Within-group nonlinear registration improves …Within-group nonlinear registration improves...

Within-group nonlinear registration improvesbetween-group Voxel-Based Morphometry

S. Duchesne, N. Bernasconi, A. Janke, K. Worsley, A. Bernasconi and D.L. Collins

McConnell Brain Imaging Centre, Montreal Neurological Institute, McGill University

3801, University St., Montreal, Canada H3A 2B4

tel:(514) 398-1730 fax:(514) 398-2975�duchesne, neda, rotor, keith, andrea, louis � @bic.mni.mcgill.ca

December 22, 2003

Key words: voxel-based morphometry, nonlinear registration, reference target, isotropic

Gaussian kernel, temporal lobe epilepsy

Abstract

Accurate registration is imperative for VBM methodologies. Typically, linear and/or non-

linear registration is used to conform all brains to the same shape, orientation and size. We

suggest disease-specific reference targets to reduce normal inter-subject anatomical variability

while at the same time enhance pathologically-induced differences between groups. These

targets can be created by averaging subjects following linear registration, and we propose

to use nonlinear registration of subjects to their respective group target prior to performing

VBM analyses. Our results demonstrate that: (A) this methodology increases the number,

extent and statistical significance of clusters; (B) a smaller smoothing kernel can be used to

improve spatial localization; and (C) there is no detectable increase in the false-positive rate.

Within-group nonlinear registration therefore improves the detection ability in between-group

voxel-based morphometry.

Abbreviations used: CDA (community dwelling adults), GLM (generalized linear model), GM (grey matter),

HC (hippocampus), HA (HC atrophy), IGK (isotropic gaussian kernel), MRI (magnetic resonance imaging), SPM

(statistical parametric mapping), TLE (temporal lobe epilepsy), VBM (voxel-based morphometry), WM (white matter)

1

S. Duchesne et al. Within-group NL registration improves VBM 2

1 Introduction

Voxel-based morphometry (VBM) consists in the statistical analysis of generalized linear model

(GLM) results performed on a voxel-by-voxel basis on combined cohorts of co-registered sub-

ject imaging data. VBM’s detection accuracy is limited by sources of spatially dependent and

independent noise which compromise the statistical results. Misregistration is a key factor which

has already been discussed [5] [2] and addressed using linear and nonlinear registration in recent

VBM implementations [1]. The techniques reviewed in the literature employ a single reference

volume as their registration target, usually an average of a large ensemble of images from healthy

individuals.

Ashburner et al [1] have proposed an adaptation of their statistical parametric mapping (SPM)

technique, initially designed for functional magnetic resonance imaging. For VBM analyses, they

proposed to examine grey or white matter (GM,WM) concentration volumes across subjects in lieu

of longitudinal activation maps. SPM has since become the de facto standard software package for

VBM. It addresses the issue of normal, anatomical variability in cortical and sub-cortical structures

by relying on global linear and local nonlinear registration, conforming all brains (irrespective of

grouping) to the same template.

While normal variability forms the basis of some VBM anatomical analyses, it is undesir-

able in cases where the goal is to highlight pathology-induced focal changes between populations,

changes which are hypothesized to be independent of normal variability. Reducing anatomical

variance would thus improve the detection of statistically significant changes between populations.

Techniques that normalize all subjects to a common reference by nonlinear registration risk elimi-

nating those very effects it is wished to detect by artificially conforming all differences regardless

of origin. In the extreme case, if nonlinear registration was perfect, all subjects would become

identical, and VBM analyses would show no difference between groups. This overconformisation

was pointed out in a recent SPM optimisation study by Wilke [18].

Smoothing is generally used as a panacea to account for local misregistrations in the analysis

as well as reducing noise in the input data. This in turn improves the detection of regions of

differences but comes at the cost of decreasing localization accuracy. If local variability is reduced,

the positional accuracy of the data is improved [13] and thus a smaller smoothing kernel size

could be used. This leads to a better localization of focal differences while maintaining statistical


significance.

