Macro–Micro structural integration for characterizing severity-related structural alterations in mild cognitive impairment

Abstract

Mild cognitive impairment (MCI) is a clinically heterogeneous condition characterized by substantial variation in structural abnormalities and cognitive impairment. However, existing neuroimaging-based approaches are limited by insufficient modeling of coordinated gray–white matter alterations and vulnerability to site effects in multi-center data. Here, we propose a Macro–Micro Structural Integration (MMSI) framework for characterizing structural-deviation heterogeneity and identifying imaging-derived MCI subgroups. The framework integrates gray-matter morphological features derived from structural magnetic resonance imaging and white-matter microstructural features derived from diffusion MRI. A Dual-Condition Variational Autoencoder was developed to separate biological variation from site-related effects and learn a site-robust normative representation using cognitively normal participants. Tract-specific MMSI scores were subsequently derived to quantify each participant's structural deviation from the normative reference. In a multi-center clinical cohort (N = 860), Gaussian mixture modeling of the tract-wise MMSI profiles identified lower- and higher-deviation MCI subgroups that exhibited significant differences in global cognition, delayed memory, and word recognition. Comparisons with conventional imaging biomarkers, machine-learning classifiers, and statistical harmonization methods further supported the value of the proposed framework. Evaluation in the Alzheimer's Disease Neuroimaging Initiative cohort demonstrated a concordance accuracy of 0.769 between the imaging-derived groups and the clinically predefined early- and late-MCI categories, exceeding the gray matter–only and white matter–only models by 7.7 and 12.3 percentage points, respectively. Transcriptomic association analysis identified KRT77 and CACNA1B as significantly associated with tract-specific MMSI scores after false discovery rate correction. Functional enrichment of the PLS-derived MMSI-associated gene set implicated biological processes related to neural signal transduction, learning and memory, calcium signaling, and immune responses. Together, these findings indicate that the MMSI framework provides a site-robust and interpretable approach for characterizing cross-sectional structural-deviation heterogeneity in MCI and offers preliminary biological support for the identified imaging patterns.

Graphical abstract

Highlights

• •A normative model integrates gray- and white-matter structural features.
• •Site effects are reduced while disease-related information is preserved.
• •Imaging-derived scores reveal heterogeneity in mild cognitive impairment.
• •External validation supports generalizability across centers and cohorts.
• •Gene expression analysis provides biological support for imaging deviations.

1. Introduction

Mild cognitive impairment (MCI) represents a heterogeneous and transitional stage between normal aging and Alzheimer's disease (AD), affecting approximately 10–20% of older adults, with an annual progression rate of 10–15% to AD (Feldman and Jacova, 2005; Gauthier et al., 2006). Its high prevalence and risk of conversion underscore the clinical importance of accurate subgroup identification. Progressive stages of MCI can be divided into early MCI (EMCI) resembling normal control (NC) and late MCI (LMCI), which tends to AD (Risacher et al., 2017). While LMCI is associated with a substantially higher likelihood of progression to AD, EMCI remains amenable to interventions that may slow or halt cognitive decline. However, the accurate identification of MCI subgroups (Wang et al., 2009; Yu et al., 2014) remains challenging as current methods largely rely on clinicians' evaluations of cognitive assessments, which are often subjective and may be insensitive to subtle biological heterogeneity (Rossini et al., 2022).

In this context, neuroimaging provides a more objective and biologically grounded way to characterize disease-related brain alterations, offering the potential to improve subgroup stratification beyond behavioral or clinical observations alone. Among available imaging modalities, white matter (WM) integrity is particularly relevant to the progression of AD (Zhang et al., 2009; Harrison et al., 2020), because WM tracts support large-scale brain connectivity and are highly vulnerable to neurodegenerative processes. Diffusion MRI (dMRI), especially diffusion tensor imaging (DTI), has been widely used to probe WM microstructure through metrics such as fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), and axial diffusivity (AxD), which reflect tissue organization, water mobility, myelination, and axonal integrity (Pierpaoli et al., 1996; Le Bihan et al., 2001; Tournier et al., 2011). Beyond voxel-wise analyses, tract-based methods enable anatomically informed assessment of microstructural abnormalities along major fiber bundles, while radiomics can further complement WM characterization by extracting quantitative descriptors of intensity and texture from DTI-derived maps (Chen et al., 2020; Yeatman et al., 2012). In particular, radiomic features derived from FA, MD, RD, and AxD may capture subtle regional heterogeneity and complex microstructural alterations that are not fully represented by conventional summary measures (Neher et al., 2024; Zhao et al., 2020).

Nevertheless, WM features alone are insufficient to comprehensively depict the complex and heterogeneous pathological changes associated with AD and prodromal stages. Gray matter (GM), which is more directly linked to cognitive function, also undergoes early and progressive degeneration in AD (Wang et al., 2009; Falgàs et al., 2019). Structural MRI provides a powerful tool for assessing GM abnormalities, and morphological features such as cortical thickness, regional volume, and surface characteristics can effectively describe macroscopic structural damage (Zhao et al., 2021). Therefore, integrating complementary information from GM and WM may offer a more comprehensive and in-depth understanding of AD-related pathology. Such joint analysis is particularly important because neurodegeneration does not affect isolated tissue compartments, but rather involves coordinated alterations across cortical regions and their connecting fiber pathways. However, traditional multi-modal fusion strategies often rely on simple feature concatenation or linear association analyses (Bhattacharya et al., 2025). As a result, they may fail to capture the coordinated gray–white matter covariation and overlook the spatial correspondence between WM tracts and anatomically related GM regions (Savadjiev et al., 2014; Liang et al., 2021). Beyond imaging-based characterization, genetic factors that influence both GM and WM alterations also warrant investigation. Alongside structural alterations, genetic variation and gene expression also play important roles in the neurodegenerative processes underlying AD and MCI. Imaging genomics has emerged as a promising approach for linking genetic information with disease-related imaging phenotypes (Li et al., 2022). Given that AD-related degeneration affects both gray matter atrophy and white matter microstructural disruption, gene-level influences may operate across GM and WM rather than within a single tissue compartment. However, previous imaging genomics studies have mainly focused on candidate variants or global imaging measures, with limited attention to coordinated multi-gene effects and their spatial correspondence with multi-modal brain alterations (Wu et al., 2022; Shen et al., 2010). Consequently, the relationship between gene expression and integrated GM–WM features in MCI remains relatively underexplored.

Beyond these challenges, multi-center studies often introduce site effects that manifest as distributional discrepancies across centers, which may obscure true biological signals and reduce model generalizability (Da-Ano et al., 2020; Orlhac et al., 2022; Stamoulou et al., 2022). To address this issue, we turn to variational autoencoders (VAEs). VAEs, originally introduced to approximate complex latent distributions through probabilistic inference, provide a principled framework for learning latent representations that can reduce nuisance variability (Kingma, 2013; Kingma and Welling, 2019). By learning a shared latent space across sites, VAEs are well-suited to mitigating site-related confounds while preserving biologically relevant information (Vivek, 2023; Huang et al., 2022).

In this study, a Macro–Micro Structural Integration (MMSI) framework was developed to characterize neurodegeneration-related structural deviations across NC, MCI, and AD and to identify imaging-derived MCI subgroups with different degrees of deviation from normative structural patterns. First, we establish anatomically corresponding gray–white matter pairs and then integrate gray matter morphological features with the radiomic features of their connected white matter tracts into a unified representation, thereby capturing coordinated macrostructural and microstructural alterations. Second, we develop the Dual-Condition VAE to reduce site-specific effects while preserving disease-related information, thereby reducing the impact of multi-center heterogeneity. Third, we construct an interpretable MMSI score that enables effective stratification of MCI subgroups. The effectiveness and generalizability of the proposed framework are validated in both our in-house multi-center cohort and the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. Finally, we analyze subgroup-associated genes to explore the potential molecular basis underlying imaging-defined heterogeneity in MCI. These findings demonstrate that the proposed framework improves MCI subgroup identification, as well as provides insight into the relationship between multi-modal neuroimaging patterns and genetic mechanisms.

