MRI‐based axis‐referenced morphometric model corresponding to lamellar organization for assessing hippocampal atrophy in dementia

Abstract

Research on the local hippocampal atrophy for early detection of dementia has gained considerable attention. However, accurately quantifying subtle atrophy remains challenging in existing morphological methods due to the lack of consistent biological correspondence with the complex curving regions like the hippocampal head. Thereby, this article presents an innovative axis‐referenced morphometric model (ARMM) that follows the anatomical lamellar organization of the hippocampus, which capture its precise and consistent longitudinal curving trajectory. Specifically, we establish an “axis‐referenced coordinate system” based on a 7 T ex vivo hippocampal atlas following its entire curving longitudinal axis and orthogonal distributed lamellae. We then align individual hippocampi by deforming this template coordinate system to target spaces using boundary‐guided diffeomorphic transformation, while ensuring that the lamellar vectors adhere to the constraint of medial‐axis geometry. Finally, we measure local thickness and curvatures based on the coordinate system and boundary surface reconstructed from vector tips. The morphometric accuracy is evaluated by comparing reconstructed surfaces with those directly extracted from 7 T and 3 T MRI hippocampi. The results demonstrate that ARMM achieves the best performance, particularly in the curving head, surpassing the state‐of‐the‐art morphological models. Additionally, morphological measurements from ARMM exhibit higher discriminatory power in distinguishing early Alzheimer's disease from mild cognitive impairment compared to volume‐based measurements. Overall, the ARMM offers a precise morphometric assessment of hippocampal morphology on MR images, and sheds light on discovering potential image markers for neurodegeneration associated with hippocampal impairment.

We presents an innovative axis‐referenced morphometric model based on 7 T ex vivo hippocampal atlas. The model follows anatomical lamellar organization of the hippocampus, reshaping its formation by precise and consistent curving long‐axis. We calculate morphological measurements and validate its accuracy by comparing reconstructed surfaces with those directly extracted from MRI hippocampi.

1. INTRODUCTION

The human hippocampus is a crucial brain structure responsible for memory processing, learning, spatial navigation, and emotions (Chauhan et al., 2021). It is especially vulnerable to the neurocognitive diseases (Baazaoui & Iqbal, 2022). For instance, a prominent structural biomarker for Alzheimer's disease (AD) progression is the accompanying atrophy of the hippocampus (Dubois et al., 2014; Frisoni et al., 2010; Hill et al., 2014). Extensive researches have focused on local atrophy to improve the sensitivity and specificity of this marker for early AD detection (Adler et al., 2018; Braak & Braak, 1997a, 1997b; Chauveau et al., 2021; Gabere et al., 2020; Kerchner et al., 2010; Martin et al., 2010; Scheff et al., 2007; Tang et al., 2015; Zhang et al., 2020). Imaging studies utilize morphological methods to detect variations in the early stages of disease by quantifying the location and extent of atrophy through large scale validations. These methods achieve point‐wise correspondence across individuals through geometric mapping to measure local morphological variations. However, accurately quantifying complex curving hippocampus by the existing methods remains challenging, leading to incorrect quantification of subtle morphological changes.

The challenge in describing the curved morphology of the hippocampus lies in the variable small folds, knowns as digitations, on its boundary surface and the medial curvature, particularly in the uncus of the hippocampal head (Figure 1). To address the issues, the current morphological methods can be categorized into two main approaches: the boundary‐based method (DeKraker et al., 2018; DeKraker et al., 2022; Fang et al., 2019; Styner et al., 2006; Tang et al., 2015) and the skeletal representations (Gao et al., 2023; Pizer et al., 2022). The boundary‐based method builds geometric mapping among individuals by surface reparameterization or deformation. The former performs a unified reparameterization rule on the boundary surface. For instance, the widely used spherical harmonic description point distribution model (SPHARM‐PDM) achieves accurate reconstruction of hippocampal morphological details by reparameterizing its boundary surface through area‐preserving conformal optimization of spherical mapping (Fang et al., 2019; Styner et al., 2006). The registration method, such as the large deformation diffeomorphic metric mapping (LDDMM), provides a biologically more plausible mapping from a template hippocampus to the targets by finding point‐wise displacement field that minimizes shape differences in a diffeomorphic transformation space (Tang et al., 2015). However, the variability in the number of digitations poses challenges for the both methods, as it requires a larger number of corresponding points in hippocampi with multiple digitations than those with fewer digitations (DeKraker et al., 2021). A recent boundary‐based method addresses the issue by unfolding the hippocampus onto a planar coordinate system (DeKraker et al., 2018, 2022). However, the technique heavily relies on subfield segmentation, particularly the stratum radiatum, lacunosum, and moleculare, which can be challenging to distinguish on clinical images. Different from above boundary‐based methods, the skeletal representation provides a comprehensive evaluation of the three‐dimensional volumetric properties of an anatomy and offers a statistically stable correspondence regardless of the number and extent of small folds. However, since the skeleton of the hippocampus is deformed from its approximating ellipsoid, the generated longitudinal axis of hippocampus deviates from its natural curvature in the head, leading to inaccurate thickness measurements. Overall, due to the difficulties of existing MRI‐based methods in characterizing the complex curvature of the hippocampal morphology, there is an urgent need to develop a mapping technique with morphological correspondence guided by biological consistent characteristics of the hippocampus, enabling precise computation of its morphology.

FIGURE 1.

Anatomical longitudinal organization of the hippocampus. The CA and DG form an “interlocking C” profile on each lamella along the entire long axis. Each lamellar slice contains a transverse functional unit across DG (red), CA1 (green), CA2 (orange), and CA3 (blue). Longitudinal interlamellar connection, dominated by mossy fibers and granule cells in DG and pyramidal cells in CA3 and CA1, are intensively existed along the long axis. The strip‐formed lamellar structure (yellow) is distributed nearly perpendicular to the long axis of the hippocampus (crimson). Functional and anatomic connectivity with extra‐hippocampal structures shows a gradient along the longitudinal dimension (Anterior, magenta; dark blue, posterior). A, anterior; CA, cornu ammonis; DG, dentate gyrus; EC, entorhinal cortex; L, lateral; M, medial; P, posterior; SRLM, stratum radiatum lacunosum moleculare; SUB, subiculum; Vert. unc, vertical uncus. The image is adaped from (Duvernoy et al., 2013)

Despite of variable complex curvature among individuals, there exists a consistent lamellar organization in the hippocampus (Andersen et al., 1971; Andersen et al., 2000; Pak et al., 2022; Sloviter & Lomo, 2012). The lamellae are distributed along the longitudinal axis, which well captures its medial curvature. the longitudinal axis of the hippocampal formation remains stable. Generally, the main curvature in the longitudinal dimension of human hippocampus follows a typical curved trajectory that forms a “crescent” shape (Genon et al., 2021). Ding and Van Hoesen (2015) has inspected the subfields in the uncus, a part of the hippocampal head that curves medially and superiorly to the amygdala, and shows that all subfields continuously follow this curvature throughout the head (Figure 1, crimson line from the posterior to anterior terminating in “vert. unc”). Adler et al. (2018) and Gross et al. (2020) also demonstrate quite similar inner architecture along the entire length of the hippocampus, an “interlocking C” profile formed by the principal cell layers of cornu ammonis (CA) and dentate gyrus (DG) (Figure 1, the three‐dimensional curved surface of CA and DG). The lamellar organization is discovered in neuroelectrophysiological experiments that the neuronal layers within the hippocampus are arranged along the longitudinal axis. Specifically, the fiber orientations of principal cell axons in the hippocampus are distributed in parallel, forming a thin strip‐like fashion oriented nearly perpendicular to the longitudinal axis. These thin transverse slices, called the lamellae, could represent a functional unit of the hippocampus. Across lamellae, longitudinal neuron connections have been discovered along the longitudinal axis. Recent studies have discovered more enriched information flow in the longitudinal plane than the transverse plane (Pak et al., 2022), highlighting the important role of longitudinal organization. We illustrate the lamellae and longitudinal interlamellar connections in the hippocampal body in Figure 1. Based on these evidences, representing the hippocampus based on its lamellar organization offers a precise and consistent characteristic of the hippocampal formation compared to boundary‐based methods and skeletal representations, which helps provides a more accurate characterization of its curving morphology.