In order to perform meaningful cluster analysis of the data, as opposed to peak finding, the

issue of data nonisotropy must be successfully resolved [20]. Concentration volumes of GM /

WM are highly nonisotropic since the noise component has nonconstant smoothness. One needs

to correct the image and make the data isotropic in a statistical sense [20] before assessing re-

sults. Whereas many studies do not explicitly mention such correction, one must take care to

incorporate a methodology of the kind proposed by Salmond [14] or Worsley [20] before reporting

cluster statistics. These authors overcome nonisotropy by measuring cluster size in resels - reso-

lution elements - rather than voxels. This is shown in eq. 1, where the total cluster size � equals

the summation of resels at those voxels � above the cluster t-statistics threshold. Unitless resels

are calculated by taking the ratio of the voxel volume �� in �� over the cubed effective

smoothing kernel full-width at half-maximum ( �� ) at that point, also in �� [20]:

��

(1)

2 Hypothesis and objective of research

We hypothesise that intra-class, inter-individual variability can be reduced by relying on nonlinear

registration of subjects to their group specific target averages, rather than registering all subjects to

the same template. This would have the effect of decreasing within-group anatomical variability

while preserving pathologically-induced deformations. The decreased within-group variance may

result in increased inter-group separation, thus improving the statistical detection of differences;

on the other hand it may also increase the false-positive rate.

To test our hypothesis, we used as a study group patients with temporal lobe epilepsy (TLE).

The most commonly described pathological findings in TLE are neuronal loss and gliosis of the

hippocampus and the parahippocampal region [3] [9]. Hippocampal neuronal loss found in sur-

gical specimens obtained from patients with pharmacologically intractable TLE has been shown

to correlate with hippocampal atrophy on volumetric MRI [6]. Volumetric studies in TLE have

also shown volume reduction ipsilateral to the side of the seizure focus in the parahippocampal re-

gion [4]. Previous VBM studies in TLE, using cluster statistics, have produced conflicting results.


In one study no abnormalities were found in the hippocampus [19]. Another study [11] reported

significant areas of GM decrease in the hippocampus and other brain areas.

The goal of our study was to implement a VBM methodology based on within-group non-

linear registration, validate the false-positive rate and apply it to a group of patients with TLE and

hippocampal atrophy.

3 Methods

3.1 Subjects

We selected 42 patients with pharmacologically intractable left TLE (mean age: 35 years; 29

males) and 51 community dwelling adults (CDA) (mean age: 33 years, 27 males). The Ethics

Committee of the Montreal Neurological Institute and Hospital approved the study and informed

consent was obtained from all participants. Lateralization of seizure focus in TLE patients was

determined by a comprehensive evaluation including prolonged video-EEG telemetry. MRI volu-

metric analyses was performed using a previously published protocol [4] and showed hippocampal

atrophy (HA) ipsilateral to the seizure focus in all patients.

3.2 MRI acquisition and initial processing

The initial processing steps in our VBM methodology are similar to the standard approach [1]

(Fig. 2). Volumetric data consisted of T1-weighted MRI acquired on a 1.5 T scanner using a fast

field echo sequence ( �� , 1 acquisition average pulse sequence, flip angle= �� ,

matrix size= �� , �� , slice thickness= � �� ). Following acquisition, intensity

inhomogeneities due to scanner variations were corrected [15]. Grey-level intensities were then

normalized to a common scale across subjects. A 12-degrees of freedom linear registration was

then used for global alignment [8] into a standard reference space. The data was finally resampled

onto a � �� isotropic grid [8].

The reference image used for the linear registration and resampling is an average (Fig. 3(a)) of

152 normal subjects in Talairach space taken from the International Consortium for Brain Mapping

(ICBM) study [12](mean age: 24.8 yrs; 86 males).


3.3 Nonlinear registration

Nonlinear registration attempts to match image features from a source volume to those of a given

target at a local level, typically in a hierarchical fashion, with the aim of reducing a specific cost

function. Whereas many nonlinear registration processes exist, the one chosen for this study was

ANIMAL, developed by Collins et al. [7]. This algorithm attempts to match image grey-level

intensity features at a local level (voxel) in successive blurring steps, by minimizing the cross-

correlation function of voxel intensities between the source and target images. The result is a

dense deformation field capturing the displacements required to align the two images.

