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eDiscipline of Psychiatry, School of Medicine & Trinity College Institute of Neuroscience ... Hospital (AMNCH), Trinity College, University of Dublin, Ireland.
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Journal of Alzheimer’s Disease 20 (2010) 477–490 DOI 10.3233/JAD-2010-1386 IOS Press

Diagnostic Utility of Novel MRI-Based Biomarkers for Alzheimer’s Disease: Diffusion Tensor Imaging and Deformation-Based Morphometry Uwe Friesea,b,∗ , Thomas Meindlc , Sabine C. Herpertzd , Maximilian F. Reiserc , Harald Hampele,f and Stefan J. Teipela,g a

Department of Psychiatry, University of Rostock, Germany Institute of Psychology, University of Osnabrueck, Germany c Department of Radiology, University of Munich, Germany d Department of General Psychiatry, University of Heidelberg, Germany e Discipline of Psychiatry, School of Medicine & Trinity College Institute of Neuroscience (TICN), Laboratory of Neuroimaging & Biomarker Research, The Adelaide and Meath Hospital incorporating the National Children’s Hospital (AMNCH), Trinity College, University of Dublin, Ireland f Alzheimer Memorial Center, Department of Psychiatry, University of Munich, Germany g Deutsches Zentrum fu¨ r neurodegenerative Erkrankungen (DZNE), Germany b

Accepted 31 December 2009

Abstract. We report evidence that multivariate analyses of deformation-based morphometry and diffusion tensor imaging (DTI) data can be used to discriminate between healthy participants and patients with Alzheimer’s disease (AD) with comparable diagnostic accuracy. In contrast to other studies on MRI-based biomarkers which usually only focus on a single modality, we derived deformation maps from high-dimensional normalization of T1-weighted images, as well as mean diffusivity maps and fractional anisotropy maps from DTI of the same group of 21 patients with AD and 20 healthy controls. Using an automated multivariate analysis of the entire brain volume, widespread decreased white matter integrity and atrophy effects were found in cortical and subcortical regions of AD patients. Mean diffusivity maps and deformation maps were equally effective in discriminating between AD patients and controls (AUC = 0.88 vs. AUC = 0.85) while fractional anisotropy maps performed slightly inferior. Combining the maps from different modalities in a logistic regression model resulted in a classification accuracy of AUC = 0.86 after leave-one-out cross-validation. It remains to be shown if this automated multivariate analysis of DTI-measures can improve early diagnosis of AD in predementia stages. Keywords: Alzheimer’s disease, biomarker, deformation-based morphometry, diagnostic utility, diffusion tensor imaging, MRI

INTRODUCTION

∗ Correspondence

to: Uwe Friese, University of Osnabrueck, Institute of Psychology, Seminarstrasse 20, D-49076 Osnabrueck, Germany. Tel.: +49 (0) 541/969 6213; Fax: +49 (0) 541/969 4470; E-mail: [email protected].

Dementia is defined as a clinical syndrome characterized by a decline of memory functions and additional other cognitive abilities which is severe enough to interfere with daily life. Alzheimer’s disease (AD) is the most common cause of dementia accounting for at least

ISSN 1387-2877/10/$27.50  2010 – IOS Press and the authors. All rights reserved

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60% of cases in patients older than 65 years [1]. The definite diagnosis of AD requires autopsy and the neuropathological confirmation of characteristic amyloid plaques and neurofibrillary tangles. Deriving the clinical antemortem diagnosis of AD is a labor intensive process and requires the exclusion of numerous other possible causes for the syndrome. Thus, the development of accurate non-invasive biomarkers which could improve the assessment of AD – especially in early stages of the disease – is of great importance for selecting adequate treatment. Considerable progress has been made to establish biomarkers for AD based on magnetic resonance imaging (MRI). One important aspect is the development of processing methods and statistical procedures which can be applied to whole brain volumes without requiring major manual user input (such as manual drawing of regions of interests or manual measurement of certain structures). Another advancement is related to the modality of MR measurement, i.e., to the question of what is actually measured. In this study, we directly compare two relatively new and potentially complementing approaches with respect to their capability to distinguish between patients with AD and healthy control subjects. On the one hand, we derived images reflecting water diffusion properties in the brain by diffusion tensor imaging (DTI). On the other hand, we characterized macroscopic morphological changes with deformation-based morphometry (DBM) maps on the basis of high-resolution T1-weighted images from the same samples. For the analysis, we built on standard multivariate statistics which take all voxels of an image into account at once instead of performing mass univariate tests at each voxel. Early MR-based techniques to quantify structural brain changes in AD were mostly based on timeconsuming manual volumetry of key brain structures which show volume decline during the progression of AD. The hippocampus or the enthorinal cortex have been typical target structures in these studies [2–4]. In contrast, more recent approaches aim at minimizing manual user input and try to establish more or less automated analyses [5]. So far the most frequently applied automated method to study brain atrophy in AD is voxel-based morphometry (VBM) [6]. In VBM, individual brain scans are transformed to a common reference template with low-resolution normalization algorithms. Afterwards the signal intensities are interpreted as a measure of gray matter concentration which can be compared voxel by voxel using statistical parametric mapping. This method has been repeatedly used to demonstrate gray matter atrophy in

