Brain Imaging and Behavior (2014) 8:292–299DOI 10.1007/s11682-013-9254-z

SI: GENETIC NEUROIMAGING IN AGING AND AGE-RELATED DISEASES

Local termination pattern analysis: a tool for comparingwhite matter morphology

M. Cieslak · S. T. Grafton

Published online: 3 September 2013© Springer Science+Business Media New York 2013

Abstract Disconnections between structures in the brainhave long been hypothesized to be the mechanism behindnumerous disease states and pathological behavioral phe-notypes. Advances in diffusion weighted imaging (DWI)provide an opportunity to study white matter, and there-fore brain connectivity, in great detail. DWI-based researchassesses white matter at two different scales: voxelwiseindexes of anisotropy such as fractional anisotropy (FA) areused to compare small units of tissue and network-basedmethods compare tractography-based models of whole-brain connectivity. We propose a method called local termi-nation pattern analysis (LTPA) that considers informationabout both local and global brain connectivity simultane-ously. LTPA itemizes the subset of streamlines that passthrough a small set of white matter voxels. The “local termi-nation pattern” is a vector defined by counts of these stream-lines terminating in pairs of cortical regions. To assess thereliability of our method we applied LTPA exhaustivelyover white matter voxels to produce complete maps of localtermination pattern similarity, based on diffusion spectrumimaging (DSI) data from 11 individuals in triplicate. Herewe show that local termination patterns from an individualare highly reproducible across the entire brain. We discusshow LTPA can be deployed into a clinical database and used

This work was supported by the David and Lucile PackardFoundation, PHS Grant NS44393 and the Institute for Collabo-rative Biotechnologies through contract no. W911NF-09-D-0001from the U.S. Army Research Office

M. Cieslak (�) · S. T. GraftonDepartment of Psychological and Brain Sciences, UCSB,Santa Barbara, CA, USAe-mail: matthew.cieslak@psych.ucsb.edu

S. T. Graftone-mail: scott.grafton@psych.ucsb.edu

to characterize white matter morphology differences due todisease, developmental or genetic factors.

Keywords DSI· Tractography· Databases· White matter ·Individual differences

Introduction

Classical behavioral neurology is rich with descriptions ofdisconnection syndromes secondary to an impairment offunctional integration between different cortical modulesdue to subcortical lesions (Geschwind and Kaplan 1962).Diffusion-weighted magnetic resonance imaging (DWI) isa popular technique for continuing this research in vivo.DWI samples the diffusion of water molecules along a pre-determined set of directions. Myelinated axon bundles insubcortical white matter constrain the directions in whichwater molecules can diffuse, producing a signal changein the image sampling the direction parallel to the axonbundle’s orientation. DWI signal from all the sampled direc-tions is combined to estimate an empirical distribution suchas an Orientation Distribution Function (ODF) or to fit amodel such as the well-known diffusion tensor used in DTI(Basser and Jones 2002) and quantify directional diffusionanisotropy in each voxel.

These characterizations of diffusivity are typically usedto study white matter at two different scales. At the level ofa single voxel, a scalar value reflecting the strength of diffu-sion along a single direction versus all other directions (suchas Fractional Anisotropy, FA), is often used as proxy for“white matter integrity” and statistically compared betweengroups of individuals. At the whole-brain scale, tractogra-phy follows the peak diffusion orientations through multiplevoxels to reconstruct long-range pathways between distant

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cortical regions (Basser et al. 2000). These pathways, orstreamlines, cannot be directly equated to axonal projec-tions, but when combined with high resolution imaging andrecent ODF modeling techniques, successfully reproduceknown tracts (Fernandez-Miranda et al. 2012). Streamlinesare often used to model connectivity between a set of graymatter regions. Both scales of analysis are widely used, buteach method has its own set of difficulties.

