white matter atlas generation using hardi based automated ... · oof 1 white matter atlas...

1

2Q1

3

456

7

89101112131415161718192021

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

NeuroImage xxx (2011) xxx–xxx

YNIMG-08628; No. of pages: 9; 4C:

Contents lists available at SciVerse ScienceDirect

NeuroImage

j ourna l homepage: www.e lsev ie r .com/ locate /yn img

OF

White matter atlas generation using HARDI based automated parcellation

Luke Bloy a,⁎, Madhura Ingalhalikar a, Harini Eavani a,b, Robert T. Schultz b,Timothy P.L. Roberts c, Ragini Verma a

a Section of Biomedical Image Analysis, Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USAb Center for Autism Research, Children's Hospital of Philadelphia, Philadelphia, PA 19104, USAc Lurie Family Foundations MEG Imaging Center, Department of Radiology, Children's Hospital of Philadelphia, Philadelphia, PA 19104, USA

⁎ Corresponding author at: Section of Biomedical ImSuite 380, Philadelphia PA 19104, USA.

E-mail address: [email protected] (L. Bloy).

1053-8119/$ – see front matter © 2011 Published by Eldoi:10.1016/j.neuroimage.2011.08.053

Please cite this article as: Bloy, L., et al., Wdoi:10.1016/j.neuroimage.2011.08.053

Oa b s t r a c t
a r t i c l e i n f o
22

23

24

25

26

27

28

29

30

31

Article history:Received 16 June 2011Revised 16 August 2011Accepted 19 August 2011Available online xxxx

Keywords:DiffusionAtlas generationHARDI templateWhite matter parcellation

32

33

34

35

TED P

RMost diffusion imaging studies have used subject registration to an atlas space for enhanced quantification ofanatomy. However, standard diffusion tensor atlases lack information in regions of fiber crossing and arebased on adult anatomy. The degree of error associated with applying these atlases to studies of childrenfor example has not yet been estimated but may lead to suboptimal results. This paper describes a novel tech-nique for generating population-specific high angular resolution diffusion imaging (HARDI)-based atlasesconsisting of labeled regions of homogenous white matter. Our approach uses a fiber orientation distribution(FOD) diffusion model and a data driven clustering algorithm. White matter regional labeling is achieved byour automated data driven clustering algorithm that has the potential to delineate white matter regionsbased on fiber complexity and orientation. The advantage of such an atlas is that it is study specific andmore comprehensive in describing regions of white matter homogeneity as compared to standard anatomicalatlases. We have applied this state of the art technique to a dataset consisting of adolescent and preadoles-cent children, creating one of the first examples of a HARDI-based atlas, thereby establishing the feasibilityof the atlas creation framework. The white matter regions generated by our automated clustering algorithmhave lower FOD variance than when compared to the regions created from a standard anatomical atlas.

36

age Analysis, 3600 Market St,

sevier Inc.

hite matter atlas generation using HARDI b

© 2011 Published by Elsevier Inc.

3738

C

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

UNCO

RRE

Introduction

The use of brain atlases in neuroimaging studies allows researchers toregister, identify and perform measurements on individual subjectswithin a common spatial coordinate system enabling large scale groupstudies with greater statistical power to elucidate smaller or more subtleanatomical differences that exist in specific diseases. Since the introduc-tion of the Talairach (Talairach, 1988) human cortical atlas, a number ofMRI atlases have been introduced to assist with these measurementissues. T1-weighted MR atlases (Collins et al., 1995; Mazziotta et al.,1995; Lancaster et al., 2000; Mazziotta et al., 2001; Lancaster et al.,2007; Ashburner, 2009) from the Montreal Neurological Institute(MNI) and the International Consortium of Brain Mapping (ICBM) havebeen used extensively to illustrate differences in gray matter anatomyas well as to localize functional signals within these structures. WhileT1-weighted MRI provides detailed information concerning corticalanatomy it provides considerably less information concerning whitematter anatomy (Toga et al., 2006), thus these atlases have focusedprimarily on the identification of GM regions, possessing limitedinformation concerning WM regions.

80

81

82

83

84

By providing an in-vivoWMcontrastmechanism, built on the recog-nition of the imaging consequences of diffusion anisotropy (Moseleyet al., 1990), diffusion tensor imaging (DTI) (Basser et al., 1994) hasreinvigorated the study of WM pathologies and more recently DTIbased WM atlases (Wakana et al., 2004; Mori et al., 2008; Oishi et al.,2009) have been introduced to address the relative lack of informationprovided by the existing cortical atlases.While DTI is able tomodelWMregions possessing a singlefiber population, it is ill suited tomodel areasof more complex WM, such as fiber crossing. This limitation makesdelineating boundaries within these regions difficult and the labelingwithin them suspect. More complex high angular resolution diffusionimaging (HARDI) data models (Frank, 2002; Tournier et al., 2004;Tuch, 2004; Anderson, 2005; Descoteaux et al., 2007) have beendeveloped to improve modeling in areas of complex WM. These newmodels provide contrast in areas of fiber crossing and orientationchange that is unavailable from conventional DTI and better reflectsthe underlying structure of the WM tissue. This paper presents anovel methodology for building WM atlases by utilizing the HARDIcontrast to identify and automatically label regions of homogenousWM. The utilization of an automated data driven clustering algorithmfor region labeling permits the generation of population/study specificatlases without the need for manual delineation of anatomical regions.

In general, the utility of atlases is two-fold. First, an atlas provides atemplate image, either a population average or a single subject image,to serve as a spatial normalization target and thus defines a common

ased automated parcellation, NeuroImage (2011),

http://dx.doi.org/10.1016/j.neuroimage.2011.08.053

mailto:[email protected]


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


T

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149Q2150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169 Q3170

171

172

173

174

175

176

177

178 Q4179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197198199200201202203204205

206

207

208

2 L. Bloy et al. / NeuroImage xxx (2011) xxx–xxx

UNCO

RREC

spatial coordinate system. Secondly, each atlas identifies regionsconsisting of voxels that meet some conceptual criterion of sameness.The majority of imaging atlases attempt to label regions based onnamed neuroanatomical constructs, such as the prefrontal cortex orthe internal capsule. This requires a neuroanatomist/neuroradiologistto manually label the template image to identify each region and isinherently variable, as human neuroanatomical boundaries are quitevariable. Recent work within the registration community (Zhang et al.,2007; Hecke et al., 2008;Hammet al., 2010; Hecke et al., 2011) suggeststhat choosing a registration template from the population under studyimproves the accuracy of spatial normalization. However the laborintensive labeling process makes the accurate transfer of atlas definedregions to a population specific atlas difficult, a particularly acute issuewhen the population has unique characteristics (such as being of ayounger age than the anatomical atlas) or when the new imagingmodalities, such as HARDI, are being used.

