Improving alignment in Tract-based spatcxuial statistics: …homepage.tudelft.nl/h5u3d/papers/Imporving_alignment_TBSS.pdf · OOF Q81 Improving alignment in Tract-based spatcxuial

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NeuroImage xxx (2013) xxx–xxx

YNIMG-10248; No. of pages: 12; 4C: 3, 4, 7, 8, 10

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NeuroImage

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Improving alignment in Tract-based spatcxuial statistics: Evaluation andoptimization of image registration

Marius de Groot a,b,⁎, Meike W. Vernooij a,c, Stefan Klein a,b, M. Arfan Ikram a,c, Frans M. Vos d,Stephen M. Smith e, Wiro J. Niessen a,b,d, Jesper L.R. Andersson e

a Department of Radiology, Erasmus MC, University Medical Center, Rotterdam, The Netherlandsb Department of Medical Informatics, Erasmus MC, University Medical Center, Rotterdam, The Netherlandsc Department of Epidemiology, Erasmus MC, University Medical Center, Rotterdam, The Netherlandsd Imaging Science and Technology, Faculty of Applied Sciences, Delft University of Technology, The Netherlandse FMRIB Centre, University of Oxford, UK

⁎ Corresponding author at: Erasmus MC, Biomedicroom Ee2102, PO box 2040, 3000 CA Rotterdam, The

E-mail address: [email protected] (M. d

1053-8119/$ – see front matter © 2013 Published by Elhttp://dx.doi.org/10.1016/j.neuroimage.2013.03.015

Please cite this article as: de Groot, M., et al.,registration, NeuroImage (2013), http://dx

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Article history:Accepted 6 March 2013Available online xxxx

Keywords:TBSSRegistrationEvaluationDiffusion imagingFNIRTElastix

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RECTED PAnatomical alignment in neuroimaging studies is of such importance that considerable effort is put into im-

proving the registration used to establish spatial correspondence. Tract-based spatial statistics (TBSS) is apopular method for comparing diffusion characteristics across subjects. TBSS establishes spatial correspondenceusing a combination of nonlinear registration and a “skeleton projection” that may break topological consistencyof the transformed brain images. We therefore investigated feasibility of replacing the two-stage registration-projection procedure in TBSS with a single, regularized, high-dimensional registration.To optimize registration parameters and to evaluate registration performance in diffusion MRI, we designedan evaluation framework that uses native space probabilistic tractography for 23 white matter tracts, andquantifies tract similarity across subjects in standard space. We optimized parameters for two registration al-gorithms on two diffusion datasets of different quality. We investigated reproducibility of the evaluationframework, and of the optimized registration algorithms. Next, we compared registration performance ofthe regularized registration methods and TBSS. Finally, feasibility and effect of incorporating the improvedregistration in TBSS were evaluated in an example study.The evaluation framework was highly reproducible for both algorithms (R2 0.993; 0.931). The optimal regis-tration parameters depended on the quality of the dataset in a graded and predictable manner. At optimalparameters, both algorithms outperformed the registration of TBSS, showing feasibility of adopting such ap-proaches in TBSS. This was further confirmed in the example experiment.

© 2013 Published by Elsevier Inc.

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UNCOIntroduction

Diffusion imaging of the brain provides insight into architecturalproperties, and developmental and degenerative processes of the whitematter (Basser et al., 1994; Beaulieu, 2002; Lebel et al., 2010). Quantita-tive features derived from diffusion imaging, such as fractional anisotro-py (FA) and mean diffusivity (MD), allow for comparison of diffusionproperties across different subjects (Basser and Jones, 2002). This canbe achieved in a number of ways, for example region of interest-basedor voxel-based.

Voxel-based analyses offer a fast and automated means of analyzingdiffusion data (Büchel et al., 2004; Buchsbaum et al., 1998; van Heckeet al., 2010). They do however require the images to be in a commonspace in which anatomical correspondence across subjects is assured.

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al Imaging Group Rotterdam,Netherlands.e Groot).

sevier Inc.

Improving alignment in Trac.doi.org/10.1016/j.neuroima

Establishing correspondence by bringing images into a common spaceis a non-trivial task, for which image registration techniques are com-monly employed. However, image registration approaches in generaldo not achieve perfect anatomical correspondence due to anatomicalvariability. In an attempt to account for the residual misalignment,increase sensitivity and to satisfy the assumptions of parametrictests (if applied), voxel-based analyses often rely on smoothing.The extent of this smoothing ideally needs to be matched to theexpected effect size, which can be spatially varying and not knowna-priori (Jones et al., 2005). In 2006, an alternative approach for an-atomical alignment of diffusion data was proposed. Tract-based spa-tial statistics (TBSS) (Smith et al., 2006, 2007) was introduced tomitigate the influence of residualmisalignment in registration of diffusiondata, and to overcome the need to set smoothing extent in voxel-basedanalyses. In TBSS, following an initial nonlinear registration step(of “medium” dimensionality), voxels that are local maxima for FAare mapped onto a skeleton composed of sheets of maximum FAvoxels, and statistical analysis is performed on skeleton voxels.

t-based spatcxuial statistics: Evaluation and optimization of imagege.2013.03.015

http://dx.doi.org/10.1016/j.neuroimage.2013.03.015

mailto:[email protected]


http://www.sciencedirect.com/science/journal/10538119


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Constraining the analysis to the white matter skeleton results in adimensionality reduction, ameliorating the issue of multiple testing.Over the past years, TBSS has beenwidely adopted, aided by its availabil-ity within FSL (Smith et al., 2004; Woolrich et al., 2009) and ease of use.The projection stage in TBSS however, is a spatially local operation, withthe voxels containing locally maximal FA projected onto the skeleton in-dependently; therefore it does not enforce spatial consistency of thewarped images. This may result in an undesirable loss of anatomical to-pology of tracts in the projection stage. The main aim of this work is toinvestigate if it is feasible to replace the two registration + projectionstages by a single regularized high-dimensional registration approach in-side the TBSS method (while still aiming to carry out cross-subjectvoxelwise testing on the skeleton, to help minimize correspondenceerrors).

