Comparison of Spatial Normalization Procedures and Their Impact On

᭜HumanBrainMapping16:228–250(2002)᭜

ComparisonofSpatialNormalization ProceduresandTheirImpacton FunctionalMaps

FabriceCrivello,1* ThorstenSchormann,2 NathalieTzourio-Mazoyer,1 PerE.Roland,5 KarlZilles,3,4 andBernardM.Mazoyer1,6

1Grouped’ImagerieNeurofonctionnelle,UMR6095,CNRS-CEALRC36VUniversite´deCaen& Paris5,Caen,France 2InstituteofNeuroanatomy,HeinrichHeineUniversity,Du¨sseldorf,Germany 3CecilandOscarVogtInstituteofBrainResearch,HeinrichHeineUniversity,Du¨sseldorf,Germany 4InstituteofMedicine,ResearchCentre,Juelich,Germany 5DepartementofNeuroscience,DivisionofHumanBrainResearch,TheKarolinskaInstitute, Stockholm,Sweden 6Unite´IRMCHUdeCaenandInstitutUniversitairedeFrance,Caen,France

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Abstract:Thealignmentaccuracyandimpactonfunctionalmapsoffourspatialnormalizationprocedures havebeencomparedusingasetofhighresolutionbrainMRIsandfunctionalPETvolumesacquiredin 20subjects.Simpleaffine(AFF),fifthorderpolynomialwarp(WRP),discretecosinebasisfunctions(SPM), andamovementmodelbasedonfullmultigrid(FMG)approacheswereappliedonthesamedatasetfor warpingindividualvolumesontotheHumanBrainAtlas(HBA)template.Intersubjectaveragedstruc- turalvolumesandtissueprobabilitymapswerecomparedacrossnormalizationmethodsandtothe standardbrain.Thankstothelargenumberofdegreesoffreedomofthetechnique,FMGwasfoundto provideenhancedalignmentaccuracyascomparedtotheotherthreemethods,bothforthegreyand whitemattertissues;WRPandSPMexhibitedverysimilarperformanceswhereasAFFhadthelowest registrationaccuracy.SPM,however,wasfoundtoperformbetterthantheothermethodsforthe intra-cerebralcerebrospinalfluid(mainlyintheventricularcompartments).Limiteddifferencesinterms ofactivationmorphologyanddetectionsensitivitywerefoundbetweenlowresolutionfunctionalmaps (FWHMϳ10mm)spatiallynormalizedwiththefourmethods,whichoverlappedin42.8%ofthetotal activationvolume.Thesefindingssuggestthatthefunctionalvariabilityismuchlargerthantheanatom- icaloneandthatprecisealignmentofanatomicalfeatureshaslowinfluenceontheresultingintersubject functionalmaps.Whenincreasingthespatialresolutiontoapproximately6mm,however,differencesin localizationofactivatedareasappearasaconsequenceofthedifferentspatialnormalizationprocedure used,restrictingtheoverlapofthenormalizedactivatedvolumestoonly6.2%.Hum.BrainMapping16: 228–250,2002. ©2002Wiley-Liss,Inc.

Keywords:neuroanatomy;spatialnormalization;registration;linearandnonlinearwarping;probability maps;brainatlas

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Contractgrantsponsor:EuropeanUnionBiotechnology;Contract rel,BP5229,14074CaenCedex,France. grantnumber:BT04-CT96-0177. E-mail:[email protected] ThisworkwaspresentedinpartattheﬁfthInternationalConfer- Receivedforpublication17April2001;accepted27March2002 enceonFunctionalMappingoftheHumanBrain,June1999. DOI10.1002/hbm.10047 *Correspondenceto:FabriceCrivello,PhD,Grouped’ImagerieNeu- Publishedonline00Month2002inWileyInterScience(www. rofonctionnelle,UMR6095,GIPCyceron,BoulevardHenriBecque- interscience.wiley.com).

INTRODUCTION though the answer to this question depends on many parameters, including the primary goal of the study, it Spatial normalization is a necessary and crucial step also relies partly on the relative merits of each proce- in the analysis of both structural and functional neu- dure. Interestingly, studies comparing normalization roimaging data because it allows us to bring brain procedures are rather scarce in literature [Fischl et al., volumes acquired in different individuals in a com- 1999; Gee et al., 1997; Grachev et al., 1999; Minoshima mon neuroanatomical reference space. In this refer- et al., 1994; Roland et al., 1997; Senda et al., 1998; ence space, image statistics may be computed over a Sugiura et al., 1999] and have so far dealt with the sample of subjects, and anatomical labeling performed dispersion metric of selected landmarks, spatial ho- in a standardized manner across subjects, studies, and mogeneity of selected anatomical features such as ma- laboratories. Given the large variability between indi- jor sulci, or with overlap percentage of restricted vol- viduals in their brain anatomy, both at the microscopic umes of interest. This is probably due to a natural and macroscopic levels, considerable efforts have been feeling that using a high degree of freedom normal- devoted over the past years to the development of ization approach will obviously surpass the alignment more and more refined spatial normalization proce- accuracy of lowest degree of freedom approaches. If dures. Several such procedures are now available that such differences exist, however, it is important to try perform brain warping with various degrees of accu- to quantify them, particularly in the growing field of racy. The original Talairach linear transformation [Fox statistical neuroanatomy. In the present study, con- et al., 1985] translates, reorients, and normalizes the dimensions of a brain volume to fit it in the so-called ducted as part of the ECHBD project, we performed a Talairach box [Talairach and Tournoux, 1988]. This cross-comparison of four published normalization simple linear procedure has been superseded by non- procedures, using 3D tissue probability maps derived linear ones that aim at a more sophisticated matching from high resolution brain MRI datasets acquired in of the structural characteristics of a given brain vol- 20 subjects and the Human Brain Atlas as a standard ume to a target one, using nonlinear deformations brain [Roland et al., 1994], and inter-subject averaged based on high-order polynomials [Woods et al., 1997a] functional maps derived from the four normalization or discrete cosine basis functions [Ashburner and Fris- methods. ton, 1999]. These nonlinear procedures, although they may lead to considerable deformations, do not, how- MATERIALS AND METHODS ever, change the topology of the brain volume to which they are applied. More recently, a new class of Subjects spatial normalization procedures of a new kind have appeared that aim at realizing a full warp of a brain volume on another one [Christensen et al., 1994; High-resolution MRI brain volumes were collected Ϯ Schormann and Zilles, 1998], or contour/surface- in 20 young healthy volunteers (age: 22.0 2.4, mean Ϯ based alignment that cannot fulfill the purpose of a SD, range: [19,28]) as part of the PET brain activa- full warp because a lot of grey-value information is tion study they participated in. All subjects were free not taken into account [Davatzikos et al., 1996; Fischl from cerebral abnormality as assessed on their brain et al., 1999; Thompson et al., 2000a, 2001]. These are T1-weighted MRI images. The protocol was accepted designed to perform high precision cortical matching by our local ethic committee and all subjects gave their between different brains. As a consequence, these pro- informed written consent. cedures have the power to modify the topology of the original brain volume. MRI data Considering the conceptual differences between these spatial normalization procedures, the issue of which procedure should be chosen to analyze a neu- MRI acquisitions were performed on a 1.5 T Signa roimaging dataset is critical, as it was for the Euro- Horizon LX scanner (General Electric, BUC, France). pean Computerized Human Brain Database (ECHBD) High-resolution T1-weighted MRI volumes were ac- [Fredriksson et al., 2000; Roland and Zilles, 1996], a quired using an inversion recovery SPGR-3D se- consortium of European laboratories that joined ef- quence (TR ϭ 12.4 msec, TE ϭ 2.2 msec, FA ϭ 10°,TI forts to gather cytoarchitectonic, MRI, and functional ϭ 600 msec) sampling the whole subject head in 0.94 maps to study relationships between microscopically ϫ 0.94 ϫ 1.5 mm3 voxels. The image volume was and macroscopically defined functional areas. Al- reconstructed as a 256 ϫ 256 ϫ 124 matrix.