As we wished to investigate pathologically-induced differences between populations as op-

posed to normal, inter-individual anatomical variability, we relied on nonlinear registration to re-

move the latter by conforming each individual to its group average (Fig. 2). Those averages were

built using the preprocessed, linearly registered data in standard reference space from either all

patients with left HA or all CDA (Fig. 3(b),(c)).

3.4 Concentration map creation

Following nonlinear registration, the brain was separated from scalp by a simple extraction process

using a cerebrum/cerebellum mask defined on the ICBM average. The extracted brain was then fed

to an artificial neural net classifier [21] which separated the volume into GM, WM and cerebro-

spinal fluid tissue components. The GM component map was then smoothed using an isotropic

Gaussian kernel (IGK) of specified full-width at half-maximum (FWHM) ( � and �� ), forming

a concentration map - spatial extent of GM in the brain - also called “density map” [1].

3.5 Statistical analysis

Student’s t-test statistical maps were derived from analysis of the concentration maps between

groups using GLM [17]. Thresholds for statistical significance were calculated [20] and include

correction for multiple comparisons as well as the random fluctuations of a nonisotropic FWHM

volume (Fig. 5) used to correct statistical variations due to data nonisotropy. In order to reduce the

number of comparisons as well as increase the reliability in the determination of class membership

(TLE or CDA), cluster analysis included only those voxels with a brain matter GM or WM con-


centration �� as determined on an average concentration map created using all subjects in

the study (Fig. 4). This mask defines the volume of interest for each experiment.

3.6 Experiments

Two experiments were performed to demonstrate the improvements in VBM using within-group

nonlinear registration.

A specificity test was designed in which the CDA group (51 subjects) was split in two sub-

groups ( �� subjects, �� subjects) which could then be compared to each other.

As both groups were composed of healthy individuals, it was hypothesized that no statistically

significant differences would be found in a VBM analysis of GM concentration maps following

within-group nonlinear registration. CDA sub-group averages were computed from linear regis-

tered data and each sub-group subject was subsequently nonlinearly registered to its sub-group

average as per the proposed methodology. VBM analyses were conducted on the linear and non-

linear within-group data for comparison, each smoothed using a � �� IGK FWHM.

In order to check the sensitivity of our methodology, a second experiment was designed where

we wished to determine improvements in the detection of statistically significant zones of GM at-

rophy in TLE subjects under four conditions: (a) following linear registration only to the ICBM

average (linear), at � �� IGK FWHM; (b) following nonlinear registration of all subjects to the

ICBM average (nonlinear ICBM) at � �� IGK FWHM; and (c),(d) following within-group non-

linear registration (nonlinear within-group) at � and �� IGK FWHM.

4 Results

4.1 Nonlinear registration

Improvements in data registration are seen in Fig. 6 (a) through (l). Each row represents a different

combination of population and registration technique. All left and middle column images are

transverse slices ( � �� ) through standard deviation maps associated with their respective group

averages, with the left column representing linear registration and the middle column nonlinear

registration. The rightmost column displays a similar transverse slice through the ratio of (middle


column / left column) for that row.

On the first row, for the left HA group, are shown standard deviation maps of the linear and

nonlinear ICBM registered data. The second row is also for the left HA group, this time comparing

linear and nonlinear within-group registration results. In a similar fashion, the last two rows

compare results for the CDA groups.

If nonlinear registration is successful in reducing variability, then the ratio (nonlinear / linear)

should be smaller than 1. This is evidenced in all cases, and within-group registration is seen to

reduce the variability in similar areas as common target registration.

4.2 Specificity experiment

VBM results for � �� FWHM IGK linear and nonlinear within-group registered data are pre-

sented in Fig. 7(a) and (b). Peaks are voxels which meet or exceed the peak statistical threhsold

( � � �� , � �� ) while clusters are composed of at least some number or extent E of re-

sels [20] above a cluster threshold ( �� , � � � �� , � � �� resels). The threshold on E

for a non-isotropic analysis must be in resels, not voxels; a big cluster can be non-significant in

a smooth region of the brain, whereas a small cluster can be significant in a rough region of the

brain.