Since even small errors in correspondence may substantially influ-ence results (Smith et al., 2006), considerable effort has been put inimproving the registration of diffusion data (Jones et al., 2002; Parket al., 2003; van Hecke et al., 2007; Yap et al., 2009; Yeo et al., 2009;Zhang et al., 2006). In registration, a spatial transformation is deter-mined by optimizing a similarity metric. For evaluating registrationperformance across algorithms, such as performed for diffusion imag-ing byWang et al. (2011), or to optimize different registration param-eters, a similarity metric must be employed as well. This is necessarysince we do not know the ground truth anatomical correspondence oftwo images. To objectively measure registration performance however,we cannot use the same similaritymetric thatwas optimized in the reg-istration process, since this would bias the evaluation.

Similarity metrics in diffusion image registration can be based onscalar images such as FA or structural images. Metrics can, alternatively,be based on higher dimensional image features, e.g., on the full diffusiontensor or a number of its components. A third category of similaritymet-rics is defined on the results of white matter tractography. These threeclasses of similarity metrics have all been used in the objective functionsof image registration approaches for diffusion images (Guimond et al.,2002; Park et al., 2003; Xu et al., 2003; Yeo et al., 2009; Zhang et al.,2006; Zvitia et al., 2010). Analogously, similarity metrics in all three cat-egories have been employed in order to evaluate registration perfor-mance (Park et al., 2003; Wang et al., 2011; Yap et al., 2009; Yeo et al.,2009; Zhang et al., 2007; Zöllei et al., 2010).

An important advantage of a performance measure based on simi-larity of tractography results is that it is independent of any particularsimilarity metric, defined on a scalar or higher order image, which isemployed in most registration approaches. Also, optimal white mattertract alignment is most closely linked to the eventual registration aimof obtaining anatomical correspondence in white matter (Lawes et al.,2008). We therefore developed a framework to evaluate scalar orhigher-order similarity metric based registrations using tractography.Previous work using white matter tractography for this purpose wasbased either on whole brain tractography (Park et al., 2003) or onlyon a small selection of tracts (Jia et al., 2011; Xue et al., 2010; Yapet al., 2009; Zhang et al., 2006; Zöllei et al., 2010). Furthermore, allprevious work depended on deterministic tractography, which hasmore difficulty in coping with complex fiber architecture (e.g., crossingfibers) and signal noise than probabilistic tractography (Behrens et al.,2007).

In this work, we extended the use of tractography for image registra-tion evaluation to a broader range of white matter tracts, and we used aprobabilisticmodel for tractography. Parameters for twononlinear regis-tration algorithms were optimized using similarity of different subjects'warped tracts as the registration performance measure. The optimiza-tion was performed on two datasets acquired at different institutionswith different spatial resolution. Registration performance for these opti-mized approacheswas then compared to the registration performance ofthe TBSS method on a white matter skeleton. We show that the opti-mized registration reproducibly improved the alignment ofwhitematterstructures compared to TBSS.

Please cite this article as: de Groot, M., et al., Improving alignment in Tracregistration, NeuroImage (2013), http://dx.doi.org/10.1016/j.neuroima

Methods

The evaluation framework consists of an automated approach toperform probabilistic tractography and a tract-based evaluation met-ric. A schematic overview of the process is provided in Fig. 1.

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Tractography

Tractography was performed with PROBTRACKX (Behrens et al.,2003, 2007), a Bayesian approach to probabilistic tractography avail-able in FSL.

Tractography was initialized by defining standard space “seed”,“target”, “stop” and “exclusion” ROIs (masks). These masks were basedon the protocols described by Mori et al. (2002), Stieltjes et al. (2001),and Wakana et al. (2004, 2007), but had to be adapted to cope withthe more dispersing nature of probabilistic tractography. Most impor-tantly, exclusion masks were added, e.g., the mid-sagittal slice wasadded in all but the commissural tracts. All masks were transferred tosubject native space using nonlinear registrations obtained with FNIRT(Andersson et al., in preparation) with default settings for FA imagesas available in FSL.

Tracts that could robustly be identified and which would lead to areasonably uniform sampling across brain regions were selected. Thesetracts are listed in Table 1. Two tracts, the posterior thalamic radiationand the inferior fronto-occipital fasciculus, were excluded from thefinal set because of considerable overlap with other tracts. Exclusionof these tracts prevented uneven weighting of different regions in theregistration evaluation. The final set therefore consisted of 23 tracts.

Tractography was performed in subject native space while record-ing tract density at a 1 mm3 resolution and using between 2000 and30,000 samples per seed ROI voxel to account for differences in thenumber of seed voxels and tract geometry. These parameter settingswere selected to aim for robust extraction of the tracts, and werebased on the observed number of fiber-particles that were includedin the tract together with visual inspection of tractography outputs.Commissural tracts were tracked a second time (adding both runs)with inverted seed-target ROIs to ensure symmetry of the resultingtract. The acoustic radiations and the superior longitudinal fasciculuswere also tracked in both directions to increase robustness. After track-ing, the tract density image was normalized by dividing with the totalnumber of particles.

An example of an individual subject's tracking result, thresholded forthe purpose of visualization, for all tracts is shown in Fig. 2. Tractographywas performed for each subject and for each structure. The resultingmaps of white matter structures reside in subject native space, andwere used for all evaluations.

Tract-based evaluation metric

The registration performance measurement was based on cross-subject similarity of the warped tract maps. Non-thresholded tract den-sity images in subject native space were warped to common space, andthen tract similarity was assessed.

To avoid differences in image characteristics between individualand group mean tract maps influencing the results, tract similarity wasevaluated on a subject-to-subject basis. Tract similarity was assessedfor each structure individually, and then averaged for all structures ineach pair of subjects. In order to provide an even weighting over tractsin this averaging, similarity of left–right homologue structureswas joint-ly given an equalweight as that of the commissural tracts and themiddlecerebellar peduncle. If a particular tract could not be identified in one ofthe subjects with the automated tractography approach (i.e. no particlesfulfilled the criteria imposed by the protocol masks), the tract was omit-ted in the aggregation of the subject–subject similarity score.