2. Materials and methods

The proposed MMSI framework integrates multi-modal neuroimaging features to learn a unified representation of disease-related structural deviations and heterogeneity within MCI. The overall architecture is illustrated in Fig. 1 and consists of four main components: (i) multi-modal feature extraction (Section 2.1), (ii) the Dual-Condition Variational Autoencoder (Section 2.2), (iii) biomarker construction and clinical analysis (Section 2.3), and (iv) External validation on the ADNI dataset (Section 2.4).

Fig. 1.

Overall workflow of our framework. (a) Construction of the TractRegion, which integrates the extraction of white matter radiomic features and gray matter morphological features. (b) Training pipeline and validation strategy of the proposed Dual-Condition VAE framework for disentangling biological and site-related information. (c) In-house multi-center dataset validation strategy. (d) MMSI score computation and MCI subgroup clustering. (e) External validation on the ADNI dataset, followed by MMSI-based gene association and pathway enrichment analyses.

2.1. Features extraction

2.1.1. Participant population

Our in-house multi-center dataset was from 7 MRI scanners (S01–S07) across 4 hospitals in China. After rigorous quality control, a total of 860 subjects were retained for analysis (283 NC, 267 MCI, and 310 CE), with exclusions applied to participants exhibiting excessive head motion, incomplete or poor-quality imaging data, or missing demographic/clinical information. Demographic and clinical characteristics are summarized in Table 1, and further details are available in prior publications (Zhao et al., 2020; Zhao et al., 2023).

Table 1.

Demographics for the multi-center dataset used in this study, * indicates p < 0.005.

Site	Total	Subject Number			MMSE (mean ± standard deviation(SD))
		NC	MCI	AD	NC	MCI	AD
S01	124	43	35	46	28.51 ± 1.37	26.54 ± 2.44	17.04 ± 6.52 *
S02	85	26	25	34	28.92 ± 1.00	26.88 ± 1.82	20.29 ± 3.34 *
S03	100	24	35	41	28.75 ± 1.13	25.46 ± 3.11	15.61 ± 5.71 *
S04	118	42	15	61	28.48 ± 1.72	24.87 ± 1.50	18.84 ± 3.49 *
S05	235	84	101	50	28.23 ± 2.41	23.78 ± 3.59	16.38 ± 6.17 *
S06	76	22	19	35	28.50 ± 1.31	22.05 ± 4.80	10.09 ± 6.33 *
S07	122	42	37	43	28.81 ± 1.22	26.27 ± 2.55	15.74 ± 5.58 *
Total	860	283	267	310	28.60 ± 1.41	25.12 ± 2.83	16.28 ± 5.31 *

To assess the robustness of the proposed model, it was further evaluated using an independent cohort from ADNI. A total of 97 participants were included, comprising NC (n = 32), EMCI (n = 43), and LMCI (n = 22) groups. Detailed demographic information is summarized in Table 2. Participants were included if they had a diagnosis of NC, EMCI, or LMCI; available T1-weighted and diffusion MRI data; and complete demographic and cognitive information. The corresponding imaging data were required to pass quality control and to be successfully processed through registration, segmentation, and tract-level feature extraction. Participant data were excluded from the analysis if either imaging modality was unavailable, if severe artifacts or incomplete brain coverage were identified, or if any essential preprocessing stage failed. For the transcriptomic analysis, participants were additionally required to have available gene-expression data that could be successfully matched to their imaging data using the ADNI subject identifier.

Table 2.

Demographics for ADNI used in this study, * indicates p < 0.005.

Group	Subject Number	Age(Mean ± SD)	Male/Female	MMSE(Mean ± SD)
NC	32	74.0 ± 6.0	14/18	28.8 ± 1.2
EMCI	43	74.8 ± 7.6	22/21	27.9 ± 1.8
LMCI	22	73.6 ± 5.9	13/9	25.9 ± 2.1
Total	97	74.3 ± 6.7	49/48	27.7 ± 2.0*

2.1.2. Magnetic Resonance Imaging data acquisition

All MRI data were acquired on 3.0 Tesla scanners, and the acquisition protocols varied across sites. For diffusion MRI, all sites used a b-value of 1000 s/mm², but differed in scanner manufacturer, number of diffusion directions (12–64), repetition time (6000–11,000 ms), echo time (85–98 ms), slice number/thickness (29–60 slices; 2–4 mm), and in-plane resolution (0.86 * 0.86 to 2.0 * 2.0 mm²). For T1-weighted imaging, inter-site variability was also observed in scanner manufacturer, head coil configuration (8–20 channels), repetition time, echo time (2.2–3.43 ms), flip angle (degree 7–degree 9), slice number/thickness (166–192 slices; 1.0–1.2 mm), and in-plane resolution (0.5 * 0.5 to 1.0 * 1.004 mm²). Most protocols were clustered around 1.0–2.0 mm² spatial resolution, but notable differences remained across centers. Supplementary Table S1 and S2 show the acquisition parameters of DTI and T1-weighted (T1w) imaging of our multi-site dataset.

2.1.3. Data preprocessing

For the DTI data of each subject in the dataset, the preprocessing steps were performed using the MRtrix3 toolbox (Tournier et al., 2019), including skull stripping, motion correction, linear registration, and eddy current correction. Whole-brain tractography was conducted for all subjects using the two-tensor Unscented Kalman Filter (UKF) method in the SlicerDMRI (version 5.6.1) toolbox (Fedorov et al., 2012). The parameters used for tractography were consistent with those used for generating tractography in the O'Donnell Research Group (ORG) atlas (O'Donnell and Westin, 2007; O'Donnell et al., 2012; Zhang et al., 2018). After the tracking was completed, fiber streamlines longer than 10 mm and shorter than 200 mm were retained. The tractogram of each subject consisted of approximately one million streamlines. Subsequently, we registered the whole-brain tractograms to the ORG space using the Advanced Normalization Tools (ANTs) (Avants et al., 2011). For each subject, a total of 10,000 fibers were retained. Finally, DTI metrics, including FA, MD, AxD, and RD, were calculated using the least squares method, and were registered to the ORG space.

For the T1w data of each subject, Freesurfer (version 7.4.1) was used to preprocess the images by performing operations such as motion correction, Talairach transformation, non-uniform intensity correction, and intensity normalization (Fischl, 2012). Finally, T1w images were skull-stripped and registered to the ORG space to ensure that all imaging data from the same subject were aligned within a common spatial framework. Specifically, through FreeSurfer, the cerebral cortex of each subject was partitioned based on the Desikan-Killiany Atlas after the cortical reconstruction of the images (Fischl et al., 2004).

2.1.4. Multi-modal feature extraction and integration

The feature extraction part can be seen in detail in Fig. 1(a). By using the Anatomically-guided Superficial Fiber Segmentation (Anat-SFSeg) framework (Zhang et al., 2024), we obtained 33 Deep White Matter (DWM) fiber tracts and 8 Superficial White Matter (SWM) fiber tracts (including both the left and right hemispheres) from the whole-brain tractograms. Meanwhile, Radtract is an advanced tool for extracting radiomics biomarkers from DTI metrics based on fiber tracts (Neher et al., 2024). It uses hyperplanes to parcellate fiber tracts effectively and extract 1106 DTI radiomics features for each parcellation. In this study, we used the radiomics metrics of all parcellations of each fiber tract, and the average indicators of each fiber tract parcellation to represent the white matter information. The specific method for determining the number of parcellations is provided in the Supplementary Table S3.

