Amygdalar Atrophy in Symptomatic Alzheimer's Disease Based on Diffeomorphometry

Neurobiology of Aging 36 (2015) S3eS10

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Neurobiology of Aging

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High-dimensional morphometry Amygdalar atrophy in symptomatic Alzheimer’s disease based on diffeomorphometry: the BIOCARD cohortq

Michael I. Miller a,b,c,*, Laurent Younes a,b,d, J. Tilak Ratnanather a,b,c, Timothy Brown a, Huong Trinh a, David S. Lee a,c, Daniel Tward a,c, Pamela B. Mahon e, Susumu Mori f, Marilyn Albert g, the BIOCARD Research Team a Center for Imaging Science, Johns Hopkins University b Institute for Computational Medicine, Johns Hopkins University c Department of Biomedical Engineering, Johns Hopkins University d Department of Applied Mathematics and Statistics, Johns Hopkins University e Department of Psychiatry, Johns Hopkins University School of Medicine f Department of Radiology, Johns Hopkins University School of Medicine g Department of Neurology, Johns Hopkins University School of Medicine article info abstract

Article history: This article examines the diffeomorphometry of magnetic resonance imaging-derived structural markers Received 2 May 2013 for the amygdala, in subjects with symptomatic Alzheimer’s disease (AD). Using linear mixed-effects Received in revised form 29 May 2014 models we show differences between those with symptomatic AD and controls. Based on template Accepted 8 June 2014 centered population analysis, the distribution of statistically significant change is seen in both the vol- Available online 29 August 2014 ume and shape of the amygdala in subjects with symptomatic AD compared with controls. We find that high-dimensional vertex based markers are statistically more significantly discriminating (p < 0.00001) Keywords: than lower-dimensional markers and volumes, consistent with comparable findings in presymptomatic Amygdala fi fi MCI AD. Using a high- eld 7T atlas, signi cant atrophy was found to be centered in the basomedial and Alzheimer’s disease basolateral subregions, with no evidence of centromedial involvement. Shape 2015 The Authors. Published by Elsevier Inc. All rights reserved. MRI

1. Introduction associated with likelihood of progression from MCI to AD dementia (Atiya et al., 2003; Kantarci and Jack, 2004). Magnetic resonance imaging (MRI) studies have substantially To date, most MRI studies of subcortical gray matter nuclei have advanced our knowledge of brain atrophy in Alzheimer’s disease defined a single measure of structural volume (Bossa et al., 2011; (AD). MRI measures are an indirect reflection of the neuronal injury McEvoy et al., 2011; Roh et al., 2011). Although this has the that occurs in the brain as the AD pathophysiological process advantage of being quantitative, it does not give specific informa- evolves. Several MRI measures are known to be altered among in- tion about subregions of atrophied nuclei. This information would dividuals with AD dementia or mild cognitive impairment (MCI). In be useful to determine whether morphometric results correlate the initial stages of AD, atrophy appears to have a predilection for with neuropathologic studies, define better the subregional distri- brain regions in the medial temporal lobe with heavy deposits of bution of atrophy, and correlate pathologic changes with clinical neurofibrillary tangles (Arnold et al., 1991; Braak and Braak, 1991; features of AD. Price and Morris, 1999). Consistent with this pattern of neurofi- Diffeomorphometry and geodesic positioning in computational brillary pathology, the volume of the entorhinal cortex and hip- anatomy (Miller et al., 2014) for the study of the distribution of pocampus have been shown to discriminate patients with AD functional and structural change in neurodegeneration has already dementia or MCI versus cognitively normal subjects and to be proved to be very powerful. Statistical shape analysis has been useful for studying normal age-related changes in subcortical q This is an open access article under the CC BY-NC-SA license (http:// nuclei, and a number of other diseases (Ashburner et al., 2003; creativecommons.org/licenses/by-nc-sa/3.0/). Csernansky et al., 1998, 2000; Qiu et al., 2010; Thompson et al., * Corresponding author at: Center for Imaging Science, The Johns Hopkins 2004; Wang et al., 2007). The study described here follows our University, 3400 N Charles St, Baltimore, MD 21218, USA. Tel.: þ1 410 516 3826; fax: þ1 410 516 4594. previous work (Miller et al., 2013), in which we used diffeo- E-mail address: [email protected] (M.I. Miller). morphometry to measure subregional atrophy in 3 temporal lobe

