Genetic influence of apolipoprotein E4 genotype on hippocampal morphometry: An N = 725 surface‐based Alzheimer's disease neuroimaging initiative study

Abstract

The apolipoprotein E (APOE) e4 allele is the most prevalent genetic risk factor for Alzheimer's disease (AD). Hippocampal volumes are generally smaller in AD patients carrying the e4 allele compared to e4 noncarriers. Here we examined the effect of APOE e4 on hippocampal morphometry in a large imaging database—the Alzheimer's Disease Neuroimaging Initiative (ADNI). We automatically segmented and constructed hippocampal surfaces from the baseline MR images of 725 subjects with known APOE genotype information including 167 with AD, 354 with mild cognitive impairment (MCI), and 204 normal controls. High‐order correspondences between hippocampal surfaces were enforced across subjects with a novel inverse consistent surface fluid registration method. Multivariate statistics consisting of multivariate tensor‐based morphometry (mTBM) and radial distance were computed for surface deformation analysis. Using Hotelling's T ² test, we found significant morphological deformation in APOE e4 carriers relative to noncarriers in the entire cohort as well as in the nondemented (pooled MCI and control) subjects, affecting the left hippocampus more than the right, and this effect was more pronounced in e4 homozygotes than heterozygotes. Our findings are consistent with previous studies that showed e4 carriers exhibit accelerated hippocampal atrophy; we extend these findings to a novel measure of hippocampal morphometry. Hippocampal morphometry has significant potential as an imaging biomarker of early stage AD. Hum Brain Mapp 35:3903–3918, 2014. © 2014 Wiley Periodicals, Inc.

INTRODUCTION

The decline of cognitive skills to a functionally disabling degree is a sign of the clinical onset of Alzheimer's disease (AD), but optimizing disease modification strategies requires early intervention against appropriate therapeutic targets that may vary with disease stage. Current therapeutic failures in patients with symptomatic memory loss may reflect intervention that is too late, or else targets that represent secondary effects less relevant to disease initiation and early progression (Hyman, 2011). For therapy to be successful, timing may be critical.

In presymptomatic subjects, determining whether AD is present is challenging. The apolipoprotein E (APOE) e4 allele is the most prevalent risk factor for AD (Corder et al., 1993; Saunders et al., 1993), and is present in roughly 20–25% of North Americans and Europeans (Gerdes et al., 1992). This discovery has made it possible to study large numbers of genetically at‐risk individuals before the onset of symptomatic memory impairment and has led to the concept of preclinical stage AD (Sperling et al., 2011), a concept validated in autopsy studies of nondemented elderly subjects with neuropathological evidence of AD at autopsy (Bennett et al., 2009; Caselli et al., 2010; Dickson et al., 1992; Gouras et al., 1997; Kok et al., 2009), magnetic resonance imaging (MRI) studies of infants at differential genetic risk (Dean et al., 2013; Knickmeyer et al., 2013), fluorodeoxyglucose positron emission tomography (PET) studies of APOE e4 carriers that have revealed AD‐like patterns of reduced CMRglucose (Reiman et al., 1996, 2005), amyloid ligand binding studies using Pittsburgh Imaging Compound B that show evidence of cerebral amyloidosis in APOE e4 carriers (Reiman et al., 2009), cerebrospinal fluid levels of beta amyloid that begin to fall, suggesting the onset of AD, in the early 50s in e4 carriers (Morris et al., 2010), and neuropsychological studies showing the accelerated decline of memory scores in a gene‐dose pattern in APOE e4 carriers beginning between age 55 and 60 (Caselli et al., 2009) that is further accelerated in APOE e4 homozygotes by cerebrovascular risk factors (Caselli et al., 2011).

So far we lack a widely available, highly objective brain imaging biomarker that can identify abnormal degrees of cerebral atrophy and accelerated rate of atrophy in preclinical individuals at high risk of AD for whom early intervention is needed. A biologically grounded approach is vital to identify reliable biomarkers, consolidate all information, reduce the sheer number of statistical tests, and improve statistical power. In AD research, structural magnetic resonance imaging (MRI)‐based measures include whole‐brain (Chen et al., 2007; Fox et al., 1999; Stonnington et al., 2010), entorhinal cortex (Cardenas et al., 2011), hippocampus (den Heijer et al., 2010; Jack et al., 2003; Reiman et al., 1998; Thompson et al., [Link]; Wolz et al., 2010), and temporal lobe volumes (Hua et al., 2010), as well as ventricular enlargement (Jack et al., 2003; Thompson et al., [Link]; Wang et al., 2011). These correlate closely with differences and changes in cognitive performance, supporting their validity as markers of disease progression. Although many current studies examine cortical and substructural volumes (den Heijer et al., 2010; Dewey et al., 2010; Holland et al., 2009; Jack et al., 2004, 2003; Ridha et al., 2008; Vemuri et al., 2008a, 2008b; Wolz et al., 2010), recent research (Apostolova et al., 2010b, 2010c; Chou et al., 2009; Costafreda et al., 2011; Ferrarini et al., 2008; Madsen et al., 2010; Morra et al., 2009b; Qiu et al., 2010; Styner et al., 2005; Thompson et al., [Link]) has demonstrated that surface‐based subregional structure analysis offers advantages over volume measures, in some respects. For precise analysis of MRI patterns of hippocampal deformation for preclinical AD research, a subregional analysis would be beneficial.