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Fig. 1. Schematic overview of the evaluation framework. Diffusion data in subject-native space (box 1) for N subjects are registered to an appropriate template image (box 2). Thisregistration can be based on FA images, the full tensor, or on any other DTI metric. This set of N registrations obtained with a particular registration algorithm is the registrationunder evaluation. Separately, standard space seed, target, stop and exclusion masks (box 3) that initialize the probabilistic tractography are transformed to subject native spaceusing a conservative nonlinear registration. Tractography for the total set of 23 structures is performed in subject native space (box 4). The registration under evaluation is usedto warp the tract-density images to standard space for all N subjects (box 5). The similarity of the warped tract-density images in standard space is quantified via spatial correlation,for each structure and for each pair of subjects (NxN). The similarity is averaged over all structures (box 6), and then averaged over all subject pairs to yield the registration per-formance for the particular registration under evaluation (box 7).

Table 1t1:1

t1:2 Overview of tracking protocols for different tracts in the evaluation framework. Tractst1:3 with left/right homologues are listed under ‘l/r’. If a stop mask is used, its relative loca-t1:4 tion to the tract is given under the ‘stop’ column. The number of seed points per voxel ist1:5 listed under ‘seed #’. Tracts that were generated twice with inverted target-seed regionst1:6 are listed under ‘invert’. References (‘refs’) translate to a: Stieltjes et al. (2001), b:Wakanat1:7 et al. (2004), c: Mori et al. (2002), d: Wakana et al. (2007).

t1:8 l/r Stop Seed # (*1000) Inv. Refs

t1:9 Tracts in brainstemt1:10 Middle cerebellar peduncle − 2 + a,bt1:11 Medial lemniscus + Sup. 4 − a,bt1:12

t1:13 Projection fiberst1:14 Corticospinal tract + 10 − a,b,dt1:15 Acoustic radiation + Med. 10 +t1:16 Anterior thalamic radiation + Post. 2 − b,c,dt1:17 Superior thalamic radiation + Inf. 2 − bt1:18 Posterior thalamic radiation + 30 − b,ct1:19

t1:20 Association fiberst1:21 Superior longitudinal fasciculus + 2 + b,c,dt1:22 Inferior longitudinal fasciculus + Ant. 2 − b,c,dt1:23 Inferior fronto-occipital fasciculus + 4 − b,c,dt1:24 Uncinate fasciculus + 4 − b,c,dt1:25

t1:26 Limbic system fiberst1:27 Cingulate gyrus part of cingulum + Ant. & post. 30 − b,dt1:28 Parahippocampal part of cingulum + Sup. & inf. 4 − b,dt1:29

t1:30 Callosal fiberst1:31 Forceps minor − 2 + b,dt1:32 Forceps major − 2 + b,d

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Similarity was assessed with the spatial correlation similaritymetric,

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which is similar to the Pearson correlation coefficient, and provides ameasure of voxelwise similarity of the continuous tract density imageintensities (J and K) for two subjects, computed over all voxels (i),and is bound on a 0–1 scale. Similarity was calculated on the tract den-sity images.

The probabilistic nature of tractography means that the intensityin the tract map varies; more support for the tract will translate intohigher intensity. Increased uncertainty will conversely translate intolower tract-density. The information that is thereby encoded in thetract-density image is related to the anatomy of the tract. The similarity,asmeasured by the spatial correlation similaritymetric, across two sub-jects therefore provides valuable feedback on alignment of the tracts inthose subjects.

Evaluation on the skeleton

To investigate the feasibility of replacing the registration-projectionin TBSSwith a regularized, high-dimensional registration,we comparedregistration performance for both registration algorithmswith the stan-dard TBSS approach. The registration evaluation framework described



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Fig. 2. Automated tractography result for one individual in the Rotterdam dataset. The same subject is shown in four different views. (a). Continuous probabilistic tractographyoutput used in the evaluation for all structures combined. (b). Probabilistic tractography output thresholded for visualization purposes only. The threshold was applied on the nor-malized tract-density images, rejecting voxels containing less than 0.5% of the total number of tracts per structure.


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above was therefore further tailored for both approaches to enable thiscomparison.

First, for the high-dimensional registrations, the registration perfor-mancemeasurement had to be constrained to the TBSS skeleton. Hence,the warped continuous tract-density images that resulted from the reg-ularized high-dimensional registration were masked using the TBSSwhite matter skeleton mask, producing skeletonized tract density im-ages for each structure, for each subject, which were used to evaluateregistration performance.

Next, for assessing registration performance of TBSS, the measure-ment also needed to be constrained to the skeleton. Hence, the contin-uous tract density images for all structures were (separately) projectedonto the white matter skeleton using the non-FA-image pipeline avail-able within TBSS (Smith et al., 2006); this allows the initial registrationand the skeleton projection, both derived from the FA data, to be ap-plied to other scalar images starting in the same space as the FA data.This produced skeletonized tract density images for each structure, foreach subject, were used to evaluate registration performance.

Optimization experiments

Diffusion MRI data

Two sets of scans from two different MRI centers were used in theexperiments. The first dataset represents a “low-end” diffusion acquisi-tion; the second dataset is representative of a state-of-the-art, thoughstill relatively “off-the-shelf”, high resolution, high signal-to-noise diffu-sion acquisition.

Lower resolution: Rotterdam dataThe first dataset was derived from the Rotterdam Scan Study

(Ikram et al., 2011), a neuroimaging study embedded in the larger,


prospective population-based Rotterdam Study (Hofman et al., 2011)composed of middle aged and elderly subjects. The diffusion data ispart of a multi-sequence MRI protocol on a 1.5 Tesla GE Signa Excitescanner. For DTI, single shot, diffusion-weighted spin echo-planarimaging data were acquired (repetition time (TR) = 8575 ms,echo time (TE) = 82.6 ms, field-of-view (FOV) = 210 × 210 mm,matrix = 96 × 64 (phase encoding) (zero-padded in k-space to256 × 256) slice thickness = 3.5 mm, 35 contiguous slices). b-valuewas 1000 s/mm2 in 25 non-collinear directions (number of excitations(NEX) = 1), and three volumes with no diffusion weighting were ac-quired. Acquisition time was 5 min. A sample of 30 subjects from thestudy population was rescanned on average 19.5 (SD 10.0) days afterthe baseline scan. These subjects were on average 76.7 years old(SD 4.8); 15 were female. The set of 30 baseline scans was used inthe registration optimization experiments; the set of rescanned data(30 scans)was used to evaluate reproducibility of the evaluation frame-work. This dataset will be referred to as the Rotterdam data, with thetime-points being labeled as “baseline” and “rescan”.