It is also important to consider if labeling based on anatomical bound-aries provides sufficient demarcation, particularly in areas of complexWM, for applications such as region of interest (ROI) basedWManalysis.For instance,most large anatomicalfiber bundles are known to traverse avariety ofWMarchitectures and thusmay not bewell suited for region ofinterest studies where they are represented by a single diffusion modelor a single scalar feature, such as diffusion fractional anisotropy.

In this work we address these limitations of existing white matteratlases by presenting a framework to generate a population-specificHARDI atlas based on one of the prominent HARDI data models, thefiber orientation distribution (FOD) (Tournier et al., 2004; Anderson,2005) function. The framework uses a non-linear spatial normalizationalgorithm to spatially transform the population into a common coordi-nate system and to create a population average FOD image. While weadopt a suitable registration algorithm, similar HARDI based registrationtechniques (Geng et al., 2011; Raffelt et al., 2011; Yap et al., 2011) couldbe used in its place, without compromising the atlas framework andparcellation capability. The advantages of algorithms of this type (i.e.based on HARDI) have been shown in registering areas of complexwhite matter when compared with state of the art DTI registrationmethods (Yap et al., 2011).

An automateddata driven clustering routine is then applied to create alarge number of spatial regions, each consisting of homogeneousWM ar-chitecture asmeasured by the FOD image. As regional homogeneity is thedriving force behind the cluster process, each region is able to be confi-dently represented by its average, making these regions ideal forregion of interest (ROI) statistical studies or for the extraction of spatialWM features for use in a classification framework. While neuroanatomi-cal labelingmay not provide suitable delineation of boundaries needed toidentify homogeneous WM regions, it does aid in interpretability byproviding researchers and clinicians with a means of investigating thestructure/function of these regions as well as a comparative basis toother published studies. For this reason, in addition to determininghomogeneous WM regions, we assign to each neuroanatomical labelsbased on its spatial overlap with an existing WM atlas. While notdesigned merely to identify these named anatomical constructs, theneuroanatomical relabeling of the data-based atlas, allows for describingthe ROI as belonging to the anatomical region, thereby instilling it withjoint information of the underlying fiber orientation as well as the globalanatomy and function, facilitating interpretability.

We illustrate the application of our framework by generating a HARDIatlas fromadataset consisting of typically developing pediatric and youngadolescent subjects, although the method is generalizable to any popula-tion under study. By comparing regional FOD spatial variances inanatomical labels to the variances computed from the regions determinedby our clusteringmethod,we demonstrate the ability of our algorithms togenerate atlases consisting of homogeneous WM regions well beyondwhat is achievable using the neuroanatomical labeling available inexisting WM atlases. Average measures in these homogenous regionscan then be used for subsequent statistical analysis and as the basis for

Please cite this article as: Bloy, L., et al., White matter atlas generatiodoi:10.1016/j.neuroimage.2011.08.053

ED P

RO

OF

between group and longitudinal within-group investigations. Anatomicalinterpretability of these study specific atlases generated by ourmethod isimparted by establishing a correspondence with an existing atlas such asthe EVE-DTI (Oishi et al., 2009) atlas in the presented case, but this could,in principle, be replacedby any anatomical atlas deemedof importancebythe hypotheses of the study for which the atlas is being created.

Methods and materials

This paper presents an automated method for creating a HARDI-based WM atlas for a given clinical population which will establish acommon spatial reference frame to facilitate further investigation ofWM differences. The generation of the WM atlas consists of a numberof steps. First, an image of fiber orientation distribution (FOD) functionsis computed for each subject's diffusion-weighted (DW)-MRI dataset. Anon-linear spatial normalization process (Bloy and Verma 2010; Genget al., 2011) is applied to deform each subject's FOD image into thespatial domain defined by a single individual, chosen to act as thepopulation template. Following registration, a population averagedFOD image is computed and a data driven clustering algorithm isapplied (Bloy et al., 2011a, 2011b) to divide the white matter intoregions of homogenous WM architecture. This parcellation algorithmis designed to determine spatially compact regions that have a lowspatial variance in the normalized FOD space and thus are comprisedof voxels possessing both a similar orientation as well as a similarlevel of complexity (as imaging surrogates of low biological/tissuevariance). These traits make these regions ideal candidates for regionalstatistical analysis (Kubicki et al., 2002; Alexander et al., 2007; Lee et al.,2007; Fletcher et al., 2010) or as input features to a pattern classificationmethod (Bloy et al., 2011a, 2011b; Ingalhalikar et al., 2011). Theseregions are not necessarily intended to correspond directly to namedanatomical structures provided by conventional labels such as theinternal capsule, corpus callosum etc., but might for example exposesub-parcellation within such structures. To impart this additionalanatomical information a labeling procedure is applied to assign WMlabels derived from the EVE-DTI atlas ((Oishi et al., 2009) http://cmrm.med.jhmi.edu/cmrm/atlas/human_data/) to each region.

Fiber orientation distribution function

The fiber orientation distribution function (FOD) is the HARDI datamodel used in this work to quantify the WM architecture at each voxel.The FOD model (Tournier et al., 2004; Anderson 2005) represents eachvoxel's DW-MRI signal as the spherical convolution of the FOD and theDW-MRI signal that would bemeasured for a single fiber bundle alignedalong the z-axis. We utilized the constrained spherical deconvolutionmethod (Tournier et al., 2007) to compute the real spherical harmonic(RSH) representation of FOD, which is then normalized to have unitintegral. Under this formulation the normalized FOD f is represented as

f θ;ϕð Þ ¼ ∑l¼0

∑l

m¼−lf̃ l;mRl;m θ;ϕð Þ, where Rl,m(θ,ϕ) are the RSH basis func-

tions and f̃ i;m are the corresponding RSH coefficients. This representa-tion allows for the efficient computation of the difference between twoFODs using the L2 norm of the RSH coefficients as well as a means torotate the FOD by the use of the Wigner D rotation matrices (Wigner,1931; Edmonds, 1960). The FOD model is of particular interest in thiswork, as it contains information concerning both the orientation andpartial volume fraction of any fiber bundles present within a voxel,making it well suited to model WM architecture in complex regions aswell as those constituting a single fiber population.