Recently, we introduced surface multivariate tensor‐based morphometry (mTBM) system (Shi et al., 2013a, 2013b; Wang et al., 2012, 2011, 2010) and applied it to study AD effects on hippocampal morphometry (Shi et al., 2013a; Wang et al., 2011). Based on our experience assessing APOE e4 effects in preclinical populations (Caselli et al., 2011, 2009, 2010; Reiman et al., 2001, 1996, 2009; Stein et al., 2012) and the relatively large sample size in the Alzheimer's Disease Neuroimaging Initiative (ADNI; Jack et al., 2008; Miller, 2009; Mueller et al., 2005a, 2005b) dataset, we applied a novel hippocampal morphometry method to a large cohort of MR images of individuals with known genotype. Subregional variations in hippocampal surfaces in 725 subjects (167 AD, 354 MCI, and 204 controls) were examined for relationships with APOE e4 dose information, from APOE e4 noncarriers, people heterozygous and homozygous for APOE e4 allele. We hypothesized that the degree of hippocampal deformation would relate to genetic risk groups for AD, including adults who carry one or two copies of the APOE e4 allele, a major AD susceptibility gene.

SUBJECTS AND METHODS

Subjects

Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu). The ADNI was launched in 2003 by the National Institute on Aging (NIA), the National Institute of Biomedical Imaging and Bioengineering (NIBIB), the Food and Drug Administration (FDA), private pharmaceutical companies and non‐profit organizations, as a $60 million, 5‐year publicprivate partnership. The primary goal of ADNI has been to test whether serial magneticresonance imaging (MRI), positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of mild cognitive impairment (MCI) and early Alzheimer's disease (AD). Determination of sensitive and specific markers of very early AD progression is intended to aid researchers and clinicians to develop new treatments and monitor their effectiveness, as well as lessen the time and cost of clinical trials.

The Principal Investigator of this initiative is Michael W. Weiner, MD, VA Medical Center and University of California – San Francisco. ADNI is the result of efforts of many coinvestigators from a broad range of academic institutions and private corporations, and subjects have been recruited from over 50 sites across the U.S. and Canada. The initial goal of ADNI was to recruit 800 subjects but ADNI has been followed by ADNI‐GO and ADNI‐2. To date these three protocols have recruited over 1500 adults, ages 55 to 90, to participate in the research, consisting of cognitively normal older individuals, people with early or late MCI, and people with early AD. The follow up duration of each group is specified in the protocols for ADNI‐1, ADNI‐2 and ADNI‐GO. Subjects originally recruited for ADNI‐1 and ADNI‐GO had the option to be followed in ADNI‐2. For up‐to‐date information, see http://www.adni-info.org.

At the time of downloading (September 2010), among the 843 subjects in the baseline dataset, 738 subjects were genotyped and classified as APOE e4 carriers or noncarriers. All subjects underwent thorough clinical and cognitive assessment at the time of acquisition, including the Mini‐Mental State Examination (MMSE) score (Folstein et al., 1975), Clinical Dementia Rating (Berg, 1988), and Delayed Logical Memory Test (Wechsler, 1987).

In this study, all T1‐weighted images from ADNI baseline dataset were automatically segmented using FIRST software¹ to segment the hippocampus substructure. We reconstructed hippocampal surfaces based on binary segmentations (Shi et al., 2013a). As a quality control, we manually checked all the constructed meshes and excluded five AD, five MCI, and three healthy control subjects with wrong surface topologies (Shi et al., 2013a). As a result, a total of 725 ADNI baseline subjects with APOE information, including 167 AD (age: 75.5 ± 7.6 years), 354 MCI (age: 75.1 ± 7.2 years), and 204 controls (age: 76.2 ± 4.9 years) were studied using the new system for this article. Table 1 gives detailed demographic data information on the subjects.

Table 1.

Demographic information of studied subjects in ADNI baseline dataset

	ApoE genotype	Number of subjects	Gender (M/F)	Education	Age	MMSE at baseline
AD	e2/e2	0	—	—	—	—
	e2/e3	4	1/3	15.00 ± 2.24	74.25 ± 8.26	22.00 ± 1.58
	e2/e4	4	0/4	15.75 ± 1.79	79.25 ± 5.12	24.75 ± 2.17
	e3/e3	52	27/25	15.15 ± 2.05	76.96 ± 8.58	23.23 ± 2.05
	e3/e4	73	44/29	14.62 ± 3.16	75.93 ± 6.43	23.42 ± 2.00
	e4/e4	34	20/14	14.71 ± 2.67	71.92 ± 7.17	23.44 ± 1.83
Control	e2/e2	1	1/0	16	70	30
	e2/e3	24	12/12	15.83 ± 3.14	76.13 ± 5.68	28.83 ± 1.14
	e2/e4	2	2/0	13.00 ± 1.00	76.50 ± 5.50	27.50 ± 2.50
	e3/e3	125	69/56	16.20 ± 2.71	76.29 ± 4.83	29.18 ± 0.89
	e3/e4	48	25/23	16.13 ± 2.73	76.50 ± 4.48	29.25 ± 0.83
	e4/e4	4	2/2	16.75 ± 1.92	73.75 ± 3.34	29.00 ± 0.71
MCI	e2/e2	0	—	—	—	—
	e2/e3	15	7/8	15.93 ± 2.86	76.67 ± 7.44	27.60 ± 1.50
	e2/e4	10	7/3	16.50 ± 2.33	74.20 ± 8.58	28.00 ± 1.26
	e3/e3	145	95/50	15.81 ± 2.94	76.20 ± 7.71	27.23 ± 1.77
	e3/e4	141	91/50	15.61 ± 3.06	74.82 ± 6.63	26.94 ± 1.76
	e4/e4	43	25/18	15.81 ± 2.57	71.81 ± 5.91	26.84 ± 1.95