The acquisition of gray matter information is obtained through 8 indicators of the reconstructed cortex in different brain regions from the preprocessed T1w data, including cortical surface area, gray matter volume, average thickness from the average white matter surface to the meningeal surface, standard deviation of the average thickness, average curvature of the surface, gaussian curvature, complexity of cortical folding, and index of cortical curvature. For the integration of gray and white matter information, we aligned the two atlases (ORG atlas and DK atlas) according to the corresponding position information of fiber tracts and brain regions to form a partial connection diagram of fiber tracts and corresponding brain regions. As shown in Supplementary Table S4, the WM information contained in the fiber tracts and the GM information contained in the two brain regions connected by the corresponding fiber tracts are spliced together (if a fiber tract connects more than two brain regions, only the two brain regions with the largest contact area are selected for the sake of format alignment), forming the input feature named fiber Tracts and brain Regions (TractRegion).

The detailed procedure for selecting brain regions connected by each fiber tract is as follows. First, the DK atlas was registered to the ORG space. Subsequently, for each fiber tract, we counted the number of streamlines passing through each brain region defined by the atlas. The two brain regions with the largest number of traversing fibers were selected as the primary connected regions for that fiber tract. This procedure ensured that gray matter and white matter features were integrated according to their underlying anatomical associations before network input, rather than being directly concatenated without considering gray–white matter correspondence.

2.2. Dual-condition variational autoencoder

2.2.1. Input representation and network overview

In this study, each input sample is defined as a TractRegion unit, our proposed analysis unit that explicitly incorporates gray–white matter anatomical correspondence, rather than as an isolated fiber tract. Specifically, for each white matter tract, we concatenate tract-level diffusion MRI-derived features with the gray matter morphological features of its anatomically connected cortical regions, thereby forming a joint gray–white matter representation. The white matter component includes tract-specific features derived from diffusion MRI metrics, including FA, MD, AxD, RD, while the gray matter component consists of morphological descriptors extracted from the connected cortical regions. These multi-modal features are combined into a unified representation that encodes tract–region coupling and serves as the input to the proposed model. All input features are normalized using Z-score statistics computed from the training set to ensure consistency across subjects and imaging centers. Based on this TractRegion representation, we propose the Dual-Condition VAE for learning structured latent representations that capture biological, site-related, and demographic factors. The model consists of a multi-scale encoder, a factorized latent space, and a conditional decoder with explicit disentanglement constraints, aiming to improve cross-center robustness while preserving biologically meaningful disease-related information.

2.2.2. Multi-scale encoder and latent factorization

The encoder is built upon a 1D multi-scale convolutional neural network with residual blocks, which progressively extracts hierarchical representations through increasing channel dimensions and multi-scale receptive fields. Multi-scale pooling is applied to aggregate features at different resolutions, followed by a fully connected projection layer that produces a shared latent embedding capturing both local microstructural variations and global tract-level structure. From this shared representation, the model learns three latent variables corresponding to biological, site-related, and demographic factors. The biological latent space encodes disease-related variability and is regularized with a standard Gaussian prior. The site latent space models inter-center variability using a center-conditioned prior bank, explicitly capturing scanner- and acquisition-related effects. The demographic latent space encodes age and gender information, where age is modeled through an MLP and gender is represented using an embedding layer; this component is used as conditional input for decoding.

2.2.3. Decoder design and disentanglement strategy

The decoder is designed to reconstruct tract-level features using only the biological latent representation together with demographic information, explicitly excluding the site-related latent variable during training. Specifically, the input to the decoder consists of the concatenation of the biological latent variable and demographic embeddings, while the site latent variable is intentionally omitted by setting it to zero or removing it from the decoding pathway.

The decoder is composed of fully connected layers followed by residual refinement blocks, and it outputs reconstructed four-channel tract representations. By preventing the site-related latent variable from participating in the reconstruction process, the model is encouraged to attribute all reconstructive capacity to the biological latent space.

This design encourages the model to rely primarily on biological latent representations for reconstruction, where the reconstruction objective enforces that the biological latent representation alone is sufficient to recover tract features. As a result, the learned biological latent space becomes less sensitive to site-specific variations, while still preserving subject-level anatomical and disease-related information. Demographic variables are retained as auxiliary conditional inputs to guide reconstruction and stabilize representation learning. For a detailed architecture of the Dual-Condition VAE, please refer to the Supplementary Fig. S1.

2.2.4. Training strategy and optimization

We adopt a leave-one-center-out strategy for cross-site evaluation, where one imaging center is sequentially used as the test domain while all remaining centers are used for training. Only normal control subjects are included in training to learn normative TractRegion representations, such that deviations in patient populations can be interpreted as disease-related alterations. A total of 41 tract-specific models are independently trained across 7 centers. For each tract, data are divided into training and validation subsets, and model selection is based on the lowest validation reconstruction error. To improve representation disentanglement and cross-center robustness, the training process incorporates multiple regularization mechanisms. These include Kullback–Leibler divergence constraints for both biological and site-related latent variables, as well as explicit disentanglement losses that reduce statistical dependence between the two latent spaces. Specifically, covariance-based, cosine-similarity–based, and mutual-information–based constraints are jointly applied to encourage the biological latent representation to remain invariant to site-specific variation while preserving disease-related information. In addition, probabilistic regularization terms are progressively activated during early training using a warm-up strategy to stabilize optimization.

Hyperparameters were optimized using grid search rather than Bayesian optimization. Within each leave-one-center-out fold, candidate configurations were evaluated using only NC participants from the development centers, and the held-out center was not involved in hyperparameter selection. The search included the network dimensions, latent-space dimensions, dropout rate, learning rate, weight decay, batch size, and regularization weights. The configuration with the lowest validation reconstruction error was selected. The final model used AdamW with a learning rate of 1 × 10⁻⁴, a weight decay of 1 × 10⁻⁴, a batch size of 128, and a dropout rate of 0.2. The weights for reconstruction, biological KL divergence, site KL divergence, covariance, cosine-similarity, mutual-information, and center-smoothness losses were 3.0, 0.3, 0.3, 0.3, 0.2, 0.2, and 0.2, respectively. KL warm-up was applied over the first 50 epochs. Each model was trained for a maximum of 300 epochs, with early stopping after 20 epochs without improvement in validation performance. All Dual-Condition VAE models were implemented in PyTorch and trained on a workstation equipped with a single NVIDIA RTX 3090 GPU.

2.2.5. Loss function

The loss function consists of three parts, including the Mean Squared Error (MSE) reconstruction loss, Kullback-Leibler divergence (KLD) loss that constrains the similarity between the potential distribution and the prior distribution of the encoder output and latent disentanglement constraints. First, the reconstruction loss is used to deal with the reconstruction of normal TractRegions. When training fiber tracts, the MSE loss is used, as shown in Eq. (1):

$$\mathit{MSE}=\sum _{i=1}^n{\left(x-\widehat{\mathrm{x}}\right)}^2\ast \frac{1}{n}$$ (1)

where $x$ represents the original TractRegion features, and $\widehat{\mathrm{x}}$ represents the reconstructed TractRegion features, n represents number of samples.