patients with AD in mediotemporal, temporo-parietal, and parietal regions [7–9]. VBM has been criticized because it provides no theoretical framework to discriminate between spatial effects on a local or a global scale. As an alternative to VBM, DBM has been proposed that provides spatial transformation of data on a high-resolution scale. Originally applied to anatomical MRI data, DBM has also been applied to DTI acquisitions. In DBM, the transformation of individual brain scans into a standard space provides information about relative reduction of brain volume with high spatial resolution [10]. In contrast to the low-resolution spatial normalization used in VBM, DBM is based on high-resolution image warping which preserves the intensities of voxels during the transformation. Hence, the normalized brain images are almost identical, and the information of interest (regional volume decline) can be derived from the so-called deformation fields. These deformation fields contain information about the positional difference between every voxel of the source brain and the reference brain. DTI is an advancement of diffusion weighted imaging (DWI). DWI measures the rate of water diffusion within each voxel. With DTI, diffusion weighted images are acquired in multiple spatial orientations to characterize the diffusion in three dimensional space (diffusion tensor ellipsoid). Depending on properties of the surrounding, this space can be shaped more like a sphere (isotropic diffusion) or rather like a cigar (anisotropic diffusion). There is evidence that the diffusion of water molecules in white brain matter is biased in the direction of the fibers and is thus anisotropic [11]. The impairment of fibers then, as it supposedly occurs in AD [12,13], leads to more unconstrained, isotropic diffusion as a consequence of progressive neurodegeneration [14]. Therefore, DTI measures can be assumed to reveal fiber tract integrity. DTI scans and deformation fields derived with DBM can be analyzed with various statistical procedures to detect patterns of degenerative changes in the whole brain without hypothesis-driven manual selection of regions of interest [15–17]. From the clinical perspective, it is important to know how these different approaches compare with respect to their ability to differentiate between the brains of healthy controls and brains of AD patients. A direct comparison of already published studies is difficult, though, because of the use of different samples and varying methodology. Often, studies differ with respect to several factors which can seriously affect the comparability of results. For instance, the diagnostic criteria to define subject samples, scanner equipment, image

U. Friese et al. / Diagnostic Utility of DBM and DTI Table 1 Sample characteristics Mean age in years (SE) Gender (female/male) Mean MMSE score (SE)

AD patients 76 (1.61) 12/9 22.9 (0.64)

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MRI aquisition Healthy controls 67 (1.64) 9/11 29 (0.15)

processing, and statistical analyses are usually not uniform across studies. For a reliable comparison it would be necessary to study the different modalities (DBM vs. DTI) within the same group of patients and controls. The objectives of the current study were to establish which method discriminates with the highest accuracy between the two groups (AD vs. control) and to evaluate if a combination of modalities may further increase diagnostic utility. To these aims, we applied DBM and DTI to the brain scans of the same sample of patients with AD and healthy control participants. We followed a multivariate statistical analysis approach which has been demonstrated to successfully reveal brain atrophy and decrease of white matter integrity in AD patients as compared to healthy control patients [16,17] and which has also been applied to the analysis of PET data [18, 19]. METHODS Participants MRI and DTI data were obtained from 21 patients with clinically probable AD and 20 healthy control participants. Neuropsychological testing included the Mini Mental State Examination (MMSE) [20] and the CERAD battery [21]. AD patients fulfilled the criteria of the National Institute of Neurological Communicative Disorders and Stroke and the Alzheimer Disease and Related Disorders Association (NINCDS-ADRDA) criteria for clinically probable AD [22]. Healthy control participants reported no cognitive deficits and performed within one standard deviation from the age- and education-adjusted means of the neuropsychological tests applied. Table 1 depicts sample characteristics and average MMSE scores of the participant groups. There was no significant difference between groups with respect to gender distribution (Pearson χ 2 = 0.61, df = 1, p = 0.54). AD patients were significantly older than controls (t 39 = 3.98, p < 0.01) and had inferior scores on the MMSE (t39 = 9.04, p < 0.01). All participants volunteered and gave written informed consent. The study was approved by the institutional review board.

MRI acquisitions of the brain were conducted with a 3.0 Tesla scanner with parallel imaging capabilities (Magnetom TRIO, Siemens, Erlangen, Germany), maximum gradient strength: 45 mT/m, maximum slew rate: 200 T/m/s, 12 element head coil. Participants were scanned in a single session without changing their position in the scanner. The following sequences were used: for anatomical reference, a sagittal highresolution 3-dimensional gradient-echo sequence was performed (magnetization prepared rapid gradient echo MPRAGE, field-of-view 250 mm, spatial resolution 0.8 × 0.8 × 0.8 mm 3 , repetition time 14 ms, echo time 7.61 ms, flip angle 200, number of slices 160). To identify white matter lesions a 2-dimensional T2weighted sequence was performed (fluid attenuation inversion recovery FLAIR, field-of-view 230 mm, repetition time 9000 ms, echo time 117 ms, voxel size 0.9 × 0.9 × 5.0 mm, TA 3.20 minutes, flip angle 1800, number of slices 28, acceleration factor 2). Diffusionweighted imaging was performed with an echo-planarimaging sequence (field-of-view 256 mm, repetition time 9300 ms, echo time 102 ms, voxel size 2.0 × 2.0 × 2.0 mm 3 , 4 repeated acquisitions, b-value 1 = 0, b-value2 = 1000, 12 directions, slice thickness 2.0 mm, 64 slices, no overlap). MRI data processing The processing of MRI data to derive DTI- and DBM-based brain maps was implemented with SPM2 (Wellcome Department of Imaging Neuroscience, London, UK, http://www.fil.ion.ucl.ac.uk/spm/) in Matlab 7 (Mathworks, Natwick). The detailed procedure is described elsewhere [16,17], and only the major processing steps are summarized below. First, a group specific template was created by averaging the individual anatomical images after low-dimensional normalization to the standard MNI-152 template. One good quality MRI scan of a healthy control subject then was normalized to this anatomical average image using highdimensional normalization with symmetric priors [23] resulting in a pre-template image. The MRI scan in native space of the same subject was then normalized to this pre-template image using high-dimensional normalization to produce the final group specific template. The individual anatomical scans in standard space (after low-dimensional normalization) were normalized to the anatomical template using high-dimensional image warping [23]. These normalized images were resliced