In our study, following prior work (Morra et al., 2009a, 2009b; Shi et al., 2013a), we pooled both the subjects who are heterozygous APOE e4 carriers (e3/e4) and homozygous APOE e4 carriers (e4/e4) together to form the APOE e4 carriers group and correlated presence of the APOE e4 allele with hippocampal morphometry, both (1) in the entire sample and (2) in nondemented (pooled MCI and controls) subjects. Throughout the article, we call these two populations as the full ADNI cohort and nondemented cohort, respectively.

Processing Pipeline

Figure 1 shows our overall sequence of processing. First, given the three‐dimensional (3D) MRI scans from the ADNI baseline dataset, hippocampal substructures were segmented with FIRST (Patenaude et al., 2011) and hippocampal surfaces were automatically reconstructed based on the segmentations (Han et al., 2003). Second, a conformal grid was generated for each surface with the holomorphic 1‐form based surface conformal parameterization (Wang et al., 2011). With this conformal grid, we computed the conformal representation of the surface (Gu and Vemuri, 2004), i.e., the conformal factor and mean curvature, which represent the intrinsic and extrinsic features of the surface, respectively. The “feature image” of a surface was computed by combining the conformal factor and mean curvature and linearly scaling the dynamic range into [0, 255]. Third, we registered the feature image of each surface in the dataset to a common template with an inverse consistent fluid registration algorithm (Shi et al., 2013a). With conformal parameterization, we essentially converted a 3D surface registration problem into a 2D image registration problem. The flow induced in the parameter domain establishes high‐order correspondences between 3D surfaces. Finally, we studied the differences between different diagnostic groups with the mTBM statistics (Leporé et al., 2008; Wang et al., 2010), which retain the full tensor information of the deformation Jacobian matrix, together with the radial distance, which retains information on the deformation along the surface normal direction.

Figure 1.

A chart showing the key steps in our system. MR images were automatically segmented by FIRST to extract the hippocampal substructure (a). After the hippocampal surfaces were constructed from FIRST segmentations (b), we computed their conformal parameterizations with holomorphic 1‐forms (c and d). Then feature images were generated by combining the local conformal factor and mean curvature that were computed from the conformal parameterizations. After the inverse consistent fluid registration was done in the feature image domain, we deformed the surfaces using the obtained displacements (e). The new statistics consisting of radial distance and multivariate TBM were computed at each point on the resultant matching surface (f). Then the Hotelling T ² test was applied to study genetic influence of APOE e4 allele (g). [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Hippocampus Segmentation and Surface Reconstruction

All T1‐weighted MR images were automatically segmented using FIRST (Patenaude et al., 2011). FIRST is a model‐based subcortical structure segmentation and registration tool developed as part of the FSL library, which is written mainly by members of the Analysis Group, FMRIB, Oxford, UK. We ran the run_first_all routine with default parameters tuned by FIRST as optimal for hippocampal segmentation. Among the results of the routine, we took the three‐phase image which contains the labels of the left and right hippocampi as shown in Figure 1a. Then the binary image for each side was obtained by a simple thresholding process. Hippocampal surfaces were constructed with a topology‐preserving level set method based on the binary segmentations (Han et al., 2003) and triangular surface meshes were obtained based on the marching cubes algorithm (Lorensen and Cline, 1987). After mesh refinement (Shi et al., 2013a), we obtained smooth surfaces that are suitable for generating conformal grids as shown in Figure 1b. Finally each of the smoothed meshes was aligned into the MNI standard space using a global affine transformation with a nine‐parameter (three parameters for translation, three parameters for rotation, and three parameters for scaling) matrix that was computed by FIRST (Patenaude et al., 2011).

Conformal Grid Generation

To facilitate hippocampal shape analysis, we generated a conformal grid on each surface and used it as a canonical space for the following surface registration and multivariate statistical analysis. To generate a planar surface conformal parameterization for a closed hippocampal surface, we applied an automatic algorithm, topological optimization, to introduce two cuts on a hippocampal surface to convert it into a genus zero surface with two open boundaries (Shi et al., 2013a). The locations of the two cuts are at the front and back of the hippocampal surface, representing its anterior junction with the amygdala, and its posterior limit as it turns into the white matter of the fornix. They are biologically valid and consistent landmarks across subjects. Given the hippocampal tube‐like shape, these landmark curves are automatically determined by checking the extreme points when searching along the first principle direction of geometric moments of surface (Elad et al., 2004; Wang et al., 2011; Zhang and Lu, 2004). For quality control purposes, we have manually checked the consistency of all landmark curves. Then the exact 1‐form basis was computed with the open boundary surface (Wang et al., 2010). Later we computed the basis for all closed but nonexact 1‐forms. The harmonic 1‐form basis is the union of the exact 1‐form basis and the closed but nonexact 1‐form basis. By solving a linear system with the harmonic 1‐form basis, we obtained the conjugate of the exact 1‐form basis. The exact 1‐form basis and its conjugate 1‐form form the holomorphic 1‐form basis, which induces a conformal grid on the hippocampal surface. Figure 1c,d shows two example hippocampal surfaces with their conformal grids. In both pictures, the overlaid checkerboard texture is used to demonstrate the angle preserving property, i.e., the right angles on the planar checkerboard texture are well preserved after they are overlaid on hippocampal surfaces.