Voxelwise FA comparisons have been used in a broadspectrum of research projects relating structure, functionand performance and are particularly germane for this spe-cial issue on the relationship between genetics and whitematter organization. Recent studies have examined the con-sistency of FA values in large twin studies and shownheritability to explain up to 80 % of FA variability insome regions (Chiang et al. 2011). Heritability of DTI FAmeasures can also be demonstrated in genetically abnor-mal populations such as Turner syndrome (Yamagata et al.2012). However, FA comparisons can be difficult to inter-pret due to some fundamental limitations of the diffusiontensor model (see (Jones et al. 2013) for an instructivereview). For example, while low FA may reflect abnormal-ities in white matter microstructure, it can also be due tonormal fiber crossings, partial voluming effects or a numberof other non-pathological causes. Higher angular resolu-tion scans and more nuanced models of diffusivity such asHARDI/Q-BALL (Tuch 2004), DSI (Wedeen et al. 2005)and GQI (Yeh et al. 2009) address some of these limitationsbut are still not as widely used as DTI.

Tractography provides a way to build network models ofstructural connectivity using streamlines and a discrete setof gray matter regions (Sporns et al. 2005; Bullmore andBassett 2011). The strength of connectivity between pairsof regions is estimated as a function of the streamlines thatterminate within their boundaries. The resulting structuralconnectivity matrix has become the defacto model for thehuman connectome (Van Essen and Ugurbil 2012). Thisapproach has recently been used to test for genetic influ-ences on network properties such as “global efficiency” ingenetically at-risk populations (Shi et al. 2012). Unfortu-nately, this global parcel and count methodology utilizes asmall subset of information about the physical shape of thestreamlines, namely the cortical regions in which they ter-minate. Most of the rich detail available from tractographyis lost.

In a recent critique of current DWI methodology, Joneset al. (2013) suggest that for DWI-based connectomics tobe more biologically relevant “methods need to be devel-oped that compensate for differences in both length andshape of tracts. Until such time as these methods are devel-oped, it may be dangerous to compare even the streamlinecount in white matter structures that have different shapes”.We propose a new method for analyzing DWI at the local

and whole-brain scales simultaneously – in doing so, boththe regional connectivity and the shape of white matterstructures become units of comparison.

Our method is based on an intuition commonly usedwhen checking tractography results. Tractography visual-ization tools such as trackvis (Wang et al. 2007) typicallysupport a “sphere dissection” feature, where the user canmove a sphere through space while the software renders thesphere and all streamlines passing through it in a 3D viewer.With a quick sphere placement the user can, for example,check that a sphere placed in the internal capsule stream-lines connecting primary motor cortex to the brainstem. Wehave encapsulated this notion – of selecting only stream-lines passing through a local neighborhood of voxels andexamining their endpoints – into an algorithm called localtermination pattern analysis (LTPA, Fig. 1).

LTPA operates on spatially normalized tractographydatasets from multiple individuals. A search sphere isdefined around a coordinate in white matter and all stream-lines intersecting this sphere are collected (Fig. 2a). Thesestreamlines and the pairs of gray matter regions they con-nect are used to construct a streamline termination patternfor each individual. Termination patterns are N element vec-tors where N is the total number of unique region pairsconnected by streamlines passing through the search sphereacross all individuals. It is essentially the flattened uppertriangle of a structural connectivity matrix (Fig. 2b). Withtermination patterns for each individual in hand, a numberof techniques may be applied depending on the researchquestion. If the goal is to contrast a group of individu-als with a specific neurological condition to a group ofhealthy individuals, a machine-learning analysis can be per-formed to see if termination patterns are separable betweengroups. The correlation between genes and the presence orabsence of a connection passing through the search spherecan be computed. In the present study, we compute thecorrelation coefficients of termination patterns within andbetween individuals to demonstrate the robustness of ourmethod. Regardless of the analysis chosen, the procedureis repeated for spheres centered on every voxel in whitematter. Results of each comparison are saved in the centralvoxel of each sphere, producing an LTPA map much likethe “information map” produced by the fMRI searchlightmethod (Kriegeskorte 2006). It is therefore possible to pro-duce an LTPA correlation map (Fig. 3), an LTPA GWASmap or an LTPA classification accuracy map.

