the pulvinar(green corresponds to P ˆ 05) By contrast the lack ofconnections between V4 and the more caudal medialpulvinar indicated by the superposition analysis appearsto repoundect an actual absence of connectivity (To create thismap we assumed a value of 05 for the prior (seeAppendix A) which assumes no prior knowledge ofconnections between the cortex and pulvinar beyondwhat is stored in the database)

One of the principal uses of XANAT is to compareconnectivity zones for diiexclerent parts of the brain such asdiiexclerent visual cortical areas In centgure 4a we show theresult of a superposition analysis for connections betweenthe pulvinar and the ventral stream (V4IT (infero-temporal cortex)) Within the pulvinar these connectionsconsistently appear in the inferior and ventral^lateralnuclei indicating a role for these regions in form proces-sing This pattern of connections is in contrast to thatfound between the pulvinar and posterior parietal cortex(centgure 4b) Here we centnd connections most predominantlywithin the medial pulvinar and more dorsal portions ofthe lateral pulvinar indicating a role for these nuclei inprocessing spatial information (corresponding to the so-called `wherersquo stream) These patterns of connectivityillustrate how diiexclerent pulvinar nuclei may be involved

in processing diiexclerent kinds of visual information (suchas form versus spatio-temporal)

Diiexclerent cortical areas within the same processingstream can also have diiexclerent patterns of pulvinarconnectivity In centgure 5 we use superposition analysis toexamine how visual area V4 (centgure 5a reproduced fromcentgure 3a) and inferotemporal cortex (centgure 5b) both ofthe `formrsquo processing stream are connected with thepulvinar These small panels show that the connectionsbetween inferotemporal cortex and pulvinar are signicent-cantly more caudal and ventral than those between areaV4 and pulvinar The diiexclerence in locations of these twoprojections is highlighted by a subtractive second-orderanalysis (centgure 5c) in which the results shown in centgure5b are subtracted from the results shown in centgure 5aBlue regions such as ventromedial caudal pulvinar indi-cate where inferotemporal cortex connects with thepulvinar more consistently than does area V4 redregions such as more lateral and rostral pulvinar indicatewhere V4 connects with the pulvinar more consistentlythan does inferotemporal cortex Figure 5d shows a multi-plicative second-order analysis formed by multiplyingthe results shown in centgure 5a with the results shown incentgure 5b Most regions in this multiplicative second-orderanalysis are near zero indicating little overlap betweenthese two sets of projections

4 DISCUSSION

(a) AnalysesOne method for analysing a collection of studies is to

examine each study individually developing a `mental



(a) (b)

Figure 3 (a) Superposition analysis of connections between all of visual area V4 and the pulvinar The left end of the colourspectrum (blue) represents minimal weight and the right end (red) represents the maximal weight (b) A probabilistic analysis ofconnections between a small zone in the middle of V4d and the pulvinar The left end of the colour spectrum (blue) represents anear 0 probability of there being such a connection and the right side (red) represents a near 100 probability chance (green)is in the middle of the heatmap colour bar and is indicated by the black tick mark

modelrsquo of similarities and diiexclerences across the entire setSuch an analysis is certainly possible using XANAT infact it is facilitated by all of the data being in a singlecommon representation However human memory islimited and subject to personal biases XANAT can thusaid the process of understanding connectivity trendsthrough analysis routines that combine data across manydiiexclerent studies in an objective fashion

The superposition analysis is computationally simplerand substantially faster than the probabilistic analysisThis is because a superposition analysis examines eachinjection only once per analysis and the size of the searcharea has no eiexclect on how long the analysis takes Bycontrast the probabilistic analysis evaluates separately theconnectivity of every point in every image with everypoint in the search area a search area larger than a fewpixels thus requires an impractical amount of time toanalyse Furthermore because of the nature of the compu-tations involved and because each pixel in the search areagenerates its own set of probabilities combining theseprobabilities over a large number of search area pixels canpotentially dilute the result For this reason probabilisticanalyses should generally be constrained to small searchareas (such as a single point or pixel in an area) whereassuperposition analyses can be eiexclectively used for analysingconnections with entire areas