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to a final isotropic voxel size of 1.0 mm 3 . Next, for the DBM analysis, we derived Jacobian determinant maps from the voxel-based transformation tensors. These Jacobian maps contain information about regional volumetric atrophy or hypertrophy effects, i.e., each voxel value denotes a shrinkage or expansion of the source voxel with respect to the reference brain. The Jacobian determinant maps were masked for gray and white brain matter excluding cerebrospinal fluid (CSF) spaces (subsequently called BRAIN maps), and we additionally created corresponding maps for CSF spaces (CSF maps). The masks were obtained by segmenting the template image into gray and white matter and CSF spaces using SPM2. We took the logarithm of the masked maps of the Jacobian determinants [24] and then applied a 10-mm full width at half maximum isotropic Gaussian kernel. For the DTI analysis, we employed fractional anisotropy (FA) and mean diffusivity (MD) as measures of white matter integrity [25]. FA values summarize the directionality of the diffusion movement, ranging from 0 (isotropy) to 1 (anisotropy). The MD values inform about the overall diffusivity of a tissue. Processing of DTI data was performed with FSL and the FMRIB’s Diffusion Toolbox FDT (http://www.fmrib.ox.ac.uk/fsl/fdt/index.html). After applying corrections for eddy currents and head-motion to the images of the diffusion-weighted sequence, diffusion tensors were calculated, and maps of FA- and MD-values were produced. FA- and MD maps were restricted to white matter only by using a white matter mask derived from the segmentation of the template image. Statistical analysis For the statistical analysis, we followed an approach which is based on standard multivariate statistical procedures (PCA, MANCOVA, CVA [18,19]). A key advantage of this multivariate approach, in contrast to mass univariate analyses, is that the former considers all voxels from the entire brain volume at once. This is a particularly useful feature considering the propagation of AD pathology in distributed brain systems or networks. It also allows characterization, summarization, and comparison of distributed patterns in the volumes, instead of making voxel-by-voxel comparisons. This analysis has been demonstrated to reveal effects of atrophy and decrease of fiber tract integrity in AD patients [16,17]. Starting point was the application of principal component analysis (PCA) to the FA-, MD-, BRAIN-, and CSF-maps separately to reduce the di-

mensionality of these data. Secondly, to reveal general differences between the data of AD patients and control participants (effect of diagnosis), separate multivariate analyses of covariance (MANCOVA) were conducted. Thirdly, the spatial distribution of atrophy effects and effects of decreased fiber tract integrity was illustrated using canonical variate analysis (CVA). Finally, the diagnostic utility of the different modalities was assessed by estimating receiver operating characteristic curves (ROC) based on the principal component scores of the components which showed the highest correlations with diagnosis. A combination of modalities was evaluated with logistic regression analysis. In the context of statistical analyses of neuroimaging data, a major problem is that the number of dependent variables (usually the number of voxels in the order of tens or hundreds of thousands) greatly exceeds the number of observations (i.e., scans). One way to deal with this problem is to find a limited number of patterns within the original data – which, if combined, closely approximate the original data – and to perform the statistics on these patterns. PCA is frequently applied to simplify complex and correlated data as it exists in neuroimaging. The procedure can be viewed as projecting the original images into a new space in which the so-called principal components represent the axes of an orthogonal coordinate system with fewer dimensions than the original data. The principal components can also be interpreted as images with the first image explaining the largest amount of variance in the original data. Subsequent images then represent orthogonal components of the residual variance of the original data. Here, we determined the eigenvectors, also called eigenimages, and the associated eigenvalues of the covariance matrices of each modality (FA-, MD-, BRAIN-, and CSF-maps) by means of singular value decomposition. The resulting eigenvectors are the principal components, and the eigenvalues correspond to the amount of variance in the data explained by these components. In our analysis we only used eigenimages associated with an eigenvalue greater than unity. The expression of a principal component in each scan is called the principal component score (pc-score) and represents the projection of the scan in the new space. After reducing the dimensionality of the original data, we used MANOVAs to test on a global level if there were differences between AD patients and controls. The significance of the overall effect diagnosis (AD vs. controls) was tested through the ratio between the covariance matrix of the effect to the error covariance matrix under the null hypothesis, known as Wilk’s lambda.