In this article, we propose an MRI‐based axis‐referenced morphometric model (ARMM) corresponding to lamellar organization of the hippocampus. The backbone of the method is to establish an interior coordinate system within the hippocampus, where coordinate lines corresponding to longitudinal axis and lamellar distribution. The coordinates of arbitrary hippocampus are built through diffeomorphic transformation from the template hippocampus to the target space. Morphological measurements from the ARMM include the location, curvature and length of the long axis, digitations, local thickness and width along the longitudinal and transverse axes, subfield distributions, and surface curvatures. To validate ARMM, we collected five 7 T ex vivo MRI from a public dataset (Adler et al., 2018) and 813 longitudinal 3 T T1‐weighted MRI scans of 271 subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to assess its morphometric accuracy. The results demonstrate the superiority of ARMM over state‐of‐the‐art methods and its ability to discriminate dementia. The ARMM offers an anatomically motivated morphological model that has the potential to reveal novel image markers for diseases associated with hippocampal damage. The code for this project, including the ARMM template and the automated pipeline, is available at https://github.com/calliegao/ARMM.

The main contributions of this study include:

1. We propose an ARMM for alignment of different hippocampi based on the consistent lamellar organization.

2. The method provides precise measurement of hippocampal morphology and its detailed variations in MR images.

3. The unique hippocampal atrophy pattern measured by ARMM can discriminate early AD from the Mild Cognitive Impairment patients.

2. METHODS

We aim to characterize the hippocampus from structural MR images based on its lamellar organization to improve detailed morphological quantification in its curving surface and medial curvature. An axis‐reference morphometric model (ARMM) is proposed to align different hippocampi and perform morphological measurements on their surfaces. The framework of ARMM consists of two stages. First, we establish an interior “axis‐referenced coordinate system” through conformally reparameterizing planar orthogonal coordinates to the inscribed medial surface (IMS) and boundary surface of a histologically‐derived atlas of hippocampus. Second, this coordinate system in the template hippocampus is utilized to automatically generate lamellar representations of arbitrary hippocampi through diffeomorphic spatial deformation while adhering to the constraints of medial‐axis geometry. We perform morphological measurements on the reconstructed surfaces of hippocampi and evaluate the accuracy of these measurements by comparing the reconstructed surface to the surface borders directly extracted from images. The details of our methods are described as follows.

2.1. Data preparation

We employ an atlas of hippocampus that captures average anatomy derived from a large cohort of ex vivo 7 T MRI and histological datasets (Adler et al., 2018). This 3D probabilistic atlas, capturing the average anatomy and anatomic variability of hippocampal subfields, is created by combining high‐resolution (0.2 mm × 0.2 mm × 0.2 mm) ex vivo MRI scans of 31 human hippocampal specimens using a groupwise diffeomorphic registration approach. The data repository is located at https://www.nitrc.org/projects/pennhippoatlas/. The voxel size of the image is 0.2 mm × 0.2 mm × 0.2 mm. The atlas includes six hippocampal subfields: cornu ammonis (CA) 1, 2, and 3, stratum radiatum lacunosum moleculare (SRLM), dentate gyrus (DG), and the subiculum (SUB). This atlas is defined as a cross‐sectional hippocampal atlas (CHA) and is used as a template that we aim to accommodate (Figure 2a).

FIGURE 2.

The two primary steps of the ARMM methodological framework: first, establishing an axis‐reference model within a hippocampal atlas; and second, utilizing this model as a template to generate axis‐reference models for any given hippocampi through spatial deformation. Left: The first step including building an axis‐referenced coordinate system of the hippocampus and reshaping the reconstructed surface to obtain laminar distribution along the long axis. To achieve this, a hippocampal boundary surface (a) is extracted from the MR image. (b) The surface is then used to calculate the IMS (pink) by NURBS surface fitting with Voronoi diagram vertexes (yellow) that generate from the hippocampal boundary surface mesh. The blue mesh in (c) is a reparameterized IMS, with the centermost axis (red) manually fitted to be generally agree with the CA‐DG border of the hippocampus. (d) Spokes calculated according to geometric constrains on IMS (yellow) and boundary surface. The superior and inferior spokes, colored in magenta and cyan, respectively, pointing from the IMS to the gray boundary surface. (e) A hippocampal surface with transversal lamellar and longitudinal axes is generated from the IMS and spokes. Note that the boundary surface is composed of the superior and inferior parts colored in magenta and cyan, respectively. Right: The approach to automated generate axis‐reference model of an arbitrary hippocampus, with consideration on longitudinal hippocampi. Ant, anterior; CA, cornu ammonis; DG, dentate gyrus; IMS, inscribed medial surface; Lat, lateral; Med, medial; NURBS, non‐uniform rational B‐splines; Post, posterior; SRLM, stratum radiatum lacunosum moleculare; SUB, subiculum.

To evaluate our method in measuring comprehensive morphology of the hippocampus during a time period, we adopt a longitudinal hippocampal atlas (LHA) derived from the same study as the atlas (Adler et al., 2018). The LHA captures anatomic variabilities corresponding to the transition from nondementia control (NC) to Alzheimer's disease (AD). Specifically, in creating the LHA, Adler et al. (2018) visualize the shape variability between control and AD hippocampi by comparing landmarks in the MRI atlas space to corresponding landmarks in each input specimen using geodesic shooting and a three‐step registration procedure. Then, statistical shape analysis, including principal component analysis and a support vector machine classifier, was employed to discriminate between AD and control groups, and the resulting initial velocity field was used to generate a longitudinal atlas illustrating the shape change between the two groups. This image series includes 21 images (voxel size: 0.2 mm × 0.2 mm × 0.2 mm).

To evaluate the accuracy of our model in representation of 7 T MRI hippocampus, we collect five samples from the study (Adler et al., 2018). The demographic information is presented in Table 1. Furthermore, to evaluate our method on 3 T T1‐weighted MRI and to verify its clinical value in discrimination of disease, we collect images from the opensource ADNI database (http://adni.loni.usc.edu) with three scans for 1 year intermittent. Three groups are included in this study, the progressive mild cognitive impairment (pMCI), the stable mild cognitive impairment (sMCI) and the normal control. All participants have provided informed written consent before recruitment and filled out questionnaires approved by the respective Institutional Review Board (IRB). A subject is labeled as amyloid‐β positive based on CSF Aβ 1–42 measurement (<192 pg/mL) (Landau et al., 2013; Shaw et al., 2009). Only the pMCI subjects who diagnosed as AD at their third visits and have positive status of CSF Aβ measurement at baseline are selected. The collected CN and sMCI subjects are age and gender matched with pMCI group. The selected sMCI subjects remain CSF Aβ positive and CN subjects remain Aβ negative through all the three visits. All enrolled sMCI and CN subjects keep the same diagnosis through all visits. According to above criteria, a total of 236 subjects are involved in this study, including 81 CN controls, 88 sMCI, and 67 pMCI patients. The demographic information of their baseline examination is presented in Table 1.

TABLE 1.

Demographic information of subjects and MRI resolution.

	7 T MRI	3 T MRI
MRI resolution (mm × mm × mm)	0.2 × 0.2 × 0.2	1.2 × 1.2 × 1.2
Group (number of subjects)	CN/AD (3/2)	CN Aβ − (87)	sMCI Aβ + (102)	pMCI Aβ + (82)
Gender	1 F/4 M	40 F/47 M	54 F/48 M	19 F/63 M
Age a	75.8 ± 10.57	76.02 ± 5.92	75.96 ± 6.08	76.25 ± 7.42

Abbreviations: AD, Alzheimer's disease; CN, cognitive normal; F, female; M, male.

^a Mean ± standard error.