The probabilistic analysis does oiexcler a signicentcant advan-tage over the superposition analysis in two main respects(i) it allows one to distinguish evidence against a connec-tion versus a lack of evidence for or against a connectionand (ii) it combines multiple datasets in a way that repoundectsproperly the total evidence for connectivity rather thanthe number of studies per se This is not the case with a

superposition analysis since all heatmap values start atzero and data are combined additively Thus no datawould appear the same as data showing evidence against aconnection In addition if there happen to be many morestudies for one particular area (eg more IT injectionsthan V1 injections) then the results of the analysis will besignicentcantly skewed in that direction In the probabilisticanalysis by contrast the heatmap value repoundects the prob-ability of there being a connection (05 being chance)Thus the lack of observed labelling lowers the probabilitywhereas those regions for which no observations existleave the probability unaiexclected Also although the obser-vation of labelling increases the probability of a connec-tion multiple studies do not combine additively but ratherasymptote towards 10 These distinctions are importantbecause most studies do not include information for allregions of the atlas and not all regions of the atlas arecovered uniformly by the data

Conversely a probabilistic analysis requires that onehas properly assigned uncertainties to the data and sothe overall conclusions resulting from such an analysis areonly as good as the assumptions used in assigning theuncertainties in the centrst place The particular method forassigning uncertainties we have chosen here is onlyintended as a beginning and could conceivably beimproved upon if there were a principled basis forassigning them based on known uncertainties in the data(eg information about sensitivity or false-positive rates ofdye transport from a particular study)

Second-order analyses provide the added poundexibility ofcombining and comparing diiexclerent analysis resultsincluding past second-order analyses The additive second-order analysis allows one to superimpose on analysis



(a)

(b)

Figure 4 A centrst-order analysis comparison of pulvinar connections with ventral and dorsal visual processing streams(a) Superposition analysis of ventral-stream (V4IT (inferotemporal cortex)) connectivity with the pulvinar shows most of theseconnections are with the inferior and ventral^lateral nuclei of the pulvinar (b) By contrast posterior parietal cortex connectsmostly with medial and dorsal lateral nuclei This comparison illustrates how diiexclerent pulvinar nuclei may have a role in distinctprocessing streams

results the original data that generated them howeverthey do not provide as strong a contrast between twoanalyses The subtractive second-order analysis showsmore clearly the relative connections of two analyses Onecaveat though is that a diiexclerence of zero could resultfrom any two identical results whether or not they indicateevidence for connectivity These two alternatives can bedistinguished using the multiplicative second-orderanalysis which displays exclusively those areas with

connections coincident between the two original analysesGiven the diiexclerent capabilities of each second-orderanalysis technique they are often best used in concert withone another to illustrate a given comparison

Using these centrst-order and second-order analysis toolsdistinct subdivisions within a structure can be distin-guished by connectivity independent of anatomicalfeatures Furthermore they can be used to discover novelconnections not immediately apparent in the original



(a)

(b)

(c)

(d)

Figure 5 A centrst-order and second-order analysis of pulvinar connections with diiexclerent levels of the ventral processing stream(a) The superposition analysis of V4^pulvinar connections (same as centgure 3a) (b) A superposition analysis of visual area IT(inferotemporal cortex) shows connections with more caudal and ventral zones of the pulvinar (c) A subtractive second-orderanalysis highlights the diiexclerence between these two projections (d) A multiplicative second-order analysis illustrates only a smallamount of overlap

data and to suggest possible areas of interest for futureinvestigation

(b) The graphical representationThe results of the above-described centrst-order and

second-order analyses are meaningful only in so far as thedatabase entries accurately repoundect the original data Oneadvantage of the graphical representation used byXANAT is that the representation of neuroanatomicaldata is not dependent on how the structures involved arepartitioned into areas This is signicentcant as area designa-tions often vary between laboratories and can have alarge amount of variability Also relying on area designa-tions to analyse data for connection-based area designa-tions reveals a troubling circularity