The conformal parameterization of a surface contains a number of geometric features about the surface. In our system, we computed the local conformal factor and mean curvature, which uniquely determine a closed surface in 3D, up to a rigid motion (Gu et al., 2004). Conformal factor is the area ratio of an infinitesimal region around a point on the surface and an infinitesimal region around the same point on the planar parameter domain. It represents the intrinsic features of a surface. By contrast, the mean curvature represents the extrinsic features of a surface. Both measurements, the conformal factor and mean curvature, are local features which are defined on each surface vertex. Since the conformal factor and mean curvature encode both intrinsic structure and 3D embedding information, we call them the surface conformal representation. In our framework, conformal representation is adopted as surface features for automated surface registration. As shown in Figure 1e, we summed up the conformal factor and mean curvature and linearly scaled the dynamic range of the summation into [0, 255] to form the feature image of the surface.

Hippocampal Surface Registrations

Similar to other tensor‐based morphometry (TBM) work (e.g., Chung, 2012; Davatzikos et al., 1996; Hua et al., 2011), we need to register each individual hippocampal surface to a common template surface for morphometric analysis. With the conformal parameterization and conformal representation, we convert the 3D surface registration problem into a 2D image registration problem. The well‐studied image fluid registration algorithm (Bro‐Nielsen and Gramkow, 1996; D'Agostino et al., 2003) can be easily applied to induce a deformation flow in the parameter domain, which in turn enforces a high‐order correspondence in 3D. We introduced a correction term in the traditional Navier–Stokes equation to compensate for the parameterization area distortion. With conformal parameterization, the correction term was simply the conformal factor and the surface fluid registration can be easily developed by extending the Navier–Stokes equation to drive flows on general surfaces, regardless of the underlying parameterizations. We call this method surface fluid registration (Shi et al., 2013a).

Furthermore, most image registration algorithms in the literature are not symmetric, i.e., the correspondences established between the two images depend on which image is assigned as the deforming image and which is the nondeforming target image. An asymmetric algorithm can be problematic as they tend to penalize the expansion of image regions more than shrinkage (Rey et al., 2002). Thus, in our system, we further extended the surface fluid registration method into an inverse consistent framework (Leow et al., 2005). The obtained surface registration is diffeomorphic. An example is as shown in Figure 1e. For details of our inverse consistent surface fluid registration method, we refer to (Shi et al., 2013a).

Surface Multivariate Morphometry Statistics

Our multivariate morphometry statistical analysis consists of mTBM (Leporé et al., 2008; Wang et al., 2009) and radial distance analysis (Pizer et al., 1999; Thompson et al., [Link]). This combines complementary information from mTBM, which measures deformation within surfaces, and radial distance, which measures hippocampal size in terms of the surface normal direction.

The mTBM statistics have been carefully studied in brain structure morphology analyses and they can demonstrate improved signal detection power relative to more standard Jacobian matrix statistics (Shi et al., 2013a, 2013b; Wang et al., 2012, 2011, 2013). As mTBM retains the full information in the deformation tensor fields, it is very sensitive to deformations such as rotation, dilation, and shear along the surface tangent direction, which is perpendicular to the surface normal. Given the hippocampal tube‐like shape, its atrophy and enlargement directly affect the distance from each surface point to its medial core (analogous to the center line in a tube). We call this distance the radial distance of a hippocampal surface. Radial distance mainly describes morphometric changes along the surface normal direction and has been applied in many subcortical studies (Bansal et al., 2000; Gerig et al., 2001; Morra et al., 2009b; Pizer et al., 1999; Thompson et al., [Link]). Thus, these two statistics are complementary to each other. In this article, we adopted the multivariate statistics proposed in (Wang et al., 2011) to study shape differences between groups with different diagnosis, APOE e4 dose, and healthy controls.

As in our prior work (Wang et al., 2011), the mTBM was computed as a 3 × 1 vector consisting of the “Log‐Euclidean metric” (Arsigny et al., 2006), computed as the matrix logarithm of the deformation tensor. Given a hippocampal surface with the conformal parameterization as described in Conformal Grid Generation section, the radial distance was computed as the distance from each parametric surface point to the center of 3D positions of the iso‐u curves in the parameter domain (Wang et al., 2011), as shown by the red curves in Figure 1f. We formed the new multivariate surface morphometry statistic as a 4 × 1 vector consisting of the mTBM and radial distance.

Statistical Group Difference

To assess group differences with multivariate statistics, we applied Hotelling's T ² test (Cao and Worsley, 1999; Hotelling, 1931; Kim et al., 2012; Thirion et al., 2000) on sets of values in the log‐Euclidean space of the deformation tensors. For each surface vertex, given two groups of n × 4‐dimensional vectors, $S_{i,}i=1,2,\dots ,p,T_{j,}j=1,2,\dots ,q,$, we used the Mahalanobis distance M to measure the group mean difference,

$$M=\frac{N_S{N}_T}{N_S+N_T}\left(\overline{S}-\overline{T}\right){}^T{\Sigma }^{-1}\left(\overline{S}-\overline{T}\right).$$

where N _S and N _T are the numbers of subjects in the two groups, $\overline{S}$ and $\overline{T}$ are the means of the two groups and Σ is the combined covariance matrix of the two groups (Leporé et al., 2008; Wang et al., 2011, 2010).