Creating a population average FOD image

Once the FODmodel has been fitted to each subject's DW-MRI data-set, a single subject is chosen to act as a template image for spatial

n using HARDI based automated parcellation, NeuroImage (2011),

http://cmrm.med.jhmi.edu/cmrm/atlas/human_data/

http://cmrm.med.jhmi.edu/cmrm/atlas/human_data/


T

209

210

211

212

213

214Q5215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230231232

233234235236237238239

240

241

242Q6243

244245246247248249250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265 Q7266

267

268

269

270

271

272273274

275

276

277

3L. Bloy et al. / NeuroImage xxx (2011) xxx–xxx

EC

normalization. Although any subject can be used to define the templatespatial coordinate frame, it is generally best to choose the individualmost representative of the population under study to act as the templatesubject. For instance, in generating the adolescent atlas in the sectionResults: development of a population atlas (an illustrative example), atwelve year old male subject served as the registration template.

With the template defined, the normalized FOD image of each subjectis registered to the template FOD image via a two phase registrationmethod (Fig. 1), each phase utilizing a different similarity measure. Thecore of both registration phases is the multichannel diffeomorphicdemons framework (Thirion, 1998; Vercauteren et al., 2009), discussedin the Appendix A. The demons framework is designed to minimize anenergy functional based on the difference metric between the fixed(template) and moving (subject) FOD images, F and M. By representingF and M in different feature spaces, the contribution of orientationinformation to the demons algorithm can be managed in each registra-tion phase, controlling the sensitivity of the registration method to theorientations of the FODs.

In the first phase, the demon's registration framework isused to minimize an orientation invariant metric between the FODsof the fixed and moving images (F and M), at each voxel,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑IMax

I¼0;leven ∑m

f̃ l;m� �2

−∑m

g̃l;m� �2

� �s. As the basis functions of each

RSH order (l level) span a subspace which is closed under rotations (Ed-monds, 1960; Frank, 2002; Green, 2003; Bloy and Verma, 2010), the

spectral power in the lth order,∑lm¼−1 ˜f i;m xð Þ� �2 is a rotationally invari-

ant feature of f. Therefore using the above metric in the spectral powerspace yields a registration process that is insensitive to rotations of theFODs of each image, allowing the computationally expensive reorienta-tion process to be removed from this registration phase increasing itscomputational efficiency.

The second, orientation sensitive, registration phase uses the full vec-tor of RSH coefficients to represent the FOD at each voxel,minimizing

the L2 metric in the full RSH space,

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑IMax

I¼0;leven

�∑m

f̃ l;m− g̃l;m� �2

s¼

∮dw fθ;ϕð Þ−g θ;ϕð Þ. This metric measures the total amplitude differencebetween the two spherical functions, f and g, and is inherently sensitive

UNCO

RR

Fig. 1. FOD registration is accomplished using a two phase registration scheme. First spectrala second registration phase where the FODs are directly registered while reorienting the FO


ED P

RO

OF

to the orientations of both. Because of this sensitivity, during the de-mons optimization process, we reorient the moving image, using the fi-nite strain reorientation scheme (Alexander et al., 2001), when applyingthe transformation at the current iteration. It may be noted that our reg-istration algorithm can be replaced by similar HARDI based registrationtechniques (Geng et al., 2011; Raffelt et al., 2011; Yap et al., 2011).

Following spatial normalization, each subject's FOD image hasbeen registered into the same spatial coordinate system allowingthe computation of the average FOD image for the population aswell as the covariance matrix computation for the FOD coefficients.This average is obtained by averaging each RSH coefficient indepen-dently, which equates to the geometric mean performed in the RSHspace. These mean and covariance images can serve both as aregistration target for newly acquired subjects, as well as a simplefirst level analysis for identifying strong acute WM abnormalitiessuch as lesions.

White matter parcellation

The process of parcellating the WM volume into spatially homoge-nous regions begins with the population average FOD image, as well asa binary image mask indicating which voxels consist of whitematter tissue. Regions are then determined by using a spatially coherentnormalized cuts algorithm (Bloy et al., 2011a, 2011b) to cluster theWMvolume. The algorithm, based on the superpixel (Mori, 2005) methodol-ogy, works by iteratively dividing the most heterogeneous region intospatially connected parts until each of the resultant regions meet ahomogeneity criterion. A region's heterogeneity (Φ(R)) is representedby the average squared distance between the mean FOD (μ) and theFOD (fi) of every voxel in the region.

Φ Rð Þ ¼ 1n∑i∈R

tfi−μt2L2:

This measure is related to the normalized trace of the FOD covari-ance matrix, and can therefore be interpreted similar to a variance.

The white matter volume is initially divided into a collection ofregions, C, using a seed growing algorithm (Appendix C) to identify

power features are computed and registered. This registration is then improved duringD at each iteration.



T

278

279

280

281

282

283

284

285

286

287288289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397


UNCO

RREC

any spatially disconnected components. From C we choose the regionof the highest heterogeneity (Φ(R)), which is then bipartitioned usingthe normalized cuts (N-cut) algorithm, discussed in Appendix B. TheN-cut algorithm is mediated by the chosen form of the similarityfunction (k(xi,xj)). In this work we measure the similarity betweentwo white matter voxels, with FODs and spatial locations given by fiand pi, using a product of a Gaussian kernel over the normalizedFOD domain (standard deviation σf) and a Gaussian kernel (standarddeviation σs) over the voxels' spatial locations.

k xi; xj� �

¼ etfi−fjt

2L2

2σf etpi−pjt

2L2

2σs :

The seed growing algorithm is then applied to each of the resultantregions, dividing any region that contains spatially disconnected com-ponents. Thus at each iteration, the region with the highest degree ofnon uniformity is replaced by spatially compact sub-regions. Thisprocess is repeated until every region has heterogeneity below apredefined threshold (ϵ). In order to control the generation ofexceedingly small regions (b5 voxels) that may be occasionally created,we apply a post processing step that identifies small regions andcombines them with the neighboring region with the most similarmean FOD.

At the completion of automated clustering routine, theWMvolume isdivided into regions that have a degree of heterogeneity, asmeasured viathe FODs, below the prescribed threshold. The boundaries of theseregions are determined by the HARDI FOD contrast that is availablewithin the data itself and thus takes full advantage of the contrastavailable from the HARDI.

Anatomical labeling

It is advantageous, for instance when interpreting the location ofabnormalities, to know the anatomical label of a specific region. Thisrequires the additional step of labeling each of these data defined ROIswith anatomical labels provided by a co-registered anatomical atlas. Weaccomplish this by using an existing WM anatomical atlas, for instancethe ICBM-DTI-81 (Mori et al., 2008) or EVE-DTI atlases, to provideanatomical labels to each of the homogeneous WM regions that wedetermine. This is accomplished by using non-linear registration tospatially normalize the atlas' structural image to the population averagestructural image. The percent overlap between each WM region and theexisting anatomical atlas regions is computed. For each WM region anyanatomical label with greater than a 10% overlap is assigned to that WMregion allowing for the possibility of multiple anatomical labels beingassigned to regions that span the boundaries of anatomically definedregions.