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PET data 1. The classical 12 parameters affine transformation (AFF) as performed by the “alignlinear” routine Using a standard 15O-labeled water PET activation included in the Automated Image Registration protocol, nine sequential measurements of the re- package (AIR 3.0) [Woods et al., 1997b]. gional cerebral blood flow were obtained from each 2. The fifth order, 168 parameters nonlinear poly- subject on an ECAT Exact HR ϩ PET camera and nomial warp algorithm (WRP), also included in reconstructed as a series of 63 contiguous, 2.5-mm- the AIR 3.0 package [Woods et al., 1997b]. thick cross-sectional images, replicating three times a 3. The “linear & nonlinear” combined procedure series of three experimental conditions presented in a implemented in the 1996 version of the Statistical randomized order: 1) listening to a factual story (Story); Parametric Mapping software (SPM) [Ashburner 2) covert generation of the most verbs semantically and Friston, 1999]. related to listening nouns (Verb); and 3) a rest condi- 4. A recently proposed multi grid technique based tion (Rest) that consisted in lying silently in the dark on Navier-Lame´ continuum mechanics theory eyes closed, with no particular instruction except to (FMG) [Schormann and Zilles, 1998], first imple- refrain from moving and avoid a specific mental ac- mented to co-register histological and MRI sec- tivity [Papathanassiou et al., 2000]. All conditions tions [Schormann et al., 1996]. were performed in darkness. During the Verb condi- These four approaches are voxel intensity-based meth- tion, the nouns were delivered through earphones at ods, meaning that they are not driven by shape or any 0.1 Hz and were of common use, most of them refer- model constraint matching, and are all fully automated, ring to objects and some of them to animals. The thereby ensuring an unbiased comparison of their rela- subjects were instructed to covertly retrieve as many tive performances. It must be stressed that the four meth- verbs semantically related to those nouns as possible. ods were used in their original “default setting,” and Three different noun lists were used for each replica- only options essential for a correct utilization of the tion. Only the Verb and Rest conditions were used in algorithms with respect to the characteristics of our MRI this study to compute the Verb minus Rest contrast in datasets were modified. All normalized volumes were the functional comparison part of the study. resliced using tri-linear interpolation and a 1 ϫ 1 ϫ 1 mm3 voxels size. Our method’s modifiable options are Standard anatomical format detailed in the four followings paragraphs. AFF The standard anatomical format used in this study was the MRI standard brain of the Human Brain Atlas This procedure was the only linear transformation [Roland et al., 1994] and of the European Computerized used in this comparison. The 12 parameters models is Human Brain Database [Fredriksson et al., 2000; Roland a superset of the simplest nine parameters registration and Zilles, 1996]. This standard brain is a single young method originally defined by Talairach. In addition to male brain high-resolution T1-weighted MRI volume, the six parameter rigid body rotation and translation, having isotropic millimeter resolution, and a 137 ϫ 181 this model allows independent rescaling parameters ϫ 146 size. This volume was selected from a sample of 21 along three arbitrary chosen coordinate axes of the male brain MRI, as being the most “representative” in reference volume. This procedure does not preserve terms of shape, size, and gyral as well as sulcal pattern. angles and distances but preserves the parallelism of This template was scalp edited, oriented and scaled ac- lines after the transformation has been applied. The cording to the stereotaxic coordinate frame defined by criterion used for aligning two images is referred to as the Talairach atlas [Talairach and Tournoux, 1988]. the ratio image uniformity (RIU) cost function, first introduced by Woods et al. [1992] for intra-subject and Intersubject spatial normalization registration intra-modality alignment. The image is divided by the target image on a voxel-by-voxel basis to create a ratio Before any spatial transformation, each subject MRI image. The uniformity of this ratio image is then mea- scan was semi-automatically segmented to remove the sured by computing the ratio of its standard deviation extra cranial structures (i.e., scalp, skull, and menin- divided by its mean, thereby providing a normalized ges) using our in-house ATOMIA software [Verard et cost function value. The minimization of this criterion al., 1997]. allows the two images to be registered. The “Initial- The 20 MRI volumes were then spatially normalized sampling” parameter was set to 81, controlling how using the following four 3D procedures: densely data was sampled during the first iterative

᭜ 230 ᭜ ᭜ Comparing Spatial Normalization Procedures ᭜ cycle of the algorithm. The “Final-sampling” parame- scribed by 1,536 parameters representing the coeffi- ter was set to 1 meaning that the alignment was cients of the deformations in three orthogonal direc- achieved at the best resolution. Twenty-five iterations tions (83 for each one). Sixteen iterations per cycle were used for each iterative cycle. Final convergence were used. Ϫ threshold was set to 10 5. FMG WRP As for the WRP algorithm, this procedure also starts The initialization step of the complete WRP normal- with the AFF linearly aligned image in our study. The ization procedure consists in applying first the AFF nonlinear part appears as follows: the brain image to method described above so that the linearly aligned be normalized is modelled as an elastic medium by image is the starting step of the WRP algorithm. This applying the principles of Navier-Lame´ continuum nonlinear approach proposed by the same authors has mechanics theory [Schormann et al., 1998; Schormann been established so as to estimate the model parameters and Zilles, 1998]. Then, the theory is extended to a of the spatial transformation in a rapid and reproducible movement model enabling the correction of large spa- manner. This model can be seen as a natural evolution of tial differences. In the elastic model, the resulting de- the classical linear model, bringing it to higher order formation is only a compromise between the internal polynomial warping models. The fifth order polynomial strain of the object and external forces. For this reason, warp algorithm used in the present study has 168 spatial only small deformation can be calculated. In this ap- transformation parameters. The cost function to be min- proach a 3D nonlinear deformation field directly re- imized by the WRP algorithm is the average across vox- sults from the solution of a system of coupled partial els of the squared difference between the resliced and the differential equations describing for each voxel the reference images. An additional parameter is included in unique movement (the spatial deformation) of the in- the cost function to account for global intensity rescaling dividual brain onto the reference volume. In this pro- of the images relative to one another. Initial-sampling cess, the total number of degrees of freedom in one was set to 81 and the final one was set to 9. Fifty itera- direction (x axis) is equal to the total number of voxels tions were used for each iterative cycle. Final conver- in the volume (for example, normalizing a 137 ϫ 181 gence threshold was set to 0.5. ϫ 146 MRI volume generates a deformations field of 10,861,086 parameters). The movement of the source SPM image onto the reference standard brain image is subject to some specific constraints imposed by the con- This approach works by minimizing the average tinuum theory of movement model. In the present across voxels of the squared difference between the vol- approach, the investigation was focused on minimiz- ume to be normalized and a template volume. For the ing computation time by applying an adapted full least-squares registration to produce an unbiased esti- multi grid technique (i.e., a multiresolution descend- mate of the spatial transformation, the intensity contrast ing approach) [Schormann et al., 1996]. Information of both images should be similar. The registration simply and support for the FMG software are available at searches for an optimum solution. The first step of the [email protected]. Note that in one normalization finds the optimum 12 parameters affine case, there was a large grey-value difference between transformation by appropriate weighting of the template both volumes (the template and the volume to nor- voxels. Although this approach does not require scalp malized), which made the FMG approach fail to con- editing that discounts the confounding effects of skull verge, so that the total number of normalized MRI and scalp differences, we have used it on the edited volumes was 20 for the AFF, WRP, and SPM proce- reference brain described above, smoothed with an 8 dures and only 19 for the FMG procedure. mm FWHM isotropic Gaussian kernel to investigate only the effect of the normalization algorithm (because Comparison of spatial normalization procedures this procedure begins with smoothing the images to be normalized by the same Gaussian kernel). The af- To quantify the relative merits of the four spatial fine registration is followed by nonlinear deforma- normalization procedures previously described, we tions defined by linear combinations of 8 ϫ 8 ϫ 83D used the HBA template as a gold standard and com- discrete cosine transform basis functions [Ashburner puted several images and figures of merits. Note that and Friston, 1999; Friston et al., 1995a]. This option brains were scalp edited before spatial normalization. results in each of the deformation fields being de- This is important because the segmentation performed