A textual alternative to area-based spreadsheet tabula-tion is to represent data by their corresponding coordi-nates This technique is commonly used in functionalimaging studies and databases (Fox et al 1994) in whichregions of activation are described by the Talairachcoordinates of each regionrsquos centre A limitation of thistechnique though is that identical coordinates in twoindividuals do not necessarily correspond to identicalstructures This is because spatially decentned coordinatesystems do not account for individual variability

Although a graphical representation overcomes some ofthese problems it has its own set of limitations Onelimitation of XANAT is that not all studies are equallyamenable to being transferred onto a given atlas In ourpulvinar^cortex implementation for example the atlasconsists of eight coronal slices of the pulvinar spaced by05 mm However some data may come from slicesspaced by diiexclerent distances and sectioned at diiexclerentangles (possibly even in diiexclerent planes) This variabilityis partially accounted for by the concentdence measureassigned to each record

Another limitation is the resolution of the atlas As thedata come from a number of diiexclerent studies andanimals and are entered into one canonical referenceframe it is likely that the centne structure in connectivitypatterns will become blurred For example Hardy ampLynch (1992) show that projections from pulvinar tocortical areas LIP and 7a arise from intercalated hori-zontal zones in the medial pulvinar If a number of suchinjections are entered into the database out of phase withone another this centne lamination will probably not beseen in analysis results though the location of LIP and 7aprojections as a group will be

(c) Future developmentXANATrsquos function ranges from a simple anatomical

database to an analytical tool capable of educing simpleintuitive results out of a complex dataset Although it hasproven to be useful for comparing connectivity betweendiiexclerent structures of the brain it should be viewed as aninitial eiexclort that has room for growth and improvement

One important area for development is to representvolumetric structures such as the pulvinar volumetri-cally instead of as a series of slices In doing so datapresented as slices could be incorporated into the atlasvolume at its appropriate angle presently we are limitedto the atlasrsquos planes of section Furthermore analysescould be performed volumetrically instead of being

limited to slice surfaces A volumetric representationwould also be more informative and easily interpretablethan the current slice representations and would providethe opportunity to view arbitrarily orientated planes ofsection

An additional area for future development is auto-mated data entry Instead of manually mapping publishedor collected data onto our canonical representations awarping algorithm (such as Christensen et al 1997) couldbe used to automate the procedure Recent anatomicalsoftware packages such as reported in Funka-Lea ampSchwaber (1994) and Van Essen et al (1998) have startedincorporating this technique How such warping wouldbe implemented in XANATdepends in part on whetherthe canonical structure is represented by slices (as in thecurrent version) or by a volume Regardless of the parti-cular implementation though a warping algorithmwould provide the means to transfer anatomical data intothe database in an objective and consistent manner andwould also facilitate the sharing of these data with otherdatabases and atlases Furthermore any distortions intro-duced by warping could be directly incorporated into ourmeasure of concentdence

Finally we have not dealt up to this point with theissue of quality control as our emphasis has been to centrstaddress the issues of representation and inference ofneural connectivity per se Clearly if XANAT is to be usedas a universal repository of neural connectivity informa-tion for the greater scienticentc community then somemeans must be taken to control submissions to the data-base such as approval by referees (similar to the processof publishing a paper) In addition standards should beadopted for assigning concentdence values and uncertaintyto data for example by having a standard set of exemplardata available for which concentdence values have beenagreed upon by a panel of experts Thus future develop-ment will require providing the means to document morecarefully the data entry and approval process in order forXANAT to serve as a general neuroscience resource

