Classification of Alzheimer's disease based on hippocampal multivariate morphometry statistics

Abstract Background Alzheimer's disease (AD) is a neurodegenerative disease characterized by progressive cognitive decline, and mild cognitive impairment (MCI) is associated with a high risk of developing AD. Hippocampal morphometry analysis is believed to be the most robust magnetic resonance imaging (MRI) markers for AD and MCI. Multivariate morphometry statistics (MMS), a quantitative method of surface deformations analysis, is confirmed to have strong statistical power for evaluating hippocampus. Aims We aimed to test whether surface deformation features in hippocampus can be employed for early classification of AD, MCI, and healthy controls (HC). Methods We first explored the differences in hippocampus surface deformation among these three groups by using MMS analysis. Additionally, the hippocampal MMS features of selective patches and support vector machine (SVM) were used for the binary classification and triple classification. Results By the results, we identified significant hippocampal deformation among the three groups, especially in hippocampal CA1. In addition, the binary classification of AD/HC, MCI/HC, AD/MCI showed good performances, and area under curve (AUC) of triple‐classification model achieved 0.85. Finally, positive correlations were found between the hippocampus MMS features and cognitive performances. Conclusions The study revealed significant hippocampal deformation among AD, MCI, and HC. Additionally, we confirmed that hippocampal MMS can be used as a sensitive imaging biomarker for the early diagnosis of AD at the individual level.


| INTRODUC TI ON
Alzheimer's disease (AD) is the most prevalent cause of dementia, posing a significant threat to human health. Mild cognitive impairment (MCI) is considered as an intermediary stage between AD and normal cognitive function. Studies suggest that clinical intervention at this stage can be beneficial in delaying the onset of AD. 1 Thus, it is of great theoretical significance and potential clinical application value to explore the pathogenesis of AD using new technologies and establish reliable imaging markers for early individual diagnosis of AD. 2 Previous neuroimaging studies have highlighted the crucial role of the hippocampus in memory processes. [3][4][5] Using various magnetic resonance imaging (MRI) methods, many studies have revealed AD-associated hippocampal abnormalities, including volume atrophy, 6,7 hypometabolism, 8 decreased spontaneous activation, 9 and decreased functional connectivity. [10][11][12][13][14][15] Structural imaging can provide accurate anatomic structures up to 1 mm with relatively stable and repeatable results. In this study, we focused on structural analysis and attempted to capture subtle structural changes in the hippocampus during the early stages of AD.
Although numerous studies have focused on analyzing hippocampal volumes, [16][17][18][19] recent researches have suggested that surface-based subregional structure analysis could offer advantages over volume measures. [20][21][22][23][24][25][26] In the previous studies from our team, 11,27 we proposed a novel method to analyze the hippocampal surface deformations, which was multivariate morphometry statistics (MMS), including multivariate tensor-based morphometry (mTBM) representing morphometry within surfaces and radial distance (RD) representing distances from the medial core to each surface point. By employing a group MMS analysis strategy, the differences in hippocampal morphometry deformations demonstrated stronger statistical power than volume measures. 11,[27][28][29][30] However, it has become increasingly important to derive a personalized accurate classification model for AD based on sensitive image features and advanced algorithms, rather than group analysis. 31 In this study, we sought to search for a new biomarker to differentiate AD, MCI, and healthy controls using the hippocampal MMS analysis and support vector machine (SVM) method on individual levels.
In this work, based on MMS, we first studied hippocampal surface deformation in the AD, MCI, and HC groups, and identified the key subregions that showed significant differences among the three groups. Second, the SVM algorithm was used to construct a binary and triple-classification model based on the selected MMS features.
Finally, we examined correlations between regional hippocampal deformation and neuropsychological test scores to validate the clinical significance of the biomarker.