The figure shows series of transverse, sagittal and coronal images for both experimental condi-

tions, on which voxels above the cluster significance level are shown superimposed on the ICBM

average for anatomical reference.

There was one significant cluster in the linear results (right insular cortex) and none in the non-

linear within-group results, while no voxels reached the peak significance level in either condition.

One can readily observe a decrease in the number of voxels above the cluster t-stat threshold (but

not reaching the resels extent criteria � ) to the point in nonlinear within-group results that they are

anatomically irrelevant and probably due to random variations in subject selection and MR signal

over the lifetime of the study.


4.3 Sensitivity experiment

VBM results were obtained for the series of experimental conditions described in Table 1, and can

be seen in Fig. 8, using the same image convention as the previous experiment. Clusters in the

mesial temporal lobe will be examined more closely since atrophy in that region was determined

using MR volumetry.

For the linear registration (Fig. 8(a)), 8 clusters reached statistical significance. There was one

significant cluster in the temporal lobe area (shown as two clusters in figure as the connection is

made on other slices), showing HC atrophy but with poor localization accuracy. In the nonlinear

ICBM registration (Fig. 8(b)) , 10 significant clusters are reported, yet the HC cluster did not reach

significance. In the nonlinear within-group results at � �� (Fig. 8(c)), 12 clusters are found. The

significance level and extent of the HC cluster improves over that of the ICBM target registered data

but does not yet reach significance; a parahippocampal (PHC) atrophy cluster on the other hand is

quite well defined. Finally, the best results can be found in the nonlinear within-group registration

results at �� smoothing (Fig. 8(d)). 17 significant clusters are reported throughout the brain. In

the temporal lobe area, both HC and PHC atrophy clusters reach significance, thus demonstrating

improved performance and localization accuracy over all other experimental conditions.

5 Discussion

Our results indicate that nonlinear registration diminishes anatomical variability, as evidence in the

standard deviation images. Additionally, our experiment using two groups of community dwelling

adults shows no increase in false-positive rate when nonlinear registration is used. Finally, our

proposed methodology based on nonlinear within-group registration using a small IGK of ��yielded the best performance in terms of sensitivity in our VBM analysis of left HA patients versus

CDA. In that experiment, the highest number of cluster was reported, as well as accurate detection

and localization of HC and PHC atrophy.


5.1 On nonlinear registration, specificity and sensitivity

Due to the large number of subjects in each group, we felt confident that on average inter-group

anatomical variability would be equal in areas untouched by the pathology while affected zones

would be substantially different. The latter can be readily verified when one compares the two

averages of linearly registered subjects in Fig. 3(b) and (c).

The standard deviation maps shown in Fig. 6 demonstrate the ability of nonlinear registration to

reduce the spatial variance within a given population. It also demonstrated that the choice of target

did not severely influence this ability; rather, subtle differences between the two groups (left HA

and CDA) are kept. Note that if nonlinear registration was perfect, then the within-group variance

would be equal to zero. The fact that it is not is a result of the imperfection of the process, itself

mainly due to the coarseness of the registration; this coarseness is directly related to the size of the

neighbordhood being optimized in the hierarchical nonlinear fitting process. The neighborhood

size chosen for this study was � �� , on the order of the expected differences in HA; a similar

thinking applies to the size selection for the IGK (see sec. 5.2).

Anatomical noise reduction is shown in Fig. 7 if one compares the decrease in statistically

significant clusters from VBM analysis of linear to nonlinear registration of two groups of com-

munity dwelling adult subjects. It also shows that there are no statistical differences between the

two groups if nonlinear registration is used. This confirms our hypothesis that nonlinear registra-

tion diminishes normal, anatomical noise and therefore can be used to improve the quality of VBM

results in the presence of pathology. Of course the sample size for both groups in the specificity

experiment was smaller ( �� ) than that for the sensitivity experiment but

still larger than many other validated fMRI and VBM studies found in the literature. This leads us

to wonder if the lack of differences would be maintained if the sample size was increased, in and

of itself an interesting experiment which other authors are attempting [16].