0197-4580/$ e see front matter 2015 The Authors. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.neurobiolaging.2014.06.032 S4 M.I. Miller et al. / Neurobiology of Aging 36 (2015) S3eS10 structures, entorhinal cortex, hippocampus, and amygdala, in sub- assessments, collect blood, and evaluate the previously acquired jects with preclinical AD, that is, individuals who were clinically and MRI scans, cerebrospinal fluid, and blood specimens. To the best of cognitively normal at the time of their MRI scans. This approach our knowledge, this is the only study in participants who were allows for a fine-scale high-dimensional analysis of nonuniform cognitively normal at entry, with this set of measures, and with change patterns in the structures and complements coarser mea- such a long duration of follow-up. sures, such as measures of total volume. Despite its proximity to the At baseline, all participants completed a comprehensive evalua- hippocampus, relatively little is known about the role of amygdala tion at the Clinical Center of the National Institutes of Health (NIH). in MCI and AD. Following earlier histopathologic findings This evaluation consisted of a physical and neurologic examination, (Arriagada et al., 1992; Herzog and Kemper, 1980; Scott et al., 1991, an electrocardiogram, standard laboratory studies (e.g., complete 1992; Tsuchiya and Kosaka, 1990), neuroimaging studies of AD blood count, vitamin B12, thyroid function, and so forth), and neu- patients suggest that amygdala volume may correlate with that of ropsychological testing. Individuals were excluded from participa- the hippocampus (Poulin et al., 2011). Further, recent shape analysis tion if they were cognitively impaired, as determined by cognitive (Cavedo et al., 2011; Qiu et al., 2009) suggests there is substantial testing, or had significant medical problems such as severe cere- atrophy within the amygdala in AD. brovascular disease, epilepsy, or alcohol or drug abuse. Five subjects The study described here focuses on the examination of the did not meet the entry criteria and were excluded at baseline, leaving amygdala via diffeomorphometry. By mapping features across co- a total 349 participants who were followed over time. ordinate systems, it was possible to identify morphometric changes fi obtained in 1.5 T scans within high- eld 7T parcellations of the 2.3. MRI assessments amygdala. We demonstrate that the location of statistically significant change is distributed across the core amygdala, including the The MRI scans acquired at the NIH were obtained using a standard basolateral and basomedial nuclei, in subjects with symptomatic multimodal protocol using GE 1.5 T scanner. The scanning protocol AD compared with controls. included localizer scans, axial fast spin echo sequence (repetition time [TR] ¼ 4250, echo time [TE] ¼ 108, field of view [FOV] ¼ 512 512, 2. Methods thickness/gap ¼ 5.0/0.0 mm, flip angle ¼ 90,28slices),axialfluid- attenuated inversion recoverysequence (TR ¼ 9002, TE ¼ 157.5, FOV ¼ 2.1. Study design 256 256, thickness/gap ¼ 5.0/0.0 mm, flip angle ¼ 90,28slices), coronal spoiled gradientecho (SPGR) sequence (TR ¼ 24, TE ¼ 2, FOV ¼ In the present study, known as the BIOCARD study, all subjects 256 256, thickness/gap ¼ 2.0/0.0 mm, flip angle ¼ 20, 124 slices), were cognitively normal when they were recruited. The mean age and sagittal SPGR sequence (TR ¼ 24, TE ¼ 3, FOV ¼ 256 256, of the BIOCARD subjects at baseline was 57.1 years. MRI scans were thickness/gap 1.5/0.0 mm, flip angle ¼ 45, 124 slices). The analyses acquired during the period 1995e2005. The participants have now described here used the coronal SPGR scans. A total of 805 scans were been followed for up to 17 years. Table 1 provides summary of the acquired from the participants with a mean of 2.4 scans per person. demographic characteristics of the subjects. 2.4. Clinical and cognitive assessment 2.2. Selection of participants The clinical and cognitive assessments of the participants have A total of 354 individuals were initially enrolled in the study. been described elsewhere (Moghekar et al., 2013). The cognitive Recruitment was conducted by the staff of the Geriatric Psychiatry assessment consisted of a neuropsychological battery covering all branch of the Intramural Program of the National Institute of major cognitive domains (i.e., memory, executive function, language, Mental Health (NIMH). Subjects were recruited via printed adver- spatial ability, attention, and processing speed). A clinical assess- tisements, articles in local or national media, informational lec- ment was also conducted annually. This included the following: a tures, or word-of-mouth. The study was designed to recruit and physical and neurologic examination, record of medication use, follow a cohort of cognitively normal individuals who were pri- behavioral and mood assessments, family history of dementia, his- marily in middle age. By design, approximately three quarters of the tory of symptom onset, and a Clinical Dementia Rating (CDR), based participants had a first degree relative with dementia of the Alz- on a semi-structured interview (Hughes et al., 1982; Morris, 1993). heimer type. The overarching goal was to identify variables among cognitively normal individuals that could predict the subsequent 2.5. Consensus diagnoses development of mild to moderate symptoms of AD. Toward that end, subjects were administered a comprehensive neuropsycho- Each case included in these analyses has received a consensus logical battery annually. MRI scans, cerebrospinal fluid, and blood diagnosis by the staff of the BIOCARD Clinical Core at Johns Hopkins. specimens were obtained approximately every 2 years. The study This research team included: neurologists, neuropsychologists, was initiated at the NIMH in 1995 and was stopped in 2005. In research nurses, and research assistants. During the study visit, 2009, a research team at the Johns Hopkins School of Medicine was each subject had received a comprehensive cognitive assessment jointly funded by the National Institute on Aging (NIA) and NIMH to and a CDR, as well as a comprehensive medical evaluation reestablish the cohort, continue the annual clinical and cognitive (including a medical, neurologic, and psychiatric assessment).