The second Kullback–Leibler divergence (KLD) term in the proposed Dual-Condition VAE serves as a probabilistic regularizer for both the biological and site-related latent spaces. It constrains the learned posterior distributions to match their corresponding priors. The KLD loss is formulated in Eq. (2) and Eq. (3) as follows:

$$\begin{array}{c}{\mathit{Loss}}_{\mathit{KLD}}^{\mathit{bio}}=D_{\mathit{KL}}\left(q\left(z_{\mathit{bio}}|x\right)\right.‖N\left(0,I\right))\end{array}$$ (2)

where $q\left(z_{\mathit{bio}}|x\right)$ denotes the approximate posterior distribution of the biological latent variable conditioned on input x, and it is assumed to follow a Gaussian distribution parameterized by mean ${\mu }_{\mathit{bio}}$ and ${\sigma }_{\mathit{bio}}^2$. The prior distribution is a standard normal distribution $N\left(0,I\right)$.

$${\mathit{Loss}}_{\mathit{KLD}}^{\mathit{site}}=D_{\mathit{KL}}\left(q\left(z_{\mathit{site}}\left|x,c\right)\right)\left.‖p\left(z_{\mathit{site}}\left|c\right)\right)\right)\right)$$ (3)

where $q\left(z_{\mathit{site}}|x,c\right)$ denotes the approximate posterior distribution of the site related latent variable conditioned on both input x and site label c, parameterized by mean ${\mu }_{\mathit{site}}$and${\sigma }_{\mathit{site}}^2$. The prior distribution $p\left(z_{\mathit{site}}|c\right)$ is a site-conditioned Gaussian prior that models inter-site variability.

The third component of the objective introduces additional regularization terms between the biological and site-related latent representations. Specifically, we compute the cross-covariance between the two latent variables and penalize its squared Frobenius norm, compute the cosine similarity between them within each mini-batch, and estimate their mutual information using Mutual Information Neural Estimation. These three terms are then jointly included in the objective function. The disentanglement loss is formulated as:

$$\begin{array}{c}{L}_{\text{disentanglement}}={‖\mathit{Cov}\left(z_{\mathit{bio}},z_{\mathit{site}}\right)‖}_F^2+E\left[\frac{z_{b\mathrm{i}o}·{\mathrm{z}}_{\mathit{site}}}{\Vert z_{\mathit{bio}}\Vert \Vert z_{\mathit{site}}\Vert }\right]+I\left(z_{\mathit{bio}};{\mathrm{z}}_{\mathit{site}}\right)\end{array}$$ (4)

where $\mathit{Cov}\left(z_{\mathit{bio}},z_{\mathit{site}}\right)$ denotes the cross-covariance matrix computed between $z_{\mathit{bio}}$ and ${\mathrm{z}}_{\mathit{site}}$ within a mini-batch. ${‖‖}_F^2$ represents the squared Frobenius norm, used to penalize second-order dependence between the two latent spaces. The expectation is taken over mini-batch samples, and this term further encourages orthogonality by reducing cosine similarity between the two latent vectors. Finally, $I\left(z_{\mathit{bio}};{\mathrm{z}}_{\mathit{site}}\right)$denotes the mutual information between the biological and site-related latent variables.

The total loss for training is calculated in Eq. (5) as follows:

$$\begin{array}{c}{\mathit{Loss}}_{\mathit{total}}=\mathit{MSE}+{\mathit{Loss}}_{\mathit{KLD}}^{\mathit{bio}}+{\mathit{Loss}}_{\mathit{KLD}}^{\mathit{site}}+L_{\text{disentanglement}},\end{array}$$ (5)

2.2.6. Evaluation protocol

To separately evaluate performance within the development centers and generalizability to unseen centers, two complementary validation settings were implemented within a leave-one-center-out framework: intra-center validation and cross-center validation. In each iteration, one imaging center was completely held out as the cross-center test domain, while the remaining centers were pooled to construct the development cohort.

For intra-center validation, 50% of the NC subjects from the development cohort were used to train the Dual-Condition VAE and establish a normative representation of healthy structural patterns. The remaining NC subjects, together with all MCI and AD subjects from the same development centers, constituted the intra-center validation set. These subjects were not used to train or update the Dual-Condition VAE, and the trained model was applied without fine-tuning. This setting assessed whether disease-related information was preserved sufficiently to differentiate NC, MCI, and AD when the training and evaluation data originated from the same set of development centers.

For each subject in the intra-center validation set, tract-wise feature distributions were compared with the normative NC reference using the Wasserstein distance. The resulting distances were aggregated into a subject-level embedding representing the spatial pattern of deviation from normative structural organization. A three-component Gaussian mixture model was then fitted using only the embeddings from the intra-center validation set, without using clinical diagnostic labels. The three components were ordered according to their mean Wasserstein distances and assigned as NC-like, MCI-like, and AD-like groups from the lowest to the highest degree of deviation. The resulting assignments were compared with the clinical diagnoses to calculate the intra-center three-group concordance accuracy.

For cross-center validation, all eligible NC, MCI, and AD subjects from the held-out center were used exclusively for evaluation. No subjects from the held-out center were involved in Dual-Condition VAE training, internal validation, hyperparameter selection, construction of the normative reference, or GMM fitting. After model development, both the Dual-Condition VAE and the GMM were fixed. The held-out subjects were processed using the same normative-deviation procedure, and their resulting embeddings were directly assigned to the fixed GMM components without refitting or domain adaptation. The predicted NC-like, MCI-like, and AD-like groups were subsequently compared with the clinical diagnoses to calculate the cross-center three-group concordance accuracy.

Accordingly, intra-center validation examined the preservation of disease-related information within the multi-center development cohort, whereas cross-center validation evaluated generalizability and robustness to unseen site effects. All dataset partitioning was performed at the subject level to prevent data leakage. Further details regarding the data-partitioning strategy, normative-model training, GMM fitting and cluster labeling, and the intra-center and cross-center validation procedures are provided in Supplementary Method S1.

2.3. Derivation of the MMSI biomarker and clinical analysis

2.3.1. Calculation of the MMSI score and clinical analysis

We propose a novel imaging-derived biomarker, termed the MMSI score, to quantify disease-related deviations in gray and white matter structural connectivity. After model training on the NC cohort, the trained Dual-Condition VAE was applied to other subjects in a testing phase. For each subject and fiber tract, the reconstruction MSE between the input features and the VAE reconstruction was computed as a measure of deviation from the learned normative model. To obtain a normalized and interpretable metric, the MSE was further transformed using a Tanh function, yielding the MMSI score constrained to the range [0,1]. In this formulation, higher MMSI scores indicate patterns closer to normative structural connectivity, whereas lower MMSI scores reflect greater deviation from the healthy baseline. Formally, the MMSI score for the r-th TractRegion is defined as:

$$\begin{array}{c}{\mathit{MMSI\; score}}_r=1-\mathit{Tanh}\left({\mathit{MSE}}_r\right),\end{array}$$ (6)

where ${\mathit{MSE}}_r$ denotes the reconstruction error of the model for r-th TractRegion.

To validate the clinical relevance of the proposed biomarker, Pearson correlation analysis was performed between the MMSI scores and a set of cognitive assessment scores. The cognitive measures included global cognitive scales and domain-specific sub-scores, namely the Mini-Mental State Examination (MMSE), Montreal Cognitive Assessment (MoCA), Delayed Memory, Original Word Recognition, New Word Recognition, as well as MoCA subdomains covering visuospatial/executive function, naming, attention, language, abstraction, delayed recall, and orientation. Detailed descriptions of these cognitive assessments can be found in previous studies (Zhao et al., 2023; Woodward and Galea, 2005).

2.3.2. Discriminating MCI subgroups and explainable analysis

For each subject and each DTI metric (FA, MD, AxD, RD), we extracted the MMSI scores of all 41 fiber tracts (33 DWM and 8 SWM), forming subject-level feature vectors of 33 and 8 dimensions for DWM and SWM tracts, respectively. These MMSI scores reflect individual-level alterations in gray–white matter structural connectivity.