Higher resolution: Oxford dataThe second datasetwas acquired in healthy adults, described in Jbabdi

et al. (2010). Scanningwasperformedona1.5 Tesla Siemens Sonata scan-ner. As described in Tomassini et al. (2007), diffusion-weighted datawereacquired using echo planar imaging (72 × 2-mm-thick axial slices; ma-trix size, 128 × 104 (phase encoding); field of view, 256 × 208 mm; giv-ing a voxel size of 2 × 2 × 2 mm). Diffusion weighting was isotropicallydistributed along 60 directions using a b-value of 1000 s/mm2. For eachset of diffusion-weighted data, five volumes with no diffusion weightingwere acquired at evenly spaced points throughout the acquisition.Three sets of diffusion-weighted data were acquired for later aver-aging to improve the signal-to-noise ratio. The total scan time forthe diffusion-weighted imaging protocol was 45 min. Data from



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30 subjects were used. Mean age for this group was 32.0 years(SD 8.5); 12 were female. This dataset will be referred to as theOxford data.

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Diffusion data preprocessing

Diffusion data was preprocessed using the FDT toolbox included inFSL. Preprocessing included affine co-registration of all acquired vol-umes in order to compensate for subject motion and eddy currents.Non-brain tissues were removed with the Brain Extraction Tool. A ten-sor was fitted to log-transformed data using a linear least squaresapproach. The tensor image was then upsampled to 1 mm3 resolution,using cubic spline interpolation of the tensor components; note thatupsampling of the tensor image is not currently done in TBSS. A highresolution FA image was then derived from the upsampled tensorimage. Interpolating the tensor instead of the FA values allows theresulting FA image to contain more spatial detail that could aid the FAbased registration algorithms, as visible in Figure 1b and e in Kindlmannet al. (2007). Higher registration accuracy (as measured with the evalua-tion framework) for the tensor-upsampled FA images was confirmed inpreliminary experiments.

Separately, following the motion and eddy current correction, aprobabilistic model of fiber orientations was fitted for each voxelusing BEDPOSTX (Behrens et al., 2007). BEDPOSTX was run withdefault parameters, as a preprocessing step for the probabilistictractography.

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Table 2 t2:1

t2:2Settings varied in the registration optimization of FNIRT. FNIRT is run as a cascade oft2:3three sets of parameters. Parameters are varied in one or two of these stages, as indicat-t2:4ed. Stage 1 in itself contains a series of 4 substages, in which an initial regularizationt2:5relaxation is performed. Warp field resolution is jointly varied in stages 2 and 3, andt2:6the final regularization level is varied in stage 3 alone.

t2:7Parameter Stage 1 Stage 2 Stage 3

t2:8Number of substages 4 1 1t2:9Warp field resolution

(cubic)10 mm Varied in stages 2 and 3: 4;

2; 1 mmt2:10Regularization at each

substageVaried:steep = 600, 125, 80, 40medium = 300, 75, 50, 40flat = 150, 60, 50, 40

Fixed (100) Varied: 70–10(steps of 10)

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Registration algorithms

For two registration algorithms, FNIRT (Andersson et al., inpreparation) and Elastix (Klein et al., 2010), the evaluation frameworkwas used for parameter optimization and performance comparison.

FNIRT (Andersson et al., in preparation), the nonlinear image registra-tion algorithm in FSL, optimizes a B-spline deformation field (Rueckert etal., 1999), and is specifically developed for brain imaging. The objectivefunction is minimization of the sum of squared differences, and in-corporates an intensity modulation term to compensate for intensitydifferences between the moving and reference images. FNIRT uses amulti-resolution strategy to increase robustness against local mini-ma in the optimization. Following each resolution level, diffeomorphicwarps are enforced. By concatenating multiple (each itself being multi-resolution) calls to FNIRT in a cascade, registration parameters can bevaried over the course of the optimization. For evaluation, warp fieldsobtained with FNIRT were used to warp tract density images using theApplywarp utility in FSL. Tract density images were warped using cubicspline interpolation.

Elastix (Klein et al., 2010) (version 4.5) also includes B-spline basednonlinear deformations, and is based on the open source ITK platform.Elastix is designed to run in a cascade of resolutions, and offers thechoice between multiple objective functions and multiple optimizersincluding an efficient adaptive stochastic gradient descent optimizer(Klein et al., 2009). When using the sum of squared differences (SSD)similarity metric, the intensity distributions of the moving and refer-ence image are assumed to be equal.While FNIRT incorporates rescalingof the image intensities to compensate for differences, Elastix does not.In order to apply the SSD,we performed a linear intensity transformationas a preprocessing step. Based on the observed FA intensity histogramsfor each 30-subject dataset, we matched the 25 and 75 percentile pointswith those of the template image. Elastix furthermore offers the optionto localize the behavior of the similarity metric by employing a regionalsampling technique (Klein et al., 2008). Spatial transformations obtainedwith Elastix were applied to the tract density images with Transformix,which is distributed with Elastix. As with FNIRT, we used a cubic splineinterpolation.


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All registrationswere performedwith the subject FA images asmov-ing image and with the FMRIB-58 FA template as reference image.

For both registration algorithms, the parameters to be optimizedwere varied in an exhaustive fashion. For FNIRT, the parameters variedin the optimization strategy are listed in Table 2; fixed parameters arelisted in the parameter supplement, which is available as Supplementarymaterial. All registrations with FNIRT contained some degree of regular-ization at all stages. The parameter space selected for the optimizationresulted in a total of 63 settings of the algorithm.

For the Elastix optimization, parameters and settings that werevaried are listed in Table 3; again, a parameter supplement is availableas Supplementary material. This parameter space resulted in a total of576 settings of the algorithm.