5 CONCLUSIONS

XANAT provides an objective framework forcombining data from diiexclerent studies and from diiexclerentlaboratories Data entry is independent from arealdistinctionsoumldistinctions that may be based on cytoarch-itecture or myelination and not functional organizationoumland its analyses yield intuitive and easily interpretableresults These results coalesced from a large pool of datamay provide insight into a structurersquos connectivity inways that may not be obvious from an unaided search ofthe literature and that may lead to area distinctions basedon functional organization It is our hope that this data-base proves useful for researchers interested in the brainrsquosanatomical connectivity and for database developersinterested in creating the tools necessary for its study

6 AVAILABILITY

XANAT is available at httpredwooducdavisedubrunoxanatxanathtml It requires a UNIX workstationrunning the X11 window system as well as a modicentable 8-bit colour map Use of the program is free and unrestricted



and independent development is encouraged It isrequested that acknowledgement be provided in propor-tion to what has already been written

APPENDIX A PROBABILISTIC INFERENCE

OF CONNECTIVITY

Given some data d(x y) which provides evidence for aconnection between x and y the posterior probability ofthere actually being a connection c(x y) is denotedP(c(x y)jd(x y)) where P(AjB) means `probability of Agiven Brsquo This is computed from Bayesrsquo rule

P(c(x y)jd(x y)) ˆP(c(x y)))P(d(x y)jc(x y))

P(d(x y)) (A1)

The denominator P(d(x y)) serves here mainly as anormalization constant and may be ignored

The prior P(c(x y)) expresses the belief that a projectionexists from x to y before the data are taken into accountIf nothing is known beforehand then P(c(x y)) is set to05 meaning that it is equally probable that a projectiondoes or does not exist from x to y If there is prior knowl-edge that alters this prior belief it can be incorporated byraising or lowering P(c(x y)) appropriately

The likelihood function P(d(x y)j(c(x y)) represents theprobability that the data d(x y) would have arisen from agiven connectivity state c(x y) A complete lack of concent-dence in the data would yield a likelihood function valueP(d(x y)j(c(x y) ˆ middot) ˆ 05 meaning that the data arecompletely uninformative about the true connectivityc(x y) ˆ middot (middot ˆ 0 or 1) Values approaching 1 indicateincreased assuredness that the data accurately repoundect thetrue underlying connectivity whereas values approaching0 indicate increased belief that the data represent theexact opposite of the true state of aiexclairs

Note that the likelihood function is not necessarilysymmetrical ie P(d(x y) ˆ 1jc(x y) ˆ 1) is not necessarilyequal to P(d(x y) ˆ 0jc(x y) ˆ 0) Letting representsuccessful label transport (d(x y) ˆ 1) and represent anunderlying connection (c(x y) ˆ 1) then P( j ) conveysthe probability that label is transported given that there isa connection present (sensitivity) whereas P( j ) conveysthe probability that label is not accidentally transportedto a location given that there is no connection present(P( j ) ˆ 17P( j ) is the false-positive rate) These twoprobabilities describe diiexclerent physical processes eg theprobabilistic nature of dye transport and therefore ingeneral warrant two separate concentdence measuresP(d(x y)jc(x y)) is thus given by the following table

c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )

In our particular implementation we take P( j )ˆ P( j )which is equivalent to assuming that the false-positiveand false-negative rates are identical (Given that one ofthe major sources of uncertainty in our data is in properlyaligning data within the atlas this is fairly appropriate)Thus we determine these values directly from the

concentdence values assigned to the data according to thefollowing formula

P(iji) ˆ

confidenceiji2 Dagger 50

100 (A2)

To combine these uncertainties across multiple studiesd1 dn each piece of data is assumed to be independentwhich is a reasonable assumption for the type of data weare dealing with and so

P(d1(x y) dn(x y)jc(x y)) ˆn

iˆ1

P(di(x y)jc(x y)) (A3)