Specifically, for each hippocampal surface point, we ran a permutation test with 10,000 random assignments of subjects to different groups to estimate the statistical significance of the areas with group difference in surface morphometry. We also used a predefined statistical threshold of P = 0.05 at each surface point to estimate the overall significance of the group difference maps by nonparametric permutation testing (Holmes et al., 1996; Nichols and Holmes, 2002). In each case, the covariate (group membership) was permuted 10,000 times and a null distribution was developed for the area of the average surface with group difference statistics above the predefined threshold in the significance map. The overall significance of the map is defined as the probability of finding, by chance alone, a statistical map with at least as large a surface area beating the predefined statistical threshold of P = 0.05. This omnibus P value is commonly referred to as the overall significance of the map (or the features in the map), corrected for multiple comparisons. It basically quantifies the level of surprise in seeing a map with this amount of the surface exceeding a predefined threshold, under the null hypothesis of no systematic group differences. The permutation test on the overall rejection areas is used to evaluate the significance of overall experimental results and correct the overall significant P values for multiple comparisons. Figure 1g shows an example of the significance p‐map with uncorrected P values, which is used to visualize the surface regions with significant differences between groups.

RESULTS

Effects of APOE e4 Genotype

To explore whether the presence of the APOE e4 allele was associated with greater hippocampal atrophy, we conducted two experiments to study the effects of APOE e4 genotype on hippocampal morphometry in two populations:

1. APOE e4 carriers versus noncarriers in the full ADNI cohort;

2. APOE e4 carriers versus noncarriers in the nondemented cohort.

The experiments aimed to determine if the APOE e4 allele was associated with hippocampal atrophy in all subjects or in subjects who have not yet developed AD. By contrast with (Shi et al., 2013a), the study in this article is more rigorous as the APOE e4 noncarriers are those subjects who are homozygous noncarriers (e3/e3). Subjects with one e2 allele, i.e., e2/e3 and e2/e4 were excluded due to the possible protective effect of e2 allele for AD (Morra et al., 2009b).

In the 725 subjects of known APOE e4 genotype, there were 322 noncarriers (all homozygous for APOE e3) and 343 APOE e4 carriers. The nondemented cohort consisted of 506 subjects who were either MCI or control subjects, including 270 e4 noncarriers and 236 e4 carriers. Figure 2 shows the statistical p‐map for the full ADNI cohort (N = 665; 322 noncarriers and 343 carriers). Nonblue colors show vertices with statistical differences at the nominal 0.05 level, uncorrected for multiple comparisons. As shown in Figure 2, the APOE e4 carriers differed significantly from the noncarriers (P < 0.0002). Figure 3 shows the p‐map for the nondemented cohort (N = 506; 270 noncarriers and 236 carriers). After correcting for multiple comparisons, the difference remained highly significant (P < 0.0027).

Figure 2.

Illustration of local shape differences (P values) between the APOE e4 noncarriers (e3/e3, N = 322) and carriers (e3/e4 and e4/e4, N = 343) in the full ADNI cohort. Nonblue colors show vertices with statistical differences, at the nomial 0.05 level, uncorrected. The overall significance after multiple comparisons with permutation test is P < 0.0002. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Figure 3.

Illustration of local shape differences (P values; a) between the APOE e4 noncarriers (e3/e3, N = 270) and carriers (e3/e4 and e4/e4, N = 236) in the nondemented cohort (MCI and controls). Nonblue colors show vertices with statistical differences, at the nomial 0.05 level, uncorrected. The overall significance after multiple comparisons with permutation test is P < 0.0027. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

APOE e4 Dose Effects: Difference Comparison Between Heterozygous and Homozygous APOE e4 Carriers

To explore whether APOE e4 allele dose affects hippocampal surface morphometry and how this atrophy is related to normal aging, we studied hippocampal morphometry between persons homozygous for the APOE e4 allele and those heterozygous for this allele. We studied group differences between heterozygous and homozygous APOE e4 subjects in the full ADNI cohort, and in the nondemented APOE e4 carrier cohort in ADNI baseline dataset.

Among the APOE e4 carriers, 81 subjects were homozygous (e4/e4) and 262 were heterozygous (e3/e4) for APOE e4 allele. Figure 4 shows the statistical p‐map for all APOE e4 subjects. The e4 heterozygotes differed significantly from the e4 homozygotes (P < 0.0129 after multiple comparisons correction with the permutation test). Excluding those APOE e4 carriers in the AD group, the nondemented APOE e4 carrier group consisted of 189 e4 heterozygotes and 47 homozygotes. Figure 5 shows the statistical p‐map for nondemented APOE e4 carriers. However, after correcting for multiple comparisons, the effect was not significant (P = 0.142). (There may be some subthreshold difference for the right hippocampus, but a larger sample size would be needed to detect it, if present.)

Figure 4.