᭜ 231 ᭜ ᭜ Crivello et al. ᭜ in the subsequent analysis was intensity driven, and different CSF brain masks even after spatial normaliza- using scalp edited brains prevented us to assign, for tion. In the same vein, voxels inside the ventricles or example, meninges to grey matter. Accordingly, only located in the deepness of sulci that were not classified as voxels included into the intra-cerebral volume were CSF, were also assigned to CSF. The lower part of Figure tissue classified. The comparison of the four proce- 1 shows that the segmentation procedure was efficient dures was conducted as follows. First, we derived and provided an adequate tissue classification of the averaged MRI volumes across subjects and visually HBA template although this segmentation algorithm compared them to the HBA template. Then, we per- was originally devoted to segment MRI brain image formed a tissue segmentation on both the template matched to the MNI template. The proportions of each and normalized volumes. The degree of spatial over- tissue class of the HBA template are presented in Table I lap between the template and individual MRI volume and can be compared to that of the MNI template. was quantified for each tissue class (grey matter, white Due to high signal to noise ratio inhomogeneities, matter, and CSF) and for each procedure. Finally, we when applied to our MRI dataset, this segmentation evaluated the impact of differences in spatial normal- procedure failed in one case, this was the case for the ization procedure on functional maps, by applying four normalization used, leading to unreasonable grey these procedures on functional maps that were ob- and white matter masks. Accordingly, the final anal- tained from the same sample of subjects. ysis steps were applied to the 18 subjects for which both the normalization and segmentation procedures Intersubject averaged images have been successfully completed. To globally quantify the relative merits of spatial normalization proce- Realigned MRI images were averaged across sub- dures at the tissue classification level, proportions of jects (n ϭ 19 for the FMG procedure and n ϭ 20 for the grey matter, white matter, and CSF composing the three other ones). For each procedure, the individual intracranial brain volume of each subject MRI were spatially normalized MRI volume was first scaled to computed for each normalization procedure and their its maximum value to normalized the intensity of the differences with corresponding figures for the HBA different MRI volumes. These volumes were then template averaged across subjects. summed across subjects and the resulting voxel values divided by the occurrence of subjects contributing to Tissue probability maps the average at every location. To further document this point, we computed two Tissue segmentation sets of probability images of grey matter, white matter and CSF over the sample of 18 subjects. These proba- The MRI template and individual normalized MRI bility maps indicate for each procedure and for each volumes were tissue classified using the segmentation tissue class, the proportion of subjects overlapping at algorithm included in the SPM99 package. The SPM each voxel location. The first set of probability maps segmentation of each individual normalized MRI is presents only voxels that were correctly classified by based on a clustering algorithm identifying voxel in- the segmentation procedure, taking the tissue classifi- tensities of particular tissue types (grey matter, white cation performed on the HBA template as a gold stan- matters, and CSF), combined with a priori knowledge dard. This means that for a specific tissue of interest, about the spatial distribution of these clusters in nor- the boundaries of the “classified” probability maps are mal subjects [Ashburner and Friston, 1997]. The result- the ones of the corresponding HBA tissue template. ing tissue segmented volumes consist of maps in The second set of probability maps presents the subject which a voxel value is the probability for this voxel to overlap corresponding to voxels that were wrongly clas- belong to the tissue class of interest, ranging from 0 sified (misclassified) with respect to the HBA tissue (low probability) to 255 (high probability). Each tissue template. probability volume was segmented by applying a The qualitative findings of these two set of maps lower threshold set at 128 (50% probability). Voxels were quantified using two 3D global criteria, C(i,j,k) classified as CSF but located outside the outer edge of and M(i,j,k) referring respectively to classified and the cortex were removed using morphological opera- misclassified voxels. tions (see upper part of Fig. 1). The number of such For each spatial normalization procedure (indexed voxels is highly dependent on the parameters em- by i), subject (indexed by j) and tissue class (indexed ployed during the semi-automated scalp edition, by k), we defined Nst(i,j,k) as the total number of voxel which can vary between subjects, leading to slightly of subject j belonging to tissue k of the template by

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Figure 1. A: Original axial section of the SPM segmentation applied to the HBA MRI template. B: Morpho- logically processed slice. This process removes the extra cerebral CSF tissue that remains after the semi-automated scalp edition and ﬁlls-in the ventricles and deepness of the sulci. C: Corre- sponding MRI slice. D: Trans- verse processed sections of the segmentation of the HBA MRI template from ϩ70 to Ϫ40 mm relative to the AC–PC plane. normalization procedure i, N (i,j,k) as the total num- N ͑i,j,k͒ s ͑ ͒ ϭ st ϫ ber of voxel of subject j belonging to tissue k by C i,j,k ͩ ͑ ͒ ͪ 100, Nt k normalization procedure i and Nt(k) as the total number of voxel of the HBA template for tissue k. Misclassified voxels criterion Classified voxels criterion

The percentage of voxels correctly classiﬁed by a The percentage of voxels misclassiﬁed by a normal- normalized-segmented MRI volume with respect to ized-segmented MRI volume with respect to the seg- the segmented template was computed as: mented template was computed as:

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TABLE I. Volumes and proportions of grey matter, meaning that the amount of misclassiﬁed voxels is white matter and CSF of the Human Brain Atlas MRI higher with FMG. template as assessed by the Statistical Parametric Mapping segmentation algorithm* Overall measures of accuracy based on correct Tissue Volume (cm3)% and incorrect classification

Grey matter 861.0 (1016.2) 59.5 (56.8) To assess the relative classification errors of the four White matter 506.7 (560.8) 35.0 (31.3) procedures tested, we computed, for each procedure CSF 78.6 (212.3) 5.5 (11.9) (indexed by i) and subject (indexed by j), the proba- Total 1446.3 (1789.3) 100 (100) bility of Type I and Type II errors for each tissue class * Corresponding figures for the Montreal Neurological Institute (indexed by k). Suppose an image consist of N voxel MRI brain are given in parentheses. classes (here N ϭ 4, because we consider an additional class that contain voxels that were not classified nei- ther in the grey matter, white matter or CSF template N ͑i,j,k͒ Ϫ ͑N ͑i,j,k͒ ͑ ͒ ϭ s st ϫ class), a confusion matrix A(i,j) of dimension N can be M i,j,k ͩ ͑ ͒ ͪ 100, Ns i,j,k constructed, where each entry AkЈk represents the number of class k voxels classified as class kЈ by the ͑ ͒ segmentation algorithm. Two error types (expressed Nt k M͑i,j,k͒ ϭ 100 Ϫ C͑i,j,k͒ͩ ͪ, N ͑i,j,k͒ in %) can thus be computed for each tissue class k, s which can both be used to described the class-by-class performances of these procedures. It must be noticed that the sum of C(i,j,k) and M(i,j,k) The multi-class Type I error is compute as: is not equal to 100% because the reference for the C(i,j,k) criterion is the number of voxels in the corresponding class of the template whereas the reference N for M(i,j,k) is the number of voxels of the correspond- ͸ AkЈk͑i,j͒ Ϫ Akk͑i,j͒ Ј ϭ ing class of the subject. ͑ ͒ ϭ k 1 ϫ MCI i,j,k 100, ΂ N ΃ Inter-individual criterion variability ͸ AkЈk͑i,j͒ kЈ ϭ 1 The inter-individual variability of these criterion was also investigated. For each procedure, subject, where the numerator represents the number of voxels and tissue class, the gain for C(i,j,k) and M(i,j,k) (in %) of tissue class k not classified as k and the denomina- provided by FMG as compared to the other proce- tor is the total number of voxels of tissue class k dures were assessed by the two following metrics [Zhang et al., 1996]. It must be noted that the Type I GC(i,j,k) and GM(i,j,k) computed as: error is the dual percentage of the correctly classified voxel criterion defined above (C(i,j,k) ϩ MC (i,j,k) ͑ ͒ Ϫ ͑ ͒ I C FMG,j,k C i,j,k ϭ 100%). G ͑i,j,k͒ ϭ ͩ ͪ ϫ 100, C C͑i,j,k͒ The multi-class Type II error is computed as:

͑ ͒ Ϫ ͑ ͒ M FMG,j,k M i,j,k MC ͑i,j,k͒ G ͑i,j,k͒ ϭ ͩ ͪ ϫ 100, II M M͑i,j,k͒ N ͸ AkkЈ͑i,j͒ Ϫ Akk͑i,j͒ where C(FMG,j,k) (respectively M(FMG,j,k)) denotes kЈ ϭ 1 the percentage of correctly classiﬁed (respectively mis- ϭ ϫ 100, classiﬁed) voxels for the FMG procedure. A positive ΂ N N N ΃ ͸ ͸ AkЈkЉ͑i,j͒ Ϫ ͸ AkЈk͑i,j͒ value of GC(i,j,k) indicates that for a subject j and a Ј ϭ Љ ϭ Ј ϭ tissue class k, the FMG procedure performs better than k 1k 1 k 1 the procedure i (AFF or SPM or WRP). In contraxt, a positive value of GM(i,j,k) indicates that for a subject j where the numerator represents the number of voxels and a tissue class k, the FMG procedure performs of other classes called class k. The denominator is the worse than the procedure i (AFF or SPM or WRP), total number of voxels of other classes [Zhang et al.,