| MRI acquisition
Magnetic resonance imaging examination was performed on a SIEMENS verio 3-Tesla scanner (Siemens, Erlangen, Germany).
The 3D T1-weighted magnetization prepared rapid gradient echo (MPRAGE) sagittal images were performed with the following pa-

| Segmentation, reconstruction, and registration
We used FIRST, an integrated tool developed as a part of the FSL library, to automatically segment all the T1-weighted brain volume MRI scans. 33 These segmented images were spatially normalized into the MNI template space with a 9-parameter (3 translations, 3 rotations, and 3 scales) linear transformation by using Minctracc algorithm 34 for the correction of head tilt and alignment. To equalize image intensities across subjects, registered scans were also histogram-matched. After segmentation for each individual hippocampus, the results were critically examined by two independent anatomists to verify their quality.
The segmentation results of all hippocampi were then processed by surface conformal slit mapping. 35 This approach allows us to efficiently analyze surface data over simpler parameter domains, which avoids the consideration of complex brain surfaces. 36 Finally, we aligned surfaces in the parameter domain with a fluid registration technique to maintain a smooth, one-to-one topology. 37,38 The one-to-one correspondence achieved between vertices allows us to accurately analyze the local information on the hippocampal surface.

| Hippocampus surface multivariate morphometry statistics
To detect group differences in the subdivisions of hippocampus, some of the previously proposed features were used. The radial distance (RD) describes the morphological changes along the surface normal direction. 39 Surface tensor-based morphometry (TBM) [40][41][42] examines the spatial derivatives (detJ, where J is the Jacobian matrix of the deformation from the registration) of the deformation maps that register each hippocampal surface to the common template.

F I G U R E 1
Whole processing pipeline is applied in this paper. First, we performed hippocampal multivariate morphometry statistics (MMS) feature extraction (A). Second, we made group comparison analysis of hippocampal MMS features and select patches based on effect Size (B). Third, based on the selected patches, we downscaled the MMS features and used it for subsequent classification (C). Finally, we made the Pearson correlation analysis between the MMSE scores and the MMS (RD and mTBM) features of hippocampus (D).
Suppose that φ: S 1 → S 2 is a map from surface S 1 to surface S 2 . The derivative map of is the linear map between the tangent spaces d : TM(p) → TM( (p)), induced by the map φ, which also defines the Jacobian matrix of φ. In the grid surface, the derivative map d is approximated by the linear map from one face v 1 , v 2 , v 3 to another w 1 , w 2 , w 3 . First, the surfaces v 1 , v 2 , v 3 and w 1 , w 2 , w 3 are isometrically embedded onto the Klein disk, 43

| Hippocampus surface MMS smoothing
The heat kernel smoothing algorithm was introduced to smooth the hippocampal surface features. 43,46 Referring to our previous work, 43 key parameters of the heat kernel smoothing algorithm were set as: smoothing parameter σ = 1 and number of iterations m = 10.

| Group-wise hippocampus surface deformation analysis
The Hotelling's T 2 test was performed to evaluate the pair-wise morphometric differences of the smoothed hippocampus surfaces in the HC-AD, HC-MCI, and MCI-AD groups. 47,48 Statistical results were corrected for multiple comparisons by using the permutation test.
We first calculated the group-level hippocampal surface differences for each vertex as the ground true group using the Mahalanobis distance, 49  We calculated the average effect of each patch using the following method: we first calculated the effect sizes of each surface vertex for HC-AD, HC-MCI, and MCI-AD groups using the Mahalanobis distance by (2), based on this, we calculated the average effect size of the three groups at each vertex and then calculated the average effect size for each patch (the average effect sizes of all vertices on each patch). (1) We tried patches in turn, with 2 as the iteration interval, and finally found that the best performance was achieved with a patch size. Figure 2A visualizes the patches selected on the bilateral hippocampus surface, and we reshaped the MMS features contained in each patch into an m-dimensional vector x i , and all the vectors x i constituted a matrix X = x 1 , x 2 , … , x n ∈ R m×n , x i ∈ R m , i = 1, 2, … n by column, where n is the total number of patches.