Anatomically relevant reduction in GM for left TLE patients is found in expected regions as

shown in Figure 8, where we notice that for equal input parameters and thus identical thresholds

of statistical significance, more clusters emerge when one moves from linear to nonlinear within-

group registration, and from a � �� to a �� IGK.

The spatial location of the main atrophy clusters in the temporal lobe is also improved as one

uses nonlinear within-group registration. In fact the only result concurrent with our volumetry


assessments in terms of HC atrophy (sec. 3.1) is achieved using our improved methodology and

a small kernel value. Standard linear approaches lack spatial localization accuracy, probably due

to the increase in anatomical noise between CDA and subject groups. Same-target nonlinear reg-

istration does not detect them at all, most probably due to conformisation of all subjects to the

symmetrical target. Finally a nonlinear within-group approach but with big kernel value ( � �� )

missed a key element (HC atrophy), although in this case, while the cluster results are borderline

in terms of statistical significance, many peaks can be located within the HC region.

5.2 On IGK size and data nonisotropy

VBM analyses in TLE usually report IGK sizes of �� and higher [19] [11]. The ultimate IGK

size should be commensurate with the effect being investigated, that is comparable to the spatial

extent of the expected regional differences between the groups [1]. In the case of TLE, the largest

atrophy is typically measured in the HC, which has a radius of nearly � �� . Salmond et al [14]

showed that lower kernel sizes ( �� ) are realistic if one uses balanced study designs, such

as the one we have. Therefore reducing IGK size closer or smaller than the HC radius should

have improved localization accuracy while maintaining statistical significance. This hypothesis

was confirmed if one observes our VBM results where we used a smaller kernel value ( �� ) in

concert with nonlinear within-group registration (Fig. 8(d)). One notices a sheer increase in cluster

count, better spatial localization (e.g., temporal area) of the clusters as well as the ability to extract

regions of known atrophy (e.g. hippocampus), as opposed to the same methodology but with a

bigger IGK size (Fig. 8(c)). Signal detection is thus optimal with a “matched” filter in terms of

IGK size.

Since our statistical testing takes into account the nonisotropy of our concentration images by

measuring cluster size in resels rather than voxels or �� [20], it allows us to report zones of

atrophy, commensurate with our volumetric results, rather than individual peak elements which

may not appear connected. This problem has also been discussed in Salmond et al [14]. Readers

should note that SPM99 does not correct for data nonisotropy even though it can report cluster

results.

Decreasing smoothing kernel size radically diminishes the data nonisotropy, as evidenced in

Fig. 5(a) and (b) and serves as another justification to use a smaller IGK.


5.3 On the use of nonlinear registration to improve VBM

Nonlinear registration with a sufficiently large local neighborhood is not unlike local linear regis-

tration. Therefore, fine-scale changes, smaller than the neighborhood of the nonlinear registration,

should not be warped to the point of disappearing and therefore remain detectable. In our nonlinear

registration the neighborhood was set at �� , as compared to our IGK FWHM of � or �� , itself

scaled to match the expected effect. Nonlinear average images have better detail and contrast than

linear averages; however, there is still much blurring, indicating that the anatomy is not perfectly

aligned and that the registration residuals are correlated with group membership.

In our methodology nonlinear registration is used in the same manner as SPM approaches it; the

change here resides in the choice of the target. Having a group-specific target, while maintaining a

large population target, reduces anatomical variability everywhere except where pathology is most

common.

A recent article by Wilke [18] presented a study in the variation of SPM99 parameters, in-

cluding the addition of modulation as suggested by Good [10]. Their results indirectly confirm

our hypothesis as they report that by reducing the neighborhood of the nonlinear registration a

higher normalization takes place and at some point differences disappear. As they used the same

target for both groups, regions of significance diminish as pathological differences are warped into

normality.

In TLE, to the spatial concept of anatomical variability one can oppose that of pathological sta-

bility. That patterns of atrophy are common between subjects has been proven by many volumetric

studies, and it is precisely the objective of VBM to find their location. Using a large ensemble

of subjects to form two targets implies that both share the same anatomical variability but not the

same pathological stability, as one may expect if one of the two groups is composed of healthy

community dwelling adults. It is the pathological spatial signal (or loss thereof) that we wish to

extract over the anatomical noise. We therefore suggest, as an antidote to anatomical variability,

the use of disease-specific targets composed of a large number of individual images sharing the

same disease spatial signature. While other studies than TLE (e.g., Alzheimer’s disease) may ben-

efit from this approach, it is also clear that this may not prove useful elsewhere where the disease

spatial characteristics are ill-defined and not well understood, such as multiple sclerosis.