The final result of the entire parcellation algorithm is a hierarchicaltwo level white matter atlas. Each white matter voxel is first assigneda label representing which data driven ROI it belongs to. Secondlyeach of these ROIs is assigned a combination of anatomical labelsbased on the regional overlap to an existing anatomical atlas. Thefiner data driven ROIs are designed to consist of homogenous WM, asmeasured by a low FOD variance and may be useful for statisticalanalysis or to extract regional features to comprehensively represent asubject'sWM architecture. The anatomical labels provide a more globalanatomical context to each ROI allowing both the location and in somecases function of each ROI to be ascertained and communicated to otherresearchers.

Results: development of a population atlas (an illustrative example)

The problemof atlas generation or region of interest (ROI) delineationoccurs in any population study where regional imaging measures servefor the basis of group comparison, such as ROI statistical analysis orsubject based classification. The problem is however most acute when


ED P

RO

OF

new imaging modalities, such as HARDI, are being utilized (for whichno anatomical atlases exist) or when the population under study hasnot been used for generating atlases previously (such as in a youngerpopulation). For this reason, we illustrate the application of our WMatlas generation framework by creating a population atlas from a datasetof typically developing adolescent and preadolescent healthy subjects (6–18 years). This specific population is of interest to manyWM researchersinvolved in studies of younger populations at varying developmentalstages, specifically those studying autism spectrum disorder andschizophrenia,which are believed to effectWMarchitecture anddevelop-ment (Kubicki et al., 2007; Verhoeven et al., 2010). This is an illustrativeatlas, and may need to be regenerated with a larger sample size, or tosuit specific clinical purposes.

Imaging dataset

The dataset consisted of 23 typically developing children (TDC)between the ages of 6 and 18 years (mean 11.2±2.7 years). All partici-pants were carefully screened, using parent report questionnaires anda telephone interview, to insure that they did not have a history ofcurrent or prior neuropsychiatric symptomatology. Moreover, T1weighted brain images were evaluated clinically by a board certifiedneuroradiologist and all participants in this study were found to becompletely anomaly free. For each subject a whole brain HARDI datasetwas acquired using a Siemens 3TVerio™MRI scanner using amonopolarStejskal-Tanner diffusion weighted spin-echo, echo-planar imaging se-quence (TR/TE=14.7 s/110 ms, 2 mm isotropic voxels, b=3000s/mm2, number of diffusion directions=64, 2 b0 images, scan time18 min). In order to facilitate tissue segmentation as well the coregistra-tion with an existing atlas lacking a HARDI component, such as the EVE-DTI or the ICBM-152, a structural image was acquired, using an MP-RAGE imaging sequence (TR/TE/TI=19 s/2.54 ms/0.9 s, 0.8 mm inplane resolution, 0.9 mm slice thickness).

DW-MRI and structural preprocessing

Prior to computing the FOD image from each subject's DW-MRIimage a number of preprocessing steps were performed in order toreduce imaging artifacts and improve signal to noise. First, the DW-MRIimages were filtered using a joint linear minimum mean squared errorfilter to remove Rician noise (Tristán-Vega and Aja-Fernández, 2010).This was followed by eddy current and motion correctionperformed via the affine registration of each DW-MRI volume to thenon diffusion-weighted (b0) image (Jezzard et al., 1998). The normalizedFOD image for each subject was then computed using theconstrained spherical deconvolution method (Tournier et al., 2007) andnormalized to have unit integral.

Using each subject's structural MP-RAGE image, their white mattersegmentation was determined by the following procedure. Skull-strip-ping and bias field correction were performed using the BET (Smith,2002) tool andN3 bias correction (Sled et al., 1998). Tissue segmentationwas then performed, to identify cerebrospinal fluid, gray and whitematter voxels, using an adaptive K-means clustering (Pham and Prince,1999). A rigid body registration, between the b0 image and the biascorrected structural image was performed. Using this deformationfield, the white matter segmentation mask was then resampled intothe diffusion space yielding a white matter segmentation mask foreach subject.

Registration

The FOD image of each subject was then non-linearly registered tothat of a 12 year old male, who was chosen to serve as the templatesubject. An affine registration between the b0 images, was performedusing the FLIRT (Jenkinson and Smith, 2001) software tool. Thistransformation was then used to initialize the two phase registration



T

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414415416417418

419

420

421

422Q8423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492


CO

RREC

method described in the section Creating a population average FODimage. Once this process was completed for each of the 23 subjects, apopulation average FOD image was computed by averaging each RSHcomponent of the registered subject FOD images individually. Usingthe computed deformation fields, each subject's WM segmentationmask was deformed into the template coordinate frame and then aver-aged and thresholded to yield a binary mask describing the voxels thatwere considered WM in over 40% of the subjects. These 2 images, thepopulation average FOD image and the population WM mask are thenused to determine the atlas regions.

The benefits of using nonlinear spatial registration to determine thepopulation template image, as opposed to affine registration used inseveral of the existing population atlases (Mazziotta et al., 1995; Moriet al., 2008), are illustrated through a marked decrease in the voxelwiseFOD variance across the sample. The FOD variance at a voxel, x, is deter-

mined by v xð Þ ¼ 1n∑

itfi−μt2

L2. Variance maps computed following the

affine registration (Panel A) and our registration method (Panel B) areshown in Fig. 2. These results show a global decrease in the FOD variancewhile drastically reducing the variance in key central WM regions,indicating a clear benefit from using the non-linear registrationalgorithm.

Region delineation

The key aspect of our atlas generation framework is the methoddescribed in the White matter parcellation section used to delineateregions of spatially homogeneous WM. Our automated WM parcella-tion method was applied using the population average FOD image tomodel the WM architecture and using the population WM mask toidentify WM voxels.

An investigation of the parameters used to define theWM similaritykernel, σf and σs, as well as the stopping variance threshold, ϵ, wasperformed. Adjusting theσf andσs parameters had the expected behav-ior of controlling the spatial smoothness of the determined regions.Similar results, in terms of both the number of regions, average regionsize, and average regional FOD variance were found when varying σf

in the 0.1–0.3 range and σs in the 6 mm–10 mm range. Adjusting ϵhas themost direct effect on the resulting parcellations as it determinesat what point the subdivision process is halted. Fig. 3 shows the resultsof our method as ϵ is changed between 0.06 and 0.1. As ϵ is decreasedthere is a clear decrease in the regional variance as well as an increasein the number of regions determined, resulting in a coarser regionaldelineation. This relationship, between the achieved regional varianceand the number of regions, suggests that in practice this parametermust be tailored to the population under study as well as to theintended use of the derived atlas regions.