Table 1 Participant characteristics stratiﬁed by outcome status

Variable Control group MCI during scan AD dementia during (N ¼ 230) (N ¼ 9) scan (N ¼ 7) Age at time of baseline MRI scan, mean 55.4 (9.8) 64.3 (9.96) 63.8 (8.04) number of years (SD) Gender, females (%) 61 33 57

Key: AD, Alzheimer’s disease; MCI, mild cognitive impairment; MRI, magnetic resonance imaging; SD, standard deviation. M.I. Miller et al. / Neurobiology of Aging 36 (2015) S3eS10 S5

For the cases with evidence of clinical or cognitive dysfunction, a In each scan, the amygdala was segmented using the land- clinical summary was prepared that included information about mark region-of-interest template-based Large Deformation Dif- demographics, family history of dementia, work history and past feomorphic Metric Mapping (LDDMM) pipeline comparable with history of medical, psychiatric, and neurologic disease, medication previous work (Csernansky et al., 1998; Munn et al., 2007). A use, and results from the neurologic and psychiatric evaluation. The representative elderly cognitively normal subject was selected as reports of clinical symptoms from the subject and collateral sour- the template, and left and right structures were segmented ces, based on the CDR, were summarized, and the results of the manually. The principal axis was identiﬁed by placing the head neuropsychological testing were reviewed. Thus, the diagnostic landmark at the center of the inferior boundary of the entorhinal process for each case was handled in a similar manner: (1) clinical sulcus (on the most anterior coronal plane showing the limen data were examined pertaining to the medical, neurologic, and insula), with the tail landmark placed at the center of the most psychiatric status of the subject; (2) reports of changes in cognition caudal aspect of the basomedial nucleus (on the most caudal by the subject and by collateral sources were examined; and (3) coronal plane showing the amygdala). Equidistant sections were decline in cognitive performance was established. These data were selected perpendicular to this principal axis, with landmarks on used to: (1) determine whether the subject had become cognitively each section placed at the dorsal lateral and dorsal medial extent impaired; (2) determine the likely etiology of any impairment; and of the amygdala, and at an intermediate point on the dorsal (3) determine the age at which the clinical symptoms began, based amygdala boundary, as well as at the ventral lateral and ventral primarily on the reports of clinical symptoms from the subject and medial extents of the amygdala, and intermediate point on from collateral sources. These diagnostic procedures are identical to ventral amygdala boundary. Please see http://caportal.cis.jhu.edu/ those implemented in the Alzheimer’s Disease Research Centers wiki/tutorials/amygdala/amygdala.html for a description of the program, supported by the NIA. It is acknowledged that, as this landmark placements. Inter-rater reliability for 9 scans yielded a process is dependent on the clinical and cognitive data available at mean kappa score of 80.95 for left and right segmentations. any one point in time, some subjects who are diagnosed as having Landmarks encompassing the amygdala were used to calcu- MCI may subsequently be diagnosed as normal or as impaired not late a rigid transformation (Umeyama, 1991) between the tem- MCI. This represented 4 of the subjects in the total sample. plate followed by LDDMM landmark matching (Joshi and Miller, During the acquisition of the scans at the NIH, 7 subjects were 2000) and image matching (Beg et al., 2005). These trans- diagnosed with dementia of Alzheimer’s type (DAT), and 9 subjects formations were subsequently used to move the template seg- were diagnosed with MCI. We term this set of subjects the mentation onto each subject’s MR scan yielding segmentations “symptomatic” cohort, that is, subjects who had MCI or DAT at the for each subject. time the scans were taken. Four or more years later, when the study Segmentations were individually inspected, manually corrected was re-initiated at Johns Hopkins, an additional number of subjects where necessary and then converted into triangulated surfaces had developed MCI or DAT. During the entire period, 230 subjects using the open source iso2mesh software. Fig. 1 shows the amygdala continued to be cognitively normal whom we deﬁned as the control relative to the hippocampus and entorhinal cortex and their group. In the analyses described in the following (Section 2.8.3.4), embedding in a section in one subject. we included age and gender as covariates to adjust for any differences in these parameters between the groups. 2.7. Amygdalar nuclei parcellation