Illustration of local shape differences (P values) between the heterozygous APOE e4 carriers (e3/e4, N = 262) and the homozygous APOE e4 carriers (e4/e4, N = 81) in the full ADNI cohort. Nonblue colors show vertices with statistical differences, at the nomial 0.05 level, uncorrected. The overall significance after multiple comparisons with permutation test is P < 0.0129. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Figure 5.

Illustration of local shape differences (P values) between the heterozygous APOE e4 carriers (e3/e4, N = 189) and the homozygous APOE e4 carriers (e4/e4, N = 47) in the nondemented cohort. Nonblue colors show vertices with statistical differences, at the nomial 0.05 level, uncorrected. The overall significance after multiple comparisons with permutation test is P < 0.142. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

APOE e4 Dose Effects: Difference Comparison Between APOE e4 Noncarriers and Carriers With Different APOE e4 Dose

To further study the APOE e4 dose effects, we divided the subjects into three groups, APOE e4 homozygotes, heterozygotes, and noncarriers. We performed group difference analysis between two groups and compared the statistical power. We hypothesized that morphometric differences would be greater in APOE e4 homozygotes than heterozygotes, who would in turn show greater deformities compared to e4 noncarriers.

Figures 6 and 7 show how APOE e4 noncarriers differ in hippocampal shape from APOE e4 heterozygotes and homozygotes in the full ADNI cohort and the nondemented cohort, respectively. Figure 6 shows the statistical p‐map for the full ADNI cohort. Nonblue colors show vertices with statistical differences, at the nominal 0.05 level, uncorrected. As shown in Figure 6a, the APOE e4 heterozygotes differed from e4 noncarriers (P < 0.0031). Figure 6b shows the statistical p‐map for the full ADNI cohort and demonstrates that the APOE e4 homozygotes differed from e4 noncarriers (P < 0.0001). Figure 6b also shows more extensive statistically significant areas of difference than those in Figure 6a, for both the left and right hippocampal surfaces.

Figure 6.

Illustration of local shape differences (P values) between the APOE e4 noncarriers (e3/e3, N =322) and heterozygous carriers (e3/e4, N = 262; a), between the APOE e4 noncarriers (e3/e3, N = 322) and homozygous carriers (e4/e4, N = 81; b), in the full ADNI cohort. Nonblue colors show vertices with statistical differences, at the nomial 0.05 level, uncorrected. The overall significances after multiple comparisons with permutation test are P < 0.0031 for (a) and P < 0.0001 for (b). [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

Figure 7.

Illustration of local shape differences (P values) between the APOE e4 noncarriers (e3/e3, N = 270) and heterozygous carriers (e3/e4, N = 189; a), between the APOE e4 noncarriers (e3/e3, N = 270) and homozygous carriers (e4/e4, N = 47; b), in the nondemented cohort. Nonblue colors show vertices with statistical differences, at the nomial 0.05 level, uncorrected. The overall significances after multiple comparisons with permutation test are P < 0.017 for (a) and P < 0.006 for (b). [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

After excluding AD subjects from these three groups, we repeated the group difference analysis among APOE e4 noncarriers (e3/e3, N = 270), e4 heterozygotes (e3/e4, N = 189), and e4 homozygotes (e4/e4, N = 47). Figure 7a shows the statistical p‐map for the nondemented cohort [N = 459; 270 noncarriers (e3/e3) and 189 APOE e4 heterozygous carriers (e3/e4)]. The APOE e4 heterozygotes differed from the e4 noncarriers (P < 0.017). Figure 7b shows the p‐map for the nondemented cohort [N = 317; 270 noncarriers (e3/e3) and 47 APOE e4 homozygous carriers (e4/e4)] and showed that the APOE e4 homozygotes differed from the e4 noncarriers (P < 0.006). Similar to Figure 6, the homozygous vs. noncarrier comparison showed more extensive areas of difference in the uncorrected p‐maps.

In Figure 8, the cumulative distribution functions of the P values observed for the contrast of APOE e4 carriers versus noncarriers are plotted against the corresponding P value that would be expected, under the null hypothesis of no group difference, for the four experiments shown in Figures 6 and 7. For null distributions, the cumulative distribution of P values is expected to fall approximately along the dotted line. Large deviations from that curve are associated with significant signal, and greater effect sizes represented by larger deviations. The theory of false discovery rates (Benjamini and Hochberg, 1995) gives formulae for thresholds that tend to control false positives at a known rate. This protocol was adopted in several of our prior articles (Shi et al., 2013a, 2013b; Wang et al., 2011, 2013, 2010) as an empirical standard to compare effects in group difference analysis. We note that the deviation of the statistics from the null distribution generally increases from heterozygotes vs. noncarriers to homozygotes vs. noncarriers in both the full ADNI cohort and nondemented cohort studies.

Figure 8.

Illustration of cumulative distribution functions of the P values observed for the contrast of APOE e4 carriers versus noncarriers, plotted against the corresponding P value that would be expected under null hypothesis of no group difference, for the four experiments shown in Figures 6 and 7. We note that the deviation of the statistics from the null distribution generally increases from heterozygotes vs. noncarriers to homozygotes vs. noncarriers in both the full ADNI cohort and nondemented cohort studies, suggesting that the APOE e4 allele dose may be associated with more accelerated atrophy of hippocampus. [Color figure can be viewed in the online issue, which is available at http://wileyonlinelibrary.com.]