To stratify the MCI cohort, we employed a Gaussian Mixture Model (GMM) to probabilistically characterize the distribution of subject-level MMSI features. By modeling latent heterogeneity with multiple Gaussian components, the GMM enabled the identification of biologically meaningful high deviation and low deviation MCI subgroups. Specifically, the distribution of subject-level MMSI feature representations was modeled as a mixture of Gaussian components, where each component captures a distinct disease-related pattern. The model parameters were estimated using the Expectation–Maximization (EM) algorithm, enabling flexible modeling of complex data distributions. For each subject, the posterior probability of belonging to each component was computed, and subgroup assignment was determined by maximum a posteriori estimation. This probabilistic formulation allows soft clustering and provides a principled framework for capturing heterogeneity within the MCI population. To evaluate the clinical significance of the identified subgroups, Mann–Whitney U tests were conducted on cognitive scores to assess differences between the resulting clusters. To identify the TractRegions contributing to the imaging-derived MCI grouping, we trained XGBoost as a post hoc explanatory model using tract-level MMSI scores as input features and the GMM-derived cluster assignments as target labels. Subject identifiers and center information were excluded. Importantly, XGBoost was not used to generate the MCI subgroups or as a primary diagnostic classifier; the subgroups were determined independently by unsupervised GMM clustering. XGBoost was used only to model the relationship between MMSI features and the clustering assignments, enabling estimation of the contribution of each TractRegion.

XGBoost hyperparameters were selected based on stratified five-fold cross-validation. The final model used 200 estimators, a maximum tree depth of 4, a learning rate of 0.05, a subsampling ratio of 0.8, and a column-subsampling ratio of 0.8. The model was subsequently fitted to the complete dataset for SHAP interpretation. Feature importance was quantified as the mean absolute SHAP value across participants, and TractRegions were ranked accordingly. The 10 TractRegions with the highest mean absolute SHAP values were identified as the features contributing most strongly to the GMM-derived grouping and were subsequently examined across the different structural imaging parameters.

2.4. External validation on the ADNI cohort

For external validation, the Dual-Condition VAE was first pretrained using NC participants from the in-house multi-center dataset. ADNI was then treated as a new imaging center, and only ADNI NC participants were used for domain adaptation. All trainable parameters of the Dual-Condition VAE were fine-tuned for 20 epochs using the same learning rate and batch size as those used during model training on the in-house multi-center dataset. This adaptation aimed to reduce acquisition- and cohort-related distribution shifts between the in-house multi-center dataset and ADNI and to establish a cross-cohort normative reference.

After adaptation, the model was applied to ADNI EMCI (n = 43) and LMCI (n = 22) subjects. For each subject, MMSI scores were computed based on reconstruction errors, and subject-level feature representations were constructed by aggregating MMSI scores. Unsupervised clustering using a GMM was then performed to identify latent subgroups within the MCI population.To quantitatively evaluate the stratification effectiveness, the clustering results were compared with the original clinical labels (EMCI vs. LMCI). The consistency between clustering assignments and clinical staging was used as an indicator of the method's ability to capture disease progression patterns.

Finally, to investigate the biological relevance of the MMSI biomarker, we analyzed its association with gene expression profiles available in the ADNI dataset. Pearson's correlation analysis was first performed between MMSI scores and gene expression levels across subjects. Based on these associations, partial least squares (PLS) analysis was applied to identify genes showing the strongest contribution to the covariance between imaging-derived MMSI scores and gene expression profiles (Krishnan et al., 2011). PLS regression was performed using the gene-expression matrix as the predictor matrix and the tract-specific MMSI matrix as the response matrix. Models containing 1–10 components were evaluated using five-fold cross-validation, and the two-component model with the highest mean cross-validated $Q^2$ was selected. Model significance was evaluated by permuting the subject correspondence between the two matrices, using 500 permutations for the latent-variable and gene-level Variable Importance in Projection (VIP) analyses and 500 permutations for cross-validated $Q^2$. Ranking stability was additionally assessed using 500 bootstrap resamples. Genes were ranked according to their overall VIP scores, which integrated contributions from both retained PLS components rather than using PLS1 weights alone. The top 500 genes were selected for enrichment analysis, and genes appearing among the top 500 in at least 50% of the bootstrap resamples were considered ranking-stable. Gene enrichment analysis was conducted using Metascape (Zhou et al., 2019) to identify biological pathways and functional modules significantly associated with the MMSI-related gene set, providing insights into the potential molecular mechanisms underlying imaging-defined MCI heterogeneity.

3. Results

3.1. Evaluation of cross-center generalization and latent disentanglement

As shown in Table 3, the proposed Dual-Condition VAE demonstrates stable and consistent performance across different centers under the leave-one-center-out evaluation setting. First, the intra-center three-class classification accuracy (NC vs. MCI vs. AD) achieves relatively high performance across all centers, ranging from 0.7286 to 0.8602, indicating that the model can effectively capture disease-related structural patterns within each center. In comparison, the cross-center accuracy based on $z_{\mathit{bio}}$ is lower, reflecting the increased difficulty under domain shift conditions. However, the performance remains robust, indicating moderate cross-site generalization under domain shift. Second, the site classification accuracy based on $z_{\mathit{site}}$ is consistently high, demonstrating that the site-related latent space successfully captures scanner- or center-specific variations. In contrast, the site classification accuracy using $z_{\mathit{bio}}$ remains low, indicating that the biological latent representation is largely invariant to site information. Furthermore, the Pearson correlation between $z_{\mathit{bio}}$ and $z_{\mathit{site}}$ is consistently low across all centers, confirming effective disentanglement between biological and site-related factors. This result suggests reduced dependency between biological and site-related representations in separating disease-related signals from confounding site effects. Overall, these findings demonstrate that the proposed Dual-Condition VAE successfully achieves a balance between discriminative capability and domain generalization, while maintaining strong disentanglement between biological and site-specific representations.

Table 3.

Performance evaluation of the proposed Dual-Condition VAE under leave-one-center-out validation. This table reports intra-center three-class classification accuracy (Acc), cross-center classification accuracy based on biological latent representation $z_{\mathit{bio}}$, site classification accuracy using site-related latent representation $z_{\mathit{site}}$, site classification accuracy using biological latent representation $z_{\mathit{bio}}$, and the Pearson correlation between $z_{\mathit{bio}}$ and $z_{\mathit{site}}$. Results are presented as mean ± standard deviation across repeated experiments.

Held-out Center	Intra-center Acc (NC vs MCI vs AD)	Cross-center Acc ($z_{\mathit{bio}})$ (NC vs MCI vs AD)	Site Acc ($z_{\mathit{site}})$	Site Acc ($z_{\mathit{bio}})$	Corr($z_{\mathit{bio}},z_{\mathit{site}})$
1	0.729 ± 0.015	0.584 ± 0.026	0.901 ± 0.018	0.274 ± 0.059	0.053 ± 0.009
2	0.803 ± 0.063	0.645 ± 0.019	0.863 ± 0.045	0.288 ± 0.044	0.033 ± 0.011
3	0.816 ± 0.051	0.684 ± 0.026	0.869 ± 0.016	0.261 ± 0.043	0.065 ± 0.012
4	0.860 ± 0.022	0.659 ± 0.020	0.866 ± 0.015	0.244 ± 0.054	0.015 ± 0.013
5	0.846 ± 0.051	0.605 ± 0.025	0.853 ± 0.031	0.244 ± 0.043	0.050 ± 0.015
6	0.786 ± 0.040	0.571 ± 0.035	0.848 ± 0.026	0.264 ± 0.018	0.071 ± 0.012
7	0.730 ± 0.032	0.548 ± 0.029	0.827 ± 0.040	0.222 ± 0.051	0.080 ± 0.011

3.2. Correlation between MMSI score and cognitive scores

Fig. 2 presents the Pearson correlations between tract-specific MMSI values and cognitive measures, averaged across five independent experiments. To harmonize cognitive variables across centers, the MMSE reading, writing, and visuospatial items were analyzed as a single composite measure because separate item-level scores were unavailable for some centers. In the MCI group, MMSE-Commands, MMSE-Memory, and MMSE-Naming showed no interindividual variation and were therefore excluded from the correlation analysis.