2.6. Region-of-interest analysis A 7T MRI scan of resolution 0.8 mm was used to reconstruct high-field parcellation of the population amygdala. The 7T sub- Statistical shape analysis requires a preliminary alignment phase, ject is a 42-year-old male who is healthy by self-report. The which produces a high-dimensional representation in a fixed coor- subject was scanned using a standard MPRAGE protocol in a dinate system. A common approach in this framework is to register Philips Achieva 7.0 T scanner (TR ¼ 4.3 ms, TE ¼ 1.95 ms, flip all shapes to a single one, called the template, defining each anatomy angle ¼ 7,FOV¼ 220 220 180). The amygdala was sub- by its position relative to the template. This is achieved via diffeo- divided into 4 nuclei: lateral, basolateral, basomedial, and cen- morphic mapping methods. It is important, in this context, to ensure tromedial nuclei using definitions based on the Paxino Atlas of that the template is as close as possible to the population, and it will the Human Brain (Mai et al., 2004) and illustrated in detail at be defined as representing the population average. http://caportal.cis.jhu.edu/wiki/tutorials/amygdala/amygdala.html.

Fig. 1. Left: surface reconstruction of amygdala (green), entorhinal cortex (red), hippocampus (blue), ventricle (gray) from one BIOCARD subject. Right: corresponding MRI section with reconstructed structures embedded in the MRI volume. Abbreviation: MRI, magnetic resonance imaging. S6 M.I. Miller et al. / Neurobiology of Aging 36 (2015) S3eS10

2.8. Diffeomorphometry shape analysis via surface-based the distance being given by the optimal deformation cost (Vaillant morphometry and Glaunes, 2005). The second error term computes a norm between surfaces. The construction is based on the representation of 2.8.1. Template averaging surfaces as geometric currents. Using rigid registration (rotation and translation) each amygdalar surface (from Section 2.6) was aligned to a common spatial 2.8.3. Shape statistics position. Rigid registration computes an optimal transformation During the preprocessing phase, each subject’s left structure was between vertices of 2 surfaces S0 and S1, by minimizing a score registered to the template, resulting in the computation, at each combining registration and soft assignment, given by:. vertex k of the template surface, and for each subject s, of a defor- Z mation marker Yk(s) that measures the expansion and/or atrophy at 2 vertex k in subject s relative to the template. This is defined as the Fðw; R; TÞ¼ wðx; yÞkRx þ T yk ds1ðxÞds2ðyÞ logarithm of the local expansion and/or reduction in surface area S S 1 2 Z around vertex k entailed by template registration and can be interpreted mathematically as a log-jacobian on the population þ l wðx; yÞln wðx; yÞds1ðxÞds2ðyÞ template surface. See Figs. 3e5 for examples of such markers. These S S 1 2 markers were then transformed into a sequence of shape indicators Here, R and T are a rotation matrix and a translation vector, at different resolution as follows: respectively; s1 and s2 are area forms on S1 and S2, respectively; and fi w is a soft assignmentR function de nedR on S1 S2, which is positive 2.8.3.1. High resolution. The vertex Jacobian marker Yk(s), which and satisfies wðx0; yÞds ðxÞ¼ wðx; y0Þds ðy0Þ¼1 for all has 750 dimensions associated to the number of vertices. S1 1 S2 2 ðx; yÞ˛S1 S2. Right subvolumes were flipped before alignment to facilitate comparison of left and right structures in fixed coordinates. 2.8.3.2. Projection on Laplace-Beltrami eigenbasis. The first 25 ei- The rigidly aligned volumes were used to generate a population genvectors of the surface Laplacian are computed (on the popula- template (Ma et al., 2010) based on a generative shape model, inwhich tion template) and the 25-dimensional projection of the surface an observed surface is modeled as a random deformation of a tem- log-Jacobian of the deformation. plate with additive noise. Given this model, the population template is estimated from the surface population data using the mode approx- 2.8.3.3. High-field defined subnuclei markers. Four amygdala sub- imation to the EM algorithm, subject to the topology constraints that fields are defined from the 7T high-resolution images, which are the population template is a diffeomorphic transformation of a fixed mapped onto the population template using LDDMM surface reference shape called the hypertemplate. In the Bayesian viewpoint, matching. This transports the labelled high-field template to the the population template is considered as a random deformation of the population template allowing the labeling of the vertices. The dif- hypertemplate. The population template becomes the coordinate feomorphic surface mapping generates the bijection between the system and is computed by applying the algorithm to the population 1.5 T population template and the high-field 7T atlas on the con- of 173 baseline scans and is therefore blind to labels. tinuum of the 3D coordinate system allowing us to transfer the labeled information between the 2 coordinate systems. The tem- 2.8.2. LDDMM surface registration plates were highly sampled so that vertices are small, thereby Non-rigid registration between the population template and all allowing precise transfer of information between the vertices of the surfaces is done via LDDMM surface registration (Vaillant and 2 coordinate systems as defined by the diffeomorphic bijection as Glaunes, 2005) which computes a smooth and invertible trans- shown in Fig. 2. The labeled vertices of the subfields are used to formation that deforms the template to a surface that is very close develop an integrated Jacobian marker for each of the 4 nuclei to the target. More precisely, it minimizes a 2-term energy function basolateral, basomedial, centromedial and lateral. These nuclei will taking the form be denoted belowas 1, 2, 3 and 4 respectively. This is a 4-dimensional marker shown in Fig. 3. Note that the values are all positive, indi- 2 ; ; cating that group difference is only associated with atrophy. E ¼ Distshape Stemp Sdef þ l Error Sdef Sobs Global: logarithm of the structure volume. where Stemp is the population template surface, Sobs is the observed fi surface, and Sdef is the deformed population template. The rst 2.8.3.4. Linear mixed-effects model. The statistical analyses com- term, Distshape, is a geodesic distance in shape space, which compared subjects with symptomatic AD (i.e., subjects with MCI and AD putes and optimizes a least-deformation path between 2 surfaces, dementia) versus cognitively normal individuals. The analyses