U. Friese et al. / Diagnostic Utility of DBM and DTI

Under the null hypothesis, the values of Wilk’s lambda can be transformed and tested for significance using the χ2 -distribution with the degrees of freedom equal to the product of the number of eigenimages with a corresponding eigenvalue greater than unity and the rank of the design matrix [18]. To illustrate the nature of significant effects with respect to spatial topography, CVA was performed. CVA finds the eigenvectors that are maximally correlated with the explanatory variables. In our case, CVA identifies the principal component that best discriminates between AD patients and controls. To this end, we identified canonical images such that the variance ratio between the effect of interest and the total error sum of squares was maximized. Each canonical image has an associated canonical value that corresponds to a variance ratio and can be compared to an F distribution with numerator degrees of freedom equal to the rank of the design matrix and denominator degrees of freedom equal to the degrees of freedom of the error term. The canonical images with canonical values exceeding the critical F -value threshold for p < 0.05 characterize the differences in the respective parameter maps of AD patients versus controls. We verified whether positive or negative loadings in the canonical images represent decreased white matter integrity and atrophy by conducting directed t-tests with the respective maps of AD patients and healthy controls (data not shown). To summarize the output of the analysis: – principal components represent the original scans (as linear combinations). – principal component scores indicate to what extent a principal component is expressed in a given scan. – MANOVA tests for global differences between data from AD patients and controls. – CVA identifies the principal component that best discriminates between AD patients and controls (canonical image). Note that in this multivariate approach, the statistical inference is about the whole image volume. Consequently, in contrast to mass-univariate approaches to neuroimaging data (e.g., statistical parametric maps, SPMs), there is no need to correct for multiple testing. One drawback of the multivariate analysis is that statistical inferences about local regional changes are not valid. However, there is evidence that the regional pattern of results obtained with the aforementioned multivariate analysis closely mirror the effects of massunivariate analyses, in the sense that the peak values obtained with both methods occur in the same re-

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gions [16]. An advantage of the multivariate approach is that it allows the characterization of rather complex patterns across the entire brain volume by single scalar values. These, in turn, can be subjected to further statistical analyses to assess the diagnostic utility of the input modalities. To determine the diagnostic utility of individual FA-, MD-, BRAIN-, and CSF-maps, we identified the principal component that was significantly associated with diagnosis (AD vs. controls) by correlating the principal component scores of each scan with diagnosis. The scores from the principal component that were significantly correlated with diagnosis were entered in ROCanalyses as result variable. Diagnosis served as the state variable, and the estimated area under the curve (AUC) was chosen as a measure of discrimination accuracy. A logistic regression analysis with diagnosis (controls vs. AD) as dichotomous outcome measure was conducted. The principal component scores of DBM-Brain, DTI-MD, and DTI-FA maps, as well as patient age were used as predictor variables to estimate the classification performance of the combination of modalities. The validity of the results was evaluated with leaveone-out cross validation. This was done by conducting 41 logistic regression analyses, specified as described above, leaving out data from one subject per iteration. The predicted values of the left-out subjects were later on used as result variable in another ROC-analysis to estimate cross-validated discrimination accuracy.

RESULTS Multivariate analysis See Table 2 for details on the main statistical results. Applying principal component analysis reduced the dimensionality of the data of FA-, MD-, CSF-, and BRAIN-maps to between 8 (CSF) and 12 (FA, MD) eigenimages with eigenvalues greater than unity. Separate MANOVAs revealed that the overall effect of diagnosis (AD vs. control) was significant for all dependent variables (FA, MD, CSF, BRAIN) with p < 0.01. Moreover, canonical variate analyses allowed us to identify the components which accounted for the effects of diagnosis. For each modality there was exactly one canonical image significantly associated with diagnosis (p < 0.01 for FA, MD, CSF, and BRAIN). Figure 1 shows effects of atrophy or decrease of fiber tract integrity in AD patients in comparison to healthy controls as they were revealed by the different

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U. Friese et al. / Diagnostic Utility of DBM and DTI Table 2 Results of the statistical analyses DTI

DBM BRAIN

FA

MD

CSF

MANCOVA Number of eigenvectors Wilk’s Λ ap

12 39.04 < 0.01

12 50.54 < 0.01

8 36.52 < 0.01

11 34.85 < 0.01

Canonical variate analysis Canonical value bp

−88.23 < 0.01∗

−141.37 < 0.01

−71.71 < 0.01

−71.37 < 0.01

0.37 0.02

0.60 < 0.01

0.54 < 0.01

0.61 < 0.01

0.75 0.08 0.86/0.65

0.88 0.06 0.86/0.95

0.82 0.07 0.81/0.80

0.85 0.01 0.90/0.70

c Correlation

with diagnosis

r p ROC-analysis Area under curve, AUC Standard errors d Sensitivity/Specificity

Abbreviations: FA: fractional anisotropy, MD: mean diffusivity, CSF deformations fields masked to show effects within CSF spaces, BRAIN deformations fields masked to show effects within white and gray matter (excluding CSF spaces). a χ2 -test with df = number of eigenvectors. b F -test with numerator df = 39 and denominator df = 2. c Correlation of principal component scores of each scan with diagnosis. d Maximum of the average sensitivity/specificity coordinate pairs of the respective ROC-curve.