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Ϯ 3 ϭ 1996]. In MCI(i,j,k) and MCII(i,j,k), each tissue class is (1,421 98 cm , coefficient of variation 6.9%) and its weighted equally. average value was not significantly different from that of the Human Brain Atlas template (1,446 cm3, P Impact of spatial normalization procedures on ϭ 0.11, Student’s t-test, degree of freedom ϭ 19), functional maps ensuring comparability between the individual MRI datasets and the HBA template. Finally, to evaluate how spatial normalization af- fects functional maps, we applied the four procedures Intersubject averaged images on the PET functional data of the 18 subjects for which both the normalization and segmentation procedures Figure 2 shows axial, sagittal, and coronal sec- have been successfully completed. Using AIR3.0 tions derived from the mean volumes obtained with [Woods et al., 1997a], each individual PET dataset was each procedure. The same sections are also pre- realigned together for correcting for intra-individual/ sented for the template volume. The visual inspec- intra-modality movements, and co-registered to the tion of these slices clearly indicates that the three subject MRI volume for intra-individual intermodality nonlinear approaches dramatically improve the alignment. For each subject, the MRI normalization alignment of the normalized volumes as compared parameters obtained for each of the four methods to the simplest affine one. Looking at the three were applied to the corresponding PET images to nonlinear procedures, the FMG approach improves spatially normalize them to the HBA template. Four the delineation of the different sulci and therefore sets of functional images per subject were thus avail- the spatial homogeneity of the observed sample. A able. All PET images were resliced using linear inter- better definition of the brain outer edge is observed polation to provide 2 ϫ 2 ϫ 2mm3 voxel size volumes. as well as of internal anatomical landmarks. This To investigate the cross-effect of smoothness and spa- improvement is obvious particularly at the level of tial normalization, we used two versions coming from the superior frontal, precentral and central sulcus the original set of functional images. First, the normal- on the axial slice, or at the level of the post-central ized PET images were smoothed with a 3D Gaussian and central sulcus on the sagittal slice. These results filter of 8 mm full with half maximum (FWHM), lead- demonstrate qualitatively that individual brain ing to a “low resolution” functional dataset. Activa- anatomy is globally better matched using nonlinear tion detection was performed on each of the four spatial deformation, the highest gain being appar- normalized blood flow difference volumes “Silent ently obtained with the FMG procedure. verb generation minus Rest” using the SPM99 software for the ensuing statistical analysis. Significance level Tissue segmentation was set at 0.05 corrected for multiple comparisons (degree of freedom ϭ 140). Then, the original normal- Table II presents, the differences (mean and stan- ized PET volumes were re-smoothed witha4mm dard deviation) between tissue class proportions FWHM Gaussian filter to generate a “high resolution” obtained for each normalization procedure and the functional dataset. The same statistical analysis was tissue class proportions of the HBA template. Note, performed for the AFF, SPM, WRP, and FMG func- first, that all procedures led to overestimation of the tional datasets. Resulting smoothness estimated on the size of the grey matter class (in the order of 4%) and functional maps at the lowest resolution with AFF, to underestimation of both the white matter (Ϫ1to SPM, WRP, and FMG through the x, y, and z direc- Ϫ2.5%) and CSF classes (Ϫ2toϪ3%). The FMG tions were [8.5 9.4 10.8], [8.6 9.5 10.9], [8.5 9.5 10.7], [8.9 procedure gave grey matter segmentation figures 9.5 10.8] mm, respectively. When looking at the high- that were the closest to that of the HBA template. est resolution, these values fell to [5.7 6.4 7.4], [5.8 6.5 No significant difference for the grey matter tissue 7.5], [5.6 6.5 7.3], [6.1 6.5 7.5] mm. Note that in both volume, however, was found between the four pro- cases, the different normalization procedures led to cedures (P ϭ 0.34, ANOVA). In contrast, significant very comparable global smoothness values. differences were found between procedures regarding the white matter and CSF tissue volumes (P RESULTS ϭ 0.005 and P Ͻ 0.0001, respectively, ANOVA, 17 d.o.f). Post-hoc Student’s paired t-test showed The distribution of the global brain volume in the that, for the white matter, WRP and FMG were sample of 20 subjects, computed before applying any significantly better than SPM and AFF (P Ͻ 0.006 spatial normalization, was found very homogeneous and P Ͻ 0.04, respectively), with no differences

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Figure 2. From left to right: transverse (z ϭϩ50 mm), sagittal (x ϭϪ44 mm) and coronal (y ϭϩ20 mm) sections of the HBA MRI template (top row) and of the intersubject average volumes computed for the four normalization procedures. Coordinates are relative to the Talairach space. AFF, affine transformation (n ϭ 20); SPM, SPM linear and nonlinear routines of the SPM package (n ϭ 20); WRP, affine and fifth order polynomial normalization of the AIR package (n ϭ 20); FMG, affine and nonlinear fluid transformation (n ϭ 19). between WRP and FMG (P ϭ 0.15). Note also that Tissue probability maps the FMG approach again provided the segmentation figures closest to that of the HBA template. No Figures 3–5 show, for each of the four normaliza- differences were observed between AFF and SPM (P tion procedures, probability maps of the grey mat- ϭ 0.44). Finally the CSF tissue type exhibited the ter, white matter and CSF classes computed across opposite feature: AFF and SPM were significantly the subset of 18 subjects. The “Classified voxels” better than WRP and FMG (P Ͻ 0.0001 for both), maps give for each voxel and for each procedure, with no differences between either AFF and SPM (P the percentage of subjects for which the tissue class ϭ 0.91) or WRP and FMG (P ϭ 0.38). was in accordance with the corresponding tissue