Additionally each piece of data only provides informationfor a limited region of x- and y-values and so onersquos beliefin c(x y) should only be updated for those particularpoints If U denotes the region of injection uptake andL denotes the valid region in which to look for label (egoutside the halo of injection) then for an anterogradetracer P(d(x y)jc(x y)) is decentned for all x 2 U and y 2 Lwhereas for a retrograde tracer datum it is decentned for allx 2 L and y 2 U

Finally to calculate the total probability for a givensearch region we calculate the average probability of anypoint within the search area being connected to any otherpoint in the atlas

P(search y) ˆ1

area(search)x2search

P(c(x y)jd(x y))

P(x search) ˆ1

area(search) y2search

P(c(x y)jd(x y))

(A4)

where a b denotes `a connects to brsquo

We thank Chris Lee and Harold Burton for helpful advice dur-ing the building of the database Supported by ONR AASERTgrant no 11 SP93R0334 (WAP) and National Institutes ofHealth grant no MH57921 (BAO)

REFERENCES

Baizer J S Desimone R amp Ungerleider L G 1993 Com-parison of subcortical connections of inferior temporal andposterior parietal cortex in monkeysVis Neurosci 10 59^72

Brodmann K 19091994 Localisation in the cerebral cortex LondonSmith Gordon [Translated by L J Garey]

Christensen G E Joshi S C amp Miller M I 1997 Volumetrictransformation of brain anatomy IEEE Trans Med Imag 16864^877

Cusick G C Scripter J L Darensbourg J G amp Weber J T1993 Chemoarchitectonic subdivisions of the visual pulvinarin monkeys and their connectional relations with the middletemporal and rostral dorsolateral visual areas MT and DLrJ Comp Neurol 336 1^30

Dashti A E Ghandeharizadeh S Stone J Swanson L W ampThompson R H 1997 Database challenges and solutions inneuroscienticentc applications NeuroImage 5 97^115

Felleman D J amp Van Essen D C 1991 Distributed hierarchicalprocessing in the primate cerebral cortex Cereb Cortex 1 1^47

Fox P T Mikiten S Davis G amp Lancaster J L 1994BrainMap a database of human brain mapping In Functionalneuroimaging (ed R W Thomas) pp 95^105 San DiegoAcademic Press



Funka-Lea G D amp Schwaber J S 1994 A digital brain atlasand its application to the visceral neuraxis J Neurosci Meth54 253^260

Gary D Gutierrez C amp Cusick C G 1999 Neurochemicalorganization of inferior pulvinar complex in squirrel monkeysand macaques revealed by acetylcholinesterase histochem-istry calbindin and Cat-301 immunostaining and Wisteriapoundoribunda agglutinin binding J Comp Neurol 409 452^468

Grenander U amp Miller M I 1993 Representations of knowl-edge in complex systems J R Statist Soc B 56 549^603

Hardy S G amp Lynch J C 1992 The spatial distribution of thepulvinar neurons that project to two subregions of the inferiorparietal lobule in the macaque Cereb Cortex 2 217^230

Jones E G 2000 Human brain project brain atlas See httpneuroscienceucdaviseduHBP

Kusama T amp Mabuchi M 1970 Stereotaxic atlas of the brain ofMacaca fuscata University of Tokyo Press

Schwaber J S Due B R Rogers W T Junard E OSharrna A amp Hefti F 1991 Use of a digital brain atlas tocompare the distribution of NGF- and bNGF-protected choli-nergic neurons J Comp Neurol 309 27^39

Stephan K E Zilles K amp KIcirctter R 2000a Coordinate-independent mapping of structural and functional data byobjective relational transformation (ORT) Phil Trans R SocLond B 355 37^54

Stephan K E Hilgetag C C Burns G A P OrsquoNeill M AYoung M P amp KIcirctter R 2000b Computational analysis offunctional connectivity between areas of primate cerebralcortex PhilTrans R Soc Lond B 355 111^126