All trials were performed on both datasets. Registration performance,as measured by the tract based similarity measure, was comparedbetween the optimized registration settings for both registration al-gorithms. To statistically examine the difference between two differ-ent sets of registrations, we computed, for each subject, the averagesimilarity to all other subjects in the dataset as defined in Tract-basedevaluation metric. We then performed paired t-tests, pairing subjectsacross both algorithms (30 pairs).

To be able to interpret the registration performance measure, weinvestigated the relationship between warp distance and this measure.Hereto, we applied the (optimum) nonlinear transformation obtainedwith FNIRT, but scaled it by a fraction between 0.8 and 0.995, and com-puted the resulting impact on the registration performance. For eachsubject in the Rotterdam and Oxford datasets, the spline coefficientsof thewarpfieldweremultiplied by thewarp fraction, leaving the affinecomponent of the transformation unchanged. All tract density imageswere transformed with these fractional warps. Then, for each subject,tract similarity was computed between the partially and fully warpedtracts.

We also compared deformation fields obtained with both registra-tion algorithms operating at optimal parameters. This was done to in-vestigate the difference between the algorithms.

Reproducibility of the performance measurement

As optimization introduces the risk of overfitting to the specificdata used in the optimization, we used the unseen rescan data, avail-able for 30 subjects in the Rotterdam data, to test reproducibility ofthe evaluation framework. This evaluation involved running the pre-processing, the tractography, and the registrations for all settings ofboth algorithms, and all evaluations on this set of scans. Two tests wereperformed on these reproducibility measurements. First, for both algo-rithmswemeasured the correlation between the performancemeasure-ments on the two sets of scans. Second, we focused on the optimalsettings for both registration algorithms, and compared the performancewith the performance obtained on the rescan data.



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t3:2 Settings varied in the registration optimization of Elastix. Elastix is run as a single cas-t3:3 cade of substages.

t3:4 Parameter Setting

t3:5 Warp field resolution (cubic) – 15 mm– 10 mm– 5 mm– 3 mm

t3:6 Similarity metric – Normalized cross correlation– Mutual information– Sum of squared differences

t3:7 Multiresolution strategy(of the image data)

– None– Pyramidal downsampling moving image– Pyramidal downsampling both images

t3:8 Regularization weight – None, 1, 10 or 100t3:9 Optimizer – Stochastic gradient descent

– Adaptive stochastic gradient descentt3:10 Localized metric Yes–no


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Comparison with TBSS

To test feasibility and effect of replacing the registration-projectionapproach in TBSS (v1.2) with a regularized high-dimensional registra-tion method, we performed three experiments. First we determinedwhether constraining the performancemeasurement to thewhite mat-ter skeleton (as described in Evaluation on the skeleton) altered the be-havior of the performancemeasure for the two registration approaches.Second, we compared the skeletonized registration performance to theTBSS performance on both datasets (Rotterdam and Oxford), and alsobetween the registration algorithms. Third, we conducted an exampleanalysis to investigate the influence of replacing the registration andprojection stageswith the improved registration, in a real-life study set-ting. For this experiment, we used MRI data of 50 female subjects fromthe Rotterdam Scan Study, aged 68–80 (mean 74.8, SD 2.9). These datawere acquired and processed in a manner identical to the Rotterdamdata that was used for the registration optimization but the subjectsused for this example applicationwere not included in the optimizationexperiment.We investigated the established (Sullivan and Pfefferbaum,2006; Vernooij et al., 2008) association between age and FA, with headsize as a confound regressor, with both TBSS and TBSS using the im-proved registration using FNIRT. Further details are provided in Supple-mentary Fig. 1.

Results


For optimization of the two registration algorithms, 639 registrationsettings (63 for FNIRT, 576 for Elastix) on both the Rotterdam data andOxford data were performed and evaluated, adding up to a total of 639sets of 60 registrations each. For Elastix, some combinations of parame-ters resulted in aborted registrations due to non-convergence for oneormore subject images. In this case, the particular setting of the registra-tion algorithm (30 for the Rotterdam data, 34 for the Oxford data) wascompletely excluded from the analysis. The resulting 1214 performancemeasurements therefore contained no cases of non-convergence, andare presented in three ways.

To illustrate the results of the optimization procedure for one ofthe four combinations of registration algorithm and dataset, the optimi-zation of Elastix on the Oxford data, performance as a function of themost influential parameters is shown in Fig. 3. This graph shows all per-formance measurements for the combination of algorithm and dataset,as a function of the parameters that influenced registration perfor-mance most (three parameters are not discernible in this figure).Warp field resolution is presented on the horizontal axis, regularizationis indicated with a symbol, and registration similarity metric is indicated


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by color. The graph shows that the optimal amount of regularizationdepended on the similaritymetric. The graph also shows that robustnesswith respect to the indiscernible parameters (multiresolution strategy,optimizer and localization of the similarity metric) depended on warpfield resolution, as indicated by the distribution of similarmarks general-ly fanning out for increasing resolution. For conciseness, graphs for theother three combinations of registration algorithm and dataset are omit-ted and summarized results are presented in Figs. 4 and 5. To visualizeparameter dependence, themarginal variation of the performance mea-surementwhen varying parameters around the optimumpoint is shownin Figs. 4 and 5. Based on the optimal registration parameters, thesegraphs show the influence of each of the parameters under investigation.These figures show that thewarp field resolution, regularization, and, forElastix, similarity metric were the most influential parameters in theoptimization.

Optimal registration parameters for FNIRT depended on the resolu-tion of the data that was being registered (Fig. 4), even though the op-timum settings for both datasets is in relatively flat segments of theparameter-performance curves and the dependence is therefore fairlyweak. For the Rotterdam data, optimal resolution for the final B-splinegrid was 4 mm, compared to 2 mm for the higher-resolution Oxforddata, although in both cases either choice would not result in a largechange in performance. The optimal regularization at the last cascadeof the registration was 60 for the Rotterdam data, compared to 30 forthe Oxford data. The relaxation speed for the regularization was theleast influential parameter, butwas different for both datasets nonethe-less; flat for the Rotterdam data compared to medium steep for theOxford data.