In the study, we manually select images with minimal movement artifacts for each subject at the same time point. All raw T1 images are directly segmented using the Synthseg toolkit to obtain bilateral hippocampi, as this tool has been proven to be robust to scans without preprocessing and exhibits high segmentation accuracy on the ADNI dataset (Billot et al., 2023). The segmented hippocampi are then used to extract contour surfaces using ITK‐SNAP (Yushkevich et al., 2006). No data are excluded from our quality control process in this study.

2.2. Template model preparation

In order to build a template axis‐referenced model, which adapts to the lamellar organization of the hippocampus, we implement two primary steps, as illustrated in the Figure 2. The first step involves the establishment of an axis‐referenced coordinate system within a template hippocampus following the medial geometry. In the second step, we reshape the hippocampal surface reconstructed in the first step to obtain lamellae along the long axis. The details of our method are described below.

2.2.1. The axis‐referenced coordinate system of the hippocampus

The skeleton is a kind of geometric symmetry used to simplify a complex shape. Mathematically, the symmetry axis of the hippocampus can be represented as an internal medial surface by the medial axis geometry (Pizer et al., 2022; Siddiqi & Pizer, 2008). We have made some modifications to the medial axis for application in this study, and the details are described in the Supporting Information. One important modification involves smoothly extending the medial surface outward until it reaches the object's boundary surface. These results in an inscribed medial surface (IMS) used to represent the symmetry of the object. Here, we generate the IMS of the template hippocampus in three steps. First, we calculate the Voronoi diagram according to the boundary surface of the hippocampus. The diagram consists of Voronoi regions, which are sets of points located closer to a particular generating point than to any other generating point. The points on a Voronoi diagram from a 3D object's boundary agree with the medial surface (Siddiqi & Pizer, 2008). Second, we create a Non‐Uniform Rational B‐Splines (NURBS) surface that best fits the Voronoi points inside the hippocampus. The NURBS, a flexible and powerful geometric fitting method widely used in 3D modeling, creates a smooth surface approximate to the medial surface of the hippocampal shape. Finally, we smoothly extend the medial surface to meet the boundary surface of the hippocampus, as shown in Figure 2b.

A rectangular mesh on a two‐dimensional plane is conformally mapped to the IMS, where the centermost longitudinal line is manually adjusted to best approximate the intersection between the IMS and the CA‐DG border (the CA region includes subfield CA 1, 2, 3 and the DG includes the SRLM). The conformal mapping is performed by methods described in (Meng et al., 2016), with four manually defined landmark vertices on the border of the IMS corresponding to the four corners of the planar rectangle. A reparameterized IMS is illustrated in Figure 2c. Due to the conformal mapping, the transversal (medial‐lateral) axes are ensured to be nearly vertical to the longitudinal axes on the IMS. These orthogonal curvilinear coordinate lines serve as a reference to reshape the hippocampal boundary surface.

A radial flow from the reparameterized IMS to the boundary surface of the hippocampus can provide a way to index any position within the hippocampus. We specify the target of the radial flow to be on the boundary surface, and then the radial mapping can be represented as a vector field. These vectors are called “spokes” in medial axis geometry. Let $S$ denote the original surface boundary of the target hippocampus, and $\tilde{S}$ be the reconstructed surface. Spokes on the IMS need to satisfy the following conditions: (1) $\tilde{S}$ should agree with $S$; (2) spokes are vertical to the boundary surface; and (3) the lengths of superior spokes are equal to the corresponding inferior spokes. We initialize the spokes on the IMS by unit normal vectors on the IMS. Then, we use an iterative scheme to refine the initial spokes. First, to ensure the accuracy of the reconstructed shape, we need condition (1) to strictly hold. Second, we set a proper threshold to measure the non‐orthogonality of spokes to the boundary surface, that is, $1-\cos \left({\theta }_p\right)$, where ${\theta }_p$ denotes the angle between the spoke direction at vertex $p$ on the IMS and the normal vector of the boundary surface at the nearest vertex to the spoke tips. Third, because the spokes at bends of the hippocampal head often cross the boundary surface, pointing to wrong places, we solve the problem by enforcing condition (3), then gradually adjust these spokes directions to be approximately orthogonal to the boundary surface. Finally, we iterate above three steps and once more implement condition (1) to get the final refined spokes.

Suppose that the medial surface $m$ is parameterized by $\left(u,v\right)$, and a spoke $U$ is placed at each location $m\left(u,v\right)$. Then, any points on the hippocampal surface can be uniquely indexed by $\left(m,U\right)$ in this coordinate system. Figure 2d shows the superior and inferior spokes attached on the IMS of the hippocampus.

2.2.2. Reshaping the boundary surface

Theoretically, the hippocampal boundary surface can be reconstructed by smoothly connecting all spoke tips. However, in digital shape models, it is hard to satisfy all three geometric conditions described above. The self‐overlap of spokes will occur at the bending part (e.g., the folds on the hippocampal head), leading to self‐intersecting faces on the reconstructed surface mesh. To refine the surface representations, the superior and inferior surfaces are first roughly reconstructed by superior and inferior spokes, respectively. The two triangular surface meshes are corrected and subdivided automatically using the MeshLab toolkit (Cignoni et al., 2008). Then, each surface is conformally reparameterized by $\left(u,v\right)$ in a two‐dimensional rectangular domain. We rearrange the mapped spoke tips to be uniformly distributed on the two‐dimensional plane. These inverse mapped spokes can overcome self‐overlap at the folds. By connecting the spoke tips that correspond to the same transverse axis, we get a “border” of a “lamellae,” which is ensured to be perpendicular to the long axes on the IMS by the conformal reparameterization. An example refined boundary surface mesh of the hippocampus with 22 lamellae and 2 mm intervals is shown in Figure 2e. The thicknesses between each of two neighboring lamellae can be manually designed by implementing interpolation or down‐sampling of the spoke density.

Since the conformal mapping builds correspondence between the IMS and the planar rectangle, and the radial mapping corresponds the superior/inferior surfaces and the IMS, subfield distributions and local curvatures on hippocampal boundary surface can be projected onto the two‐dimensional plane through these correspondences. This process equals to unfold the hippocampal surface to the two‐dimensional plane while remaining the geometric properties of surface textures. An unfolded hippocampal surface is presented in Figure 2f and fitted with a two‐dimensional coordinate system. Each straight line of the same u‐value in this coordinate system corresponding to a lamella on the hippocampus. When inspecting the topography of the hippocampal subfields, the SRLM forms a typical “C shape” on transverse slices, with subfields CA 1, 2, 3, SUB, and part of DG cutting off the external dorsal portion of the “C” shape into five parts. The ventral part of the “C” shape consists DG and part of CA3. Therefore, the unfolding of the hippocampal surface keeps topography of subfields that distributes around the external dorsal part of the SRLM, including all the CA1, 2, SUB, most part of CA3, and part of DG. Therefore, through this unfolding, any points on these subfields can be uniquely indexed and identified on the two‐dimensional orthogonal coordinate system. By mapping the surfaces of a group of hippocampi, the unfolding onto this uniform rectangle facilitates point‐wise morphological correspondence across individuals.

2.3. Automated ARMM generation

Although the morphology of the hippocampus varies among individuals, it follows a consistent long axis organizational pattern. Therefore, we can deform the ARMM of the template hippocampus to match different hippocampal shapes. The right panel of Figure 2 illustrates how to derive an axis‐referenced coordinate system for any given hippocampus based on the template.

The ARMM consists of the IMS and spokes, which are distributed within the space of hippocampal surface. Therefore, to achieve this deformation, we employ a spatial transformation method that utilizes control points on the surface to guide the diffeomorphic deformation from the template space to the target space. For each target hippocampus, we computed the deformation in two steps. First, we established correspondences between the boundary surfaces of different hippocampi using the SPHARM‐PDM correspondence method. We selected surface vertices as control points, which do not require strict anatomical correspondence but should be sufficient to guide the deformation in the local neighborhood. Next, we utilized a control‐points‐based instance of the Large Deformation Diffeomorphic Metric Mapping framework, as introduced in previous works (Durrleman et al., 2014; Fishbaugh et al., 2017). This framework allowed us to continuously adjust the velocity and momentum fields to obtain the template‐deformed morphological model that best matches the target hippocampus.