Toga A W 1989 Digital rat brain a computerized atlas BrainRes Bull 22 323^333

Van Essen D C Drury H A Joshi S amp Miller M I 1998Functional and structural mapping of human cerebralcortex solutions are in the surfaces Proc Natl Acad Sci USA95 788^795

Van Essen D C Lewis J W Drury H A Hadjikhani NTootell R B H Bakircioglu M amp Miller M I 2001Mapping visual cortex in monkeys and humans using surface-based atlasesVision Res 41 1359^1378

Young M P 1993 The organization of neural systems inthe primate cerebral cortex Proc R Soc Lond B 25213^18



immediately obvious whether it is due to there being nolabelling observed in an experiment that would revealsuch a connection or whether the experiment simply hasnot yet been done

For the investigator braving a foray into the literature inorder to learn the specicentcs of certain connection patternsthere is yet another problem lurking namely diiexclerentauthors often use diiexclerent nomenclatures to describe thesame brain region (eg Brodmann 1909 Felleman amp VanEssen 1991) The pulvinar nucleus of the thalamus is anexcellent example of where there is wide disagreementamong authors as to the placement of borders delineatingvarious subnuclei What constitutes the lateral pulvinar toone author may be the medial pulvinar to another Otherregions such as inferior pulvinar are constantly under-going further subdivision (Cusick et al 1993 Gary et al1999) Thus one cannot simply trust a verbal report in apaper claiming to have found `evidence for connectionsbetween V1 and lateral pulvinarrsquo One must examine thescored cross-sections and compare the actual label siteswith onersquos own `mental databasersquo of these various regionsAlthough such work is routine for a skilled neuroanato-mist it cannot reasonably be expected of the wider class ofinvestigators that need access to detailed informationabout neural connectivity Thus there is a need for toolsthat allow for the objective analysis and comparison ofcentne-scale neuroanatomical data

Our eiexclort to build a neuroanatomical database wasinitially stimulated by an interest in the patterns ofconnectivity between the pulvinar and visual cortex inthe macaque monkey The dicurrenculties encountered inintegrating information across multiple studies due to themultiplicity of partitioning schemes used for both cortexand the pulvinar motivated our development of agraphically orientated database The idea behind agraphical database as opposed to a conventional textorientated database is that data are represented within acanonical neuroanatomical atlas irrespective of parti-tioning schemes Our database program called XANATallows injection and label sites from multiple experimentsand across diiexclerent laboratories to be entered onto asingle consistent graphical representation of the anato-mical structures of interest The connectivity trendswithin the entire set of data may then be revealed usinganalysis routines which display the cumulative evidencefor connectivity between user-specicented regions of interestin a colour-coded `heatmaprsquo that is superimposed on theneuroanatomical atlas In this way one can summarizethe evidence for connectivity between any arbitrarilychosen locations in the brain accumulated from all datawithin the database without relying upon (thoughpossibly guided by) previous area-partitioning schemes

Graphical representations of data have found success ina number of anatomical applications including volu-metric atlases (Toga 1989 Jones 2000) and volumetricreconstruction of data collected from a series of slices(Schwaber et al 1991 Funka-Lea amp Schwaber 1994) Inaddition graphical representations at the macroscopiclevel have been shown to allow for the translation of oneparcelization scheme to another (Stephan et al 2000a)Perhaps most closely paralleling our own eiexclorts is theprogram NeuARt (Dashti et al 1997) which allows sitesof various types of anatomical labelling (not necessarily

connectivity related) to be scored within a canonicalatlas The implementation of graphical search capabilityfor this program is still in progress

Another capability that we have attempted to buildinto our database is the ability to represent and combinedata probabilistically This capability is importantbecause there are uncertainties inherent in the data dueto both the probabilistic nature of dye transport and theprocess of registering injection and labelling sites withinthe canonical atlas Thus rather than simply super-imposing multiple datasets one would actually like toobtain a measure of the probability that a connectionpathway exists between one area and another given allthe data available XANATdoes this by using the rules ofBayesian inference to combine evidence from multipledatasets thus taking into account both the structure andvariability inherent in the data in a principled manner(Grenander amp Miller 1993) Such a probabilistic approachhas recently been employed successfully for combininginformation about areal boundaries in the cortex fromdiiexclerent animals (Van Essen et al 2001)