Optimal registration parameters for Elastix also depended on thedataset being optimized. Two of the most influential parameters werethe same for both datasets; warp field resolution was optimal at 3 mmand normalized cross correlation (NCC) was the optimal similaritymetric.Optimal regularization weight depended on the dataset; for theRotterdam data a weight of 10 was optimal, and for the Oxford data aweight of 1. Of the least influential parameters, two parameters hadthe same optimum for both datasets; the optimal optimizer (adaptivestochastic gradient descent), and localization of the similarity metric(yes). One parameter differed; for the Rotterdam data, the optimalmultiresolution strategy was to not smooth to any of the images, andfor the Oxford data, decreasing smoothing for the subject image, withno smoothing of the template image, was the optimal strategy.

To center on the aforementioned optimization results, Fig. 6 showsthemaximumperformance as a function of the twomost influential pa-rameters (warp field resolution and regularization) for both datasetsand both algorithms. Each point on these graphs represents the maxi-mumperformance across a set of 36 settings for Elastix, or three settingsfor FNIRT.

The performances with optimal parameter settings are listed inTable 4. The table shows that optimal registration performance forElastix was slightly higher than for FNIRT with a difference in perfor-mance of 0.004–0.006. Although the differences were very small, theywere statistically significant (Table 4; p-values for all datasets b10−4).

To be able to interpret these distances, the relationship betweenregistration performance and deformation distance is shown in Fig. 7.A difference in performance of 0.01 translates to an average deformationdifference of about 0.2 mm; this is twice the difference in registrationperformance between FNIRT and Elastix.

For both algorithms operating at the optimal parameters for bothdatasets, the mean deformation distance is shown in Fig. 8. For eachdataset, the figure also shows the Euclidean difference between theoptimal deformations of FNIRT and Elastix, including group wise dif-ferences in registration along white matter structures. The mediandifference for the Rotterdam data was 1.19 mm (IQR 0.91–1.71) andfor theOxforddata 1.70 mm(IQR 1.14–2.52). Confined to the TBSS skel-eton this corresponded to 1.10 mm (IQR 0.91–1.39) and 1.48 mm (IQR1.03–1.98).



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Fig. 3. Scatterplot of registration performances for all settings evaluated on the Oxforddata with the Elastix registration algorithm. Each point represents registration perfor-mance (vertical axis) on the entire Oxford dataset as a function of the most influentialparameters: warp field resolution (horizontal axis), regularization weight (symbol)and similarity metric (color). Repeated appearance of the same symbol and color corre-sponds to variations in multiresolution strategy, optimizer and localization of the similaritymetric.


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Reproducibility of the performance measurement

The optimization experiment was repeated on the rescan data. Thisresulted in a second, independent performance-measurement for eachof the registration parameter settings of FNIRT and Elastix, calculatedon a different set of scans of the same subjects. Scatterplots of perfor-mance measurements for both datasets are shown in Fig. 9. For FNIRTthe scatterplot shows that the absolute performance on the rescandata was slightly reduced (mean difference 0.0105), but this differencewas very consistent (SD 6.4 × 10−4), indicating a slightly lower dataquality in the rescan data. Both measures showed an excellent correla-tion,which is reflected in the R2 value of the OLS regression of 0.993. For

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Fig. 4. Registration performance (vertical axis) of FNIRT, for each of the parameters around tdata (solid). The optimum points are indicated with dots. Registration performance is separfinal regularization (higher means more regularization).


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Elastix the scatterplot shows that a similar performance difference wasobtained (mean difference 0.0099), but at an increased variability(SD 8.9 × 10−3) which is reflected in a lower R2 value of 0.931.

For the rescan data, registration performance was also measuredfor the optimal parameters determined on the baseline data. Perfor-mance measurements are listed in Table 4, showing that the smallFNIRT — Elastix difference was exactly reproduced, albeit that the ab-solute performance measures for both algorithms were again slightlyreduced.

Comparison with TBSS

Constraining the evaluation to the TBSS skeleton had little influenceon the optimal parameters, especially around the optimal settings.While the optimal registration parameters evaluated on the wholetract did not exactly match the optimal parameters evaluated on theskeleton, this had very little influence on performance. The differencein registration performance between parameters obtained in the regis-tration optimization (Optimization experiments), and the optimal reg-istration according to a skeletonized optimization was at maximum2.6 × 10−3.

To compare the performance of both FNIRT and Elastix to TBSS,Table 5 lists the registration performance for both DTI datasets re-stricted to thewhitematter skeleton. Performance differences betweenFNIRT or Elastix and TBSS were all significant and ranged from 0.038 to0.046 (all p-values for paired t-tests between both nonlinear registra-tion algorithms and TBSS were b10−6). This indicates that registrationperformance was significantly better on the white matter skeleton forFNIRT and Elastix than for TBSS; the difference in performance betweenFNIRT and Elastix (in different directions in different datasets) was anorder of magnitude smaller than the extent to which both performedbetter than TBSS.

Table 5 also contains a comparison between FNIRT and Elastix inthe skeletonized evaluation. For the Rotterdam data, Elastix repro-ducibly outperformed FNIRT, but for the Oxford data, FNIRT was sig-nificantly better than Elastix.

Supplementary Fig. 1 shows the results of the association between ageand FA in the 50 aging female subjects, comparing TBSS to TBSS with im-proved registration using FNIRT. Replacing the registration-projection ap-proach in TBSSwith the improved registration yieldedmore symmetry inthe clusters of significant association between higher age and lower FA.Also, clusters were larger and more clusters were found (50% morevoxels) when using the improved registration. Bland–Altman plots ofthe t-values and the cluster enhanced t-values for both approaches(Supplementary Fig. 1) further show that at the cluster level, TBSSwith improved registration rendered average higher t-values than TBSS.

Discussion

We developed a method to determine the accuracy of establishedanatomical correspondence of white matter tracts between different

he optimum parameter setting. Shown for the Rotterdam data (dashed) and the Oxfordately shown as a function of warp field resolution, regularization relaxation speed and



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Fig. 5. Registration performance (vertical axis) of Elastix, for each of the parameters around the optimum parameter setting. Shown for the Rotterdam data (dashed) and the Oxforddata (solid). The optimum points are indicated with dots. Registration performance is separately shown as a function of warp field resolution, similarity metric, multiresolutionstrategy, regularization weight, optimizer, and localization of the similarity metric.