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TABLE II. Difference between segmented tissue class the superiority of the three nonlinear procedures proportions computed across the 18 subjects and the when compared to AFF (P Ͻ 0.0001 for each proce- corresponding tissue class proportions of the Human dure) for both grey and white matter. In addition, Brain Atlas MRI template for the four spatial FMG was found significantly better than WRP for normalization procedures* grey matter overlap (P ϭ 0.025), and better than Procedure Grey matter White matter CSF both WRP and SPM for white matter overlap (P ϭ 0.0003 and P ϭ 0.0002, respectively). On the op- AFF 4.49 (1.89) Ϫ2.54 (1.81) Ϫ1.96 (0.60) posite, the best overlap for the CSF class was ob- SPM 4.38 (1.55) Ϫ2.42 (1.48) Ϫ1.96 (0.61) tained with SPM (P Ͻ 0.0001 for all comparisons), WRP 4.58 (1.66) Ϫ1.89 (1.46) Ϫ2.69 (0.64) the other three methods showing similar perfor- FMG 3.88 (2.26) Ϫ1.08 (1.95) Ϫ2.79 (0.67) mances. Considering the individual variability of this criterion, Figure 6 clearly demonstrates that * Values are mean (SD). AFF, affine transformation; SPM, linear and non-linear routine of the Statistical Parametric Mapping package; FMG provided a better alignment of tissue compart- WRP, affine and fifth order polynomial normalization of the AIR ment than the three other methods in almost all package; FMG, affine and non-linear fluid transformation. subjects both for grey and white matter. Note that for these two tissues, SPM and WRP were remark- class of the HBA template. The “misclassified vox- ably similar and that AFF was clearly surpassed by els” correspond to voxels found outside the bound- the nonlinear approaches. These findings demon- aries of the tissue template. Note the better subject strate also that the differences pointed in Table III overlap obtained with FMG for both the grey and were not driven by one or two subjects but remain white matter tissues, and the very similar results valid at the individual level. The lower part of Fig- provided by WRP and SPM. The spatial accuracy ure 6 illustrates that SPM performed a better CSF visible in the FMG maps indicates that this proce- alignment than all other methods for all subjects dure aligns high-resolution MRI images from differ- included in this comparison study. ent subjects in such a way that internal structures, such as sulci in their deepness, are better aligned to the structural model of the template. For the CSF Misclassified voxels tissue class, FMG does not appear to be superior to either SPM or WRP, although the extent of overlap Table IV and Figure 7 present the average results for in the CSF “misclassified voxels” map seems to be the misclassified voxels M(i,j,k) criterion (see the Ma- dramatically reduced (see Fig. 5). Nevertheless, Fig- terials and Methods section). For grey matter, white ures 3–5 clearly demonstrate that any of the nonlin- matter, and CSF, FMG provides the lowest error clas- ear approaches used in this study provides better sification rate, respectively from (0.9–6%), (1–4.9%) results than the classical linear AFF procedure. and (2–13.3%). As for the classified voxels statistic, This is confirmed in a quantitative manner in Table significant differences between procedures were ob- III and Figure 6 for the classified voxels and in Table served for all tissues (P Ͻ 0.0001 for each one, IV and Figure 7 for the misclassified ones. ANOVA, 17 d.o.f.). Post-hoc Student’s paired t-tests show the same pattern for the three tissue types. Each Classified voxels nonlinear procedure leads to a lower ratio of misclassified voxels than AFF (P Ͻ 0.0001 for each proce- Table III gives, for each tissue class and normal- dure). In addition, FMG and WRP were found supe- ization procedure, the mean and standard deviation rior to SPM for the grey matter (P ϭ 0.0005 and P of the classified voxels criterion (C(i,j,k), see the ϭ 0.012, respectively), for the white matter (P ϭ 0.020 Materials and Methods section above for details). and P ϭ 0.044, respectively), and for the CSF (P The FMG procedure provides the best overlap fig- Ͻ 0.0001 for both). Finally no significant differences ures for both grey matter (close to 79%) and white were found between FMG and WRP for the grey mat- matter (71%). Interestingly, the gain in overlap pro- ter, white matter and CSF (P ϭ 0.095, P ϭ 0.093, P vided by FMG as compared to the other methods is ϭ 0.063, respectively). The investigation of the inter- more pronounced for the white matter class (4–7%) individual variability of this metric reveals that in almost than for the grey matter class (1–5%). Significant all subjects, FMG exhibits the lowest rate of classification differences between procedures were found for all errors (negative gain for the misclassified), a feature tissue (P Ͻ 0.0001 for each tissue, ANOVA, emphasized in the CSF compartment. The individuals 17 d.o.f.). Post-hoc Student’s paired t-tests confirm results confirm that average results are not driven by

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Figure 3. Left column: Axial section (z ϭϩ50 mm) of the HBA MRI template and enlargement of the corresponding segmented grey matter volume focused on the superior frontal gyrus. Middle column: Grey matter probability maps (n ϭ 18) computed for the four normalization procedures. These maps are restricted to voxels located inside the corresponding HBA grey matter template and denoted “Classified voxels.” Right column: Grey matter probability maps obtained for voxels located outside the corresponding HBA grey matter template and denoted “Misclassi- fied voxels.” AFF, affine transformation; SPM, SPM linear and nonlinear routines of the SPM package; WRP, affine and fifth order polynomial normalization of the AIR package; FMG, affine and nonlinear fluid transformation. some outliers but reveal better classification patterns procedures. These results shown strong similarities using the FMG normalization procedure. with the misclassified criterion results. The only differences between the M(i,j,k) misclassified crite- Overall accuracy based on correct and rion and the MC (i,j,k) Type II error concerns the incorrect classification II white matter tissue for which no significant Type II Table V gives the results of the Type II errors error differences were found between SPM, WRP classification computed for the four normalization and FMG. Concerning the CSF tissue class, our re-

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Figure 4. Left column: Axial sections (z ϭϩ50 mm) of the HBA MRI template and of an enlargement of the corresponding segmented white matter volume focused on the superior frontal gyrus. Mid- dle column: White matter probability maps (n ϭ 18) computed for the four normalization procedures. These maps are restricted to the voxels located inside the corresponding HBA white matter template and denoted “Classified voxels.” Right column: White matter probability maps obtained for voxels located outside the corresponding HBA white matter template and denoted “Misclassified voxels.” AFF, affine transformation; SPM, SPM linear and nonlinear routine of the SPM package; WRP, affine and fifth order polynomial normalization of the AIR package; FMG, affine and nonlinear fluid transformation. sults show that the Type II error was significantly Impact of spatial normalization procedures on higher for SPM than for WRP and FMG (P Ͻ 0001 functional maps for both). This feature was also found for the grey matter tissue class, indicating that sulcal CSF and Figures 8 and 9 present the results of the analysis the surrounding grey cortical ribbon were signifi- of the functional data at low and high resolution, cantly better aligned with WRP and FMG than with respectively. The global functional activation vol- SPM (P ϭ 0.003 and P ϭ 0.0048, respectively). umes obtained with AFF, SPM, WRP, and FMG

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Figure 5. Left column: Axial sections (z ϭϩ18 mm) of the HBA MRI template and of an enlargement of the corresponding segmented CSF volume focused on the ventricles. Middle column: CSF probability maps (n ϭ 18) computed for the four normalization procedures. These maps are restricted to the voxels located inside the corresponding HBA CSF template and denoted “Classified voxels.” Right column: CSF probability maps obtained for voxels located outside the corresponding HBA CSF template and denoted “Misclassified voxels.” AFF, affine transformation; SPM, SPM linear and nonlinear routine of the SPM package; WRP, affine and fifth order polynomial normalization of the AIR package; FMG, affine and nonlinear fluid transformation. normalization of “low resolution” PET blood flow volume obtained at low resolution vs. 1.9 cm3 rep- images acquired during the Silent verb generation resenting 45% of the maximum activated volume minus Rest contrast were 38.7, 45.3, 42.1, and 42.7 obtained at high resolution). This indicates that us- cm3. Values obtained at “high resolution” were 3.4, ing too small a filter is not suited for an optimal 5.3, 3.2, and 4.9 cm3. A striking feature of these detection of PET activation, even if the criteria that results is that the range of the four activated vol- one applied on the smoothing kernel fulfills the umes increases when increasing the resolution (6.6 assumption of the Gaussian field theory (i.e., the cm3 representing 15% of the maximum activated smoothness has to be at least twice the voxel size

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TABLE III. Percentage of overlap between segmented 6.2% of their union. Actually, the activated volume tissue classes and the corresponding tissue class of the specific to each procedure (15.1, 20.4, 7.7, and 19.7% Human Brain Atlas MRI template, for the four spatial for AFF, SPM, WRP, and FMG, respectively) was normalization procedures* larger than the four functional volumes overlap (see Procedure Grey matter White matter CSF Table VI, and right side of Fig. 9). This indicates that at high resolution, spatial normalization procedures AFF 73.79 (2.12) 64.05 (2.42) 21.61 (3.20) have a non negligible impact on the localization of SPM 77.76 (1.87) 66.90 (2.24) 25.78 (3.98) activated areas. Actually, the volume of activated WRP 77.36 (2.43) 67.21 (2.16) 22.13 (4.26) areas common to the four methods was preserved FMG 79.01 (3.99) 71.13 (3.43) 22.65 (4.74) mainly for foci located near internal structures (see for example the left insula focus at x ϭϪ28 mm). * Values are mean (SD) averaged across the 18 subjects. AFF, affine transformation; SPM, linear and non-linear routines of the Statistical Parametric Mapping package; WRP, affine and fifth-order polynomial normalization of the AIR package; FMG, affine and non-linear fluid transformation.