Fig. 2. High-ﬁeld 7T amygdala template (left) mapped into BIOCARD 1.5 T population coordinates (middle); regions correspond to parcellation into 4 subnuclei: basolateral (blue), basomedial (sky-blue), centromedial (caramel) and lateral (red). These nuclei will be denoted below as 1, 2, 3 and 4 respectively. The right column shows a labeling into the 4 subﬁeld parcellation of the 1.5 T population BIOCARD atlas generated by transferring the labels in the closest vertex in the middle column to the 1.5 T coordinate system. M.I. Miller et al. / Neurobiology of Aging 36 (2015) S3eS10 S7

Fig. 3. Statistically significant family wise error rate (FWER) at 5% significance for the mixed effects modeling of the symptomatic group compared with controls, demonstrating atrophy for left and right amygdala. Left panel shows statistics depicted from medial-rostral aspect; right panel shows depiction from medial-caudal aspect. Statistically, significant vertex coloring given by the natural log of the surface Jacobian b þ b0a indexed over the template between the control versus symptomatic groups corrected at the average age. For reference only, shown are entorhinal cortex, hippocampus, and lateral ventricle. included age, gender, and log intracranial volumes as covariates, and 1 computed statistics at each vertex of the template surface, corrected q ¼ SXX SXX SXY SXY for multiple comparisons, using permutation tests. fi To estimate the variance, de ne the residual R(Ps) ¼ Y(s) X(s)q, Our statistical model is a linear mixed-effects model in which N which is an N K matrix. For a given v, letRvðsÞ¼ s R vðsÞ. Then the noise associated with the scans from the same subject is s j ¼ 1 j modeled as different than the noise associated cross-sectionally in Xn Xn 2 2 1 2 r RvðsÞ averaging to the common template. Hence the term “mixed-ef- sv ¼ kRvðsÞk N N 1 þ rN fects”. So we introduce group variables g(s) equal to 1 if subject s s ¼ 1 s ¼ 1 s belonged a disease group and 0 otherwise. These disease groups Step 2: Update r with all other parameters fixed. Compute, with will be MCI, AD, MCI þ AD for the symptomatic classification. We the notation mentioned previously. then use the linear statistical model defined as. XK 2 0 0 1 RvðsÞ Yvj s ¼ av þ a vaj s þ bv þ b vaj s g s þ gvc s þ dvd s [ s ¼ K s2 ε v ¼ 1 v þ vj s Then, br is defined as the minimizer of. where s denotes subjects/structure; j represents scan order in the ’ Xn [ Xn subject s time series; v indexes the multivariate marker (v is be- b ðsÞ r ¼ argminr r þ logð1 þ rNsÞ tween 1 and 1, 4, 7, 25, or 750); Yvj(s) is the vth coordinate of 1 þ rN s ¼ 1 s s ¼ 1 deformation marker for subject s at scan j; aj(s) is the subject’s age at scan j; g(s) is the subject’s group (control or disease); c(s) and d(s) This minimization has no closed-form solution and must be are covariates and respectively denote the subject’s intracranial performed numerically. volume and gender; εvj(s) represents the noise, modeled as εvj(s) ¼ Note that this model assumes that r is independent of the shape hv(s) þ zvj(s) where hv(s) measures between-subject variation and coordinate, v. Although extending this algorithm to a coordinate- zvj(s) measures within-subject variation. Both noise are assumed to dependent parameter would be straightforward, we have 2 2 be centered Gaussian, with variance rsv and sv , respectively. preferred not to do so to avoid the computational burden of per- 0 0 2 The parameters av; a v; bv; b v; gv; dv; sv and r are estimated by forming K nonlinear optimization procedures at each step maximum-likelihood. The estimation procedure is iterative and mentioned previously, especially in the context of permutation alternates the following 2 steps until convergence (which usually tests that are used to estimate p-values. happens after a small number of iterations). After convergence, the log-likelihood is given by (up to an ad- Step 1: Least square estimation, updating all parameters with ditive constant) fixed r. Let n denote the number of subjects, Ns the number of scans Xn for subject s, and N the total number of scans (the sum of all Ns). Let 2 L ¼ N log s þ logð1 þ rNsÞ d be the number of variables in the linear model (d 6 in our case) ¼ s ¼ 1 and K the dimension of the shape marker. Rewrite the linear model in the form: Y(s) ¼ X(s)q þ ε(s) where Y(s)isaN K matrix, X(s)is 2.9. Analysis with familywise error rates Ps fi n T Ns d and q is d K.De ne the matrices SXX ¼ s ¼ 1XðsÞ XðsÞ and P P For each type of shape marker, we perform an omnibus test for n T fi Ns SXY ¼ s ¼ 1XðsÞ YðsÞ.De ne also XðsÞ¼ XjðsÞ where Xj(s)is P j ¼ 1 the significance of the group variables, by testing the null hypoth- Ns v : 0 the jth row of X(s), and similarly YðsÞ¼ j ¼ 1YjðsÞ to set. esis H0ð Þ bv ¼ b v ¼ 0. The test statistic is the likelihood ratio between the compared models. The set of coordinates v for which Xn T the null hypothesis is rejected is computed via permutation tests SXX ¼ r XðsÞ X s ð1 þ NsrÞ and corrected for multiple comparisons within the shape marker s ¼ 1 (no correction is made across shape markers, because these are and highly correlated). Xn Letting F denote the log-likelihood ratio, the maximum value T * SXY ¼ r XðsÞ Y s ð1 þ NsrÞ over all vertices, F max Fv, is compared with those obtained by ¼ v s ¼ 1 performing the same computation several times, with group labels Then, the least square estimator of q is given by randomly assigned to subjects. The p-value is given by the fraction S8 M.I. Miller et al. / Neurobiology of Aging 36 (2015) S3eS10