Based on these results, two atlases were generated. A coarse atlaswas generated using the parameters σs=6mm, σf=0.3 and ϵ=0.15while the finer atlases used a lower halting threshold of ϵ=0.08. Theiterative nature of the parcellation algorithm yields a hierarchical

UN

A

Fig. 2. Effect of registration on lowering voxelwise population FOD variance. FOD variance mfocal decrease in population variance clearly demonstrates the importance of using the non


ED P

RO

OF

relationship between these atlases, with the ϵ=0.15 regions beingsupersets of the ϵ=0.08 regions. The finer atlas consists of 379 spatiallycompact regionswith an average regional size of 105 2 mm3 voxels anda mean regional FOD variance of 0.06, while the coarse atlas consists of94 regionswith an average regional size of 423 2 mm3 voxels andmeanregional FOD variance of 0.10. Representative coronal slices of thecoarse and fine atlases are shown in Fig. 4. The rough bilateral symme-try of the regions is clearly visible in the coarse atlas, while at the finerscale the bilaterality is less apparent particularly in complex WMregions. Fig. 5 shows representative slices of the finer atlas andcorresponding regional FOD variance maps. The orientation sensitiveaspect of the similarity kernel groups voxels with similar orientation,as seen in the genu and spleniumof the corpus callosum,while sensitiv-ity to the WM complexity aids in parcellating the cortical WM.

Comparison with anatomical atlas defined regions

Weutilized the EVE-DTI atlas to create an anatomicalWMparcellationthat would be used both as a comparison as well as to provide our datadefined regions with anatomical context as described in the Anatomicallabeling section. This was achieved by using a nonlinear spatial normali-zation algorithm to transform the structural, T1weighted image providedas part of the EVE-DTI atlas into the space defined by the group averageT1-weighed image (T1-weighted images were used for registration asthis was the common modality between the HARDI population and theDTI anatomical atlas). Using this deformation field, the anatomical labelsprovided by the EVE-DTI atlas were then transformed into the templatespace yielding an alternative parcellation. Fig. 6 shows a comparisonbetween the population atlases, generated using ϵ=0.15 and ϵ=0.08,and the anatomical regions inherited from the EVE-DTI atlas. A clearimprovement in regional FOD variance is achieved using the ϵ=0.15data driven atlas regions, with a further improvement at the expense ofgenerating a moderately larger number of regions when using the fineratlas (ϵ=0.08).

Discussion

We have proposed an automated atlas building method that utilizesHARDI data and the FOD diffusion model to provide improved contrastin complex WM regions using a non-linear spatial normalization tomore accurately determine spatial correspondence and a novel data-drivenWMparcellation algorithm that allows automated regional label-ing based on models of the local WM architecture as opposed to thetraditional time consuming anatomical labeling. The automatic natureof these methods permits researchers to generate their own atlasbased on thedatasets of their specific study. This overcomesmany issuesthat occur when attempting to use published atlases, such as differentclinical populations (ages) or imaging protocols being utilized to gener-ate the atlas.

Similar to the cytoarchitectural mapping of the brain (Brodmann,1909), where local variations in cell type are used to delineate cortical

B

aps are shown for affine (A) and non-linear registration (B) methods. The global and-linear registration algorithm for atlas generation.



T

OO

F

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

541

542

543

544

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

100

200

300

400

500

600

700

800

ε=0.6 ε=0.8 ε=0.1

Number Regions Regional Variance

Fig. 3. As the stopping variance threshold, ϵ, is decreased, the expected decrease in the regional FOD variance is seen. This decrease coincides with an increase in the number ofregions as well as an increase in the coarseness of the parcellation results.


ORREC

regions, our method uses the FOD as a non-invasive imaging measureof local tissue architecture to delineate WM regions. Through the ap-plication of this methodology to the problem of generating an agespecific population atlas, adolescent and preadolescent healthysubjects in our case, we show that these regions are more homoge-nous, with respect to WM orientation and complexity, than theregions inherited from an existing DTI based anatomical atlas. Thissuggests that these regions are better suited for regional statisticalanalysis or the extraction of regional features of WM architecture tobe used in subsequent applications such as pattern classification andare thus perhaps more faithful to the overall goal of identifyingregions of biological homogeneity.

The generation of the illustrativeWMatlas shows that both the spatialnormalization and WM parcellation methods outperform the typicalprocessing methods that are generally utilized for determining WMatlases. A comparison of voxel wise population variance maps, Fig. 2,generated from the non-linear and affine registration shows the clearimprovement in both global and focal variances when using the non-linear registration technique. This decrease in FOD variance is critical forthe accurate computation of the population average FOD image and thestability of the final atlas regions. Similarly, a comparison between theanatomical regions of the EVE-DTI atlas and those determined by ourmethod, shown in Fig. 5, indicates the benefit of using data-driven regionsto represent local WM architecture, through the marked decrease inregional FOD variance. This decrease suggests that the data determinedregions are more tightly related to the local WM anatomy, which may

UNC

A

Fig. 4. The general anatomical bilateral symmetry is apparent in the atlas regions. At a highregions obtained using a lower stopping variance of ε=0.08 (B) where the division of compthe two regions circled in panel B correspond to a single contralateral region.


ED P

Rhave significant benefits when examining clinical populations (e.g.,schizophrenia, autism spectrum disorder). While bilateral symmetry isnot considered in the region delineation process, the roughly bilateral na-ture of WM anatomy is still clearly apparent in the data defined regions,shown in Fig. 4, particularly at the coarser spatial scalars.

The proposed framework provides three parameters which affectthe regions that are determined. Of these three, the stoppingcriterion, ε, has the most pronounced affect, seen in Fig. 3, on boththe number of regions determined and, more significantly, theregional FOD variances of these regions. The other 2 parameters, σs

and σf, determine the kernels used in the similarity functions, affectingthe smoothness of the ROIs, in the spatial and feature domain and inturn, the number and size of the resulting regions but had little effecton the regional FOD variance of the regions. In practice, selection of εshould be based on the desired degree of uniformity required for theregions while the other parameters are best set based on qualitative as-sessment of the resulting atlas. This process need only be done once fora new population and requires little effort particularly when comparedwith the process of manually correcting anatomical regions.