LTPA mapping has two noteworthy properties. Suppose aclassifier is used in each sphere to distinguish between twogroups of individuals. Due to the geometric properties ofsearching a space with a fixed-size sphere as the structuringelement, differences in local termination patterns betweentwo groups will appear in the LTPA map as a cluster ofhigh classifier accuracies proportional in size to the radius

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Fig. 1 A schematic of LTPA for comparing two brains. a Assumethat there are three structures in the brain named A,B and C. We scantwo individuals and tractography reconstructs 6 streamlines in eachbrain. b The conventional network approach is taken and a whole-brain connectivity matrix is estimated (similar to Hagmann et al. 2007;Bassett et al. 2011). This matrix is converted to a vector, producingthe “Global” termination pattern in Fig. 2b. In this case the networkapproach reveals no difference between the two brains. Instead, we

use LTPA to map local termination pattern differences at three “vox-els” by computing Euclidean distance. The location at the cyan voxelobserves no difference, at the green a large difference and at the purplea subtle difference. c Local termination patterns are compared at eachvoxel using Euclidean distance and the distance value is mapped backto the brain. The map reveals differences in the voxels where the A toB connection has a different shape

of the search sphere (Viswanathan et al. 2012). If a bundleof streamlines is present in one group and missing in theother, all search spheres falling in the path of that bundlewill show high classification accuracy. This appears in theLTPA accuracy map as a cluster of high classification accu-racies in the shape of the missing bundle. Secondly, if bothgroups have statistically indistinguishable whole-brain con-nectivity matrices but the shape of a connection differs, thevoxels where the shapes differ will show high classificationaccuracy (Fig. 1c).

Local termination pattern analysis can be used as a com-plimentary tool for whole-brain connectivity comparisonsbased on age, gender, disease state, genetics or any othersystematically varying factor. However, before the methodcan be applied in a research setting to assess differencesbetween individuals or groups, we must show that termi-nation patterns are a reliable unit for comparison. To thisend, we scanned 11 individuals in triplicate and measuredthe reproducibility of termination patterns both within andbetween subjects. Due to the effects of atlas choice (Zaleskyet al. 2010; Hagmann et al. 2010) on brain connectivityestimates and the known effects of search sphere size in tra-ditional searchlight analyses (Viswanathan et al. 2012), weassessed termination pattern reproducibility at two differentatlas resolutions using two different sphere radii.

Methods

Data acquisition and preprocessing

Diffusion spectrum images (DSI, Wedeen et al. (2005))were acquired for a total of 11 subjects in triplicate (meanage 27 ± 5 years, 2 female, 2 left handed) along with aT1 weighted anatomical scan at each scanning session. DSIscans sampled 257 directions using a Q5 half shell acqui-sition scheme with a maximum b value of 5000 and anisotropic voxel size of 2.4mm (Axial acquisition, TR =11.4s, TE = 138ms, 51 slices, FoV (231,231,123 mm)).

DSI data were reconstructed in DSI Studio (www.dsi-studio.labsolver.org) using q-space diffeomorphicreconstruction (QSDR) (Yeh and Tseng 2011). QSDR firstreconstructs diffusion weighted images in native space andcomputes the quantitative anisotropy (QA) in each voxel.These QA values are used to warp the brain to a templateQA volume in MNI space using the SPM nonlinear registra-tion algorithm. Once in MNI space, spin density functionswere again reconstructed with a mean diffusion distanceof 1.25mm using three fiber orientations per voxel. Fibertracking was performed in DSI Studio with an angular cut-off of 55◦, step size of 1.0mm, minimum length of 10mm,smoothing of 0.0, maximum length of 400mm and a QA

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a

b

c

Fig. 2 a An example “sphere dissection”. Voxels in the search sphereare colored dark red. Streamlines intersecting these voxels are col-lected from one subject and rendered. The color of each streamline isdetermined by the pair of structures it connects. b Local terminationpatterns generated by the search sphere in (a) are plotted for three sep-arate scans of the same individual. The mean correlation coefficient isr = 0.95 ± 0.03. c Local termination patterns of one scan from eachsubject are plotted. The mean correlation coefficient between subjectsis r = 0.84 ± 0.13

threshold determined by DWI signal in the CSF. Determin-istic fiber tracking using a modified FACT algorithm wasperformed until 100,000 streamlines were reconstructed foreach individual.