modalities. We projected the loadings of the canonical image which characterized atrophy effects or decrease of fiber tract integrity into voxel space. In detail, FA-maps show regions in which the FA was lower for AD patients than for controls, and MD-maps show areas in which MD was higher for AD patients than for controls. CSF deformation maps depict areas with a widening of CSF-spaces in AD patients in comparison to controls. In BRAIN-deformations maps regions are shown which were atrophic in AD patients compared to controls. For purposes of clarity, we only depict voxels with values above the 95th percentile. In addition, anatomical labels associated with peak values, are presented in Table 3 for DTI-data (FA and MD) and in Table 4 for DBM-data (CSF and BRAIN). Peak values were defined as local maxima exceeding the 99th percentile with a distance of at least 10 mm to other local maxima. Figure 1, Tables 3 and 4 reveal that for FA, MD, and BRAIN differential spatial patterns of atrophy or decrease of fiber tract integrity were found. Regional effects were widespread over cortical and subcortical areas. Summarizing the regional patterns, it is noticeable that the corpus callosum and the anterior cingulate cortex were the regions in which atrophic effects or decrease of fiber tract integrity were found consistently with FA, MD, and BRAIN maps (see Fig. 2 for an overlay of effects). FA maps furthermore revealed

decreased white matter integrity in parieto-occipital regions (precuneus, cuneus), in the prefrontal lobe, and in the basal ganglia (lentiform nucleus). MD maps also indicate effects in parieto-occipital areas, in the frontal lobe (e.g., middle frontal gyrus and precentral gyrus) and in the basal ganglia, as well as in the medial temporal lobe (parahippocampal gyrus). The DBM-analysis in gray and white matter resulted in broad atrophy effects in frontal, parietal, and temporal regions. Subcortical structures (lentiform nucleus and thalamus) were also found to be affected. In contrast to the DTI measures, no effects were found in occipital regions. The CSF-maps illustrate wider CSF-spaces in AD patients along the third ventricle, the inter-hemispheric fissure, and the left sylvian fissure. For each modality, there was a principal component which was significantly correlated with diagnosis. The correlation coefficients ranged from r = 0.37 (FA) to r = 0.61 (BRAIN). To assess the diagnostic utility of the different modalities we performed ROC-analyses on the scores of the principal components which were correlated with diagnosis. We estimated the AUC for each modality as measures of discrimination accuracy, and conducted pairwise comparisons between modalities (Table 3). Statistical tests were based on a procedure which builds on the correspondence of the AUC and the Wilcoxon statistic, and which accounts for the correlated nature of different AUCs which are derived

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Fig. 1. Spatial distribution of atrophy effects revealed by diffusion tensor imaging (FA, MD) and deformation-based morphometry (BRAIN, CSF). Components of canonical images which reflect atrophy effects were projected into voxel space. Only voxel-values above the 95th percentile on the respective canonical image were overlaid on coronal slices of a normalized anatomical image according to neurological convention (left is left).

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U. Friese et al. / Diagnostic Utility of DBM and DTI Table 3 FA and MD peak loadings on the canonical images Region Fractional anisotropy FA Precentral gyrus Superior frontal gyrus Precuneus Precuneus Cuneus Anterior cingulate gyrus Lentiform nucleus Mean diffusivity MD Middle frontal gyrus Middle frontal gyrus Middle frontal gyrus Precentral gyrus Middle frontal gyrus Medial frontal gyrus Middle frontal gyrus Inferior frontal gyrus Middle frontal gyrus Middle frontal gyrus Inferior frontal gyrus Postcentral gyrus Postcentral gyrus Lingual gyrus Middle occipital gyrus Cuneus Cuneus Anterior cingulate gyrus Posterior cingulate gyrus Posterior cingulate gyrus Parahippocampal Caudate Putamen Caudate

Side

x,y,z

L R R R L R R

−42, −1, 25 20, 19, 41 16, −53, 35 16, −52, 44 −25, −73, 8 13, −2, 49 23, 3, −9

L L L L L L R R R R R L L L L L R L L L R L L R

−55, 4, 41 −45, 38, 23 −43, 13, 33 −30, −9, 48 −28, −2, 50 −12, 59, 10 23, 53, 19 33, 32, −12 37, 46, 15 44, 42, 11 45, 17, 4 −62, −27, 39 −40, −27, 47 −28, −71, 0 −27, −97, 14 −5, −86, 29 3, 86, 28 −3, 37, 0 −12, −43, 42 −7, −29, 40 28, −56, 2 −21, 17, 8 −18, 18, −3 19, 20, 7

Note: Effects reflecting decrease of fractional anisotropy (negative component of canonical image) and increase of diffusivity (positive component of canonical image) in white matter of AD patients as compared to healthy control participants. Shown are characteristics of voxels with peak loadings on the canonical image above the 99th percentile. Anatomical labels refer to nearest gray matter as reported by the talairach daemon client [48].

from the same subjects [26]. Numerically, AUC was found to be lowest for FA (0.75) and highest for MD (0.88). The aforementioned statistical test revealed that the comparison between FA and MD showed a tendency towards significance (p = 0.09). No other pair of AUC-values was associated with p < 0.10. XY-plots in Fig. 3a-c illustrate pairwise comparisons of the discrimination abilities of the pc-scores from different modalities (DBM-CSF pc-scores were not included because of high correlation with DBM-Brain scores; r = 0.85). As AD patients were significantly older than participants of the control group, we additionally analyzed the data with age as covariate. This did not have an impact on any of the statistical inferences mentioned above. In particular, the analysis of discrimination accuracy resulted in identical ROC-values, and the patterns of at-

Table 4 DBM peak loadings on the canonical images Region BRAIN-mask Inferior frontal gyrus Precentral gyrus Superior frontal gyrus Superior frontal gyrus Precentral gyrus Middle temporal gyrus Supramarginal gyrus Posterior cingulate gyrus Anterior cingulate gyrus Anterior cingulate gyrus Anterior cingulate gyrus Claustrum Lentiform nucleaus Thalamus Sub-lobar Lentiform nucleaus CSF-mask Superior temporal gyrus Superior temporal gyrus