6 Conclusion

Within-group nonlinear registration, when used in the way described in our study, reduces the

amount of normal intra-class, inter-subject anatomical variability while maintaining pathologically-

induced changes. It thus allows more subtle differences between groups under study to reach sta-

tistical significance. This addition to the list of VBM refinements furthers our ability to accurately

localize significant areas of change in brain matter concentration maps across individuals.

Acknowledgments

This work was supported by the Fonds pour la Recherche en Sante du Quebec (FRSQ), Man-

ulife Financial / Canadian Council of Professional Engineers and the Canadian Institute for Health

Research. The authors would also like to thank ICBM for permission to use the data.

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IGK cl. E sig. HC HC PHC PHC

Registration FWHM t-stat cl. cl. size cl. P cl. size cl. P

( �� ) (resels) (resels) (resels)

linear 5 3.17 208 8 901 0.046 901 0.046

nonlinear ICBM 5 3.17 208 10 797 0.07 303 0.6

nonlinear w/i gp 5 3.17 208 12 815 0.08 1521 0.002

nonlinear w/i gp 3 3.17 60 17 622 0.005 1191 7.3E-0.6

Table 1: Results from sensitivity experiment. Columns from left to right: Registration method, Isotropic Gaussian

Kernel Full-Width Half-Maximum (IGK FWHM), cluster t-statistics threshold (cl. t-stat), cluster extent (E), number

of statistically significant clusters (sig. cl.), hippocampus (HC) cluster size and P-value (HC cl. size, HC cl. P),

parahippocampus (PHC) cluster size and P values (PHC cl. size, PHC cl. P). 4 methodologies were tested, dependant

on their choice of registration and/or their choice of reference target. Temporal lobe clusters are examined more closely

as MR volumetric results had indicated hippocampal atrophy (HA). Linear registration results in one significannt

cluster of broad HA (poor localization). Nonlinear ICBM registration results in no clusters reaching significance in

the mesial temporal lobe (poor sensitivity). Nonlinear within-group registration at identical smoothing improves the

size of the HA cluster and accurately detects the presence of parahippocampal (PHC) atrophy. Finally, the use of a

smaller kernel with nonlinear within-group registration achieves both sensitivity and localization, with atrophy in HC

and PHC accurately detected.


Figure 1: Transverse ( �� ) and sagittal ( � �� ) images of community dwelling adult (CDA) (left column) and

TLE patient (right column). Notice enlargment of lateral horn of left ventricle, indicative of HC atrophy (red arrows).


Figure 2: Improved voxel-based morphometry pipeline. The standard methodology is shown in green, whilst our

modifications are displayed in red. Central to the proposed approach is (a) the creation of group averages from linearly

registered volumes, and (b) nonlinear registration of individual subjects to their group averages prior to classification

and GLM. Concentration thresholding and GM nonisotropy correction are necessary for valid cluster detection in the

statistical analysis of t-stat images.


ICBM avg Left TLE avg CDA avg

(a) (b) (c)

Figure 3: Transverse views ( � � � � ) through (a) average of 152 ICBM subjects in Talairach space; (b) average of

42 left HA subjects, linearly registered to ICBM average; and (c) average of 51 CDA matched to the left HA group.

Subtle differences can be discerned between (b) and (c) (red arrows), indicating higher local variability in TLE.


GM Concentration map GM mask

(a) (b)

Figure 4: (a) Transverse view ( � ��

) through concentration map averages for LHA and CDA ( �� )GM concentration maps following nonlinear within-group registration, �� smoothing. (b) Cluster statistics are

computed only on voxels belonging to this mask, computed by thresholding the average map in (a) with �� ,

thereby increasing the likelihood of GM presence in those voxels.