Anatomical scans were segmented using FreeSurfer(Dale et al. 1999) and parcellated according to the Lausanne2008 atlas included in the connectome mapping toolkit(Gerhard et al. 2011; Hagmann et al. 2008). Two parcel-lation schemes, scale 33 (containing 83 regions) and scale60 (129 regions) were registered to the B0 volume fromeach subject’s DSI data. The B0 to MNI voxel mapping pro-duced via QSDR was used to map region labels from nativespace to MNI coordinates. To extend region labels throughthe gray/white matter interface, both atlases were dilatedby 4mm. Dilation was accomplished by filling non-labeledvoxels with the statistical mode of their neighbors’ labels. Inthe event of a tie, one of the modes was arbitrarily selected.Each streamline was labeled according to its terminal regionpair, one label for each of the Lausanne atlases.

Discrete space indexing and local termination patternanalysis

Once in 2mm MNI space, a hash table h was generatedfor each subject where each coordinate cn = (i, j, k) ismapped to a set of tuples containing streamline id numbers,endpoint labels and their array of coordinates: h(i, j, k) →{(id1, label1,X1), . . . }. A search is conducted with a cen-ter coordinate c and a radius r. Parameters c,r are used toconstruct a set of coordinates C = {c1, c2, . . . cn} such thatc is the center and all other voxels are within r millime-ters of c. Querying h with C returns a set of streamlinesS = h(c1) ∪ h(c2) ∪ · · · ∪ h(cn)∀ci ∈ C. This formulationprevents double-counting of streamlines passing throughmultiple voxels in the search sphere. Figure 2a depicts aquery in the corticospinal tract. C(r = 2, c = (33, 54, 45))is rendered as a set of red cubes. S is plotted such that eachstreamline X is colored based on its label, not its orienta-tion in space. In this case, the label was determined by thestreamline’s termination regions in the Lausanne scale 33atlas.

Termination patterns are defined by counts of eachstreamline label in S. One termination pattern is computedfor each scan. Connections where no streamlines wereobserved in any subject were not included as elements in thetermination pattern.

Results

Figure 2b shows termination patterns returned from threeseparate scans of the same subject. Figure 2c plots ter-mination patterns from a single scan of each subject. In

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Fig. 3 A summary of the distributions of within-subject corre-lation coefficients. Columns display the mean or standard devi-ation of within-subject correlation coefficients for search spheresof 5mm radius (left columns) and radius 7mm (right columns).

Distributions displayed in the top row were observed when using thescale 33 atlas, the bottom row using scale 60. Search spheres aroundcolored voxels produced mean correlation coefficients significantlyhigher than those observed when permuting streamline counts

each sphere, local termination patterns were combined toform L, a 33-by-M matrix where rows contain the countsof streamlines connecting each of the M observed regionpairs for each the 33 scans. To establish the reproducibilityof termination patterns, we calculated Pearson’s correlationcoefficient between all pairs of rows in L. These coeffi-cients were split into two categories. If the correlation wascalculated between two scans of the same individual, thisvalue is a within-subject correlation coefficient. Correlationcoefficients between two scans from different subjects arebetween-subjects. Complete pairwise comparisons in ourdata produces 33 within-subject and 495 between-subjectcorrelation coefficients.

Both within and between-subjects correlation coefficientmeans were tested for significance using a permutationtest. Streamline counts in the local termination patterns ofeach subject were shuffled and used to compute within andbetween-subject correlation coefficient means 100 timesin each sphere. Separate sampling distributions were con-structed for within and between subject means to accountfor their different sample sizes. The actual correlation

coefficient means were compared to their correspondingsampling distributions to obtain a p-value. Colored voxelsin Figs. 3 and 4 reflect spheres where the observed correla-tion coefficient means are greater than all 100 permutations(p < 0.01).

The distribution of the 33 within-subject correlation coef-ficients reflects the reliability of local terminations fromthe same individual. Values close to 1 indicate that localtermination patterns are not corrupted by errors in ODFreconstruction or tractography. Values close to 0 indicatethat LTPA in this sphere would not be suitable for makinginferences about white matter structure. Figure 3 displaysthe mean within-subject correlation coefficients in eachsphere. These values vary depending on the radius of thesearch sphere and the spatial resolution of the atlas used todefine regions. However, within-subject correlation coeffi-cients were significantly greater than 0 across most of whitematter regardless of search sphere radius or atlas resolution.