[Friston et al., 1995b]). This implies that, independent of the spatial normalization strategy, PET intersubject statistical analysis requires a large enough kernel filter to compensate for the large interindividual functional variability and cannot be performed at very high resolution. At first, exami- nation of the activation volumes at the lowest resolution shows that the three nonlinear methods provided slightly higher activated volumes as compared to the affine procedure, indicating that improved warping of subjects neuroanatomy results in enhanced functional areas volume, despite the fact that the inter-subject averaged functional map resolution (ϳ10 mm) is far more coarse than that of the structural image (ϳ1 mm). The left part of Fig- ure 8 shows that, at low resolution, the four methods gave very similar functional maps. There was no activation found with one method that was not detected with the others. The subtle observed differences concerned the morphology of activation clusters (i.e., outside delineation of the activated areas), and the localization of their local maxima. Table VI shows that the four functional volumes overlap in 42.8% of their union, whereas activated volumes specific to one method represented 26.2% of the same volume. The right part of Figure 8 emphasizes this point and demonstrates that the different functional volumes largely overlap (white areas). These findings indicate that 10 mm spatial Figure 6. resolution functional maps are quite independent of Gain in tissue class overlap (in %) provided by FMG as compared to AFF, SPM, and WRP, for each subject, the tissue the normalization procedure used, even with a sim- segmented HBA template serving as a reference. Positive values ple linear normalization method such as AFF. Going indicate that FMG provides a better overlap of the tissue type. to higher resolution changed the results quite dra- Negative values indicates that FMG provides a worse overlap. matically. Table VI and Figure 9 highlights this phe- AFF, affine transformation; SPM, SPM linear and nonlinear rou- nomenon, showing that specific activation volumes tine of the SPM package; WRP, affine and fifth order polynomial raised to 62.9% of the total activated volume, the normalization of the AIR package; FMG, affine and nonlinear four functional volumes now overlapping in only fluid transformation.

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TABLE IV. Percentage of misclassified voxels of a [Friston et al., 1995a]; HBA [Roland et al., 1994]; and segmented tissue class with respect to the MICHIGAN [Minoshima et al., 1994]. Using size and corresponding tissue class of the Human Brain contour of the brain, as well as the course of four Atlas MRI template, for the four spatial major sulci, these authors found that SPM and HBA normalization procedures* were equivalent from the point of view of anatomical Procedure Grey matter White matter CSF homogeneity, despite the fact that SPM was used to normalize low resolution PET data only. Regarding AFF 33.41 (1.75) 32.93 (1.90) 66.98 (3.54) functional images, these authors concluded to the use- SPM 29.05 (1.87) 29.60 (1.01) 60.26 (3.26) fulness of nonlinear procedures, as compared to linear WRP 28.26 (0.86) 29.00 (1.26) 55.73 (3.27) ones, but found that it was better to perform spatial FMG 27.36 (2.48) 28.06 (2.23) 53.72 (4.71) normalization of PET images on a PET template rather than to apply a spatial normalization matrix derived * Values are mean (SD) averaged across the 18 subjects. AFF: affine transformation; SPM, linear and non-linear routines of the Statistical Parametric Mapping package; WRP, affine and fifth order polynomial normalization of the AIR package; FMG: affine and non-linear fluid transformation.

DISCUSSION

Methodological aspects

Previous comparison studies

We used an original approach for evaluating the spatial normalization performances of four linear and nonlinear inter-subject alignment procedures applied on high-resolution 3D MRI datasets. One of the main goal of our study was to derive a methodology that would be unbiased, from the acquisition of the dataset images to the comparison criterion and its interpre- tation. This issue remains under debate because at present, standard methods for evaluating the global and regional accuracy of the spatial transformations applied on brain images have not been fully developed. Although many papers have reported important and fundamental methodological improvements in spatial normalization by presenting new core algorithms, their validation has been usually very crude and limited to a comparison with the simplest linear affine transformation [Andersson and Thurfjell, 1997; Ashburner et al., 1998; Ashburner and Friston, 2000; Collins et al., 1994; Davatzikos, 1996; Kochunov et al., 1999; Lancaster et al., 1999; Meyer et al., 1999; Minoshima et al., 1994; Rizzo et al., 1997; Roland et al., 1994; Schormann and Zilles, 1998; Thompson et al., 2000a; Woods et al., 1997b]. Figure 7. Gain in misclassification (in %) provided by FMG as compared to Indeed, reports on the comparison between nonlin- AFF, SPM and WRP, for each subject. Negative values indicate that ear warping methods are very scarce, for such studies FMG provide a lower percentage of misclassified voxels. Positive require tedious processing of large image datasets. values indicates that FMG provides a higher percentage of misclas- Previous authors [Senda et al., 1998; Sugiura et al., sified voxels. AFF, affine transformation; SPM, SPM linear and 1999], for example, have compared four normalization nonlinear routine of the SPM package; WRP, affine and fifth order approaches on the same dataset composed of MRI and polynomial normalization of the AIR package; FMG, affine and PET images: linear scaling [Fox et al., 1985]; SPM 95 nonlinear fluid transformation.

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TABLE V. Multi-class Type II error (%) computed comparisons have been based on some measure of the for each class and for the four spatial dispersion of anatomical (or functional) landmarks normalization procedures* that were placed, either manually or automatically, on both the normalized and template images [Fischl et Procedure Grey matter White matter CSF al., 1999; Grachev et al., 1999; Woods et al., 1997b], AFF 11.59 (1.13) 5.14 (0.56) 0.98 (0.18) thereby restricting the evaluation to an a priori small SPM 9.97 (1.12) 4.59 (0.34) 0.87 (0.16) subset of the 3D brain volumes. In a different vein, a WRP 9.52 (0.65) 4.47 (0.34) 0.63 (0.16) surface based technique has been proposed recently FMG 9.34 (1.42) 4.54 (0.64) 0.59 (0.17) for spatial normalization evaluation [Lohmann et al., 1999], whereby an average distance is computed be- *Values are mean (SD), averaged across the 18 subjects. AFF, affine tween the segmented white matter surfaces of each transformation; SPM, linear and non-linear routines of the Statistical Parametric Mapping package; WRP, affine and fifth order polyno- normalized brain and of the template, through ran- mial normalization of the AIR package; FMG, affine and non-linear dom and roughly even sampling of both surfaces. fluid transformation. More sophisticated validation criteria have been proposed based on a blurring metric that gives the spatial from structural images (HBA). These results, however, uncertainty associated with the location of a given must be taken cautiously because not all procedures anatomical (or functional) area after spatial normaliza- were applied to the two datasets, linear and HBA tion has been applied [Fischl et al., 1999]. In fact, some being applied to MRI data (using an MRI based tem- studies have used a regional 3D criterion, such as the plate) whereas SPM and MICHIGAN were applied to overlap of volumes of interest [Cardenas et al., 2000; PET data (using a specific PET template). To pool all Fiez et al., 2000]. normalized images in a given modality, the transfor- In the present study, 3D probability tissues maps mation matrix computed in one modality was further were used to evaluate and compare alignment accu- used to normalize the other modality image. A second racy across normalizing procedures, allowing both to drawback of this study was that not all procedures derive global statistics and to focus on specific tissue were automatic, the user interactive version of HBA or areas of interest. This generic approach has similar- being used, which biased their comparison. Several ities with voxel based methods proposed recently for studies have indeed compared the performances of assessing the difference between samples of structural manual versus automated warping techniques, report- MRI images, such as “Voxel-based morphometry” ing a superiority of the latter on the former, except in (VBM) [Ashburner and Friston, 2000; Woermann et al., some cases of brain lesions [Fiez et al., 2000], and a 1999], or a method based on the permutation theory crucial dependence of the manual approach accuracy [Bullmore et al., 1999]. Both VBM and the permutation on the operator skills [Sugiura et al., 1999]. method require the image to be smoothed to a certain In the present study, we tried to avoid these pitfalls, degree to be theoretically valid (VBM) or computa- all normalization procedures being fully automatic tionally tractable (permutation), and consequently and applied to all images acquired in a given modality cannot be applied to high resolution datasets. In con- using the same template. In addition, all steps in the trast, the high resolution probability tissue maps used generation of the PET functional statistical maps were in the present study allow one to evaluate the align- automated and rigorously identical except, of course, ment accuracy at the intrinsic resolution of the nor- the MRI spatial normalization: PET–PET intra-subject malized MR images. alignment, PET–MRI intra-subject registration, filter- Another point that is worth discussing is how to ing, and statistical analysis. This ensures that the dif- evaluate the quality of matching an MRI volume to a ference observed in activation foci localization (Figs. template when brain regions are missing (i.e., in pres- 8,9) can truly be ascribed to differences in sulcal pat- ence of a lesion or abnormalities such as in Alzheimer terns of spatially normalized MRI images. disease). It is obvious that the four methods used in our comparison will be inadequate. When brain re- Comparison criterion gions are missing, these automated procedures at- tempt to reduce image mismatch between the tem- Another key point emerging from spatial normal- plate and the image to be normalized at lesion sites, ization comparison studies is the comparison criterion and this can lead to inappropriate image distortions, used for alignment performance evaluation. To our especially when nonlinear transformations are used. knowledge, no previous study has used a full 3D The higher the degree of freedom of a spatial normal- criterion for comparing alignment accuracy. Previous ization technique, the worse will be the alignment of a