Table 2 markers. As can be seen, the high-dimensional vertex based Differences between controls and symptomatic subjects markers are statistically more significantly discriminating (p < Groups Side Vertex Laplace 7T regions Volume 0.00001) than lower-dimensional markers and volumes. To more Controls versus Left <0.00001 0.002 0.0047 (1,2) 0.004 easily visualize the location of these significant differences, the symptomatic cases p-values are superimposed on a template of the amygdala, Controls versus Right 0.0001 0.005 0.01 (1,2,4) 0.002 showing the location of maximum difference between the groups symptomatic cases (see Fig. 4). Note that the images show the amount of surface Rows 2 and 3 show p-value resulting from linear mixed effects model analysis of con- atrophy relative to the template, which is expressed in percent- trols versus the combined group of symptomatic cases listed from high to low dimen- ages, 100% meaning no difference with template. The red value of sion. Columns list p-value for the vertex (750 dimensions per structure), and Laplace- Beltrami eigenvectors (25 dimensions per structure), the four 7T regions, and volume 85% means, in terms of the atrophy measure, there has been a biomarkers (1 dimension per structure). Regions in the 7T template are significant at change (a net decrease) of 15% from the original template to the 0.05 FWER after correcting for multiple comparisons. p-value testing based on geometry disease group at 85%. segment clustering gives p-values of 0.028 and 0.002 for left and right, respectively. In addition, Fig. 5 shows the location of the significant differ- (1, 2) basolateral and basomedial, (1,2,4) basolateral, basomedial and lateral nuclei. ences between the controls and the symptomatic cases in relation Key: FWER, familywise error rates. to the nuclei of the amygdala, using a high-field 7T atlas. Signifi- of times the values of F* computed after permutation is larger than cance is determined at 0.05 familywise error rates, based on Bon- < the value obtained with the true groups. Similarly, p-values are ferroni bound p 0.0125. The top row shows the left amygdala obtained for the volume except that no multiple testing correction subregions with the basomedial (p ¼ 0.0006) and basolateral (p ¼ fi fi is needed. 0.0024) signi cant, with no signi cance for the lateral (p ¼ 0.036) Permutation testing provides a (conservative) estimate of the set and centromedial (p ¼ 0.103) subregions. The bottom row shows fi of vertices v on which the null hypothesis is not valid. This set is the right amygdala, showing statistically signi cant subregions, defined by D ¼ fv:F qg where q* is the 95 percentile of the basomedial (p ¼ 0.0087), basolateral (p ¼ 0.0047), lateral (p ¼ v fi observed value of F* over the permutations (Nichols and Hayasaka, 0.0045), with no signi cance centromedial (p ¼ 0.0565). fi 2003). These results are visualized by coloring the vertices that Thus, signi cant atrophy was centered in the basomedial and basolateral subregions, with no evidence of centromedial were significant with an atrophy measure defined as ðbv;0 þ bvageÞ, involvement. where bv;0; bv are the coefficients associated to the group variable in the regression model for vertex v,andage is the average age in the Table 3 provides the p-values for the MCI and the AD dementia considered disease group population. cases, taken separately, compared with the controls. The differences between the AD cases and the controls are statistically significant for both left and right hemisphere. The differences between the MCI 3. Results cases and the controls, while in the same direction, are not significant for all markers. The results of the mixed effects models comparing the controls and the symptomatic cases, taken together as a group, are shown in Table 2, which provides the p-values for shape change 4. Discussion between the groups, as measured by the high-dimensional shape markers, based on the Jacobian statistics at the vertices and The examination of amygdalar shape analysis in this cohort has Laplace Beltrami expansions, and the low-dimensional volume revealed volumetric changes as well as non-uniform shape changes

Fig. 4. Results of mixed effects modeling of the symptomatic group compared with controls. Top and bottom rows portray left and right amygdala respectively, showing the p-value (left) and degree of atrophy shown as a percent decrease relative to the template (right) for the 7Tregions projected onto the significant high-field regions, that is, the basolateral and basomedial nuclei. Blue color in the figure on the left implies that the vertex statistic is not significant for FWER 5%. Blue in the figure on the right implies no atrophy relative to template (determinant Jacobian ¼ 1). Abbreviation: FWER, familywise error rates. M.I. Miller et al. / Neurobiology of Aging 36 (2015) S3eS10 S9