The ARMM imposes specific requirements on its spokes: (1) single measurement at a single location, (2) thickness vectors being nearly vertical to the reference surface, and (3) a completely match of the spoke tips with the target boundary. To meet these conditions, we apply the medial‐axis geometric constraint to the spokes. Then, by smoothly connecting the spoke tips, we obtain the reconstructed hippocampal surface. The coordinate lines on the reconstructed superior and inferior boundary surface intersect transversely and longitudinally with each other, and the whole boundary surface share the same coordinate system as the template hippocampus through unfolding onto a common two‐dimensional rectangle.

To address commonly encountered longitudinal data in clinical settings, we have devised a model construction method that ensures more reasonable correspondences. Each observed hippocampus represents a single time point. First, we rigidly align all the hippocampi to the baseline hippocampus. Then, we fit the baseline hippocampus with an ARMM using above deformation strategy. Finally, for each time point, we let the hippocampi share the same IMS as the baseline hippocampus while refine the spokes and location of fold curves to fit each hippocampus boundary surface.

2.4. Morphological measurement

The above methods implemented on the CHA form what we call the ARMM of the hippocampus. Local surface features, such as curvatures quantified by discrete mean curvatures on the mesh vertices, have been widely used and proved to be sensitive to local shape changes. In addition, subfield borders on the hippocampal surface can be projected onto the IMS by conformal correspondence. Volumetric features, such as thickness, width, and bending, which have also shown to be useful in disease‐affected focal locations, can be measured along the coordinate lines of the reparameterized IMS. In this study, distances from mesh vertices to the IMS are defined as local thicknesses. Since the whole hippocampal surface is cut into superior and inferior surface along the fold curve, where the IMS meets the boundary surface, vertices on each of the two surfaces have respective local thickness, called the superior thickness, and the inferior thicknesses. This definition has several advantages: (1) Any vertices on the hippocampal surface, including those with no corresponding spokes, have measurable thickness; (2) The thickness between the superior/inferior surfaces and the IMS is a straight‐line/Euclidean distance, which is more easily interpreted than the Laplace thickness (Jones et al., 2000) in terms of a sheet‐like shape; and (3) Considering thicknesses of superior and inferior portions of the object, respectively, makes it convenient to study local shape change on each portion. We have summarized all structural features that can be measured by the proposed ARMM and their corresponding descriptions in Table 2.

TABLE 2.

The structural features and how to measure them on the ARMM of hippocampus.

Features	Characterization	Measurement
Surface curvatures	The fluctuation of the hippocampal surface.	Mean curvatures measured on each vertex on the reshaped hippocampal boundary surface.
Superior thicknesses	The thickness of the superior portion of the hippocampus.	Euclidean distances from superior boundary surface vertexes to the IMS.
Inferior thicknesses	The thickness of the inferior portion of the hippocampus.	Euclidean distances from inferior boundary surface vertexes to the IMS.
Widths	The medial‐lateral extent of the hippocampus.	Lengths of transversal axes on IMS.
Lamellar thickness	Thickness between two adjacent lamellae.	Curvilinear distance between two adjacent transverse axes on IMS of the relating lamella domain.
Lengths	Lengths of the hippocampus in the longitudinal dimension.	Length of the longitudinal axes on IMS.
Length of the long axis	Length of the entire long axis of the hippocampus.	Length of the long axis on IMS.
Curvatures of the long axis	The fluctuation of the long axis trajectory.	The discrete mean curvatures measured on the long axis.
Curvature of digitations	The fluctuation of the hippocampal surface along the longitudinal axis on digitations.	Curvatures of the longitudinal lines on the boundary surface.

2.5. Model evaluation

The raw hippocampal surface extracted from the label image is used as the ground truth to test the geometric accuracy of the ARMM. The hippocampal surface is reconstructed using four shape models (ARMM, SPHARM‐PDM (Styner et al., 2006), ds‐rep (Liu et al., 2021), and cm‐rep (Yushkevich, 2009)), respectively. We test four metrics that measure the accuracy of the reconstructed hippocampi by the shape models, including surface distance, areal difference, curvedness error, and dice index.

The surface distance Q is defined as $Q=\frac{1}{n}\sqrt{{\sum }_{i=1}^n{‖p_i-q_i‖}^2}$, where $n$ is the number of vertices on surfaces, and $p_i$, $q_i$ represent the corresponding points on two surfaces. The Euclidean distance $d_i=‖p_i-q_i‖$ ($i=1,\dots n$) denotes each point‐wise distance. The correspondence related to point‐wise distance is constructed by searching for the nearest point between surfaces via the Iterative Closest Point (ICP) method. The curvedness at each vertex is defined by $c=\sqrt{\left(k_{\max }^2+k_{\min }^2\right)/2}$, where $k_{\max }$ and $k_{\min }$ represent the main curvature. Further, we convert the reconstructed surfaces into binary image labels and rigidly register the labels into the original image label of the template hippocampus, then calculate the dice index between the reconstructed shape and the ground truth. The dice index is defined as $\text{Dice}=\frac{2\times \text{Volume}\left(R\cap G\right)}{\text{Volume}\left(R\right)+\text{Volume}\left(G\right)}$, where R denotes the image label of the reconstructed shape, and G denotes the ground truth label. To evaluate the accuracy of ARMM in shape representation on different portions of the template hippocampus, we subdivide the hippocampus into head, body, and tail by 1/3 and 2/3 of the anterior–posterior extent. We cut 1/2 of the hippocampal head tip along the medial‐lateral orientation, which consists of a fold that curves medially and superiorly. We further cut 1/2 of the hippocampal tail tip along the anterior–posterior orientation.

Longitudinal local surface variations are quantified by calculating the point‐wise surface distance between the baseline and the $i^{\mathrm{th}}$ observed surface. The point‐wise surface correspondence is established by the coordinate system of ARMMs. Thickness variation is evaluated by subtracting the local superior/inferior thickness measured on each vertex of the reshaped hippocampal surface from the corresponding thickness measured on the baseline hippocampus.

To evaluate the potential improvement in discriminating disease subjects from the controls using the measurements obtained from ARMM, we employ the random forest model for classification. Specifically, to mitigate the risk of overfitting due to improper data set partitioning, we perform a five‐fold cross‐validation. The classification performance was evaluated based on sensitivity, specificity, accuracy, and the area under the receiver operating characteristic curve on the test set.

3. RESULTS

3.1. Model accuracy on template hippocampus

We applied the ARMM to the CHA and compared its accuracy with those of three other shape models (cm‐rep, SPHARM‐PDM, and ds‐rep). As presented in Table 3, the results show that the ARMM outperformed the other three models in all portions of the hippocampus in surface distance and dice, particularly in the head fold and tail tip. In these two portions, the curvature of the hippocampal surface is relatively large, and the cm‐rep, ds‐rep and SPHARM mehods all rely on deformation algorithms to generate reconstructed surfaces. However, maintaining the geometric integrity of the surface mesh during large deformation in these areas can lead to deformation errors. Conversely, ARMM focuses soly on deforming the IMS, thereby avoiding such inaccuracy. It can be observed that, although the Dice coefficient in the Head fold and Tail tip portions is slightly lower than that in the other parts, it can still reach above 0.99. In comparison, the highest Dice coefficient is in SPHARM, reaching 0.97 and 0.95, respectively, while cm‐rep has the lowest Dice coefficient, at 0.68 and 0.73. In all portions, the reconstructed surface error of ARMM is wihin 0.0004mm, which is much small than that of other mehods. In addition, the areal difference of ARMM is found to be higher than that of SPHARM‐PDM, which is expected, given the relatively sparse point distribution on the lateral of the hippocampus surface due to the fan‐out lamellae from the lateral to medial. The ARMM also performed the best on the head and tail portions of the hippocampus, as indicated by the results of curvedness and surface area. In these two locations, the surface area errors are approximately within 0.5 and 0.3 mm², much smaller than those of other methods. In contrast, the surface area errors of ds‐rep and cm‐rep can exceed 10 mm². Regarding the curvedness error in the head and tail, ARMM has the best performance among all methods with an error within 0.003(1/mm), indicating that smoothness of the reconstructed surface is closest to the ground truth surface. This further indicates that the surface curvature measured on the ARMM reconstructed surface is more consistent with the ground truth.