As such, although more rigorous statistical tests are certainly necessary, from the p‐maps and CDF plots, we can observe the trend that in all groups, APOE e4 homozygotes appear to differ more from noncarriers than do e4 heterozygotes, suggesting a clear APOE e4 dose effect.

DISCUSSION

Prior studies of APOE e4 carriers (Caselli et al., 2011, 2009, 2010; Reiman, 2007) have helped to define and characterize preclinical AD with possible implications for primary AD prevention research. Essential to this effort are sensitive biomarkers that can track disease progression in the absence of symptoms. Imaging endophenotypes are promising, but further refinement of their relevance in early stage disease is needed (Frisoni et al., 2010). MRI hippocampal morphometry may help move disease detection earlier and evaluate the effectiveness of promising disease‐slowing and prevention therapies in a shorter time and a more cost‐effective way. Much recent research has used brain imaging to study how APOE e4 allele affects hippocampal morphometry in patients and cognitively normal people (Farrer et al., 1997; Lehtovirta et al., 1995; Lemaitre et al., 2005; Morra et al., 2009a, 2009b; Mueller and Weiner, 2009; Pievani et al., 2011; Qiu et al., 2009; Reiman et al., 1996; Shi et al., 2013a).

Our study has two main findings. First, as one of the largest hippocampal morphometry studies to date, involving 725 baseline ADNI subjects, we found that, for the nondemented subjects, the APOE e4 genotype is associated with greater hippocampal deformation. Second, our novel hippocampal surface morphometry method (Shi et al., 2013a, 2013b), which involves conformal mapping, inverse consistent surface fluid registration and multivariate statistical analysis, automatically processed all ADNI baseline imaging data and was as or more sensitive to APOE e4 effects than some previously reported methods (e.g., Morra et al., 2009a, 2009b), that have used the ADNI dataset.

Our work is related to the shape modeling of hippocampal surfaces. The Large Deformation Diffeomorphic Metric Mapping (LDDMM; Joshi and Miller, 2000) has been used to deform labeled anatomical templates of the hippocampus onto new images, using a combination of manual landmarking of points on the hippocampus and 3D fluid image registration (Csernansky et al., 2000; Haller et al., 1996; Wang et al., 2007). In the LDDMM method, the surface of the hippocampus is parcellated a priori using a neuroanatomical template into three zones to approximate the locations of underlying subfields, and LDDMM is used to generate the hippocampal surfaces of all subjects and to register the surface zones across subjects. Another important shape modeling approach models the hippocampal surface using spherical harmonic functions (Gutman et al., 2009; Shen et al., 2009; Styner et al., 2004), and uses the coefficients of the harmonic expansion to infer shape differences between patient groups and controls. Other methods (Van Leemput et al., 2009; Wang et al., 2006, 2003; Yassa et al., 2010; Yushkevich et al., 2010) segment hippocampus into different regions and analyze the volume and shape changes in these subfields. These methods compute volumetric image registration between template and individual subject and translate and visualize the deformation on surfaces. In hippocampal subfield shape analysis work (Apostolova et al., 2010a; Cho et al., 2011; Morra et al., 2009a; Qiu et al., 2009; Shi et al., 2013a; Thompson et al., [Link]), the morphometry comparison was performed by registering hippocampal surfaces with geometric feature analysis. This type of methods affords the benefits of high resolution information from the hippocampal surface representation and efficient numerical solutions to register and analyze surface deformation across subjects.

In our APOE e4 carrier vs. noncarriers experiments, comparisons with both the nondemented and the full ADNI cohorts yielded significant differences that were apparently more pronounced on the left hippocampal surface. A prior study (Morra et al., 2009b), which conducted similar experiments with a smaller number of images in ADNI baseline dataset (N = 490) was only able to achieve significance for the left hippocampal surfaces on the full ADNI cohort but did not detect significant differences in the nondemented cohort. That aside, our finding of more significant areas on the left than on the right side, agree with (Morra et al., 2009b), despite differences in our image segmentation methods, surface parameterization and registration algorithms, and statistics. Our results also agree with another APOE e4 study with manually segmented hippocampal surfaces (Pievani et al., 2011).

To our knowledge, this is the first study to use a surface‐based approach to study APOE e4 gene dose effects on the hippocampal morphometry differences among subjects with two copies, one copy and no copies of the APOE e4 allele. Although most current approaches use cortical and substructural volume measures (den Heijer et al., 2010; Dewey et al., 2010; Holland et al., 2009; Jack et al., 2004, 2003; Ridha et al., 2008; Vemuri et al., 2008a, 2008b; Wolz et al., 2010), recent research (Apostolova et al., 2010b, 2010c; Chou et al., 2009; Costafreda et al., 2011; Ferrarini et al., 2008; Luders et al., 2012; Madsen et al., 2010; Morra et al., 2009b; Qiu et al., 2010; Styner et al., 2005; Thompson et al., [Link]; Yang et al., 2012) has demonstrated that surface‐based subregional structure analysis can offer some advantages over volume measures. Our work identified significant differences in hippocampal shape between subjects heterozygous and homozygous for APOE e4 allele in the full ADNI study but did not detect such a difference on the nondemented cohort. When comparing these two groups with homozygous noncarriers (e3/e3), we detected significant differences in all four experiments. Furthermore, our empirical examination of the effect size clearly suggested that the homozygous APOE e4 carriers showed greater atrophy than heterozygous APOE e4 carriers in both full ADNI and nondemented cohorts.