The stability of the clustering, in terms of specific boundarylocations, is mainly governed by the robustness of the populationaverage. For this reason it is important to ensure that a sufficientnumber of subjects are used to make up the population average. If thisnumber is suitably large the effect of additional subjects on the popula-tion average and thus on the parcellation results will be negligible. Inpractice, the study specific atlas is generated when the study is ready

B

er stopping variance of ε=0.15 (A), this symmetry is more apparent than in the finerlex regions is more heavily influence by the local characteristics of the data. For instance



T

545

546

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

607

608

609

610

611612613614615616

617618619

620

621

622623

624625626

627628629

630

631

632

633

A B

Fig. 5. Population atlas generated from 23 young adolescents generated using the parameters σs=6mm, σf=0.3 and =0.08. Representative slices are shown of the label mapindentifing homogenous WM regions (A) and the corresponding FOD variance (B) images.


UNCO

RREC

for a statistical analysis. The atlas is created once, using the sample sizedetermined by the study's power calculations, and reflects the local var-iation in the specific dataset.

While the focus of this work has been on the delineating homogenousWM regions, the ability to include global anatomical information into theregions is also important. This anatomical information not only improvesthe interpretation of any subsequent results by providing anatomical con-text to the regions, aiding in hypothesis formulation, but also facilitatesmeta-analytic studies by utilizing existing anatomical terminology. Inour case we have used the EVE-DTI WM atlas to impart this globalinformation; however, any anatomical atlas can, in principle, be used inthe method. For instance, as developmental studies progress, theinclusion of pediatric anatomical and functional atlases can be incorporat-ed for various ages. The ability to assign domain specific labels, eitherfunctional or otherwise, to the WM regions determined by our methodyields a multi-faceted approach to atlas creation, giving researcherstremendous flexibility concerning the information content available inthe atlas, which will prove extremely useful as research protocols movetoward utilizing multiple modalities.

The fact that this paper describes an atlas generation methodology asopposed to simply the description of a single population HARDI atlas, likethe ICBM-DTI-81 (Mori et al., 2008), is indicative of our belief that optimalresults from a group study are obtained when the specific traits of thepopulation anddata are utilized.Whilewehave focused onWM,develop-ing novel clustering methods based on the state of the art modeling ofWM architecture, the central theme of his work is applicable to manyother atlas building problems. For instance gray matter regions could beparcellated based on their structural and functional connectivity profiles,ostensibly generating regions that more closely respect the structure/function relationship within the population understudy.

It is important to note thatwhile themethod presented in this papermakes use of high b-value (3000 s/mm2) HARDI data, the principles ofthe clustering algorithm can be extended to other diffusion modelsand other b-values. A method that makes use of the diffusion tensormodel acquired on lower b-value data is currently under development.While such a method will prove useful to many researchers, as DTI isnow routinely acquired, it is still unclear how parcellations generatedfrom DTI will compare with those generated using HARDI. It is similarlyunclear exactly how large a role the improved angular resolving powergarnered from high b-value HARDI data plays in the WM parcellation.Based on the improvements of modeling complex WM regions usingHARDI data models at higher b-values onemight expect better delinea-tion in regions of fiber crossing etc. However the definitive comparisonwill have to wait until a technically-suitable dataset consisting of bothHARDI and DTI data has been acquired on the same subjects.

In conclusion this paper presents a methodology for creating HARDIwhite matter atlases using the fiber orientation distribution (FOD) diffu-sion model. The automated nature of the methods allows for their effi-cient application to any population without relying on the timeconsuming task of manual anatomical delineation. The resulting atlasconsists of regions designed to be homogenous with respect to the


ED P

RO

OFlocal architecture of the WM and are thus ideally suited for either statis-

tical analysis or to be used as features within a pattern classificationframework.

Acknowledgments

This research was supported by the NIH grants T32-EB000814(LB), R01-MH079938 (RV), R01-MH092862 (RV), R01-DC008871(TR), a grant from the Nancy Lurie Marks Family Foundation (TR)and the Center grant SAP#4100047863 (RS). Dr Roberts would liketo thank the Oberkircher Family for the Oberkircher Family Chair inPediatric Radiology.

Appendix A. Multichannel diffeomorphic demons

Given afixed andmoving image, F andM, the diffeomorphic demonsalgorithm seeks to determine a correction to the current transforma-tion, s, of the form exp(u). This update minimizes a global energy func-

tional, Es uð Þ ¼ ∑p∈Ω

tF pð Þ−M∘s∘exp u pð Þð ÞtL2

2 þ σiσx

� �2tut2, where p are

points in Ω, the domain of the fixed image, F. The σiσx

term accounts forimage noise and interpolation error and acts as a regularizer for deter-mining the update field. We can linearize the image similarity term inthe region of u=0 as F(p)−M ∘s∘exp(u(p))=F(p)−M∘s(p)+ Jpu andin the casewhere F andM are images of vectors, Jp is the Jacobianmatrix.With this linearization the energy functional simplifies to

Es uð Þ ¼ ∑p∈Ωt F pð Þ−M∘s pð Þ

0

þ

Jpσi

σxI

24

35u pð ÞtL2

2:

If wemake the assumption that the voxels are independent, whichis not strictly true when performing reorientations, the optimizationof Es(u) can be broken up in to individual equations for each point p.

Jtp Jp þσi

σxI

� �u pð Þ ¼ −Jtp F pð Þ−M∘s pð Þð Þ

yielding update step

u pð Þ ¼ − Jtp Jp þσi

σxI

� �−1Jtp F pð Þ−M∘s pð Þð Þ:

We use the symmetric Jp ¼ − Jp Fð ÞþJp M∘sð Þ2 computation of the Jacobi-

an, where Jp (F) and Jp (M s) are the Jacobians of the fixed and de-formed moving images at the point p. Each iteration of thediffeomorphic demons method can summarized as follows

1. compute an update step u2. smooth u with a Gaussian filter3. s← s ° u4. Deform the moving image using s



T

OF

634

635

636

637

638

639

640

641

642

643

644

645

646

647

648

649

650

651

652653654655656

657

658

659

660

661662663

664

665

666

667668669

670

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689

690

691

692

693

694

695

696

697698699700701702703704705706707708709 Q9710711712713714715716717

EveData Defined

(ε=0.15)Data Defined

(ε=0.08)Number of

Regions127 94 379

Variance0.12 0.10 0.06

Max RegionalVariance

0.30 0.15 0.08

Mean Regional

A

B

Fig. 6. Representative slices of the EVE-DTI atlas' anatomically defined regions and their corresponding regional FOD variances are shown in panel A, compared with the datadefined WM regions generated using two stopping variances ε=0.15 and 0.08. The EVE-DTI anatomical regions are conspicuously more heterogeneous, indicated by high regionalvariance, even in central WM areas. A table listing characteristics of each parcellation is shown in panel B.