The distribution of the 495 between-subject correlationcoefficients, assuming the within-subject correlations arehigh, reflect the similarity of local termination patterns

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Fig. 4 The same mapping parameters are used as in Fig. 3, but here the between-subjects correlation coefficient distributions are described

across individuals. Maps in Fig. 4 show that between-subject correlations are high along large white matter tracts,indicating that these structures produce highly consistentlocal termination patterns. Correlations are well over .6 inthe corticospinal tract, longitudinal fasciculi and genu ofthe corpus callosum. Low between-subject together withhigh within-subject correlations near the gray/white matterinterface suggest these areas are rich source of individualanatomical variability.

A similar within/between subject correlation approachhas been used previously to characterize the reproducibilityof whole brain structural connectivity matrices (Cammounet al. 2012). Each voxel in a Figs. 3 and 4 could be thoughtof as Cammoun et al.’s whole-brain graph reliability mea-sure evaluated on all possible subgraphs, each conditionedon the streamlines constituting their edges pass through thatvoxel’s neighbors.

Discussion

Extensive collections of clinical DWI data can produce largedatabases of tractography information. LTPA, combinedwith technology for storing and retrieving big data, may be

an ideal approach to exploring white matter structures.The process of searching a set of spatial coordinates, col-lecting region pair labels from intersecting streamlinesand consolidating them into termination patterns transla-tes easily into a Map/Reduce problem. A number of tech-nologies including MongoDB (www.mongodb.org) andHadoop (hadoop.apache.org,) implement Map/Reduce on alarge scale, providing the benefits of distributed computingand potentially supporting a web interface accessible toother researchers. LTPA on a smaller scale can be runon a typical desktop computer. Our present implementa-tion of LTPA uses python dictionary objects to implementthe mapping h from spatial coordinates to streamline ID’s.Similar functionality has recently been included in DiPy(Garyfallidis et al. 2011).

It is important to note that in this study we used LTPA tomap termination pattern similarity across subjects. The factthat within-subject similarity is much higher than betweensubject similarity is also a comforting reassurance that sim-ilarity is not simply being driven by consistent artifacts inreconstruction of ODFs or streamlines. This is only a firststep: multivariate measures of dissimilarity can be appliedto local termination patterns or machine learning techniquescould be used to classify individuals into groups. Machine

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learning approaches will also benefit from LTPA. The fea-ture space in a connectivity-based classification problemscales in dimensionality as a function of the N regionspresent in the atlas. For a global termination pattern anal-ysis that considers all streamlines (Richiardi et al. 2011),the feature space will span N(N − 1)/2 dimensions, rais-ing the potential for over-fitting in small datasets. An LTPAsearch sphere will contain strictly fewer connected regions,effectively acting as an anatomically-based feature selectionmechanism. Additionally, we used the simplest connectiv-ity measure possible, streamline count, as our measure ofconnectivity between region pairs. Count is one of manymeasures, such as along-track anisotropy, that could be usedalternatively.

We propose that a publicly available database of spatiallyindexed high resolution tractography could be useful inthe study of white matter conditions. An exhaustive spheresearch is a tool well-suited for exploring neurological con-ditions where no specific structure is hypothesized to beaffected a priori. The same database can be searched withsets of coordinates other than spheres - any region of interestcould be uploaded and queried so that termination patternscould be compared across many individuals.

While it is possible that less expensive, lower resolutionDWI methods may provide comparable results to DSI-basedLTPA, they are also known to fail at reconstructing U-fibersand tracts known to cross. We predict that if LTPA wererun on DTI-based tractography then Fig. 3 would resembleFig. 4: large non-crossing structures would be reproduciblebut high variability in tractography where the tensor modelfails would make U-fibers and crossing tracts unreliable.However, as tractography methods improve (Kreher et al.2008) and more nuanced ODF models are employed itmay become plausible to use low resolution DWI data withLTPA.

Acknowledgments The authors thank Dani Bassett, MarioMendoza, Philip Beach, Zsuzsi Fodor and Frank Yeh.

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