| Patch-based sparse coding and dictionary learning
To further improve calculation efficiency, we used online dictionary learning (ODL) to learn overcomplete dictionary by modeling the matrix X as a sparse linear combination of column vectors (atoms) in the learned dictionary D. 52 According to ODL, the sparse coding optimization problem for each column vector x i in X can be expressed in the form of (3): where n is the number of vectors of X, D is the learned overcomplete dictionary, each column represents a basis vector (atom) and tis the size of the dictionary. i is usually called sparse encoding. ψ is the sparse-induced regularizer and  is the constraint set of the dictionary D. ψ and  can be used in various combinations to solve different matrix decomposition problems. To prevent arbitrary scaling of the sparse encoding, the atoms d 1 of D are constrained to be  ≜ D ∈ R m×t s.t.
, and the regularizer ψ we use L1-regularization, because it ensures that the learned features are sparse, i.e., i has only a few nonzero values.
Before applying the sparse coding, we constrained the input X by columns as L2 norm, and then we can rewrite (3) as a matrix decomposition problem as follows:

| Feature reduction
The hippocampus feature of each subject after sparse coding is a high dimension and sparse vector, and based on the highly sparse nature of the information, we employed independent-samples T-test to select features in S that are more significant for classification.
The T-test-based feature ranking and feature selection method is an effective method for high-dimensional feature selection, 53 which can test whether the mean of each feature of two independent samples is significantly different from its distribution (p < 0.05).
We first divided all subjects into training and test sets and split all samples in test sets into three groups according to classes: HC-MCI, HC-AD, and MCI-AD. The test statistic p value was then calculated for each feature in each of the three groups by using the independent samples T-test, and the p value of all features was ranked in descending order. p value was chosen as an empirical value, due to the small number of subjects and high feature dimension, we only selected features with p value <0.01, so as to remove features with little difference (small difference between the two classes). We selected three groups of features that were significant for dichotomy in HC-MCI, HC-AD, and MCI-AD. After that, we merged the three groups of features selected for binary classification and removed the duplicate features and use it as the features of the HC-MCI-AD triple classification group. We applied the feature indexes selected

| Training classifier and parameter optimization
After a series of feature reduction processes, we finally obtained the low dimensional surface-based hippocampal features for classification.
In this paper, we used SVM with a nonlinear kernel function for classification and built a triple SVM classifier using One-Vs-One multiclass strategy. One-Vs-One approach splits the dataset into one data- The parameter optimization of SVM classifier is also an important aspect. The main hyperparameter optimization methods commonly used are grid search, random search, and Bayesian optimization. 54 Bayesian optimization was applied because of its more efficient than the other two search methods. 55 Ten-fold cross-validation scheme was applied to evaluate the classification performance. The scheme was repeated a total of 10 times.
Finally, we measured the performances of kinds of classifiers. And the classification performance of hippocampal MMS features was compared with volume and age features. For binary classification, we used accuracy, sensitivity, specificity, and area under the curve (AUC) in receiver operating characteristic (ROC). In total, we tested three different binary classifications, HC-AD, HC-MCI, and MCI-AD. For triple classification, we used standard performance metrics, precision, recall, F1-score, accuracy, and confusion matrix. All the ML analyses were done using scikit-learn, a python library for machine learning. 56

| Correlation analysis of hippocampus surface features and MMSE scores
The  (5): Each subject has one MMSE score, which can be expressed as a vector of n, 1 , n is the number of subjects, as in (6): We used vertex-based Pearson correlation analysis, which is calculated by successively extracting each row of matrix (5)

| Study samples
Demographics and hippocampus volume information for the AD, MCI, and HC groups were summarized in Table 1

| Hippocampus subregions definition
According to previous study related to hippocampus subregions, 21 the template of the hippocampus was subdivided into three different subregions, mainly including CA1, CA2-3, and Subiculum ( Figure 2B).

| Hippocampus morphology differences
Significant morphology differences were found in the whole bilateral hippocampus, including CA1, CA2/3, and Subiculum in the HC-MCI and HC-AD groups. For the MCI-AD group, the distribution of significant differences regions in the bilateral hippocampus was slightly different, with significant differences in the left hippocampus mainly in the CA1 region and the local area of the subiculum, and significant differences in the right hippocampus mainly in the CA1 region ( Figure 3A).

| Effect size analysis
From Figure 3B, there were significant differences of effect size of MMS between HC-AD, HC-MCI, and MCI-AD groups. The larger effect sizes indicated higher differentiation between the two groups.  Figure 4A and Table 2). Figure 4B and Table 2 showed the ROC results using hippocampal volume and age features (AUC of the classification of HC-AD, HC-MCI, and MCI-AD was 0.76, 0.66, and 0.58, respectively).