TABLE 3.

Shape errors between each reconstructed shape and the ground truth.

Portions of hippocampus	Shape similarity metrics	ARMM	Cm‐rep	SPAHRM	Ds‐rep
Whole hippocampus	Surface distance (mm)	0.0003	0.0071	0.0012	0.026
	Areal difference (mm2)	1.2404	0.4222	1.7255	9.9669
	Curvedness error (1/mm)	0.0133	5.0635	0.0326	0.0592
	Dice	0.9961	0.8313	0.9702	0.9074
Head	Surface distance (mm)	0.0002	0.0054	0.0009	0.0028
	Areal difference (mm2)	0.5217	7.4814	1.5972	11.3964
	Curvedness error (1/mm)	0.002	6.9358	0.0293	0.0643
	Dice	0.9959	0.8277	0.9732	0.9045
Head fold	Surface distance (mm)	0.0003	0.0069	0.001	0.0044
	Areal difference (mm2)	0.6414	1.2509	1.3612	17.8808
	Curvedness error (1/mm)	0.0024	14.136	0.0224	0.0573
	Dice	0.9934	0.6815	0.9706	0.8459
Body	Surface distance (mm)	0.0004	0.0106	0.0012	0.1137
	Areal difference (mm2)	0.1076	8.1713	0.127	5.4684
	Curvedness error (1/mm)	0.0679	0.0281	0.0134	0.0146
	Dice	0.998	0.8403	0.9722	0.9284
Tail	Surface distance (mm)	0.0002	0.0046	0.0012	0.0031
	Areal difference (mm2)	0.2534	17.5162	2.0229	10.8307
	Curvedness error (1/mm)	0.0029	0.0095	0.0402	0.0501
	Dice	0.997	0.8313	0.9611	0.8934
Tail tip	Surface distance (mm)	0.0004	0.008	0.0017	0.0061
	Areal difference (mm2)	0.3948	28.8729	4.0824	25.5454
	Curvedness error (1/mm)	0.0036	0.0445	0.0369	0.0037
	Dice	0.9939	0.7272	0.9517	0.7747

Figure 3a visualizes the local surface distance between the reconstructed surfaces and the ground truth. The SPHARM‐PDM and ARMM perform well in characterizing the hippocampal head and tail, while the ds‐rep and the cm‐rep models fail to capture the bending on these two portions. The ARMM shows higher accuracy than SPHARM‐PDM, particularly at the bending on the medial side of the head. Lamellar boundaries on the hippocampal surface are generated from the ARMM and visualized as black curves in Figure 3a, showing a fanned‐out distribution from the lateral to medial of the hippocampus, with no overlaps at folds (the bending part of the hippocampal head).

FIGURE 3.

Comparisons of the four hippocampal shape models. (a) Point‐wise distance maps of the models. The locations colored in red denote large errors between the ground truth surface and the reconstructed surfaces by the shape models. (b) Axes generated from the four models. In the last panel, the long axis generated from ARMM is visualized inside the 3D hippocampus. CA, cornu ammonis; DG, dentate gyrus; LA, long axis; Sub, subiculum.

Figure 3b shows the long axis of the hippocampus from the four models. The ds‐rep and SPHARM‐PDM well characterize the curved body of the hippocampus but fail to capture the bending on the hippocampal head and the end of the tail. The cm‐rep cannot generate an explicit longitudinal axis directly from its medial surface. None of the three models consider the interior anatomical structure of the hippocampus. The last panel of Figure 3b shows a 3D visualization of the subfield distribution and the long axis derived from ARMM, which agrees with the CA‐DG border and follows the orientation of the entire longitudinal curvature.

The ARMM in Figure 3b shows a local thickness map measured on the superior hippocampal vertices respecting the reparameterized IMS. The curved transverse and longitudinal coordinate lines are nearly orthogonal to each other on the IMS of ARMM. We have calculated the angular distortion of conformal reparameterizations of the IMS, where the angular distortion refers to the difference between angles of the triangle elements on the 2D rectangle and corresponding angles on the conformal reparameterization. All of the angular distortions are found to be less than one degree, ensuring that the lamellae are perpendicular to the longitudinal axes.

3.2. Model evaluation on 7 T MRI hippocampi

To evaluate the effectiveness of our method, we apply it to five 7 T ex vivo MRI scans of hippocampi (Adler et al., 2018). Our goal is to determine if the deformation field could successfully transform all elements of the ARMM to the target hippocampi while preserving the relationship between adjacent elements. The hippocampal surfaces are extracted from the label image, which are also used as the ground truth to test geometric accuracy of ARMMs by the proposed method. In addition, we compared our results with the ds‐rep (Liu et al., 2021), which is a skeletal representation similar to the ARMM. The ds‐rep also utilizes a transform‐based approach to automatically generate population representations for shapes. To ensure a fair comparison of the two models, we set the reconstructed surfaces to contain a similar number of vertices, approximately 1000 in each case.

Figure 4a shows an ARMM of a typical 7 T hippocampus. The colormap for the left panel of the figure denotes local surface distance between the reshaped surface by ARMM and the ground truth. The most severe surface distance errors are on the medial and lateral of the body, with the maximum distance 1.07 mm. The longitudinal axis on IMS well captures medial curvature on the hippocampal head, shown in the right panel of Figure 4a. Also, the transversal axes have been kept nearly orthogonal to the longitudinal axes. Population statistics of the surface distance errors between the ground truth surface and the reconstructed surface from ARMM and ds‐rep are listed in Table 4. The distance errors are measured by point‐wise surface distance Q. The ARMM outperformed the ds‐rep in both the mean and maximum of the measurement, indicating a more accurate representation of the hippocampus. As morphometry is conducted on reconstructed surfaces, this result indicates that ARMM can measure hippocampal morphology more accurately than ds‐rep.

FIGURE 4.

The ARMM of typical 7 T and 3 T hippocampi generated by the deformation‐based method. Columns from left to right: the ground truth surface extracted from MRI, the reshaped surface by ARMM, the IMS of hippocampi. (a) Surfaces and IMS of a 7 T hippocampus. (b) Surfaces and IMS of a 3 T hippocampus. IMS, inscribed medial surface.

TABLE 4.

Distance error statistics between the reconstructed surface and the ground truth surface by ARMM and ds‐rep, respectively.

	Mean (mm)	Standard deviation (mm)	Max (mm)	Group	Mean (mm)	Standard deviation (mm)	Max (mm)	Longitudinal time points	Mean (mm)	Standard deviation (mm)	Max (mm)
7 T (ARMM)	0.40	0.17	1.07
7 T (ds‐rep)	3.37	0.05	3.55
3 T (ARMM)	0.45	0.05	1.10	CN	0.45	0.05	1.10	tp 0	0.45	0.03	0.90
								tp 1	0.42	0.02	0.50
								tp 2	0.40	0.08	1.10
				pMCI	0.43	0.05	0.80	tp 0	0.43	0.03	0.50
								tp 1	0.40	0.03	0.48
								tp 2	0.48	0.08	0.80
3 T (ds‐rep)	4.43	0.58	5.9	CN	4.70	0.40	5.90	tp 0	4.85	0.40	5.90
								tp 1	4.55	0.35	5.60
								tp 2	4.60	0.38	5.75
				pMCI	4.10	0.55	5.65	tp 0	4.35	0.50	5.25
								tp 1	4.08	0.50	5.65
								tp 2	3.90	0.60	4.95

Abbreviations: AD, Alzheimer's disease; CN, cognitive normal; tp, time point.