Side

x,y,z

L L L L R L L L L L L L L L L R

−53, 29, 15 −39, 16, 40 −15, 37, 41 −14, 13, 53 35, 10, 37 −55, 7, −16 −58, −48, 36 −20, −10, 36 −17, 24, 29 −17, 44, 11 −12, 26, 16 −30, 14, −2 −27, 7, 2 −25, −34, 4 −11, 10, −11 25, 15, −1

L L

−50, 11, −12 −47, 0, −14

Note: Effects reflecting atrophy in AD patients as compared to healthy control participants. Two different masks were used: The BRAIN mask images included white and gray matter and the CSFmask images included only CSF-spaces. Shown are characteristics of voxels with peak loadings on the canonical image above the 99th percentile.

rophy or decrease of fiber tract integrity in the different modalities were not altered substantially. Therefore, we do not present the results of these analyses as they do not lead to different conclusions regarding the main objective of this study. Supplementing the results of the ROC-analyses, we conducted a logistic regression analysis with diagnosis as dependent variable. The pc-scores based on DBM-Brain, DTI-MD, and DTI-FA maps as well as age served as predictor variables. The overall fit of this logistic regression model was significant (p < 0.01, χ 2 = 35.2, Nagelkerke’s R 2 = 0.77; Hoshmer-Lemeshow test p = 0.26). The contributions of both DTI predictors were significant (MD: p = 0.04; FA: p = 0.03) whereas age and DBM-Brain scores were not significant contributors (p > 0.1). Performing an ROCanalysis with the predicted probabilities of this model resulted in AUC = 0.95, sensitivity = 1, specificity = 0.95. After leave-one-out cross-validation these values dropped to AUC = 0.86, sensitivity = 0.85, and specificity = 0.85 (Fig. 3d). DISCUSSION In this study we investigated the diagnostic utility of DBM- and DTI-based measures for the discrimination

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Fig. 2. Overlay of FA-maps (yellow), MD-maps (red), and DBM BRAIN-maps (blue). Notice the overlap of decreased white matter integrity and atrophy in the corpus callosum (coronal slice). MD-maps in the sagittal and horizontal sections illustrate widespread decrease of fiber tracts integrity reaching from the occipital cortex into the temporal lobe.

(a)

(b)

(c)

(d)

Fig. 3. XY plots of pc-scores from different modalities for AD patients (solid circles) and healthy controls (open circles): (a) DBM-Brain versus DTI-MD, (b) DBM-Brain versus DTI-FA, (c) DTI-FA versus DTI-MD. Panel (d) illustrates group separation based on the predicted probability values of the logistic regression model after leave-one out cross validation. Dashed lines indicate cut-off values determined by maximizing the average of sensitivity and specificity values of the respective ROC-curve.

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between patients with AD and healthy controls. We used a multivariate analysis approach to determine significant patterns of atrophy or decrease of white matter integrity throughout the whole brain as reflected by DBM-maps (in gray and white brain matter and in CSF spaces) as well as FA-maps and MD-maps. For individual modalities, highest accuracy was found with MD maps (AUC = 0.88) and DBM-maps in gray and white matter (AUC = 0.85). The ability of FA to reveal directionality did not result in better diagnostic utility (AUC = 0.75). Combining modalities by means of a logistic regression, we found that only FA-maps and MD-maps were significant contributors to group separation. Cross validated discrimination accuracy was associated with AUC = 0.86. It is important to note that the discrimination accuracies for DBM- and DTI-measures presented here were derived from the same group of AD patients and controls and can be readily compared to each other. The finding that overall DTI did not perform better than DBM in discriminating AD patients and controls suggests that the measurement of decreased white matter integrity by DTI adds no further useful information for the separation of the groups than the assessment of atrophy effects by DBM. In particular, the discrimination accuracy of FA-maps (AUC = 0.75) was even slightly inferior to that of DBM-based maps and MD-maps. On the other hand, direct comparisons of the discrimination performance of FA, MD, and DBM (Fig. 3a-c) suggest that combining modalities should lead to better sensitivity/specificity. Correspondingly, the logistic regression analysis indicated that FA and MD both contributed significantly to the classification when modalities were combined in one model. Hence, FA maps and MD maps can complement one another for achieving better group separation. The question in how far changes of FA and MD in white matter represent different neurodegenerative processes has been recently addressed in a study on normal aging [27]. It was proposed that concordant changes of FA and MD might indicate demyelination and axonal loss, and that discordant changes (FA decrease without MD changes) might indicate Wallerian degeneration. Hence, for increasing diagnostic utility it may be advantageous to combine FA and MD for capturing different aspects of white matter damages in AD. Our finding of relatively high discrimination accuracy of individual MD-maps is a consistent replication of the results of a former study [17] where similar discrimination accuracy with DBM-maps in gray and white brain matter was found in an independent sample