UNCO

RREC

5. Apply reorientation if needed

This process is repeated until the update steps no longer substantiallyreduce the image difference. The deformation field s is then applied tothe moving image resulting in the final deformed subject image.

Appendix B. Spatially coherent normalized cuts

The normalized cuts (N-cut) algorithm (Shi and Malik, 2000;Rahimi and Recht, 2004) is a means of partitioning a set of data pointsx, in our case a set of white matter voxels, based on a providedsimilarity measure k(x, y). Using the similarity measure we build anaffinity matrix such that Ki,j=k(xi, xj). The affinity matrix describesthe weights of a fully connected undirected graph using x as thenodes. The N-cut algorithm labels each node dividing the verticesinto 2 sets A and B. The cost Cut(A, B) is the sum of all connectionsbetween elements of A and elements of B. The goal is to find thelabeling that minimizes the normalized cut, Cut(A, B)/(Vol(A)+Vol(B)) where Vol() is the sum of the weights within a set.

The labeling is found via a relaxation to the above problem byfinding the second largest eigenvector, v, of the matrix D−1

2KD−12.

Where D is a diagonal matrix whose iith element is the sum of allelements in the ith row of K. The labels are determined by examiningthe sign of v. For a more complete discussion please see Rahimi andRecht (2004).

Our application of the N-cut algorithm concerns the ability to labelWM voxels based on their FOD. As discussed above we use a productof two Gaussian kernels with standard deviations of σf and σs as thebasis of our similarity measure yielding the following similarity mea-sure:

kðxi; xjÞ ¼e‖ fi−fj‖

2L2

2σ2f e

‖ pi−pj‖2

2σ2s

where xi and xj are WM voxels with fi, fj, pi, and pj being the corre-sponding FODs and spatial locations.

Given a collection of WM voxels we compute the affinity matrix Kusing the above similarity function. The matrix D is then computedand the second largest eigenvector, v, of D−1

2KD−12 is determined

using the SLEPc (Hernandez et al., 2005) software package. Twonew regions are then determined based on the sign of v.

These two regions are then input into a simple seed growing algo-rithm (described in Appendix C) which divides them into their spa-tially disconnected subregions yielding a set of spatially connectedregions from the single region with high variance.


ED P

ROAppendix C. Seed growing algorithm

A seed growing algorithm is used to divide a supplied region intospatially disconnected subcomponents. This insures that each of thefinal resulting regions is fully spatially connected. The algorithm issupplied with a list of voxels, X, comprising the region to be dividedand returns a list of labels, L, which identify which connected sub-component each voxel is a member of. The mechanics of the algo-rithm are shown below:

Input: list of voxels, XOutput: list of labels, L

labelValue=1labelMembers=∅for all x in X do

if x is not labeled thenadd x labelMembersrepeat

y=next element of labelMembersL[y]=labelValueAdd all unlabeled neighbors to labelMembers

Until all members of labelMembers have been visitedlabelValue=labelValue+1labelMembers=∅

References

Alexander, A.L., Lee, J.E., et al., 2007. Diffusion tensor imaging of the corpus callosum inautism. Neuroimage 34 (1), 61–73.

Alexander, D.C., Pierpaoli, C., et al., 2001. Spatial transformations of diffusion tensormagnetic resonance images. IEEE Trans. Med. Imaging 20 (11), 1131–1139.

Anderson, A.W., 2005. Measurement of fiber orientation distributions using high angularresolution diffusion imaging. Magn. Reson. Med. 54 (5), 1194–1206.

Ashburner, J., 2009. Computational anatomy with the SPM software. Magn. Reson. Imaging27 (8), 1163–1174.

Basser, P.J., Mattiello, J., et al., 1994. Estimation of the effective self-diffusion tensorfrom the NMR spin echo. J. Magn. Reson. B 103 (3), 247–254.

Bloy, L., Ingalhalikar, M., et al., 2011a. HARDI based pattern classifiers for the identificationof white matter pathologies. Med. Image Comput. Comput. Assist. Interv. Int. Conf.Med. Image Comput. Comput. Assist. Interv.

Bloy, L., Ingalhalikar, M., et al., 2011b. Neuronal white matter parcellation using spatiallycoherent normalized cuts. Proc. IEEE Int Biomedical Imaging: From Nano to MacroSymp.

Bloy, L., Verma, R., 2010. Demons registration of high angular resolution diffusion images.Proc. IEEE Int Biomedical Imaging: From Nano to Macro Symp.

Brodmann, K., 1909. Vergleichende Lokalisationslehre der Grosshirnrinde in ihrenPrinzipien dargestellt auf Grund des Zellenbaues. Johann Ambrosius Barth Verlag,Leipzig.



T

718719720721722723724725726727728729730731732733734735736737738739740

Q10742743744745746747748749750751752753754755756757758759760761762763764765

Q11

767768769770771772773774775776777778779780781782783784785786787788789790791792793794795796797798799800801802803804805806807808809810811812813814815

817


C

Collins, D.L., Holmes, C.J., et al., 1995. Automatic 3-D model-based neuroanatomicalsegmentation. Hum. Brain Mapp. 3 (3), 190–208.

Descoteaux, M., Angelino, E., et al., 2007. Regularized, fast, and robust analytical Q-ballimaging. Magn. Reson. Med. 58 (3), 497–510.

Edmonds, A.R., 1960. Angular Momentum in QuantumMechanics. Princeton UniversityPress.

Fletcher, P.T.,Whitaker, R.T., et al., 2010.Microstructural connectivity of the arcuate fascic-ulus in adolescents with high-functioning autism. Neuroimage 51 (3), 1117–1125.

Frank, L.R., 2002. Characterization of anisotropy in high angular resolution diffusion-weighted MRI. Magn. Reson. Med. 47 (6), 1083–1099.

Geng, X., Ross, T.J., et al., 2011. Diffeomorphic image registration of diffusion MRI usingspherical harmonics. IEEE Trans. Med. Imaging 30 (3), 747–758.

Green, R., 2003. Spherical harmonic lighting: The gritty details. Archives of the GameDevelopers Conference.

Hamm, J., Ye, D.H., et al., 2010. GRAM: a framework for geodesic registration on anatomicalmanifolds. Med. Image Anal. 14 (5), 633–642.

Hecke, W.V., Leemans, A., et al., 2011. The effect of template selection on diffusion ten-sor voxel-based analysis results. Neuroimage 55 (2), 566–573.