3.3. Model evaluation on cross‐sectional and longitudinal 3 T MRI hippocampi

The automatic ARMM generation algorithm is implemented entirely on a server with 64GB 8‐core CPU and 11GB 1080Ti GPU. The primary computational complexity of the model lies in the spatial deformation from the template surface to the target surface, which takes about 1 min for one case. A whole process of morphological modeling and measurement for one case takes about 2 min.

We test the proposed method on 3 T T1 MRI of a longitudinal cohort including pMCI and cognitive normal CN subjects. The objectives of the experiment are threefold: (1) to assess the accuracy of the reconstructed hippocampi from 3 T MRI scans, as this directly impacts the accuracy of measurements derived from our model; (2) to investigate if the method performs differently on diseased hippocampi, such as those exhibiting atrophy due to pathological changes; (3) to evaluate the performance of the method on longitudinal data, as the proposed method incorporates specific considerations for analyzing data collected over multiple time points.

In Figure 4b, we present the ARMM of a representative 3 T hippocampus. The left panel of the figure displays a colormap representing the local surface distance between the reshaped hippocampal surface obtained from the ARMM and the ground truth. We observed that the maximum surface distance error locates in the medial part of the hippocampal body, with a maximum error of 0.33 mm. The right panel of Figure 4b shows a longitudinal axis on the IMS, which well characterizing curvature of the hippocampal head. The transversal axes remained nearly orthogonal to the longitudinal axes. Population statistics of the distance errors are listed in Table 4. The ARMM outperformed the ds‐rep on the mean and maximum of the measurement, and our method reaches high accuracy of image resolution‐level (1.2 mm) in modeling 3 T hippocampus. In all groups, the error of ARMM reconstruction surface is nearly one order of magnitude smaller than that of ds‐rep. The average surface error of ARMM is within 0.5mm, and the maximum surface error is 1.1mm. In contrast, the error of ds‐rep is within 5mm, and the maximum error is 5.9mm. This means that there is a maximum error of about 1mm when using ARMM to measure the thickness of the hippocampus, while the error of ds‐rep may exceed 5mm. Meanwhile, the reconstructed surface by ARMM also has lower standard error of surface distance error than ds‐rep. Furthermore, there has no significant difference (F = 1.06, p = 0.36) in the surface distance error between the pMCI and CN groups. Also, there is no significant difference of surface distance error between the three time points (pMCI: F = 0.76, p = 0.15; CN: F = 0.90, p = 0.33).

3.4. Morphometrics on longitudinal shape variations

We applied the ARMM to the LHA. The features characterizing the shape variations of the hippocampus during the progression of AD are presented in Figure 5. Local surface and thickness variations at four time points (the 6th, 11th, 16th, and 21st time points) compared to the baseline (the 1st time point) hippocampus are displayed in Figure 5a,b, which show more severe atrophy on the inferior than the superior during the disease progression. The thickness variations are consistent with the surface distance variations while clearly showing which lamellae affected by atrophy. The atrophy initially occurs on the inferior lateral of the body and the tail tip, while focal atrophy is located in the medial head on the same lamella and symmetric superior and inferior. The thickness decreases are diffuse and focally distributed along the long axis of the hippocampus, gradually spreading from the middle portion of the head to the posterior during AD progression. The primary atrophy remains to be on the same lamellae symmetric superior and inferior, with the inferior hippocampus having more severe atrophy.

FIGURE 5.

Morphological features calculated from the ARMM and measurement of local shape variations on a time series of left hippocampi. (a) Local surface variations on the superior and inferior parts of the hippocampus at four selected time points. Surface contraction indicated focal atrophy is colored in red. (b) Local thickness variations on the superior and inferior parts of the hippocampus at four selected time points, where thickness decrease is colored in red. (c) Typical local surface curvature variations along the longitudinal axis. Curvature decreases/straightening (red); curvature increases/bending (blue). (d) Hippocampal width variation along the long axis (from posterior to anterior). Typical atrophy locations, where width decrease compared to the baseline, are denoted by red arrows. (e) Hippocampal length variations along transverse axes during AD progression. Note that the color red in all color bars denotes decreases of the measurements compared to the baseline, while blue denotes the increase of the measurements. AD, Alzheimer's disease; LA, long axis; NC, nondementia control; tp, time point.

In the left panel of Figure 5c, the typical locations on the hippocampus that suffer relatively large curvature variations during disease progression are shown. The red points denote where the mean curvature decreases, and blue points denote where the mean curvature increases. These points are distributed near a specific long axis, the black curve shown on the hippocampal surface. The right panel of Figure 5c shows curvature variations of these points along the longitudinal axis on the 20 observed hippocampi from NC to AD compared to the baseline hippocampus. At the locations where the surface curvature is positive (convex), such as the middle superior of the body and the top of the head, curvature tends to decrease over time. Conversely, at locations where the surface curvature of the surface is negative (concave), such as the superior bending of the head and the lateral tail, curvature tends to increase. The results reflect local atrophy at these locations of the hippocampus.

Figure 5d shows the width variations along the entire long axis of the hippocampus during disease progression. The left panel of Figure 4d explains how we measure the widths of the hippocampus along the longitudinal curvature of the hippocampus, and the red arrows point to locations where large width decrease occurs. The right panel of Figure 5d shows width variations along the long axis of the entire hippocampus across the NC to AD progression. Width decreases occur mainly at the portion near the top of the head and the end of tail, while the width near the first bending of the head increases.

Figure 5e illustrates the entire hippocampal length variations. The left panel explains how we measure these lengths, and the red curves are lengths that suffer relatively large variations over disease progression. The diagram on the right shows the lengths variations during NC to AD progression. We find that the lateral portion of the hippocampus has the greatest length decreases.

3.5. Neurodegenerative disease discrimination using morphological features from ARMM

To evaluate the potential of the extracted morphological features by ARMM in detecting neurodegenerative diseases, we applied the method to a longitudinal cohort of individuals in the AD spectrum. The pMCI subject underwent 3 T T1 MRI scans at yearly intervals over a period of 3 years, and were diagnosed as AD at their third visits. For clarity, we refer to these three time points as t0, t1, and t2 in this article.

We conduct independent two‐sample t‐tests to compare the extracted morphological features (superior thickness, inferior thickness, ventral width, dorsal width, length) between the pMCI and CN groups at each time point. The resulting p‐values are then adjusted using the false discovery rate (FDR) correction. We identify features that exhibited significant atrophy (p < 0.05) consistently across all three time points, which we considered as significant spatial features distinguishing pMCI from the control group in 2 years prior to AD conversion (Figure 6a).

FIGURE 6.

Significant spatiotemporal atrophy patterns measured by ARMM in AD progression and classification performance based on morphological measurements.

Additionally, we calculate average atrophy rates of each morphological features over the two‐year period using linear regression as temporal atrophy features. We perform independent two‐sample t‐tests to compare these features between groups, followed by FDR correction. The statistical results are shown in the second column of Figure 6a, with red indicating the Cohen's d effect size, which measures the magnitude of significant differences. We observe that the temporal features exhibited greater significance of local atrophy in the superior than the inferior portion. The most severe atrophy is observed in the portion curves medially from the body to head. Furthermore, the local atrophy rate in the right hippocampus is higher than that in the left hippocampus, which is consistent with literatures (Barnes et al., 2009; Gao et al., 2023; Jahanshahi et al., 2023).

In the right panel of Figure 6a, we present the ROC curves for classifying pMCI and CN using different combinations of features: local atrophy + volume, volume, and local atrophy features. Details of the results are listed in Table 5. The volume features include both spatial and temporal characteristics, that is, absolute volume and change rate during the 2 years. We find that the local atrophy features obtained by ARMM outperformed the volume features alone in terms of accuracy, sensitivity, and specificity for pMCI identification in 2 years prior to conversion.

TABLE 5.

Results of inter‐group classification using local atrophy from ARMM and hippocampal volume.