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subjects. Using this method, we optimized parameters for two registra-tion algorithms, and showed that alignment in TBSS can be improved byusing a regularized high-dimensional nonlinear registration approachrather than the registration-projection procedure.

We reproducibly observed substantially better alignment of whitematter structures on the white matter skeleton with the optimizedregistration algorithms than with the current approach in TBSS. Thisindicates feasibility of replacing the registration-projection approachin TBSSwith a finely optimized nonlinear registration. This replacementwould improve alignment, but also topological consistency in whitematter tracts, since this is explicitly preserved in the diffeomorphic reg-istration of FNIRT, and almost always preserved by the regularized reg-istration performed with Elastix.

The example analysis showed that TBSS with improved registra-tion producedmore symmetric, larger andmore clusters of significantassociation between age and FA, and that clusters common to bothapproaches had smaller p-values using TBSSwith improved registration.These observations do not prove that the improved registration yieldshigher sensitivity, as we do not know the ground-truth association inthis experiment. However, the results are in line with the common no-tion of widespread degeneration of white matter with age (Sullivanand Pfefferbaum, 2006; Vernooij et al., 2008), and as such serve as an il-lustration of the potential benefit offered by the improved registrationand maintained topological consistency, in the analysis of diffusiondata in future studies.

There are several methodological considerations to be discussed.First, the optimization experiments showed that optimal registrationparameters were different for both imaging datasets (low-end andhigh-resolution) used. Most notably the optimal regularization was

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Fig. 6. Maximum registration performance (vertical axis) for both algorithms and both dataFor each point on the graph, the maximum performance as a function of the other parameterlines indicate Rotterdam data, the solid lines Oxford data.


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The reproducibility of the registration, as measured with the evalua-tion on the rescan data shown in Fig. 9, is influenced by the individual re-producibility of the tractography, the registration, and the optimization/evaluation framework itself. The observed dispersion of the differencebetween performances calculated on baseline and rescan data is there-fore a combination of variances. Assuming independence of the registra-tion evaluation variance from the registration algorithm means that theexcellent reproducibility of the registration performance measures forFNIRT (Fig. 9a) provides a lower bound for the reproducibility of the reg-istration evaluation framework. It should be noted that the performanceranges for the two registration algorithms across the parameter rangesare nearly one order of magnitude apart. With Elastix spanning a largerperformance range, this also means that part of the range is covering

sets, as a function of regularization (horizontal axis) and warp field resolution (color).s is plotted. Performance for FNIRT is shown on the left, Elastix on the right. The dashed



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Table 4t4:1

t4:2 Registration performance for all datasets at the optimal registration parameters fort4:3 both FNIRT and Elastix. Performance on the Rotterdam rescan data is computed usingt4:4 the registration settings determined to be optimal based on the Rotterdam baselinet4:5 data. p-values listed are computed for paired t-tests, comparing the registration perfor-t4:6 mance for all 30 subjects across both registration algorithms.

t4:7 Algorithm Rotterdambaseline

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Oxford data

t4:8 FNIRT 0.588 0.577 0.600t4:9 Elastix 0.594 0.583 0.604t4:10 FNIRT-Elastix (p-value) −0.006 (b10−4) −0.006 (b10−4) −0.004 (b10−5)


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registrations that are so far away fromoptimal that reproducibility is lessinformative. Even so, it seems that reproducibility for FNIRT was slightlybetter than for Elastix.

It is interesting to see that for Elastix, the sum-of-squared-differences(SSD) similarity metric, which is the similarity metric implemented inFNIRT, was consistently outperformed by the mutual information (MI)and normalized cross correlation (NCC) metrics. This might have beencaused by nonlinear intensity differences between subjects across tracts.With different tracts having slightly different intensity across subjects,the assumptions of the SSD cannot be met. This might explain the differ-ence in registration performance between Elastix and FNIRT observed onthe full tract evaluation.

Registration performance on the skeleton for both registration al-gorithms showed heterogeneous behavior amongst the datasets, withElastix performing slightly better on the worse data, and FNIRTperforming slightly better on the better data. Comparison of both al-gorithms using the whole tract evaluation showed Elastix to performslightly better than FNIRT with absolute deformation differences inthe order of 1–2 mm. These differences will be a composition ofdeformation differences that do, and deformation differences thatdo not translate into registration performance differences (think e.g. oftwo sets of transformations, each with an equal amount of different ran-dom perturbations). By scaling the optimal deformations, we found thatthe obtained difference in registration performance between optimalwarp fields of both algorithms would translate to deformation differ-ences in the order of 0.1 mm, had all deformation differences translatedinto registration performance differences. While performing slightlyworse, FNIRT is diffeomorphic and therefore produces invertible warps.Invertibility of the warp field is a desirable property in a neurosciencecontext such as TBSS as this allows back-projecting points in standardspace to subject-native space and preserves topological consistency of

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Fig. 7. The relationship between tract similarity difference (based on spatial correlationbetween two aligned tract density images) and warp deformation difference for theRotterdam data (dashed) and the Oxford data (solid), computed for FNIRT operatingat optimum parameters for each dataset. The largest difference is obtained when scal-ing the warp with a factor of 0.8. This translates into a similarity drop between fullyand partially warped tracts. Deformation difference is computed by taking the deforma-tion difference (vector) image for each subject, comparing the full and partial warps.The deformation difference in the graph is then themedian Euclidean deformation differ-ence distance (vector length), averaged over all subjects in each dataset.


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the whitematter through the transformation of native space to standardspace.

Themasks that initialize the probabilistic tractography (seed, target,exclusion, and stop) are defined in standard space, and transformed tosubject space. The registration that is used for this transformation isobtained with a low degree-of-freedom registration, i.e., the same reg-istration that is used in the initial alignment of TBSS. This registrationis inverted to obtain a standard space to subject transformation. Theuse of a registration inside a registration-evaluation framework can po-tentially bias the evaluation metric. However, this bias would favortransformations similar to the one used in the tractography initializa-tion, i.e. conservative, low-degree of freedom transformations. It shouldalso be noted that tractography is only run in a preprocessing stage, andthat the same tract-sets are used to evaluate all different registration pa-rameter settings. We therefore consider bias due to this registrationstep not to be a major factor in our results.