Hecke,W.V., Sijbers, J., et al., 2008. On the construction of an inter-subject diffusion tensormagnetic resonance atlas of the healthy human brain. Neuroimage 43 (1), 69–80.

Hernandez, V., Roman, J.E., et al., 2005. SLEPc: a scalable andflexible toolkit for the solutionof eigenvalue problems. ACM Trans. Math. Softw. 31 (3), 351–362.

Ingalhalikar,M., Parker, D., et al., 2011. Diffusion based abnormalitymarkers of pathology:toward learned diagnostic prediction of ASD. Neuroimage.

Jenkinson, M., Smith, S., 2001. A global optimisation method for robust affine registrationof brain images. Med. Image Anal. 5 (2), 143–156.

Jezzard, P., Barnett, A.S., et al., 1998. Characterization of and correction for eddy currentartifacts in echo planar diffusion imaging. Magn. Reson. Med. 39 (5), 801–812.

Kubicki, M., McCarley, R., et al., 2007. A review of diffusion tensor imaging studies inschizophrenia. J. Psychiatr. Res. 41 (1–2), 15–30.

Kubicki, M.,Westin, C.F., et al., 2002. Uncinate fasciculus findings in schizophrenia: amag-netic resonance diffusion tensor imaging study. Am. J. Psychiatry 159 (5), 813–820.

Lancaster, J.L., Tordesillas-Gutierrez, D., et al., 2007. Bias between MNI and Talairachcoordinates analyzed using the ICBM-152 brain template. Hum. Brain Mapp. 28(11), 1194–1205.

Lancaster, J.L., Woldorff, M.G., et al., 2000. Automated Talairach atlas labels for functionalbrain mapping. Hum. Brain Mapp. 10 (3), 120–131.

Lee, J.E., Bigler, E.D., et al., 2007. Diffusion tensor imaging of white matter in the superiortemporal gyrus and temporal stem in autism. Neurosci. Lett. 424 (2), 127–132.

Mazziotta, J., Toga, A., et al., 2001. A probabilistic atlas and reference system for thehuman brain: International Consortium for Brain Mapping (ICBM). Philos. Trans.R. Soc. Lond. B Biol. Sci. 356 (1412), 1293–1322.

Mazziotta, J.C., Toga, A.W., et al., 1995. A probabilistic atlas of the human brain: theoryand rationale for its development. The International Consortium for Brain Mapping(ICBM). Neuroimage 2 (2), 89–101.

Mori, G., 2005. Guiding model search using segmentation. IEEE Int.Conf. Comp. Vis. 2,1417–1423.

Mori, S., Oishi, K., et al., 2008. Stereotaxic white matter atlas based on diffusion tensorimaging in an ICBM template. Neuroimage 40 (2), 570–582.

UNCO

RR

816


ED P

RO

OF

Moseley, M.E., Cohen, Y., et al., 1990. Diffusion-weighted MR imaging of aniso-tropic water diffusion in cat central nervous system. Radiology 176 (2),439–445.

Oishi, K., Faria, A., et al., 2009. Atlas-based whole brain white matter analysisusing large deformation diffeomorphic metric mapping: application to nor-mal elderly and Alzheimer's disease participants. Neuroimage 46 (2),486–499.

Pham, D.L., Prince, J.L., 1999. Adaptive fuzzy segmentation of magnetic resonance images.IEEE Trans. Med. Imaging 18 (9), 737–752.

Raffelt, D., Tournier, J.D., et al., 2011. Symmetric diffeomorphic registrationoffibre orientationdistributions. Neuroimage 56 (3), 1171–1180.

Rahimi, A., Recht, B., 2004. Clustering with normalized cuts is clusteringwith a hyperplane.Statistical Learning in Computer Vision. .

Shi, J.B., Malik, J., 2000. Normalized cuts and image segmentation. IEEE Trans. PatternAnal. Mach. Intell. 22 (8), 888–905.

Sled, J.G., Zijdenbos, A.P., et al., 1998. A nonparametric method for automatic correc-tion of intensity nonuniformity in MRI data. IEEE Trans. Med. Imaging 17 (1),87–97.

Smith, S.M., 2002. Fast robust automated brain extraction. Hum. Brain Mapp. 17 (3),143–155.

Talairach, J., 1988. Co-Planar Stereotaxic Atlas of the Human Brain: 3-D ProportionalSystem: An Approach to Cerebral Imaging. Thieme, New York.

Thirion, J.P., 1998. Image matching as a diffusion process: an analogy with Maxwell'sdemons. Med. Image Anal. 2 (3), 243–260.

Toga, A.W., Thompson, P.M., et al., 2006. Towards multimodal atlases of the humanbrain. Nat. Rev. Neurosci. 7 (12), 952–966.

Tournier, J.D., Calamante, F., et al., 2007. Robust determination of the fibre orientationdistribution in diffusion MRI: non-negativity constrained super-resolved sphericaldeconvolution. Neuroimage 35 (4), 1459–1472.

Tournier, J.D., Calamante, F., et al., 2004. Direct estimation of the fiber orientation densityfunction fromdiffusion-weightedMRI data using spherical deconvolution.Neuroimage23 (3), 1176–1185.

Tristán-Vega, A., Aja-Fernández, S., 2010. DWI filtering using joint information for DTIand HARDI. Med. Image Anal. 14 (2), 205–218.

Tuch, D.S., 2004. Q-ball imaging. Magn. Reson. Med. 52 (6), 1358–1372.Vercauteren, T., Pennec, X., et al., 2009. Diffeomorphic demons: efficient non-parametric

image registration. Neuroimage 45 (1 Suppl), S61–S72.Verhoeven, J.S., De Cock, P., et al., 2010. Neuroimaging of autism. Neuroradiology 52

(1), 3–14.Wakana, S., Jiang, H., et al., 2004. Fiber tract-based atlas of human white matter anatomy.

Radiology 230 (1), 77–87.Wigner, E.P., 1931. Gruppentheorie und ihre Anwendungen auf die Quantenmechanik

der Atomspektren. Vieweg Verlag, Braunschweig.Yap, P.T., Chen, Y., et al., 2011. SPHERE: spherical harmonic elastic registration of

HARDI data. Neuroimage 55 (2), 545–556.Zhang, H., Avants, B.B., et al., 2007. High-dimensional spatial normalization of diffusion

tensor images improves the detection of white matter differences: an examplestudy using amyotrophic lateral sclerosis. IEEE Trans. Med. Imaging 26 (11),1585–1597.
E


white matter atlas generation using hardi based automated ... · oof 1 white matter atlas...

Documents