Fig. 2.

Correlations between TractRegion-level MMSI scores and cognitive scores in the MCI and AD groups. (a) Results for the MCI group. (b) Results for the AD group. * indicates p < 0.05 after Bonferroni correction.

In the MCI group, significant MMSI–cognition associations were relatively sparse and varied across fiber tracts and cognitive domains. Associations were mainly observed for total MMSE, the combined MMSE-Reading, Writing, and Visuospatial score, MoCA-Attention, MoCA-Language, and selected memory-related measures. Both positive and inverse associations were identified, without a consistent directional pattern across TractRegions. This relatively weak and heterogeneous correlation profile is consistent with the substantial interindividual variability in structural and cognitive alterations at the MCI stage.

In contrast, the AD group exhibited a more extensive and coherent pattern of significant associations across multiple fiber tracts. These associations involved a broader range of cognitive domains, particularly total MMSE, MMSE-Attention and Calculation, MMSE-Memory, MMSE-Repetition, total MoCA, MoCA-Attention, MoCA-Abstraction, and MoCA-Language. Although the direction of the associations remained dependent on the specific tract and cognitive measure, positive correlations were more widely distributed in the AD group. Overall, the cross-sectional results indicate that tract-specific MMSI–cognition associations were less pronounced and more heterogeneous in MCI, whereas more widespread and consistent associations were observed in AD.

3.3. Comparison of feature representations for discriminating MCI subgroups

To determine the number of clusters, candidate solutions with K = 2, K = 3, and K = 4 were compared using the Calinski–Harabasz and Davies–Bouldin indices. The two-cluster solution achieved the highest Calinski–Harabasz index (740.17) and the lowest Davies–Bouldin index (0.034). The corresponding values were 437.73 and 0.142 for K = 3 and 628.01 and 0.101 for K = 4, respectively. Thus, both internal validation indices consistently supported the two-cluster solution.

Based on this two-cluster solution, Table 4 summarizes the ablation experiments evaluating cognitive differences between the lower- and higher-deviation MCI subgroups under different feature-representation settings. Using only T1-derived morphological metrics, significant subgroup differences were observed in MMSE (difference = 1.30, p = 0.0020), delayed memory (difference = 0.83, p = 0.0233), and new word recognition (difference = 0.88, p = 0.0096). The DTI-only model also identified significant but smaller differences in MMSE (difference = 1.03, p = 0.0180), delayed memory (difference = 0.84, p = 0.0245), and new word recognition (difference = 0.79, p = 0.0218).

Table 4.

Cognitive-score differences between the low- and high-deviation MCI subgroups under different feature-representation settings. Values are reported as mean differences, with the corresponding p values shown in parentheses.

Feature-representation setting	MMSE difference (p value)	Delayed Memory difference(p value)	New Word Recognition difference (p value)
T1-derived metrics only	1.30 (0.0020)	0.83 (0.0233)	0.88 (0.0096)
DTI-derived metrics only	1.03 (0.0180)	0.84 (0.0245)	0.79 (0.0218)
Without age embedding	1.78 (0.0008)	0.98 (0.0042)	0.95 (0.0050)
Without gender embedding	1.88 (0.0007)	1.05 (0.0009)	1.11 (0.0028)
Dual-Condition VAE	1.97 (0.0006)	1.08 (0.0006)	1.15 (0.0019)

The multi-modal ablation models produced larger cognitive differences than the single-modality models. Without the age embedding, the differences were 1.78 for MMSE (p = 0.0008), 0.98 for delayed memory (p = 0.0042), and 0.95 for new word recognition (p = 0.0050). Without the gender embedding, the corresponding differences were 1.88 (p = 0.0007), 1.05 (p = 0.0009), and 1.11 (p = 0.0028), respectively. The complete MMSI framework, incorporating both imaging modalities and demographic embeddings, yielded the largest differences across all three measures: 1.97 for MMSE (p = 0.0006), 1.08 for delayed memory (p = 0.0006), and 1.15 for new word recognition (p = 0.0019).

Overall, these findings indicate that the joint integration of T1- and DTI-derived features improved the characterization of cognitive heterogeneity within MCI. The further improvement achieved by the complete framework supports the contribution of both age and gender embeddings to the imaging-derived subgroup representation.

3.4. 3.4 Interpretability of MMSI-based MCI subgroup classification

The MMSI score provides a compact representation of subject-specific WM and GM alterations. As shown in Fig. 3(a), violin plots illustrate the distribution of MMSE scores across two MCI subgroups identified by clustering based on individual MMSI scores. A significant difference in MMSE score was observed between the low deviation and high deviation subgroups, indicating distinct levels of global cognitive impairment. Similarly, Fig. 3(b) shows the distribution of delayed memory scores across the two MCI subgroups, with the high deviation group exhibiting significantly lower performance than the low deviation group. These results demonstrate that the MMSI-based clustering captures meaningful cognitive heterogeneity within the MCI population, particularly with respect to both global cognition and memory-related function. To further interpret the MMSI-based classification, Fig. 3(c) shows the top 10 TractRegions contributing most strongly to MCI subgroup discrimination, ranked by mean absolute SHAP values. These discriminative TractRegions included striato-frontal (SF), thalamo-parietal (TP), middle longitudinal fasciculus (MdLF), superior longitudinal fasciculus II (SLF-II), thalamo-frontal (TF), intracerebellar input and Purkinje tract (Intra-CBLM-I-P), inferior occipito-frontal fasciculus (IOFF), inferior longitudinal fasciculus (ILF), cingulum bundle (CB), and superficial-frontal (Sup—F), covering a range of long-range association fibers, superficial white matter systems, and cerebellar pathways. Notably, several of the highest-ranking features were distributed across frontal, temporal, and parietal connectivity systems, including SF, TP, MdLF, SLF-II, TF, IOFF, and ILF, suggesting that subgroup-related structural alterations are not confined to a single anatomical territory but instead involve multiple large-scale association pathways. In addition, the presence of Intra-CBLM-I-P and CB among the most important features further points to a potential contribution of cerebellar-related gray-white matter alterations to MCI subgroup differentiation. Overall, these findings indicate that the MMSI framework captures distributed TractRegion-level patterns of white matter abnormality that jointly support discrimination between MCI subgroups, rather than relying on isolated regional effects.

Fig. 3.

Cognitive and imaging characteristics of the two GMM-derived MCI subgroups. (a) Comparison of MMSE scores between the low- and high-deviation MCI subgroups (p < 0.05). (b) Comparison of delayed memory scores between the two subgroups (p < 0.05). (c) SHAP-based interpretation of the XGBoost model trained to discriminate the two GMM-derived subgroups, showing the contribution of individual TractRegion features to subgroup differentiation. XGBoost was used for post hoc discrimination and feature interpretation, whereas subgroup assignment was determined by GMM clustering.