In this paper we describe the structure of XANATandthe tools we have built for analysing data on neuroanato-mical connectivity (see frac12 2) We then demonstrate its usein inferring patterns of connectivity between the cortexand pulvinar of the macaque monkey (see frac12 3) Finally wediscuss the lessons learned from this eiexclort and somefuture directions for improving the methods of data entryand data representation

2 METHODS

(a) The graphical representationInjection and tracer data are represented in XANAT by

their coordinates within a canonical brain atlas This represen-tation comprises three separate levels the atlas correspondingsupplementary images and explicit area-partitioning schemes

The atlas comprises a set of images onto which all data aredrawn providing a canonical representation for combiningresults across experiments and studies Ideally these images arelike those of a conventional atlas they show the structuralgeography and cytoarchitectural organization and do not relyupon explicit segmentation The atlas used in our exemplar ofcorticopulvinar connectivity includes two types of images(centgure 1ab) a poundat map of Macaca mulatta cerebral cortexgeography (gyri and sulci) and eight coronal Nissl-stainedsections through the Macaca fuscata pulvinar and associatedsubcortical regions (posterior to anterior displayed from left toright by row) The Macaca fuscata pulvinar atlas was usedinstead of one for Macaca mulatta because it was the highestquality atlas available at the time of development The corticalpoundat map was scanned directly from Felleman amp Van Essen(1991) using a Microtek poundat-bed scanner The pulvinar imageswere digitized directly from Kusama amp Mabuchi (1970) using a512 pound512 pixel charge-coupled device (CCD) camera and thusinclude Kusama amp Mabuchirsquos designated thalamic nucleusboundaries and labels These images also included stereotaxiccoordinates which were then translated into pixels in the atlas

The supplementary images used in XANAT are in registerwith the atlas images and can be toggled to be displayed intheir stead These supplementary images contain additionalinformation that aids data entry and analysis For example ourpoundat map of cortical geography (centgure 1b) has a corresponding











161 km

(b)

(a)

12

34

567 789

101112131415

12

3456

89

1011

1213

1415

16

(c)

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29

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(21)






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3 RESULTS









98

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1516

12

34567

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1011121314

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12

3456

7

98

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st1

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1cl

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injection

CIB

1 cm

POB

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12

34

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10111213

1415

16

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34

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1 cm

PS

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1415

16

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CeS






4 DISCUSSION





(a) (b)










(a)

(b)







(a)

(b)

(c)

(d)














5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES

































161 km

(b)

(a)

12

34

567 789

101112131415

12

3456

89

1011

1213

1415

16

(c)

1 cm1 cm

29

PSd

30

PO

MIP

5PIP

V3

V2d

VIPLIP

7aDPV3A

7b

2 1 3b

4 6motorMEFSMA

cingulate24 dorsal

prefrontal

946

10

32

medial prefrontal

FEF

4512

13

11

lateralprefrontal

14

25

PaII

Pro

PIR

orbito-frontal

PAC

olfactory

ER35

36ER

TF

TH

PSvCA1

CA3

V2v

V1

VPV4v

VOT

V4d

V41

PITv

PITd

CITd

CITvAITv

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subicular

GIdSII

R

dMAPA IgRLC

auditory

STPa

MSTdM

Y MSTISTPPFS1

somato-sensor

23

MDP

12

34

567 78910

1112

1314

1516

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34

5689

1011

1213

1415

16

IOS

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STSAMT

CISPOB

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HFRF

CeS

IPS

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SF 1112

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5 6 7 8

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11

10

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11

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912

13

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7RF

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L8

PO8

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CaS

C18

OTS

9
















(21)