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Figure 8. Impact of spatial normalization procedures on “low resolution” was performed on the HBA template. Right side: Sagittal sections functional activation maps. Stereotactically normalized PET vol- (x ϭϪ54, Ϫ40, Ϫ28, Ϫ3, ϩ24 mm) of the functional volumes umes were smoothed with a 3D 8 mm FWHM Gaussian filter. superimposed on the corresponding HBA template sections, illus- Functional clusters were detected in intersubject averaged (n trating activations specific or common to the four functional ϭ 18) PET difference volumes spatially normalized by the four volumes. Color code indicates which functional volume(s) a given different normalization procedures. Left side: Sagittal and coro- voxel belongs to. A, affine transformation; S, SPM linear and nal orthogonal maximum intensity projection maps of functional nonlinear routine of the SPM package; W, affine and fifth order volumes thresholded at a 0.05 significance level corrected for polynomial normalization of the AIR package; F, affine and nonlin- multiple comparisons. Note that the contour delineating the brain ear fluid transformation. is derived from the MNI template whereas the statistical analysis brain MRI with missing regions. To circumvent this Validation of tissue segmentation drawback, a method based on the masking of the lesion areas in the calculation of image difference has Our data analysis strategy heavily relied on the been developed recently and validated [Brett et al., segmentation scheme, both for each individual nor- 2001]. This approach was found superior to the clas- malized MRI volume and for the HBA template, the sical approach of this problem. In the case of Alzhei- tissue classification of the latter serving as a gold mer disease, which is characterized by a diffuse grey standard. We have used the segmentation algorithm matter atrophy, we believe that spatial normalization included in the SPM99 package [Ashburner and Fris- using a global nonlinear brain match (for example ton, 1997], a well-documented and recently rigorously SPM or WRP) are better suited for statistical neuro- validated approach [Ashburner and Friston, 2000]. anatomy studies performed to determine the in vivo The relatively high resolution of the normalized image cerebral modifications caused by this pathology. (ϳ1 mm) asserts that the partitioned images were not

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Figure 9. Impact of spatial normalization procedures on “high resolution” the statistical analysis was performed on the HBA template. Right functional activation maps. Stereotactically normalized PET vol- part shows sagittal sections (x ϭϪ54, Ϫ40, Ϫ28, Ϫ3 mm) of umes were smoothed with a 3D 4 mm FWHM Gaussian filter. functional volumes superimposed on the corresponding HBA tem- Functional clusters were detected in intersubject averaged (n plate sections, illustrating activations specific or common to the ϭ 18) PET difference volumes spatially normalized by the four four functional volumes. Color code indicates which functional different normalization procedures. Left part of the figure shows volume(s) a given voxel belongs to. A, affine transformation; S, sagittal and coronal orthogonal maximum intensity projection SPM linear and nonlinear routine of the SPM package; W, affine maps of functional volumes thresholded at a 0.05 significance level and fifth order polynomial normalization of the AIR package; F, (corrected for multiple comparisons). Note that the contour affine and nonlinear fluid transformation. delineating the brain is derived from the MNI template whereas confounded by partial volume effects in which voxels both initiated using the “alignlinear” routine of the contained mixture of different tissue types. It must be AIR package that corresponds to the AFF procedure. noticed that the SPM original standard space is the Meanwhile, SPM contains its own affine transforma- Montreal Neurological Institute (MNI) template tion that seems to perform better alignment than AFF [Evans et al., 1994], which has different size and shape for internal structures such as the ventricles, and par- compared to the HBA template used in the present ticularly to provide a better starting point for further study. As shown in Table I and Figure 1, using a priori nonlinear alignment. tissue probability maps designed for the MNI template for segmenting the HBA template was satisfac- FMG vs. other approaches tory, if one excepts the CSF tissue. As a consequence, relatively low overlap was found between CSF prob- Unlike the FMG procedure, SPM and WRP are not ability maps. Our results show that SPM was also designed to provide perfect alignment of two different superior to the AFF and WRP methods for inter-sub- brains. Indeed, because the deformations provided by ject intracerebral CSF alignment. WRP and FMG were the discrete cosine basis functions, or polynomial

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TABLE VI. Percentage of activated volume specificor brains. For example, if the brain atlas provides a pe- common to two or more normalized functional culiar sulcus with two ramifications whereas the brain volumes at a 0.05 significance level, corrected for to be deformed has only one ramification for the same multiple comparisons* sulcus, the resulting deformed sulcus will finally ex- Procedure Low resolution High resolution hibit two ramifications. This means that the original anatomy is modified in such a way that it is con- A 7.5 15.1 strained to fit the anatomy of the target one. This S 8.8 20.4 specific ability was clearly illustrated in our compari- ¥ ϭ 26.2 ¥ ϭ 62.9 son study, particularly when one looks at the shape of W 4.9 7.7 the sulcus after deformation. Furthermore, the FMG F 5.0 19.7 algorithm can be adjusted to preserve the local rela- A,S 1.0 4.3 tionship among sulci and gyri as does SPM and WRP, A,W 2.4 2.2 which was done in the present study. By increasing A,F 1.7 3.0 the grid-resolution it is also possible to fully warp one S,W 4.0 4.2 brain to another. Approximate absolute running times S,F 6.0 6.2 ¥ ϭ 31 ¥ ϭ 30.9 on a SUN-SPARC ULTRA 30 were about 15 min for W,F 1.0 1.6 SPM (including the affine transformation), 45 min for ϩ ϩ A,S,W 2.8 1.5 AFF WRP, and 100–120 min for AFF FMG. Compu- A,S,F 2.4 3.2 tation time of the actual FMG procedure is thus much A,W,F 2.4 0.4 larger and can be a drawback when analyzing large S,W,F 7.3 4.3 datasets. A,S,W,F 42.8 ] ¥ ϭ 42.8 6.2 ] ¥ ϭ 6.2 How far should we remove individual * Low (respectively High) resolution was obtained by applying a 8 mm (respectively 4 mm) three-dimensional full with half maximum anatomical variability? Gaussian filter to the PET images. A, affine transformation only; S, linear and non-linear routines of the Statistical Parametric Mapping Statistical neuroanatomy package; W, affine and fifth order polynomial warp; F, affine and non-linear fluid transformation. Because performing a quasi perfect brain match is by itself a challenge of interest, the question of its warping, are only defined by a few hundred parame- necessity in the neuro imagery field has to be dis- ters, as opposed to the millions of ones of the FMG cussed. procedure, they do not have the potential precision of New computational approaches defined to quantify more sophisticated methods. As a consequence, SPM human neuroanatomical variability require that im- and WRP offer the advantage of preserving the local ages to work on be put into a common space. Indeed, relationships among sulci and gyri after the normal- group comparison between normal patients and pa- ization has been applied, and provide a pertinent tients, such as schizophrenic or Alzheimer patients, or overall adjustment of global nonlinear size and shape between young and old subjects, requires the different brains. SPM and WRP also have the potential to be brains to be similar. But similar to what degree? At superseded by upgraded versions of the same core present, there are two majors strategies for answering algorithm (for example using higher order polynomial this question. The first one, as mentioned previously, warps (8, 10, or even 12) or more 3D discrete cosine is VBM [Ashburner and Friston, 2000] and involves a transform basis functions. Technical and computa- voxel-wise comparison of the local concentration of tional limitations, as well as biological constraints, grey or white matter density maps between two or however, restrict their use to global brain matching. In more groups. In this case, one tries to detect differ- contrast, the fluid mechanical theory implemented in ences in the regional concentration of brain tissues at FMG can model any brain onto another. In this a local scale, and if the spatial normalization is perfect, method, high-level structural information has to be then all the segmented tissue images would appear invoked to guarantee the biological validation of the identical and no differences would be detected. A resulting spatial transformation, which generally im- global nonlinear brain match (SPM, WRP) is almost plies that the relationship among anatomical land- satisfactory, therefore, and there is no need for a more marks can be lost after the matching step has been precise normalization of the brain images. VBM, using performed, depending on the amount of mismatch SPM as the gold standard spatial normalization pro- between the anatomy of the source and the target cedure, has been used already to demonstrate local