3.5. MMSI outperforms unimodal DTI radiomics and T1 morphological features in MCI subgroup discrimination

As shown in Fig. 4, MMSI scores yielded the clearest and most consistent separation between the two MCI subgroups across the five representative TractRegions with high SHAP contributions, including SF, MdLF, TP, and SLF-II,TF. In all four regions, MMSI scores exhibited the largest between-subgroup differences and the strongest statistical significance. By contrast, conventional tract-level radiomics features derived from FA, MD, AxD, and RD, as well as T1-based morphological features, showed weaker and less consistent discrimination, with significant differences observed only in selected regions and modalities. For these unimodal comparisons, DTI radiomics and T1 morphological features were evaluated separately within each modality. Specifically, modality-specific features were projected onto a single principal component using principal components analysis to provide a comparable scalar summary across modalities, and this one-dimensional summary measure was subsequently compared between subgroups. These results indicate that MMSI scores are more sensitive than conventional single-modality DTI radiomics and T1 morphological metrics for capturing subgroup-related structural alterations. Taken together, the findings support the added value of MMSI scores as a TractRegion–level biomarker for characterizing MCI heterogeneity. Furthermore, Supplementary Fig. S2 shows the distributions of MMSI scores across all TractRegions for the two identified MCI subgroups.

Fig. 4.

Comparison of MMSI and unimodal imaging features between MCI subgroups across representative TractRegions with high SHAP contributions. The selected TractRegions included MdLF, SF, SLF-II, TF, and TP. Each panel corresponds to one metric category: (a) MMSI, (b) FA, (c) MD, (d) AxD, (e) RD, and (f) T1. Boxplots show the distributions of the corresponding tract-level metric across these representative TractRegions in the two MCI subgroups. The dashed line represents the mean value of the parameters of the selected fiber bundles. Statistical significance is indicated as follows: * p < 0.05, ** p < 0.01, *** p < 0.001.

3.6. Cross-center three-class evaluation against conventional harmonization methods

Table 5 summarizes the leave-one-center-out performance for distinguishing NC, MCI, and AD. In each fold, six centers were used for model development and the remaining center was reserved for evaluation. The ComBat (Fortin et al., 2017) and CovBat (Chen et al., 2022) baselines followed the same six-center training and one-center testing protocol. The framework of Dual-Condition VAE achieved the highest mean performance across the seven held-out centers, with an accuracy of 0.614 ± 0.026 and an AUROC of 0.747 ± 0.060. Among the conventional approaches, CovBat combined with XGBoost performed best, achieving an accuracy of 0.573 ± 0.041 and an AUROC of 0.727 ± 0.042. Compared with this baseline, Dual-Condition VAE improved accuracy by 0.041 and AUROC by 0.020, supporting its effectiveness for cross-center discrimination of NC, MCI, and AD (Cortes and Vapnik, 1995; Chen, 2016; Ke et al., 2017).

Table 5.

Leave-one-center-out performance for NC, MCI, and AD classification using different harmonization and classification methods. Results are presented as mean ± standard deviation across repeated experiments.

Methods	Accuracy	AUROC
RBF-SVM (Cortes and Vapnik, 1995)	0.492 ± 0.051	0.645 ± 0.078
XGBoost (Chen, 2016)	0.523 ± 0.054	0.711 ± 0.026
LightGBM (Ke et al., 2017)	0.519 ± 0.036	0.703 ± 0.019
Combat+RBF-SVM (Fortin et al., 2017)	0.516 ± 0.071	0.687 ± 0.056
Combat+XGBoost	0.551 ± 0.056	0.720 ± 0.038
Combat+LightGBM	0.545 ± 0.054	0.710 ± 0.030
Covbat+RBF-SVM (Chen et al., 2022)	0.524 ± 0.070	0.684 ± 0.064
Covbat+XGBoost	0.573 ± 0.041	0.727 ± 0.042
Covbat+LightGBM	0.557 ± 0.037	0.711 ± 0.035
Dual-Condition VAE	0.614 ± 0.026	0.747 ± 0.060

3.7. External validation and TractRegion-associated gene enrichment analysis

To further evaluate the generalizability of the proposed method, we performed external validation in the ADNI cohort. As shown in Supplementary Fig. S3, MCI subjects were partitioned into two subgroups using the same clustering strategy, and the agreement between the resulting subgroups and clinically defined labels, namely late MCI (LMCI) and early MCI (EMCI), was assessed. The contingency matrix showed an overall accuracy of 0.769 for distinguishing LMCI from EMCI in the ADNI dataset. Notably, this performance was higher than that obtained using only T1-derived features (ACC = 0.692) or only DTI-derived features (ACC = 0.646). Additional comparisons with single-modality models and ablated variants are provided in Table 6. These findings suggest that the proposed representation captures clinically meaningful disease-related structure and generalizes well across independent cohorts.

Table 6.

Ablation study results of the proposed model on the ADNI dataset.

Feature-representation setting	ADNI Classification Accuracy of MCI
T1-derived metrics only	0.692
DTI-derived metrics only	0.646
Without Age embedding	0.723
Without Gender embedding	0.753
Dual-Condition VAE	0.769

Correlation analysis between gene-expression levels and tract-specific MMSI scores identified two genes with associations that remained significant after Benjamini–Hochberg FDR correction (p < 0.05), as shown in Supplementary Fig. S4(a). Keratin 77 (KRT77) was significantly associated with MMSI scores in the arcuate fasciculus (AF), corpus callosum 4 (CC4), inferior occipito-frontal fasciculus (IoFF), thalamo-frontal tract (TF), and superficial-occipital tract (Sup—O). Calcium voltage-gated channel subunit alpha 1 B (CACNA1B) was significantly associated with MMSI scores in the AF, TF, and Sup—O. Only associations surviving FDR correction are annotated and interpreted in Supplementary Fig. S4(a).

Separately, functional enrichment analysis of the PLS-derived MMSI-associated gene set identified biological terms related to neural signal transduction, learning and memory, calcium signaling, and immune processes, as shown in Supplementary Fig. S4(b). The enrichment network demonstrated functional interconnections among these biological modules. Supplementary Fig. S4(c) presents the statistical significance of the enriched terms, quantified as $-{\mathit{log}}_{10}\left(p\right)$, with calcium signaling, learning- and memory-related processes, and immune-response pathways showing relatively strong enrichment. Collectively, these findings provide preliminary transcriptomic support for the biological relevance of tract-specific MMSI variation.

4. Discussion

The present study addressed a central challenge in MCI research: how to identify clinically and biologically meaningful heterogeneity from multi-modal neuroimaging data while maintaining robustness across imaging sites. To address this, we developed the MMSI framework, which integrates gray matter morphology and white matter radiomics within anatomically defined TractRegion units and uses a Dual-Condition VAE to separate biological variation from site-related effects. This design was motivated by the view that MCI-related neurodegeneration is better conceptualized as a systems-level process, in which cortical and white matter alterations emerge in a coordinated manner across interconnected gray–white matter architectures, rather than as isolated abnormalities within either tissue alone.

A key methodological implication of this work is that disentangling site-related variability is not only a technical adjustment, but also a prerequisite for interpretable biomarker construction in multi-center neuroimaging studies. Scanner and protocol effects can overlap with subtle disease-related signals, particularly in prodromal populations such as MCI. The proposed Dual-Condition VAE is therefore valuable not simply because it improves representation learning, but because it encourages the learned latent space to reflect biologically meaningful variation rather than center-specific bias. This provides a principled way to construct imaging biomarkers that are more stable across multi-center datasets. In this context, the MMSI score can be interpreted as a deviation marker derived from a site-robust representation, which may facilitate subgroup discovery and cross-cohort application. More broadly, the proposed multi-modal fusion framework may be applicable to subgroup identification in other neurological and neuropsychiatric disorders, including vascular cognitive impairment, depression, and autism spectrum disorder, in which coordinated gray–white matter alterations also contribute to clinical heterogeneity (Gray et al., 2020; Itahashi et al., 2015; Liu and Zhang, 2023).