P(Djc(x y)) ˆn

iˆ1












3 RESULTS









98

1011

121314

1516

12

34567

98

1011121314

1516

12

3456

7

98

8

8

8

8

7

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7

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6

66

6

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11

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RT HF


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Cd

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MD

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st1

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lu

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2 3

laip3

2

1cl

caot

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injection

CIB

1 cm

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5 67

98

10111213

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16

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1 cm

PS

CeS

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CIS

LSSP

RF

HF

AS

1415

16

910

CeS






4 DISCUSSION





(a) (b)










(a)

(b)







(a)

(b)

(c)

(d)














5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES







































(21)






P(Djc(x y)) ˆn

iˆ1












3 RESULTS









98

1011

121314

1516

12

34567

98

1011121314

1516

12

3456

7

98

8

8

8

8

7

7

7

7

7

6

1

3

57 86

6

66

6

5 5

5

49

9

9 9

9

9

9

9

10

10

10

11

10

10

10

10

10

10

10

11

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12

12

12

13

13

1111

11

11

10111213

1415

16

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RT HF


Cd

Cd

Cd

CdCd

Cd

ST

ST

ST

ST

ST

ST

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PL

R

PLPI

PI

Br

B

MG

PM

PM

Li

MD

PL

pulvinar

cortex

database entry

st1

ioec

lu

stla

cetip

ar p

2 3

laip3

2

1cl

caot

io

injection

CIB

1 cm

POB

OTS

12

34

5 67

98

10111213

1415

16

12

34

567

1 cm

PS

CeS

AS

AMT

SF

STSIOS

LSIPS

OTS

AMT

STS

IOS

POS

CaS

IPS

CIS

LSSP

RF

HF

AS

1415

16

910

CeS






4 DISCUSSION





(a) (b)










(a)

(b)







(a)

(b)

(c)

(d)














5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES































3 RESULTS









98

1011

121314

1516

12

34567

98

1011121314

1516

12

3456

7

98

8

8

8

8

7

7

7

7

7

6

1

3

57 86

6

66

6

5 5

5

49

9

9 9

9

9

9

9

10

10

10

11

10

10

10

10

10

10

10

11

12

12

12

12

13

13

1111

11

11

10111213

1415

16

CeS

RT HF


Cd

Cd

Cd

CdCd

Cd

ST

ST

ST

ST

ST

ST

R

PL

R

PLPI

PI

Br

B

MG

PM

PM

Li

MD

PL

pulvinar

cortex

database entry

st1

ioec

lu

stla

cetip

ar p

2 3

laip3

2

1cl

caot

io

injection

CIB

1 cm

POB

OTS

12

34

5 67

98

10111213

1415

16

12

34

567

1 cm

PS

CeS

AS

AMT

SF

STSIOS

LSIPS

OTS

AMT

STS

IOS

POS

CaS

IPS

CIS

LSSP

RF

HF

AS

1415

16

910

CeS






4 DISCUSSION





(a) (b)










(a)

(b)







(a)

(b)

(c)

(d)














5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES





























4 DISCUSSION





(a) (b)










(a)

(b)







(a)

(b)

(c)

(d)














5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES

































(a)

(b)







(a)

(b)

(c)

(d)














5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES






























(a)

(b)

(c)

(d)














5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES





































5 CONCLUSIONS


6 AVAILABILITY






OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES



























OF CONNECTIVITY



P(d(x y)) (A1)





c(x y)0 1

d(x y)0 P( j ) 17P( j )1 17P( j ) P( j )



P(iji) ˆ


100 (A2)



iˆ1




P(search y) ˆ1


P(c(x y)jd(x y))

P(x search) ˆ1


P(c(x y)jd(x y))

(A4)



REFERENCES

























A graphical anatomical database of neural connectivity · Agraphicalanatomicaldatabaseofneural...

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