Connectome-Based Model of Pathology Spread

• Connectome-based models are frameworks that utilize network diffusion and reaction–diffusion equations to simulate how disease agents propagate along structural and functional neural pathways.
• These models integrate quantitative imaging data and personalized parameter inference to link network topology with clinical biomarkers in neurodegeneration and tumor invasion.
• Key insights include the role of high-degree hubs, localized forcing, and multimodal interactions that collectively shape the spatial–temporal progression of pathology.

A connectome-based model of pathology spread formalizes the hypothesis that brain-wide neurodegenerative dynamics and tumor invasion are governed not purely by region-local factors, but by disease agents' preferential migration along axonal and/or functional pathways as specified by the structural and/or functional connectome. These models leverage network diffusion, reaction–diffusion, and coupled-mechanistic frameworks, with region-to-region connectivity quantified from large-scale diffusion MRI, tractography, or fMRI correlation matrices. Contemporary work incorporates monotonic progression guarantees, nonlinear saturation, multimodal interactions, and personalized-parameter inference, providing a quantitatively precise mapping between connectome architecture and observed biomarker trajectories across neurodegenerative and oncological pathologies.

1. Mathematical Foundations of Connectome-Guided Pathology Spread

The canonical framework for connectome-based spreading phenomena is the network diffusion ODE: $\frac{dx}{dt} = -\rho L x$ where $x(t) \in \mathbb{R}^p$ encodes the pathology or biomarker burden in each brain region, $L$ is the graph Laplacian derived from the structural connectome $A$ (edge weights: streamline count, fiber density, or derived adjacency), and $\rho$ is the global diffusivity parameter (Alexandersen et al., 5 Sep 2025).

Reaction–diffusion extensions incorporate local nonlinearities, such as the Fisher–Kolmogorov term: $\frac{dx}{dt} = -\rho L x + \alpha x(1 - x/\beta)$ with $\alpha$ the local replication/growth rate and $\beta$ the saturation limit. Two-species models explicitly track healthy and misfolded protein species, e.g.,

$$\begin{aligned} \frac{du}{dt} &= -\rho L u + k_0 - k_1 u - k_2 u v \ \frac{dv}{dt} &= -\rho L u - k_3 v + k_2 u v \end{aligned}$$

where $u$, $v$ represent healthy and misfolded forms (Alexandersen et al., 5 Sep 2025, Pal et al., 2021).

Recent generalizations encode further mechanistic realism:

• COMIND model [Editor's term]: Combines connectome-transitive diffusion, region-specific forcing $f$, monotonic logistic-type saturation, and consistent scaling to imaging biomarkers (Semchin et al., 14 Aug 2025).
• Coupled-mechanisms frameworks: Introduce local production/aggregation rates modulated by region-wise topology metrics (e.g., betweenness, clustering coefficient, functional degree), coupled to standard diffusion (He et al., 2023).
• Stochastic SDE models: Add Itô noise to account for multifactorial, random effects (MacIver et al., 4 Nov 2024):

$dc = f(c)\,dt + \Sigma(c)^{1/2} dW(t)$

• Multilayer diffusion: models on SC and FC graphs with interlayer mass exchange (Dan et al., 23 Oct 2025).

2. Model Parameterization, Inference, and Scalability

Connectome-based models typically require estimation of few global, many region-specific, and no explicit edge-wise parameters:

• COMIND: Uses $2p+1$ parameters for $p$ regions: global timescale $s_t$, region scaling $s\in\mathbb{R}^p$, and external forcing $f\in\mathbb{R}^p$; no per-edge fitting (Semchin et al., 14 Aug 2025).
• Coupled-mechanism approaches (He et al., 2023): Fit per-subject diffusion $k_i$, production $\alpha_i$, and mixture weights $w_i$ over P network metrics via a Dirichlet-horseshoe prior, leveraging stochastic variational inference in high dimension.
• Functional–structural multilayer frameworks: Learn coupling parameters (e.g., $\lambda_s$, $\lambda_f$, feedback gains $(K_s, K_f)$), interlayer mass-exchange matrices, and subjectwise regional embedding parameters by end-to-end minimization of imaging error using neural ODE solvers (Dan et al., 23 Oct 2025).
• Stochastic frameworks (MacIver et al., 4 Nov 2024): Bayesian inference (ABC-MCMC) jointly recovers mean progression rates and noise levels.

Subject-specific heterogeneity is accommodated using latent time-shifts, epicenter selection, or individual parameter vectors, enabling the model to fit observed diversity in disease onset, spatial patterns, and trajectory shape (Semchin et al., 14 Aug 2025, He et al., 2023).

3. Empirical Validation: Synthetic and Clinical Cohorts

Validation occurs on both synthetic and real-world imaging cohorts:

• Synthetic studies: Model-generated connectomes and pathology vectors (e.g., random $K^*$, $f \sim$ Gamma) with numerically integrated disease trajectories permit direct ground-truth evaluation. Parameter recovery, MAE in subject time-shift, and close tracking of trajectory shapes are achieved (mean $\beta_i$ error $\sim 0.3 \pm 0.2$ over $\sim 20$ years) (Semchin et al., 14 Aug 2025).
• Clinical studies: Application to Parkinson's disease (PPMI), Alzheimer's disease (ADNI), or glioma imaging datasets using regionwise neuroimaging (e.g., cortical thickness, PET SUVR) and diffusion MRI connectomes. For the COMIND model (PPMI, $p=68$), classic neurodegenerative patterns—occipito-parietal to frontal/limbic—are quantitatively reproduced. Region-specific forcing $f$ often localizes to known vulnerable subnetworks (e.g., salience network) and external clinical scores (MoCA, Hoehn–Yahr) exhibit significant correlation with latent subject-specific disease times (Semchin et al., 14 Aug 2025).