Fig. 5. Results of mixed effects modeling of the symptomatic group compared with the controls. The figures in the left column show the 7T high-field left amygdala template (top row) with 4 subfields defined from the 0.8 mm isotropic 7T MRI; the bottom row shows right high-field amygdala. The figures in the right column show the subfields transferred to the 1.5 T population template showing statistically significant subregions. Significance is determined at 0.05 FWER, based on Bonferroni bound p < 0.0125. Abbreviations: FWER, familywise error rates; MRI, magnetic resonance imaging. in the amygdala in subjects with symptomatic AD. By leveraging a cases. The non-uniform changes in shape may explain the variation high-field amygdala atlas, significantly atrophied subregions were in volume in the relatively few neuroimaging studies of amygdala in located specifically in the basomedial and lateral nuclei. This is MCI and AD. The lateral part of the amgydala has also been noted in consistent with the histopathologic findings with the greatest cell recent shape analysis by Cavedo et al. (2011) and Qiu et al. (2009). packing density loss in the medial region and some loss in the lateral The former study is pertinent because a diffeomorphic approach region (Herzog and Kemper, 1980). It is also interesting that the re- was applied to a small sample and a parcellated amygdala atlas gion of significant atrophy illustrated in Figs. 3e5 is identical to that albeit at 3T was used. observed in autopsied amygdala with AD (Scott et al., 1991), that is, The diffeomorphometry methods described here enable transfer superiorly adjacent to the paralaminar region. The same study of the high-field amygdala parcellation ensuring anatomic consis- showed great loss of “large nerve cells” in the magnocellular regions tency. This also allows for the explicit testing of statistical signifi- of the amygdala which is deep inside the basomedial nucleus. This is cance by a subregion by subregion basis allowing us to demonstrate consistent with the hypothesis that the observed changes in the the significant changes in the affected basolateral regions. The fact surface of the basomedial nucleus reflect the underlying changes. that there are significant projections from these regions in amygdala Our results can be interpreted in terms of the core and non-core to hippocampus and entorhinal cortex also make it significant in amygdalar parcellations by Price. (1987), (2003) based on subregions light of our other findings in those structures in previous work sharing developmental, structural, and functional characteristics. Core (Miller et al., 2013). Given the temporal lobe circuitry model of the amgydala consists of the lateral, basal, and accessory basal nuclei, and degenerative processes in MCI and AD, future studies will be the non-core amygdala consists of remaining nuclei including the necessary to correlate shape changes in the amygdala with that in central, medial, and cortical nuclei (Munn et al., 2007; Sheline et al., the hippocampus, entorhinal cortex, and other structures. Such 1998). From a functional standpoint, subnuclei in the core amygdala expanded studies provide additional biomarkers to that of the are associated with a role in emotional processing and storage of hippocampus in the early stages of MCI and AD. emotional memories (LeDoux and Schiller, 2009; Price, 1981), which provide