FWHM linear FWHM nonlinear

(a) (b)

Figure 5: (a) Transverse view ( � � �� ) through effective FWHM volume for (a) linear registered data, � � �isotropic Gaussian kernel smoothing and (b) nonlinear within-group registered data at � � � smoothing. The color-

coded scale is in effective FWHM ( �� ). Nonisotropy is obvious in both cases, but decreases with kernel size. The

effective FWHM is used to calculate cluster size in resels, rather than voxels or � � �

, to avoid nonisotropy.


Linear SD Nonlinear SD Ratio

LHA to ICBM avg

(a) (b) (c)

LHA to LHA avg

(d) (e) (f)

CDA to ICBM avg

(g) (h) (i)

CDA to CDA avg

(j) (k) (l)

Figure 6: Rows of images represent different combinations of population and registration techniques. Images in

the left column ((a), (d), (g) and (j) are transverse views ( � � �� ) throught the standard deviation maps associated

with the average of linear registered subjects (LIN SD). All linear registered images use the ICBM target shown

in Fig. 3(a). Images in the middle column ((b), (e), (h) and (k)) are also standard deviation images but following

nonlinear registration (NONLIN SD). Images in the right column are ratio images of NONLIN SD / LIN SD; a

ratio �� indicates a decrease in variability. In the first row linear and nonlinear registration to the ICBM target

(Fig. 3(a)) is compared for the left HA group. The second row is also the left HA group, this time comparing linear

and within-group nonlinear registration. The third and fourth rows compare the same approaches but this time for the

CDA group. One can readily see that in all cases nonlinear registration is successful in reducing normal, anatomical

variability regardless of input subjects or target average. At the same time subtle local differences can be seen in the

within-group results between the left HA and CDA ratio maps, confirming our hypothesis that normal variability can

be reduced independently of gross pathological variability.


Linear registration CDA1 vs CDA2 5mm IGK FWHM

(a)

NL registration CDA1 vs CDA2 5mm IGK FWHM

(b)

Figure 7: In order to demonstrate the reduction in anatomical variability when one uses nonlinear registration, two

groups of CDA ( �� subjects, �� subjects) were compared following linear registration (top row)

and nonlinear registration to their respective group averages as per the proposed improved VBM methodology (bottom

row). Spatial smoothing was similar in both instances (FWHM � � � ). Voxels above the level of statistical significance

for clusters ( � � �� , � � � � � � , corrected for multiple comparisons) from VBM analysis are shown, indicative of

decreases in GM concentration (atrophy). As both groups were composed of healthy individuals, no differences were

expected. Any difference would be indicative of the misregistration of the individuals. As was expected, in neither

condition did peaks reached the significance level, while linear registration produced 1 significant atrophy cluster

(right insular cortex), compared to none for within-group nonlinear registration.


Linear, 5mm Nonlin ICBM, 5mm Nonlin w/i gp, 5mm Nonlin w/i gp, 3mm

(a) (b) (c) (d)

Figure 8: Statistically significant clusters ( � � �� , corrected for multiple comparisons) from VBM analysis show-

ing GM concentration decreases (atrophy) of LHA subjects versus CDA, overlaid on ICBM average for anatomical

reference. (Column a) Linear registration results, � � � FWHM isotropic smoothing of input data. 7 significant clus-

ters of extent � � � � voxels at � � � � �� . In the temporal lobe area, hippocampal atrophy is detected (shown as

2 different clusters on this slice). (Column b) VBM results after nonlinear registration to the ICBM average, with

10 significant clusters. Notice the disappearance of the hippocampus atrophy cluster. (Column c) VBM results after

nonlinear within-group registration of subjects, � �� FWHM smoothing of input data, with 11 significant clusters

( � � � � �� , � � � � voxels). Parahippocampal atrophy is detected in the temporal area. (Column d) VBM results af-

ter nonlinear within-group registration, this time with �� FWHM smoothing, with 17 significant clusters ( � � � � � � ,� � � � voxels). This combination of parameters yields the best results, with clear and precisely defined hippocampal

and parahippocampal atrophy clusters, concurrent with our MR volumetry observations.

Within-group nonlinear registration improves …Within-group nonlinear registration improves...

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