Tumor-spread models demonstrate improved volume overlap (Dice) between predicted and actual tumor margins when incorporating patient- or atlas-derived DTI tensors, especially for commissural butterfly gliomas (Weidner et al., 23 Jul 2025). For neurodegeneration, region-level trajectory fits, subtyping, and Braak-staging recovery (accuracy $>$80%) establish external validity (Zhang et al., 2022, He et al., 2023).

4. Mechanistic Insights, Network Topology, and Biomarker Dynamics

The connectome critically shapes pathology propagation:

• Hubs and modular structure: High-degree hubs (e.g., entorhinal cortex) accelerate regional invasion; modules with dense intra-connections display rapid within-community spread, while sparse inter-module connectivity slows propagation (MacIver et al., 4 Nov 2024, Alexandersen et al., 5 Sep 2025). Degree–arrival-time anti-correlation (corr $\sim$ –0.75) is quantitatively observed (MacIver et al., 4 Nov 2024).
• Critical vs. vulnerable regions: Regions with maximal impact on global disease burden ("critical nodes") strongly overlap high-degree, high-PageRank vertices; these outperform classical hub selection for driving whole-graph transitions to high-risk states (Zhang et al., 2022).
• Structural–functional interplay: Multi-layer models reveal stage-specific and region-specific balance of SC- vs FC-mediated tau spread, modulated by age, APOE genotype, amyloid level, and gene expression (CHUK, TMEM106B, MCL1, NOTCH1, TH), with SC dominance rising in late-stage and in specific lobes (Dan et al., 23 Oct 2025).
• Mechanistic diversity: Coupled-mechanisms models fit per-subject weights over multiple topology-driven vulnerabilities, revealing mechanistic subtypes and variable regional "seeding" sites (He et al., 2023).

5. Model Comparisons, Advantages, and Limitations

The table below summarizes salient properties of major model classes (abbreviations as above):

Model/Framework	Key Features	Notable Advantages
COMIND	Monotonic, scalable ODE; region forcing	Parsimony, monotonicity, interpretable $f$
Coupled-mechanisms	Multi-metric topology weights	Subject subtyping, heterogeneity, uncertainty
Stochastic SDE	Noise-driven, Bayesian fit	Quantifies uncertainty, captures randomness
SC+FC Multilayer	Bi-layer graph diffusion, gene linkage	Dynamic SC/FC balance, genetic correlations
Reaction–diffusion	Standard (non)linear connectome PDE	Analytical tractability, mechanistic clarity

Key strengths of connectome models include quantitative mechanistic insight, parameter economy suitable for high-resolution graphs, empirical pattern recovery, and tractable numerical and analytical properties (Semchin et al., 14 Aug 2025, He et al., 2023, MacIver et al., 4 Nov 2024, Dan et al., 23 Oct 2025). However, common limitations are static connectomes (immunity to atrophy/reorganization), lack of explicit neuronal feedback and clearance pathways, absence of patient-specific DTI in clinical application (for glioma), and in many models, single-mechanism or single-compartment limitations (Semchin et al., 14 Aug 2025, Weidner et al., 23 Jul 2025).

6. Biological, Clinical, and Predictive Significance

Connectome-based models recapitulate observed spatial-temporal disease progression: Braak staging, lobe- and hub-specific vulnerability, critical region-induced cascading, and gene-expression spatial alignment (Zhang et al., 2022, Dan et al., 23 Oct 2025). In glioma, fiber-guided migration accurately predicts cross-hemispheric spread, supporting more precise radiotherapy margins (Weidner et al., 23 Jul 2025).

Monotonic and scalable formulations (COMIND) facilitate fitting in small and medium longitudinal imaging datasets, enabling robust parameter recovery, trajectory tracking, and association with clinical staging (Semchin et al., 14 Aug 2025). Stochastic frameworks reveal that late-stage trajectory uncertainty is maximal in hypo-connected regions (frontal lobe), consistent with clinical unpredictability (MacIver et al., 4 Nov 2024).

A plausible implication is that targeting high-degree or critical regions, reducing vulnerability via network reconfiguration, or adjusting nodal forcing parameters may optimally delay network-level collapse or slow oncological spread. However, generalization to personalized, plastic, or subtyped regimes remains an open challenge.

7. Current Debates and Future Directions

Active areas include:

• Dynamic connectomics: Incorporating time-varying graphs to capture atrophy, compensatory reorganization, or adaptive therapy (Semchin et al., 14 Aug 2025, Dan et al., 23 Oct 2025).
• Explicit modeling of clearance pathways: Integration of glymphatic, proteasomal, and microglial dynamics (Alexandersen et al., 5 Sep 2025).
• Bidirectional neural-activity coupling: Capturing disease–neural oscillation feedback, e.g., using joint neural mass–pathology models (Alexandersen et al., 5 Sep 2025).
• Personalized multiparameter inference: From patient-specific DTI/fMRI to per-subject biomarker and network dynamics (He et al., 2023, Dan et al., 23 Oct 2025).
• Multi-pathology coupling: Beyond single-compartment, multi-modal models (e.g., joint A$\beta$, $\tau$, atrophy, TDP-43, $\alpha$-synuclein) (Dan et al., 23 Oct 2025, Pal et al., 2021).
• Therapeutic targeting: Using inferred $f$ or criticality to direct molecular or stimulatory intervention (Semchin et al., 14 Aug 2025, Dan et al., 23 Oct 2025).

These developments are poised to increase clinical translation and mechanistic interpretability, while ongoing work continues to expand the granularity, scope, and biological realism of connectome-based disease spread modeling.