		Local atrophy + volume	Volume	Local atrophy
pMCI versus CN (2 years prior conversion)	Accuracy	0.882 ± 0.086	0.776 ± 0.060	0.781 ± 0.02
	Sensitivity	0.879 ± 0.141	0.760 ± 0.148	0.806 ± 0.077
	Specificity	0.887 ± 0.087	0.794 ± 0.085	0.758 ± 0.077
	AUROC	0.944 ± 0.049	0.853 ± 0.055	0.886 ± 0.034
pMCI versus sMCI (2 years prior conversion)	Accuracy	0.767 ± 0.058	0.723 ± 0.038	0.701 ± 0.096
	Sensitivity	0.756 ± 0.095	0.668 ± 0.111	0.610 ± 0.089
	Specificity	0.774 ± 0.069	0.764 ± 0.067	0.773 ± 0.127
	AUROC	0.828 ± 0.058	0.747 ± 0.037	0.800 ± 0.085
pMCI versus sMCI (1 year prior conversion)	Accuracy	0.776 ± 0.024	0.687 ± 0.116	0.741 ± 0.039
	Sensitivity	0.739 ± 0.107	0.667 ± 0.139	0.657 ± 0.093
	Specificity	0.816 ± 0.122	0.706 ± 0.116	0.825 ± 0.091
	AUROC	0.800 ± 0.024	0.777 ± 0.099	0.805 ± 0.013

We further compared the intergroup differences between the pMCI and sMCI groups. The results are depicted in the left columns of Figure 6b,c and Table 5. In the 2 years prior to conversion, few significant differences are observed between the two groups. However, in the 1 year prior to conversion, we find more pronounced significant atrophic regions measured by spatial features. The ROC curves of classification results for the two groups using different combinations of features are presented in the right column of Figure 6b,c. We find that the incorporation of ARMM features improved the differentiation of pMCI from sMCI in both the 2 years and 1 year prior to conversion.

4. DISCUSSION

We propose an ARMM of the hippocampus based on MR images. The method maps the anatomical lamellar organization onto the hippocampal shape, which improve quantifications of detailed morphological changes of the curving hippocampus. The ARMM involves two key techniques: establishing coordinate system on the template hippocampus and registering it to arbitrary hippocampi. Specifically, we first reparameterize the medial surface and the boundary surface of a hippocampal atlas from 7 T ex vivo MRI with longitudinal and transverse lamellar distribution through conformal reparameterization. This allows us to establish an “axis‐referenced coordinate system” where the medial surface with attached vectors pointing to the boundary. Second, the coordinates of the template hippocampus are diffeomorphically transformed to the target space with vectors adhering to the constraint of medial‐axis geometry. We perform morphological measurement and evaluate its accuracy by evaluating shape representations on 7 T and 3 T MRI hippocampi. Additionally, we find local atrophy measurements derived from ARMM show higher discriminatory power in distinguishing prodromal AD from mild cognitive impairment (MCI) compared to volume‐based measurements. In addition, there are three aspects of the ARMM need to be highlighted: (1) the reasonability of the axis‐referenced coordinate system derived by the ARMM; (2) the point‐wise correspondence by ARMM for precise measurement of local atrophy; and (3) its clinical value in providing local hippocampal atrophy features for disease detection. In the following sections, we discuss these aspects and the limitations of our method in detail.

4.1. The ARMM provides an anatomical‐motivated consistent coordinate system of the hippocampal morphology

The tripartite model considers the anterior–posterior extent, forming a crescent shape, as longitudinal curvature of the hippocampus, which is commonly used in image studies. However, recent studies suggest that the entire length of the hippocampus should be considered in morphological analysis. Adler et al. (2018) take the medial curvature as the longitudinal axis, while Gross et al. (2020) take the lateral curvature as the longitudinal axis. DeKraker et al. (2018) and DeKraker et al. (2022) propose a method to trace the entire hippocampal length through longitudinal potential field on SRLM by Laplace equation. They demonstrate that the SRLM shape can well capture the general hippocampal shape, including the complex folding patterns on the head. However, the article also finds that the SRLM is often not visible in the most medial, vertical component of the uncus, which must be manually defined. Large cross‐individual differences in the hippocampus should also be considered in the shape model. The different number and scale of digitations on the head and tail cause the lateral/ventral curvature to fluctuate and deviate from the natural curvature of the entire hippocampus. This is also the case for the SRLM. The variable folding patterns will lead to diverse long axes among individuals, which is a disadvantage for population analysis of hippocampal morphology. Therefore, it is not practical to trace the long axis by tracing the SRLM.

Despite the many uncertainties, we can confirm that the long axis of the hippocampus has its natural anterior termination in the more medial and superior component of the uncus, and all subfields of the hippocampus contiguously follow this curvature through the hippocampal head (Ding & Van Hoesen, 2015). Generally, the curvature of the hippocampi on the longitudinal dimension remains a consistent trajectory. For example, the left hippocampus curves like a crescent from posterior to anterior, and curves medially, posteriorly, then superiorly. This trajectory moderates the folding patterns caused by variable digitations, which is more feasible for statistical analysis. Therefore, in this study, we choose the centermost longitudinal line follows the intersection between the CA‐DG border and IMS as the longitudinal axis of the atlas hippocampus, which is currently the closest approximation to its anatomically consistent longitudinal trajectory. We have also demonstrated that the proposed deformation method, by transforming this template longitudinal axis to target arbitrary hippocampus, has achieved excellent results in accurately describing the trajectory of the longitudinal curvature of the target hippocampus.

Some evidence supporting the reasonability of this long axis includes, first, Gross et al. (2020) demonstrate the internal subfield consistency inside the hippocampal head. We compare the subfields on slices along the long axis of our template hippocampus with the subfield distribution on similarly located slices of a typical hippocampus in the literature. In Figure 7, all slices from head to tail show the “interlocking C” or the “body‐like” profile discovered in Adler et al. (2018) and Gross et al. (2020). This result shows consensus inner structures along the ARMM‐long‐axis with the manual tracing method. Second, the mesoscale longitudinal cell connections support the discovered longitudinal axis location. Specifically, the long axis generated by the ARMM lies on the border between CA3 and DG, and is often within the CA3, except for the portions near the head and tail endpoints (Figure 7). The DG and CA3 serve as pivotal information processing hubs within the laminar functional units and are likely to be the main drivers of longitudinal information transmission in the hippocampus. For example, the “CA3‐centric” viewpoint of hippocampal information processing believes that CA3 pyramidal cells project diversely to all hippocampal principal cells (Scharfman, 2007), and many studies have demonstrated the existence of excitatory projecting associational pathways of dentate mossy cells and CA3 pyramidal cells (Gloveli et al., 2005; Pak et al., 2022; Ropireddy et al., 2011).

FIGURE 7.

Representative slices that cut perpendicularly to the ARMM‐derived long axis. Left: traditional subdivision method (red dotted lines) and slicing along directions perpendicular to the long axis (blue lines). Right: slices corresponding to the cutting orientations shown in the left panel.

Based on the longitudinal axis from ARMM, we are able to construct lamellar architectures in the longitudinal dimension of the hippocampus. Although Strange et al. (2014) suggest that the exact number of domains along the long axis and whether these domains are hierarchically organized in the human hippocampus is currently unknown, the longitudinal lamella of the hippocampus is expected to be very thin from mesoscopic perspective. Studies have discovered that the longitudinal mossy fibers in the DG‐DG connection often stretch up to about 2 mm (Amaral & Witter, 1989; Pak et al., 2022), while many other longitudinal connections are shorter. For example, the primary axonal fiber in CA3 producing longitudinal axons towards the subiculum bifurcates often extends up to ~400 μm (Pak et al., 2022). In the current study, we generate 23 lamellar domains with 2 mm intervals against the long axis in the results section. Further subdivision of the lamellar domains is available through spoke interpolation. The specific number of lamellar domains should be determined based on the research question and objective.

