Alzheimer's disease (AD) and Lewy body dementia (LBD) present overlapping clinical features yet require distinct diagnostic strategies. While neuroimaging-based brain network analysis is promising, atlas-based representations may obscure individualized anatomy. Gyral folding-based networks using three-hinge gyri provide a biologically grounded alternative, but inter-individual variability in cortical folding results in inconsistent landmark correspondence and highly irregular network sizes, violating the fixed-topology and node-alignment assumptions of most existing graph learning methods, particularly in clinical datasets where pathological changes further amplify anatomical heterogeneity. We therefore propose a probability-invariant random-walk-based framework that classifies individualized gyral folding networks without explicit node alignment. Cortical similarity networks are built from local morphometric features and represented by distributions of anonymized random walks, with an anatomy-aware encoding that preserves permutation invariance. Experiments on a large clinical cohort of AD and LBD subjects show consistent improvements over existing gyral folding and atlas-based models, demonstrating robustness and potential for dementia diagnosis.
Alzheimer's disease (AD) and Lewy body dementia (LBD) are two of the most prevalent neurodegenerative disorders, together accounting for a substantial proportion of dementia cases worldwide [20]. Clinically, these two conditions share overlapping cognitive symptoms and neuropathological features, particularly in early stages, which often leads to diagnostic ambiguity. However, AD and LBD differ markedly in disease mechanisms, progression trajectories, and treatment responses, making accurate differential diagnosis crucial for patient management and therapeutic decision-making [19,27]. Developing neuroimaging-based biomarkers that can reliably distinguish AD from LBD therefore remains a central challenge in dementia research. A growing body of evidence suggests that such neurodegenerative processes are not confined to isolated brain regions but instead manifest as system-level alterations involving distributed brain circuits. This view has motivated the modeling of the human brain as a complex, interconnected network, whose organization supports cognition and behavior [2,21]. Within this network-based perspective, researchers represent the brain as a graph of interacting elements, and have extensively characterized dementia-related changes through alterations in structural and functional connectivity, revealing many network-level disruptions that cannot be fully explained by local atrophy alone [31].
Recently, gyral folding patterns have emerged as an alternative and biologically grounded basis for network construction [6,32]. In particular, the threehinge gyrus (3HG), a reproducible folding configuration linked to cortical development and mechanical constraints, has been proposed as an individualized anatomical landmark for defining network nodes [4,14,30]. Gyral folding networks that use 3HGs as nodes and derive edges from structural connectivity (e.g., diffusion MRI tractography) or functional connectivity (e.g., resting-state fMRI synchronization) have demonstrated strong discriminative power in dementia diagnosis. Several recent studies have highlighted the advantages of gyral folding-based networks over conventional atlas-based representations. Prior work [18] has shown that networks constructed from gyral folding landmarks can outperform atlas-based brain networks in early AD detection, suggesting that folding-derived nodes capture disease-sensitive structural patterns that are blurred by coarse parcellation. More recent efforts [8,9] have further integrated gyral folding networks with atlas-based representations in a hierarchical manner, using representation learning to construct a unified, continuous staging framework spanning AD and LBD. These studies collectively underscore the potential of folding-informed network models for dementia characterization. Despite these advances, existing gyral folding network methods face several limitations. First, due to pronounced inter-individual variability in cortical folding, it is generally difficult to establish reliable one-to-one correspondences between folding landmarks across subjects [5,28,29]. As a result, node identities are often only weakly aligned, rendering downstream graph learning models sensitive to arbitrary node indexing or residual spatial noise. Second, the number of detected folding landmarks may vary across individuals, leading to graphs with different sizes and topologies. These properties violate the fixed-node and strict-alignment assumptions implicit in most atlas-based and conventional graph learning approaches [15,16], limiting their applicability and robustness in clinical settings.
To address these challenges, we propose a Probability-Invariant Random-Walk Learning framework (PaIRWaL) for the classification of gyral folding net-works. The method constructs cortical similarity networks from morphometric feature similarity within local neighborhoods of gyral folding landmarks, and models each network through distributions of anonymized random walks, thereby achieving graph isomorphism invariance in a probabilistic sense. Random walk sampling is guided by a minimum degree local rule (MDLR) to balance exploration across heterogeneous node degrees. We further propose an Anatomy-Aware Anonymized Walk Recording module (A 3 WR), in which each random walk is represented as an event sequence encoding structural transitions and neighborhood relations, while anatomical priors are incorporated via region-ofinterest (ROI) attribute tokens under a permutation-invariant formulation. We validate the proposed framework on a clinical cohort of AD and LBD subjects, where it consistently outperforms existing gyral folding network baselines as well as atlas-based brain network classification models, demonstrating its effectiveness and robustness for dementia diagnosis.
Dataset description and data pre-processing In this study, we analysed a cohort of T1-weighted structural MRI scans (n = 303) obtained from the University of Cambridge. A subset of th
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