The TractRegion design provides an additional conceptual advantage. Rather than simply concatenating multi-modal features without anatomical constraint, our framework explicitly links tract-level white matter properties with the gray matter characteristics of anatomically connected cortical regions. This yields a circuit-informed representation of structural organization and may be particularly relevant in MCI, where abnormalities are often subtle, spatially heterogeneous, and distributed across interconnected systems. This explicit anatomical coupling distinguishes our approach from conventional feature concatenation strategies. From this perspective, MCI heterogeneity may be better understood as variation in gray–white matter coupling, rather than as isolated alterations within a single tissue compartment. This interpretation is consistent with the broader literature suggesting that prodromal neurodegeneration emerges at the network level rather than through focal damage alone (Muthuraman et al., 2016; Trombetta et al., 2024).

The importance of this finding lies not only in the numerical separation between groups, but in the observation that the imaging-derived subgroup structure aligns with biologically meaningful dimensions of impairment, particularly memory-related function. This suggests that the proposed biomarker captures disease-relevant variation in structural organization, rather than reflecting arbitrary clustering in a high-dimensional feature space. More broadly, these findings support the view that multi-modal structural phenotypes may provide added value for resolving MCI heterogeneity beyond conventional diagnostic grouping (Eppig et al., 2017; Graves et al., 2020; Jacova et al., 2007).

The TractRegion-level interpretation further suggests that the differences between the identified MCI subgroups are distributed rather than focal. The most discriminative TractRegions were not confined to a single anatomical location, but instead involved multiple association pathways, superficial white matter systems, cerebellar-related tracts, and their connected cortical regions. This pattern suggests that MCI heterogeneity may reflect large-scale differences in coordinated gray–white matter organization spanning frontal, temporal, parietal, and cerebellar systems (Chen et al., 2020; Yue et al., 2025). Notably, the representative TractRegions highlighted by the SHAP analysis also showed systematic differences in MMSI score distributions, further supporting their relevance to subgroup separation. Together, these findings suggest that structural variability in MCI is not limited to a classical focal vulnerability pattern, but instead involves more widespread TractRegion-level alterations, which may help explain why patients with similar global cognitive performance can nevertheless differ in subgroup membership and potentially in disease-related trajectories (Machulda et al., 2021).

The external validation on ADNI strengthens this interpretation. Its significance is not simply that the identified subgroups showed agreement with EMCI and LMCI labels, but that a representation learned in a multi-center setting retained meaningful structure in an independent cohort. This suggests that the model captures aspects of disease organization that are partially shared across datasets rather than being entirely dataset-specific. At the same time, the partial rather than complete correspondence with clinical staging is also important. Imaging-defined subgroups and clinically defined categories should not be expected to be identical, as they reflect overlapping but distinct aspects of disease progression. The ADNI results therefore support generalizability without requiring overly strong claims of equivalence (Michelutti et al., 2025; Park et al., 2017).

The gene analysis extends the interpretation of the MMSI framework beyond imaging phenotype alone. The enrichment of pathways related to neural signaling, learning and memory, calcium signaling, and immune processes is biologically plausible in the context of MCI and AD, and suggests that the identified subgroups may reflect biologically relevant patterns rather than purely statistical partitions. This point is especially relevant because imaging-based subgroup analyses are often criticized for limited mechanistic interpretability. By linking MMSI-associated patterns to pathway-level signals, the present study provides preliminary support for the biological relevance of imaging-defined heterogeneity (Wang et al., 2020; Fà et al., 2015).

At the structural level, heterogeneity is expressed as disruption of gray–white matter coupling. At the clinical level, it is reflected in differences in cognitive performance. At the molecular level, it is associated with pathways implicated in synaptic communication, memory, calcium homeostasis, and immune regulation. This convergence across scales is one of the main strengths of the study and suggests that subgroup stratification may be most informative when supported simultaneously by imaging, cognition, and molecular evidence (Liu et al., 2024; Fingerhut et al., 2022).

Several limitations should be acknowledged. First, although the framework generalized to ADNI, broader validation in larger independent cohorts is required to establish the reproducibility of both the imaging-derived subgroup structure and the associated gene findings. Although both two internal clustering-validity indices supported a two-cluster solution, these indices were calculated within the discovery cohort and therefore reflect separation in the analyzed MMSI feature space rather than out-of-sample stability or clinically discrete MCI categories. Intermediate or additional subgroups may emerge in larger and more heterogeneous populations. Second, the current TractRegion definition uses only the two most strongly connected cortical regions for each tract, which improves methodological consistency but simplifies the full anatomical complexity of TractRegion relationships. Future work could incorporate probabilistic connectivity weights to better capture this complexity. Third, the present study is cross-sectional, and the identified subgroups should therefore be interpreted as imaging-defined structural phenotypes reflecting different degrees of deviation rather than definitive longitudinal progression categories. Longitudinal follow-up will be required to determine whether these subgroups differ in cognitive decline or conversion to AD. Finally, the gene analysis is associative rather than causal, and the pathway results should be interpreted as biological support rather than mechanistic evidence.

5. Conclusion

This study proposed an MMSI framework for identifying biologically meaningful MCI subgroups by jointly modeling gray matter morphological alterations and white matter microstructural abnormalities. By further introducing a Dual-Condition VAE to reduce site-related heterogeneity, MMSI achieved robust subgroup stratification in a multi-center cohort and showed good generalizability in external validation. Moreover, gene-associated analyses provided additional molecular evidence supporting the biological relevance of the imaging-defined heterogeneity. Together, these findings suggest that the MMSI framework offers a robust and interpretable approach for characterizing MCI heterogeneity, while also facilitating a more comprehensive understanding of the structural and molecular mechanisms underlying progression along the MCI-to-AD continuum. In addition to providing a useful framework for stratifying MCI patients beyond conventional clinical staging, this multi-modal fusion strategy may also have broader applicability to subgroup identification in other neurological and neuropsychiatric disorders, such as vascular cognitive impairment, major depression, and autism spectrum disorder, in which coordinated gray–white matter alterations likewise contribute to disease heterogeneity and may inform future precision medicine applications.

Consent for publication.

All authors consent for the publication.

CRediT authorship contribution statement

Qichen Zhang: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Methodology, Formal analysis, Data curation, Conceptualization. Di Zhang: Writing – review & editing, Supervision, Investigation, Data curation, Conceptualization. Ruixi Zhou: Writing – review & editing, Supervision. Kun Zhao: Resources, Project administration, Data curation. Dawei Wang: Resources, Project administration, Data curation. Hongxiang Yao: Resources, Project administration, Data curation. Bo Zhou: Resources, Project administration, Data curation. Jie Lu: Resources, Project administration, Data curation. Xi Zhang: Resources, Project administration, Data curation. Ying Han: Resources, Project administration, Data curation. Pan Wang: Resources, Project administration, Data curation. Yong Liu: Supervision, Resources, Project administration, Funding acquisition, Data curation, Conceptualization. Fangrong Zong: Writing – review & editing, Supervision, Resources, Project administration, Investigation, Funding acquisition, Data curation.

Ethics approval and consent to participate

Multi-center dataset used in the present study was collected from four hospitals. The Medical Ethics Committee of PLA General Hospital, the Medical Ethics Committee of Qilu Hospital of Shandong University, and the Medical Ethics Committee of Tianjin Huanhu Hospital approved this study. Written informed consent was obtained from each enrolled subject or their authorized guardian. The study was approved by the Medical Research Ethics Committee and Institutional Review Board of Xuanwu Hospital (ClinicalTrials.gov identifiers: NCT02353884 and NCT02225964).

Funding

We acknowledge funding provided the National Key Research and Development Program of China (No. 2023YFE0118600) and the National Natural Science Foundation of China (No. 82371910). We acknowledge all researchers for their contributions to data collection.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary material: Figure S4. External validation in the ADNI cohort and functional enrichment analysis of MMSI-associated genes. Change : functional analysis → functional enrichment analysis.

Data availability

Data will be made available on request.