Probability-Invariant Random Walk Learning on Gyral Folding-Based Cortical Similarity Networks for Alzheimer's and Lewy Body Dementia Diagnosis

Technical Deep Dive: Probability-Invariant Random Walk Learning on Gyral Folding Networks for Dementia Diagnosis

Overview

This work proposes a novel framework called PaIRWaL (Probability-Invariant Random-Walk Learning) for classifying Alzheimer's disease (AD) and Lewy body dementia (LBD) using individualized brain network models derived from cortical gyral folding patterns. Key innovations include:

• Constructing cortical similarity networks from local morphometric features of three-hinge gyri (3HGs), a biologically-grounded cortical landmark
• Modeling these variable-size, irregularly-structured networks using probability-invariant random walk sampling and anonymized walk encoding
• Demonstrating consistent improvements over existing gyral folding network and atlas-based graph learning approaches for AD/LBD diagnosis

Problem & Context

• AD and LBD are major neurodegenerative disorders with overlapping clinical symptoms, making accurate differential diagnosis crucial
• Brain network analysis using structural and functional connectivity is a promising approach, but standard atlas-based parcellations may obscure disease-sensitive individual anatomy
• Gyral folding-based networks can better capture disease-related patterns, but suffer from high inter-subject variability in node correspondence and topology

Methodology

1. Cortical Similarity Network Construction:
   • 3HG landmarks were automatically extracted from T1-weighted MRI scans
   • Cortical morphometric features were extracted within 5-ring neighborhoods around each 3HG
   • Similarity networks were built using Kullback-Leibler divergence between multivariate feature distributions
2. Probability-Invariant Random Walk Learning:
   • Random walks were sampled on the cortical networks using a conductance-based scheme that preserves isomorphism invariance
   • Each walk was encoded into an anonymized sequence capturing structural transitions, neighborhood relations, and anatomical region attributes
   • A reader neural network processed the walk encodings to output graph-level predictions
3. Architecture and Training:
   • Random walk length ℓ=64, K=8 walks sampled per graph for training, K=64 for inference
   • Reader network: 2-layer MLP with 128 hidden units, trained using cross-entropy loss

Data & Experimental Setup

• Cohort: 303 T1-weighted MRI scans, including 108 cognitively normal controls, 90 AD, and 105 LBD subjects
• Data preprocessing: cortical surface reconstruction, spherical mapping, 3HG extraction using automated pipeline
• Cross-validation: 10-fold splits for 4 classification tasks (AD/LBD/CN, AD vs CN, LBD vs CN, AD vs LBD)
• Evaluation metrics: accuracy, sensitivity, specificity, AUC, Matthews correlation coefficient

Results

• PaIRWaL consistently outperformed both gyral folding network baselines (GraphStat, GNN models) and atlas-based approaches (BrainNetCNN, BNT, CPSSM) across all tasks.
• On the challenging AD vs. LBD binary classification, PaIRWaL achieved substantial gains in both sensitivity and specificity compared to prior methods.
• Ablation studies confirmed the importance of probability-invariant random walks, anonymization, and anatomical attribute encoding for robust performance.

Interpretation

• The probability-invariant random walk representation effectively handles the high variability in cortical folding patterns, enabling reliable network-level disease classification.
• The anatomically-informed encoding captures meaningful structural relationships beyond just sequential transitions, providing interpretable insights into disease-relevant brain regions.
• The efficient sampling and aggregation strategy ensures computational feasibility while retaining strong predictive power.

Limitations & Uncertainties

• The study was conducted on a single clinical cohort, so generalization to other datasets remains to be evaluated.
• The specific choices of morphometric features, neighborhood size, and network sparsity thresholds were not extensively explored.
• While the work demonstrates improved AD/LBD classification, its impact on early detection and prognosis prediction is not assessed.

What Comes Next

• Validating the framework on independent cohorts and across different neuroimaging modalities (e.g., diffusion MRI, functional MRI)
• Extending the method to jointly model multimodal brain networks and investigate their complementary contributions
• Exploring ways to further enhance the interpretability of the learned representations, such as identifying specific folding patterns or network motifs associated with each disease