᭜ 246 ᭜ ᭜ Comparing Spatial Normalization Procedures ᭜ structural brain differences among various popula- said, “…while this current approach cannot provide tions [Abell et al., 1999; Good et al., 2001; May et al., exact matches between small cortical or deep grey 1999; Paus et al., 2000; Sowell et al., 1999; Woermann matter structures, it provides additional information et al., 1999; Wright et al., 1995]. To our knowledge, in a practical way for large subject cohorts.” The ana- however, there has been no comparison of the relative tomical residual variability was compensated in this merits of SPM and WRP to determine the differences case by the very large number of subjects of the study, observed in classical VBM statistical neuroanatomy. acting as a supplementary image smoothing process. The second class of methods aims at identifying mac- This improvement has also been implemented by Da- roscopic anatomical shape and size difference among vatzikos et al. [2001]. These authors use a very high the brains of different population. Here, statistics are dimensional elastic transformation to preserve the not carried out directly on the normalized volumes, volumetric measurements of each tissue, both locally but are applied to the parameters describing the en- and globally. This study demonstrated that the com- suing estimated nonlinear deformations. These tech- bination of high dimensional elastic transformation niques, called deformation-based and tensor-based and VBM can be used to accurately quantify very morphometry, compare the transformation fields cor- localized atrophy and volumetric changes. responding to different populations. The more precise Regarding the normalization procedures compared is the mapping between homologous features of a in our study, we confirm that smooth normalization individual brains to a target one, the more relevant is procedure such as SPM, WRP, or FMG provide an the displacement field characterizing the difference in amount of residual variability that restricts their use to the shape and the size of these specific features [Ash- traditional VBM analysis of tissues class densities. burner et al., 1998; Davatzikos, 1996; Gaser et al., VBM analysis does not measure any higher order 1999]. For this purpose, sophisticated methods are of shape characteristics and are less sensitive to spatial interest and are highly recommended to reduce sig- normalization errors in comparison with methods nificantly the anatomical residual variability between based on displacement fields. subjects after spatial normalization. The use of these high-dimensional elastic normalization approaches Functional neuroanatomy have permitted us to investigate, for example, longitudinal studies of the corpus callosum growth pat- Another field of investigation where the accuracy of terns in children [Thompson et al., 2000b] or to map spatial normalization is of relevance is the investiga- precisely morphological differences of the same struc- tion of the neural basis of higher cognitive functions. ture in schizophrenic patients [Narr et al., 2000]. The Indeed, a functional parcellation of the brain consists results obtained from our comparison study have of segregating and precisely localizing cerebral func- shown that the FMG algorithm provide a slightly bet- tional fields. A basic hypothesis underlying cognitive ter alignment of anatomical features between subjects. neuroanatomy studies is that functional fields in dif- These results, however, indicate that SPM, WRP, or ferent individuals are located at similar anatomical FMG procedures are not accurate enough, both in locations [Watson et al., 1993]. As a consequence, the terms of warping the individual to the template, to be use of warping algorithms that perform the best reg- used in deformation- or tensor-based morphometry istration of different brains should result in more ac- analysis. The use of one of these procedures combined curate alignment of functional areas and therefore with displacement measures can blur the identifica- enhance the intrinsic detection sensitivity of these tion of subtle and localized effects of brain morphol- functional fields. This characteristic has been found in ogy between populations, due to the important resid- previous studies that have related the effect of spatial ual variability remaining after spatial normalization normalization on functional datasets and have con- (Tables IV,V). In a recent work, Good et al. [2001] used cluded that the normalization procedure with higher the smooth dimensional deformation field obtained localization accuracy of structural features provide from the SPM99 normalization procedure to investi- the most accurate and sensitive functional results gate the effect of age on the volume reduction (or [Andersson and Thurfjell, 1997; Downs et al., 1999; growth) of anatomical structures in a sample of 465 Fischl et al., 1999; Gee et al., 1997; Senda et al., 1998]. subjects. This was done using a “modulation step” Our findings moderate these assertions. We did not preserving the volume of a particular tissue within a investigate the differences in terms of sensitivity be- voxel by multiplying the voxels values in the seg- tween functional maps obtained with different nor- mented images by the Jacobean determinants derived malization procedure (activated volumes, extent, and from the spatial normalization step. As the authors overlap in a common space). Using conservative sig-

᭜ 247 ᭜ ᭜ Crivello et al. ᭜ nificance level and traditional smoothing kernel for ery. It has been demonstrated that the macroscopic classical PET inter-subject analysis (ϳ10 mm final 3D anatomical variability is highly related to the micro- spatial autocorrelation), our results show that there structural one in primary cortices [Geyer et al., 1996], were only subtle differences between inter-subject but this tight relationship seems to disappear for as- maps, either linearly or nonlinearly stereotactically sociative areas [Amunts et al., 1999]. The large vari- normalized. This suggests that the blurring intro- ability of the architectural organization of the cerebral duced by the inter-individual functional variability cortex that exists at every scale requires us to ap- dominates the anatomical variability that can be re- proach this issue through probabilistic schemes and duced by precise warping strategies. Although ana- atlases rather than through single individual observa- tomical features such as sulci, were aligned with mil- tions (as was the case for the pioneer, Brodmann’s limeter resolution, the underlying functional fields map). Such studies are based on the hypothesis of identified by inter-subject PET activations (mainly the sulcal anatomical standardization and therefore re- extent of these functional sites) were spread around quire all datasets to be accurately normalized in a the anatomical center of interest. This, of course, does probabilistic space at a macroscopic level. The most not imply that the activation centers after spatial nor- accurate brain is likely to provide the most relevant malization are located exactly at the same coordinates, conclusions regarding the relative positions of func- but it shows that conclusions derived from the analy- tional landmarks and cytoarchitectural areas. This in- sis of such PET experiments are independent of the novative approach imposes the use of quasi perfect normalization scheme used to move the functional warp between brains and will be a prerequisite for the volumes in the standard space. It should be noted that analysis of very large neuroimaging databases such as the Gaussian kernel size we used was about 4 mm the European Computerized Human Brain Database lower than most filter sizes used in the functional (ECHBD) [Roland and Zilles, 1996] or the Interna- neuroimaging literature. One can easily hypothesize tional Consortium for Brain Mapping [Mazziotta et al., that using a more traditional larger kernel size will 2000]. The main goal of the ECHBD, now followed by emphasize the homologies between functional maps the NEUROGENERATOR project [Roland et al., 2001] produced with different normalization strategies and was to investigate the spatial congruence of probabi- enhance the overlap of activated volume across meth- listic map of cytoarchitectonic fields and functional ods. Tuning the significance threshold to ultra high PET and fMRI areas. These cytoarchitectonic maps are conservative thresholds should probably leave the useful and can offer precise stereotaxic information of maximum intensity activation peak, allowing the com- interindividual variability of microscopic areas only if parison of their relative localization in the stereotaxic space. This was achieved in our study by improving the surrounding macroscopic structural variability of the spatial resolution of the functional study to ϳ6 the post-mortem subjects is completely reduced using mm, which corresponds to the resolution of many a quasi perfect alignment procedure. This is what was fMRI maps. No differences were observed in terms of done in the ECHBD using a very high dimensional the number of activated areas but non-negligible vari- elastic version of the FMG procedure. The results ob- ations appeared in terms of their localizations, the served in our study concerning the impact of normal- activation volume overlap between methods being re- ization procedures on high resolution functional maps stricted to a few percents of the total activated volume. (Table VI, Fig. 9) suggest that using this high dimen- These variations can be of importance when research- sional procedure, the observed differences on the lo- ers have to distinguish precise activation areas located cation and extent of functional activations will be in the same anatomical features, but the problem of more striking than the ones observed with the actual selecting the method that gives the best “theoretical” version of the FMG procedure. To build an inter- results still remains. subject average functional map with the lowest between subjects residual variability, one has to use the Relationships between microscopic and must accurate normalization procedure to align the macroscopic areas different subject brains. Our results lead us to con- clude that new database projects integrating high res- A last topic of interest, in which a complete warp is olution functional datasets with micro- or macroscopic of crucial importance, is the analysis of the precise structural informations should be based on normaliza- relationships between macroscopic functional and cy- tion procedure providing the highest degree of accu- toarchitectonic associative areas involved in higher racy, such as FMG, to investigate close relationships cognitive function such as language or mental imag- between structure and function.

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