clues as to how they may be affected in MCI and AD. 5. Conclusion The volumetric changes are consistent with those observed in a recent study (Poulin et al., 2011) of 2 large samples of MCI and AD In summary, application of advanced computational anatomy diffeomorphometry methods detected atrophy in basomedial and Table 3 basolateral regions of the amygdala in patients with symptomatic Differences between controls (NC) and MCI subjects (rows 2, 3) and AD dementia AD. Despite the small sample size, atrophied subregions of the subjects (rows 4, 5) amygdala could be detected with p-values based on familywise Groups Side Vertex Laplace 7T regions Volume error rates which unlike false discovery rates have the advantage of MCI versus NC Left 0.01242 0.004 0.0695 0.118 not requiring additional assumptions on the data such as inde- MCI versus NC Right 0.067325 0.030 0.0746 0.097 pendence or positive dependence. These findings warrant further AD versus NC Left <0.00001 0.005 0.0003 (1,2) 0.002 investigation in a larger data set. AD versus NC Right 0.0002 0.005 0.0089 (1,4) 0.002 p-value testing based on geometric segments was significant for the AD dementia Disclosure statement cases, left and right p-value 0.024 and 0.002, respectively. (1,2) basolateral and basomedial (1,4) basolateral and lateral nuclei. Key: AD, Alzheimer’s disease; MCI, mild cognitive impairment; NC, healthy controls. All authors do not have conflicts of interest. S10 M.I. Miller et al. / Neurobiology of Aging 36 (2015) S3eS10

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Kenichi Oishi, Thomas Reigel, Elizabeth Postell, William Schneider, McEvoy, L.K., Holland, D., Hagler Jr., D.J., Fennema-Notestine, C., Brewer, J.B., and Laurent Younes), (4) the Biospecimen Core (Richard O’Brien, Dale, A.M., Alzheimer’s Disease Neuroimaging Initiative, 2011. Mild cognitive Abhay Moghekar, and Richard Meehan), (5) the Informatics Core impairment: baseline and longitudinal structural MR imaging measures improve predictive prognosis. Radiology 259, 834e843. (Roberta Scherer, Curt Meinert, David Shade, Ann Ervin, Jennifer Miller, M.I., Younes, L., Ratnanather, J.T., Brown, T., Trinh, H., Postell, E., Lee, D.S., Jones, Matt Toepfner, Lauren Parlett,April Patterson, and Lisa Las- Wang, M.C., Mori, S., O’Brien, R., Albert, M., BIOCARD Research Team, 2013. The ’ siter), the (6) Biostatistics Core (Mei-Cheng Wang, Shanshan Li, and diffeomorphometry of temporal lobe structures in preclinical Alzheimer s disease. Neuroimage Clin. 3, 352e360. Yi Lu), and (7) the Neuropathology Core (Juan Troncoso, Barbara Miller, M.I., Younes, L., Trouvé, A., 2014. Diffeomorphometry and geodesic Crain, Olga Pletnikova, Gay Rudow, and Karen Fisher). positioning systems for human anatomy. Technology (Singap. World Sci.) 02, 36e43. The authors are grateful to the members of the BIOCARD Scien- ’ fi Moghekar, A., Li, S., Lu, Y., Li, M., Wang, M.C., Albert, M., O Brien, R., BIOCARD ti c Advisory Board who provide continued oversight and guidance Research Team, 2013. CSF biomarker changes precede symptom onset of mild regarding the conduct of the study including: Drs John Csernansky, cognitive impairment. Neurology 81, 1753e1758. David Holtzman, David Knopman, Walter Kukull, and John McArdle, Morris, J.C., 1993. The Clinical Dementia Rating (CDR): current version and scoring rules. 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