of AD patients and healthy controls (AUC = 0.87 in that study vs. AUC = 0.88 reported here). The finding that DBM was not a significant contributor in the logistic regression model should not be overrated because the classification performance of the model was very high, and the algorithm sequentially picks out the predictor which explains most of the (remaining) variance. In the few studies combining DTI and morphometry measures to increase diagnostic utility, an inconclusive picture is drawn. DTI was found to be more sensitive than hippocampal volumetry for distinguishing between patients suffering from mild cognitive impairment (MCI) and healthy controls [28]. A logistic regression model with left hippocampal MD and left hippocampus volume reached a classification accuracy of 86%. Moreover, hippocampal diffusivity was a better predictor than hippocampal volumetry for the conversion from MCI to AD [29]. Comparable classification accuracies were reported for DTI indices (FA and apparent diffusion coefficients, ADC) and cortical thickness in various regions of interest [30]. While individual AUCs were in the range of 0.78 (superior temporal cortex thickness) to 0.86 (left temporal ADC), the combination of DTI and morphometry led to a maximal AUC = 0.98 for FA plus cortical thickness in the left temporal region. Partially contradicting these results, another recent study [31] combined brain metabolism (FDG-PET), morphometry (gray matter thickness), and DTI (FA). Here, morphometry data uniquely predicted diagnostic group (MCI vs. controls) when all modalities were entered simultaneously in logistic regression models for most of the nine regions of interest. For a logistic regression with all regions of interest and all modalities perfect classification accuracy (100%) was achieved. All of the aforementioned studies used region of interest approaches. In addition, the reported diagnostic accuracies are likely to overestimate the true capability of the respective method to distinguish between the diagnostic groups because no cross validation procedures were implemented. In contrast, our multivariate analysis approach takes changes across the entire brain volume into account which, on the one hand, might increase sensitivity and, on the other hand, avoids the need for manual, hypothesis-driven selection of regions of interest. Furthermore, we applied leave-one-out validation to obtain less biased estimates of discrimination accuracy. Additional indirect evidence for the validity of our procedure comes from a study in which the same multivariate analysis was applied to morphometry data from AD patients, MCI patients, and healthy

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controls [17]. There, the principal component solution used to discriminate between AD and controls was applied to the data from MCI patients (an independent sample) to predict conversion to AD. It was found that the method allowed discrimination between converters and non-converters with an accuracy of 80%. The patterns of structural changes which were found in white brain matter of AD patients were considerably different for FA, MD, and BRAIN maps, reflecting the differential aspects of the structural changes reflected by these modalities. Overlap of effects across FA, MD, and BRAIN maps occurred, for example, in the body of the corpus callosum and in the anterior cingulum. This is consistent with the abundant evidence that these structures are affected in AD [14,32–36]. The pattern of brain tissue loss revealed by DBM in the present study largely corresponds to known sites of atrophy in AD in the frontal, parietal, and temporal regions as well as in basal ganglia and in the thalamus [7,8, 17]. Many of the regions with decreased white matter integrity we found with FA- and MD-maps constitute intracortical projections from and to atrophic regions. For instance, the increase of diffusivity in the parahippocampal white matter might indicate damage to fibers connecting the hippocampus formation and enthorinal cortex with the posterior cingulate. These regions are typically affected relatively early in AD and have been demonstrated to be functionally connected [37]. Although occipital regions such as the cuneus are typically not among the most affected in AD, decreased white matter integrity and atrophy in this area have also been demonstrated [16,17,38]. This is compatible with our DTI results showing decreased FA and increased MD spreading over occipital, parietal, and temporal regions (see Fig. 2). With respect to the proposal that entire networks of areas are affected in AD [39,40], these findings are not surprising since long association fiber tracts (superior longitudinal fasciculus, inferior frontooccipital fasciculus) connect occipital visual processing areas and parietal, frontal, and temporal lobes [41, 42]. Several limitations of this study should be mentioned: Firstly, due to the rather small sample size, independent replications of the results are demanded to further validate the methods used. Additionally, although we did not observe significant direct influences of subject age as a covariate in our analyses, a closer match between patient and control group with respect to age would further increase validity. Concerning sample size and corresponding power to reveal robust effects our study cannot compete with approach-

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es such as the multicenter Alzheimer‘s Disease Neuroimaging Initiative (ADNI [43]) which provides the opportunity to study MRI data from much larger samples (e.g., [44,45]). However, no multimodal MRI data are available for ADNI or other multicenter initiatives so far. Therefore, the development of new methods has to proceed with single center data first where the findings then guide the selection of innovative acquisitions for future multicenter studies. One reason is the still relatively high amount of data processing – a second limitation of the present study concerning immediate practical implications. Clearly, an application of most likely all recently proposed MRI-based biomarkers in daily clinical use is not reasonable to date. This technical problem could be reduced to considerable degree, e.g., by extending existing analysis software as our approach builds on popular standard statistical procedures. We believe that a future application in a research context, for instance as a surrogate endpoint in clinical trials, would be conceivable. Basically, clinical application would be built on the principle component (PC) solution acquired from a larger reference population. Technically, one would estimate the PC-scores of the individual patient using the reference data. This can be seen as projecting the individual patient’s data (e.g., FA-values) into a coordinate system in which the principle components of the reference data constitute the axes. The estimated PCscore on the axis which had been shown to distinguish best between the diagnostic groups could be compared to the respective cut-off value. In this regard, the PCscore would be used as a diagnostic marker. Of course, as we have already pointed out, additional data is needed for validation. Foremost this includes the evaluation in other patient groups – particularly with MCI. As a next step it must to be shown if a multivariate analysis of DTI and DBM measures might improve early diagnosis of AD in predementia stages when atrophy effects are less distinctive than in the current study. As DTI has been shown to reveal damage to cortical projection fibers which are particularly affected in early stages of the disease [42,46, 47], our method might be suited particularly well to differentiate between converters and non-converters. In summary, we have demonstrated that multivariate analyses of MD maps in white matter and DBM maps in brain matter (excluding CSF spaces) are equally accurate in distinguishing between patients with AD and healthy controls. FA-maps were less effective for group separation. The combination of modalities in a logistic regression model resulted in a classification accuracy