In this evaluation we have included two nonlinear registration al-gorithms that were developed in the groups that contributed to thisstudy and for which primary developers were involved in the project.Though not the aim of this study, the developed framework may lenditself to a comprehensive comparison of more registration algorithms.Such a comparison of registration algorithms could e.g. include a broadselection of algorithmsout-of-the-box, such as carried out inWanget al.(2011), or could include a full optimization in which case we recom-mend involvement of developers of each algorithm to design thealgorithm-specific optimization scheme. Such an optimizationwould in-herently be very computationally intensive. Computing the registrationperformance for a single registration parameter setting, for a group of30 subjects, took on average around 50 CPU-hours. This included theactual registration, warping the tract maps, and computing the spatialcorrelation. Computations were performed on the LISA cluster inAmsterdam (www.sara.nl/systems/lisa) and on a local cluster inRotterdam. The optimal registrations of the Rotterdam data requiredon average 51 min (FNIRT), and 68 min (Elastix) of CPU time on2.1 Ghz AMD Magny Cours processors, compared to 12 min for theregistration + projection of TBSS. For the Oxford data this was 71 minfor FNIRT, 71 min for Elastix, and 12 min for TBSS.

We used probabilistic tractography for fiber tracking and evaluatedregistration performance using a spatial correlation similarity metric.This is different frompreviouswork that usedfiber tracts to quantitative-ly measure registration performance (Park et al., 2003; Xue et al., 2010;Yap et al., 2009; Zhang et al., 2006; Zöllei et al., 2010), which werebased on deterministic tractography. As a result, metrics for comparingsimilarity of warped tract maps in those methods were overlap-based,using similaritymetrics such as theDice, Jaccard and Cohen's Kappamet-ric (Stieltjes et al., 2001; Zhang et al., 2010), or distance-based metrics,related to the Hausdorff distance or the mean absolute surface distance(Park et al., 2003; Yap et al., 2009; Zhang et al., 2006; Zöllei et al.,2010). The near-continuous density information that results from prob-abilistic tractography is not so well suited for these similarity metrics.Most importantly, tract-density contains information about the tract,which would be lost if a thresholded, binary tract-mask was used. Sec-ondly, setting a density threshold for binarization would introduce an-other parameter that requires setting. Spatial correlation as a similaritymeasure does not suffer from these drawbacks. Also, we have shownthat when using the framework presented, based on multiple tractsidentified with probabilistic tractography, using spatial correlation assimilarity measurement allows for a precise and reproducible evaluationof registration quality. Investigating other evaluation metrics would bepossible within this framework, but this is beyond the scope of the cur-rent research.

Registration performancemeasurements on the rescan data showedthe difference between both nonlinear registration algorithms to behighly reproducible. Furthermore, performance measurements werehighly reproducible themselves. This is an important observation, as itshows that using the tractography output to measure registration


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Fig. 8. Average Euclidean deformation distance for the Rotterdam data (a) and the Oxford data (b). For each algorithm operating at the optimal parameters for each dataset, theindividual deformation vector images are used to compute Euclidean deformation images, which are then averaged over all subjects to produce the images shown. For both algo-rithms we included the affine transformation in the deformation field, and then subtracted the mean displacement within the template image in order to account for differences inthe coordinate definitions. The distance for both FNIRT and Elastix is shown in mm, the bottom panel in each graph shows the mean Euclidean deformation difference between bothalgorithms at their respective optimum settings.


performance in the framework presented is not prone to overfitting reg-istration parameters on the dataset that is used for training the registra-tion parameters. This in turn allows one to train registration parameterswithout the explicit need to evaluate performance on a separate datasetthat was not used in the optimization.


The optimized parameter sets that resulted fromour experiments areavailable for both registration algorithms as Supplementarymaterial. ForElastix, parameters can additionally be downloaded from the parameterfile database on the Elastix wiki page (http://elastix.bigr.nl/wiki). ForFNIRT, optimized parameter files will be distributed with FSL. Scripts


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Fig. 9. Reproducibility of the registration performance measurements for FNIRT (a) and Elastix (b) experiments on the Rotterdam data. Each point represents the registration per-formance for one registration parameter setting, as measured on two different sets of scans of the same subjects.

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Conclusions

In conclusion, firstly, we demonstrate that optimized nonlinearimage registration algorithms produce better image alignment on thewhite matter skeleton than the registration-projection approach cur-rently in TBSS.

Secondly, registration quality of diffusion imaging data can beassessed using probabilistic tractography and thus used for optimi-zation of registration parameter settings and for comparison of reg-istration algorithms. This evaluation is not in general biased towardsany particular tensor or tensor metric based registration approach,and highly reproducible.

Thirdly, optimal registration parameters depend on the quality(resolution, number of averages etc.) of the diffusion dataset in a gradedand predictable manner.

Future studies investigating cross-subject diffusion data with TBSSare expected to benefit from the improved anatomical alignment.

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.neuroimage.2013.03.015.

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Table 5Skeletonized performance at the optimum parameter settings for each dataset, com-pared to registration performance of TBSS. Performance on the Rotterdam rescandata is computed using the registration settings determined to be optimal based onthe Rotterdam baseline data. p-values listed are computed for paired t-tests, comparingthe registration performance for all 30 subjects across both registration algorithms andbetween registration algorithms and TBSS.

Algorithm Rotterdam baseline Rotterdam rescan Oxford data

FNIRT 0.685 0.674 0.690Elastix 0.689 0.677 0.686TBSS 0.643 0.636 0.647FNIRT–Elastix (p-value) −0.004 (0.002) −0.003 (0.01) 0.005 (b10−6)FNIRT–TBSS (p-value) 0.04 (b10−6) 0.04 (b10−6) 0.04 (b10−6)Elastix–TBSS (p-value) 0.05 (b10−6) 0.04 (b10−6) 0.04 (b10−6)


EDAcknowledgments

Thisworkwas sponsored through grants of theNetherlandsOrganiza-tion of Scientific Research (NWO, grants 612.065.821 and 639.031.919)and the Alzheimer Association (NIRG-09-131680). Computational facil-ities were granted by the National Computing Facilities Foundation(NCF), The Netherlands, operating with financial support from NWO.

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