Consistent with prior studies of APOE e4 effects on hippocampal surfaces (e.g., Morra et al., 2009b; Pievani et al., 2011), both heterozygous and homozygous APOE e4 patients show greater deformities for the left than the right hippocampus. By contrast with comparisons of APOE e4 carriers vs. noncarriers, differences between the heterozygous and homozygous APOE e4 groups were greater on the right side than on the left. Some prior research on hippocampal volume (Farrer et al., 1997; Lemaitre et al., 2005) also found that when comparing the heterozygous and homozygous APOE e4 groups, the right hippocampus may have more pronounced atrophy than the left side. However, contradictorily, when comparing these two groups with noncarriers, some other works (Farrer et al., 1997; Lemaitre et al., 2005) found greater atrophy on the right side. The inconsistency may be due to the algorithms used, as with surface‐based method and the new statistics we introduced, more local subtle changes may be captured, which may be missed by the global volume‐based method. More systematic validation and comparison studies are warranted.

Another important goal is to study differences between APOE e4 noncarriers and carriers within the cognitively normal group, i.e., healthy control subjects. As there were only two control subjects homozygous for the APOE e4 allele, tests of dose effects were underpowered in healthy control group. Thus we only compared APOE e4 carriers vs. noncarriers within the control group. Our experiments [N = 177, 125 noncarriers (e3/e3) vs. 52 APOE e4 carriers (e3/e4 or e4/e4)] identified greater deformities on the left hippocampus than the right side but no statistically significant differences were detected after multiple comparisons correction (P = 0.34). This is perhaps due to the low number of healthy control individuals with the APOE e4 genotype (Table 1). The association between APOE e4 and hippocampal atrophy may be detectable in a much larger sample.

In our work, we applied a nonparametric, multivariate permutation testing on Hotelling's T ² statistics. Due to the Hotelling's T ² test, comparisons of different genotype groups were only conducted pairwisely. However, the multivariate analysis of variance (MANOVA; Smith et al., 1962) may be also applicable to analyze our multivariate statistics. MANOVA is a generalized form of univariate analysis of variance. It is used when there are two or more dependent variables. MANOVA has been successfully applied to human brain mapping research (e.g., Bartley et al., 1997; Poline et al., 1996). It may be particularly useful for us to check the hippocampal morphometry differences among subjects with two copies, one copy and no copies of the APOE e4 allele. We plan to study MANOVA in our ongoing AD prevention research.

The current work focuses on describing structural differences at the group level and establishing the correlation between morphometry changes and genetic variance. The current work mainly explores the difference among multivariate statistics without considering the trends of the metric changes. Investigating the trend for multi‐variables as a whole (in the context of multivariate type analysis) might be difficult, but it would be useful for us to explore this “trend analysis” on individual statistics. For example, a medically interesting question could be that, among these three groups (noncarriers, heterozygotes and homozygotes of e4), which individual statistics is more monotonic. In our prior work (Shi et al., 2013b), we used TBM to visualize the metric trend for prematurity study but it may not be able to directly explain the outcome achieved with mTBM features. We plan to explore more along this direction in our future work. The answers to these questions will make our results more intuitive to be understood and eventually help our methods to be adopted quickly by the medical community.

This study has two limitations. First, as the participants are elderly, the ADNI subjects may not be the best representative of patient populations in clinical trials. Our ongoing work that studies the Arizona APOE cohort (Caselli et al., 2009) which consists of cognitively normal subjects with a wider age span may validate or extend our current ADNI findings. We have obtained another cohort dataset from Australian Imaging, Biomarkers and Lifestyle Study of ageing (AIBL, 2013; Ellis et al., 2009). In addition, our ongoing research on Enhancing Neuro Imaging Genetics through Meta‐Analysis (Thompson et al., in press) may potentially provide new and rich datasets for cross‐validation. Replication attempts will be made to corroborate our current biomedical discoveries. Second, because of the extremely low number of APOE e2 carriers in ADNI dataset (Table 1), we excluded them from our APOE e4 studies but did not perform any additional studies to show that APOE e2 might be protective.

CONCLUSIONS

We recently developed our MRI‐based computer‐assisted hippocampal surface morphometry system that uses conformal maps to induce well‐organized grids on surfaces. This simplifies a number of downstream computations of derivatives and metrics. In addition, the surface metric tensor, computable from the conformal grid, has a multivariate structure that contains a great deal of information on local surface geometry. Its components follow a log‐Euclidean law that affects their possible range of values and their statistical distributions. The resulting set of surface tensor methods encodes a great deal of information that would otherwise be inaccessible, or overlooked.

We applied our system to study hippocampal shape differences between subjects in the ADNI dataset with two copies, one copy, and no copies of the APOE e4 allele, a common susceptibility gene for late‐onset AD. We found significant differences between APOE e4 carriers and noncarriers in both full ADNI and nondemented cohorts, with more deformation of the left hippocampus than the right. Within the full ADNI cohort, the e4 homozygotes demonstrated more deformities than the e4 heterozygotes. Our work supports prior reports that the APOE e4 genotype is associated with accelerated brain atrophy along with disease progression, and that these differences can be mapped to morphological changes in subsections of the hippocampal surface. Future studies will test this framework in cognitively normal subjects for the detection of preclinical AD.