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of AUC = 0.86 after leave-one-out cross-validation. Future studies should reveal if multivariate analyses of DTI and DBM measures can improve early diagnosis of AD in predementia stages when atrophic changes are less distinct than in manifest AD. ACKNOWLEDGMENTS Part of this work was supported by grants of the Medical Faculty of the Ludwig-Maximilian University (Munich, Germany) to S.J.T., of the Hirnliga e. V. (N¨urmbrecht, Germany) to S.J.T., an investigator initiated unrestricted research grant from Janssen-CILAG (Neuss, Germany) to H.H. and S.J.T., and a grant from the Bundesministerium f u¨ r Bildung und Forschung (BMBF 01 GI 0102) awarded to the dementia network “Kompetenznetz Demenzen”. There are no conflicts of interest including any financial, personal or other relationships with other people or organizations, by any of the co-authors, related to the work described in the paper. Authors’ disclosures available online (http://www.jalz.com/disclosures/view.php?id=270).

1. Derivation of eigenimages by principal component analysis Data were transformed into a (n×p) matrix X, where n is the number of scans (observations) and p is the number of voxels (variables). PCA consists of finding the eigenvalues and eigenvectors of the (p × p) covariance matrix of the data matrix X. The eigenvectors are the principal components (PC) and the eigenvalues give the variance explained by the corresponding eigenvector. In the terminology of image analysis, the eigenvectors are called eigenimages. As the number of variables p is at the order of 10 5 this covariance matrix cannot be computed with up to date computers. Therefore we used singular value decomposition (SVD) to compute the PCs of X. The output data of the PCA are: – Vk : Principal Components that are the eigenvectors of the covariance matrix X T X or in other words the new axes, k runs from 1 to n, where n is the number of observations. In this case they are 3D images, termed eigenimages. – Sk : Eigenvalues of the covariance matrix X T X, giving the variance explained by PC k .

APPENDIX: DETAILS ON MATHEMATICAL PROCEDURES

2. MANCOVA

The following procedures were applied analogue to Friston et al. (1996) [16,18,19]. Images were scaled to the same mean value and standard deviation using a voxel-wise z-transformation: xi,k − x¯k zi,k = sk where xi,k is the value of voxel i in scan k, x¯ k is the mean value across all xi of scan k and s is the standarddeviation across all xi of scan k. With imaging data, the number of observations (scans) is usually very small in relation to the number of variables (voxels). This limits the application of multivariate statistics. This issue is resolved by analyzing the data not in terms of voxels, but in terms of eigenvectors (=eigenimages). The analysis proceeded in three steps. First, we determined the eigenvectors of the data covariance matrix using principal component analysis (PCA), to reduce the dimensionality of the data. Second, we determined the significance of the hypothesized effect of diagnosis (AD vs. controls) using MANCOVA. Third, we characterized the spatial distribution of these effects using canonical variate analysis in terms of the canonical vector that best captured the effect of diagnosis. The multivariate analysis followed in 3 steps:

To ensure that the number of variables is smaller than the number of observations, the dimensions of the XT X matrix were reduced through the singular value decomposition X. The matrix of the dependent variable Y then is the product of the eigenvector matrix U of the covariance matrix XX T (projections of X in the space of the observations) and the eigenvalues S of the covariance matrix X T X. Only those columns of U and Y were used that were associated with an eigenvalue greater than unity (after normalizing each eigenvalue by the average eigenvalue). The effect of diagnosis was modeled according to the general linear model with Y as multivariate dependent variable and diagnosis as binary predictor variable and the mean effect. The significance of the overall effect was tested through the ratio between the sum of squares and products due to the effect by the error sum of squares and products under the null hypothesis, i.e., discounting the effect. This ratio is known as Wilk’s lambda. After transformation under the null hypothesis Wilk’s lambda has a χ2 distribution with degrees of freedom equal to the product of the number of eigenimages associated with an eigenvalue greater unity and the rank of the matrix of the effects of interest.

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3. Canonical variate analysis (CVA) To characterize the effect in terms of its spatial topography, we aimed to find a linear combination of the compounds of Y, i.e., the eigenimages that best express the group effects when compared to error effects. To this end, we defined canonical images, c, in the observation space such that the variance ratio between the effect of interest and the total error sum of squares was maximized. The canonical images in voxel space were then found by rotating the canonical images in observation space into voxel space with the original eigenimages V: C =c∗V The matrix C now contained the voxel values of the canonical images. The kth column of C has an associated canonical value that serves to estimate whether a particular canonical image is important. The canonical value can be compared to an F distribution with nominator degrees of freedom equal to the rank of the matrix of the effect of interest and denominator degrees of freedom equal to the number of scans minus the rank of the design matrix (= degrees of freedom of the error term). We considered a canonical image important if its canonical value exceeded the critical F threshold for p < 0.05. The expression of the canonical images in each scan, i.e., the projection of the canonical image in observation space, analogous to the principal component scores of a PCA, can be determined as: Z k = Y ∗ ck where Zk represents the canonical variates of the kth canonical image, i.e., its expression in each scan, and ck is the kth canonical image in observation space.

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