| Triple classification
In Figure 5 and Table 3, the classification performance of each group was evaluated, it can be clearly seen that the classification results using hippocampal MMS features are better than the classification results using the hippocampal volume and age features.

| Correlation analysis
Positive correlations were revealed between hippocampus RD/ TBM features and MMSE scores. The presence of regions of positive correlation with MMSE scores mainly included the CA1 region, then the CA2-CA3 region and the subiculum at a moderate level (0.4 < r < 0.6), the details see Figure 6.

| Major findings
The present study showed significant deformation of hippocampus subregions during the transformation from HC to MCI/AD using MMS, which was closely associated with cognitive performance.
Additionally, when the hippocampal MMS features were used to construct the binary classification and triple classification model, relatively good classification effect was achieved.

| Hippocampal morphometric differences of AD vs. MCI vs. HC
Previous MRI studies reported significant structural changes in several brain regions in AD and MCI patients, including the wholebrain, 58  formation was the most sensitive region for the AD pathology, which was vulnerable to amyloid protein deposition, hypoxia, ischemia, and so on. 63,64 The hippocampus, composed of the CA1, CA2/3, and subiculum, was important for memory storage and retrieval. In particular, the CA1 subregion constituted the primary output of the hippocampus, which was thought to be essential for most hippocampusdependent memories. 65,66 In the present study, we found that the deformation of CA1 region was more significant during the transformation of MCI to AD, which was consistent with the previous studies. 29 In addition, interestingly, we found the deformation of the left hippocampus was more extensive than that of the right hippocampus, which was consistent with the previous studies. 67

| Binary and triple classification model construction at the individual level based on the hippocampal MMS features
Most previous studies focused on the hippocampal structural differences at the group level, especially between two groups. 11,29,70 This is the first study where surface-based hippocampal morphology measure was used to differentiate among three groups, including AD, MCI, and HC, and to classify individual subjects into diagnostic groups.
In this study, all the binary classification models based on hippocampal MMS features showed good performances, particularly presenting an AUC of 0.94 in the classification of HC-AD group. In one of our previous studies, based on the whole brain gray matter voxel as feature, the accuracy of the binary classification model on AD/HC was 0.90. 71 The current study was superior to the previous study, indicating that hippocampal MMS features could be used as better imaging indicators for AD, MCI, and HC pairwise classification. In this study, the accuracy of the triple classification model based on hippocampus deformation reached 0.85. From Table 3, this classifier of HC achieved the best precision followed by AD, and then MCI. It could be explained as follows: due to the transitional stage of MCI between AD and HC, MCI was easier to be confused with AD or HC, which might influence the accuracy of the triple classification.

| Correlation analysis of RD/TBM features of hippocampus surface vertex and MMSE scales
The correlation analysis showed that MMSE scores and hippocampus morphology feature (RD/TBM) values were positively correlated, i.e., the higher the MMSE, the more normal the hippocampus morphology, suggesting that the deformation of hippocampus could be used as an imaging marker for tracking disease progression. In addition, the area of positive correlation was mainly distributed in the CA1 region, followed by the CA2/3 region and the subiculum, which was consistent with the above result of hippocampus deformation subregions, further verifying the reliability and accuracy of using deformation characteristics of hippocampal subregions as markers for tracking AD progression.

| LI M ITATI O N S
There are some limitations to our study. First of all, this is a crosssectional study. In the future, multi-center longitudinal large sample data need to be collected and performed to confirm the current results. Second, to explore whether the surface-based hippocampal morphometry measure could discriminate AD patients in different stages, future studies will add more samples of early stages of AD patients, such as ApoE 4 carriers and subjective cognitive decline.
Finally, in this study, we only focused on the surface-based hippocampus morphometry. Future work will need to be performed on other brain regions, such as the entorhinal cortex, amygdale, posterior cingulate cortex, and so on.

| CON CLUS IONS
In conclusion, the present study found that significant deformation of hippocampus subregions occurred during the transformation

CO N FLI C T O F I NTER E S T S TATEM ENT
The authors declare no conflicts of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The raw/processed data during the study are proprietary and confidential, it cannot be shared at this time as the data also forms part of an ongoing study.