4.2. The ARMM provides accurate morphological correspondence for measurement of detailed local hippocampal atrophy

The determination of point‐wise correspondence across individuals is a key subject in morphological analysis. Ambiguous correspondences at locations with large individual variabilities may lead to completely different results in statistical analysis. According to Ding and Van Hoesen (2015), the hippocampal head has different numbers of digitations across subjects, posing a major challenge in establishing correspondences. The variability in hippocampal digitations may not be well suited for registration‐based approaches, as it is inconclusive how to align the anterior portions among populations with different numbers of digitations (DeKraker et al., 2021). Furthermore, the correspondence established by current geometric methods is not always directly related to or supported by physiopathological evidence.

Adler discovers that the hippocampal tail (the posterior 1/3 of the hippocampus), while slicing it at approximately 6/9, 7/9, 8/9 of the total hippocampal length along the curvature of the long axis, very few samples have different subfields distribution (Adler et al., 2018). This finding indicates a stable correspondence between individuals along the curved long axis. Due to difficulties in sample acquisition and manual annotation, evidence for intra‐individual correspondence based on the long axis is rare. At most scenarios, shape changes on the hippocampus of the same individual have little influence on its overall shape, so the internal skeleton of the baseline observation remains stable over time. In Section 3.2, we measured local shape variations on time series of hippocampi and find that the focal distribution measured by surface and volumetric features are highly consistent. This finding indirectly verifies the intra‐individual correspondence by the long axis.

There remain limitations for the morphological correspondence by the long axis. The hippocampus may not undergo isotropic atrophy under the effect of disease. Therefore, the length and curvature of the long axis may change, especially in the head and tail of the hippocampus, leading to deviations in the correspondence. As a result, even if the effect is not so extreme, the correspondence established based on proportions is no longer valid. In Poppenk et al. (2020), the author describes a similar mis‐correspondence example that due to the contraction of the uncus, a larger portion of anterior is redefined as posterior of hippocampus, leading to incorrect conclusion that the posterior segments grow. In this article, we solve the problem by utilizing the axis‐referenced coordinate system of a baseline hippocampus as a reference for the atrophied hippocampus of the same subject. In the atrophied hippocampus, the length of vectors representing local thickness is scaled down and their directions are adjusted to be perpendicular to the boundary surface, in order to meet the requirements of thickness measurement. This method offers improved accuracy in measuring atrophy by taking into account the morphology of the baseline hippocampus.

4.3. Clinical application of ARMM in disease detection: From anatomical atlas to 3 T in vivo MRI measures

The current most established structural imaging marker for early diagnosis of AD is the hippocampal volume (Dubois et al., 2014; Frisoni et al., 2010; Hill et al., 2014). However, the overall volume of the hippocampus has limited specificity in distinguishing the AD converters and the non‐converters (Lombardi et al., 2020; Ruchinskas et al., 2022; van Oostveen & de Lange, 2021). To address this issue, many studies have expected to develop localized features in the hippocampus into more specific and sensitive image markers than volume. Histological researches reveal that the neurofibrillary tangles associated with AD pathology initially target specific subfield of the hippocampus. The atrophy pattern of hippocampal subfields has been extensively studied, with CA1 and subiculum (SUB) being particularly vulnerable to AD pathology. These histological findings provide evidence supporting the investigation of localized hippocampal atrophy in the early stage of the disease using imaging techniques. However, achieving consistent conclusions across imaging‐based studies is challenging due to the utilization of different segmentation protocols, which limits the generalizability of the findings. Efforts have been made to standardize subfield segmentation protocols. For example, the Hippocampal Subfield Group (HSG; http://hippocampalsubfields.com/) launched in 2013 (Wisse et al., 2017; Yushkevich et al., 2015) is currently working towards establishing a consensus on the criteria for subfield delineation. Moreover, the use of 3 T MRI for subfield segmentation introduces uncertainties due to low image resolution. The reduced visibility of fine anatomical details and the difficulty in identifying certain geometric landmarks can affect the accuracy of subfield delineation. Different segmentations can lead to variations in hippocampal subfield shape measurements, potentially influencing the reliability and interpretation of statistical findings. To address the problem, this article presents a more effective method to correspond different hippocampi via a unified anatomical‐motivated coordinate system, potentially providing stable statistical analysis on local atrophy compared to the subfield‐based method. We have demonstrated that the method could provide useful structural features to discriminate AD based on clinical images, which shed lights on discovering new measures for pre‐diagnosis of neurodegenerative diseases.

In our experiment, measures related to the early progression of AD can be divided into two categories: spatial atrophy features, which refer to the reduced cortical thickness in patients compared to healthy individuals, and temporal features, which indicate the rate of localized atrophy in patients compared to normal individuals. The results reveal that, prior to the conversion to AD, patients exhibit significantly greater differences in the temporal atrophy compared to spatial atrophy (larger effect size) when compared to healthy individuals. Additionally, temporal and spatial features exhibit distinct patterns (Figure 6). Specifically, the regions where patients exhibited faster rates of atrophy, particularly in the right hippocampus, are located in the transitional lamellae between the body and head of the hippocampus. The locations where patients have less cortical thickness, occurring along the longitudinal axis, are predominantly in the intermediate region transitioning from the tail to the head, with a greater reduction in thickness observed in the superior compared to the inferior regions. Analysis of the spatiotemporal atrophy differences between patients with progressive mild cognitive impairment (pMCI) and stable mild cognitive impairment (sMCI) reveals that localized atrophy had already occurred 2 years prior to conversion, primarily in the inferior medial head and body transitioning regions of both the left and right hippocampi, with significantly greater atrophy rates observed in pMCI. Furthermore, 1 year prior to conversion, there is an emergence of numerous instances of spatial localized atrophy compared to sMCI, primarily occurring in the head of the left hippocampus and the middle regions along the longitudinal axis of the right hippocampus.

4.4. Limitations and future works

There are some limitations to the current model. First, additional validation is required to determine whether the lamellae of the hippocampus represented by ARMM exhibit the same topographical structure as the functional units they represent. This validation can be achieved through further comparative analysis involving morphological, histological, and electrophysiological experiments. While, in this study, we focused solely on utilizing the longitudinal axis and lamellar structure of the hippocampus to better characterize its curving morphology. Second, this model only accommodates a single segmentation protocol, while the diverse protocols for hippocampus segmentation may lead to different longitudinal axis and lamellar distributions. We have considered the generality of the long axis as much as possible by restricting it to the medial surface and moderating the lateral and medial curvatures. Future work will further develop and validate the method to accommodate more protocols. Third, the proposed method does not support the representation of subfield morphology within the hippocampus. It would be beneficial to include subfield morphometry in our model, such as subfield shape features on lamellae. Future directions for this work will integrate subfield morphologies for quantitative analysis of subfield variations in aging and neurodegenerative diseases.

5. CONCLUSIONS

This study proposes an MRI‐based computational morphometric model for hippocampus, enabling alignment of different individuals and detection of detailed local atrophy. This method, called the ARMM, corresponding and measuring local morphology across individuals through diffeomorphic transformation of an axis‐referenced coordinate system that follows the consistent lamellar organization of the hippocampus, which precisely captures its complex curving patterns. Compared with state‐of‐the‐art morphometric approaches, the ARMM shows supreme ability in capturing the boundary surface and medial curvature of the hippocampal formation with high accuracy. With such merit, ARMM shows powerful potential in AD early detection with hippocampal subregion atrophy. Promising application of the ARMM includes identification of new structural image markers for AD especially at early stage.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

Supporting information

Data S1: Supporting Information.

Gao, N. , Ye, C. , Chen, H. , Hao, X. , & Ma, T. (2024). MRI‐based axis‐referenced morphometric model corresponding to lamellar organization for assessing hippocampal atrophy in dementia. Human Brain Mapping, 45(10), e26715. 10.1002/hbm.26715

DATA AVAILABILITY STATEMENT

The data supporting the findings of this study is based on open‐source results from (Adler et al., 2018). The data repository is located at https://www.nitrc.org/projects/pennhippoatlas/. All code for this project, including the ARMM template, is available at https://github.com/calliegao/ARMM. The code for the pipeline will be made publicly available after acceptance.