Tau-BNO: Brain Neural Operator for Tau Transport Model

TL;DR

Tau-BNO, a Brain Neural Operator surrogate framework for rapidly approximating NTM dynamics that captures both intra-regional reaction kinetics and inter-regional network transport, is proposed, showcasing the transformative value of deep learning surrogates to accelerate analysis of large-scale, computationally intensive dynamical systems.

Abstract

Mechanistic modeling provides a biophysically grounded framework for studying the spread of pathological tau protein in tauopathies like Alzheimer's disease. Existing approaches typically model tau propagation as a diffusive process on the brain's structural connectome, reproducing macroscopic patterns but neglecting microscale cellular transport and reaction mechanisms. The Network Transport Model (NTM) was introduced to fill this gap, explaining how region-level progression of tau emerges from microscale biophysical processes. However, the NTM faces a common challenge for complex models defined by large systems of partial differential equations: the inability to perform parameter inference and mechanistic discovery due to high computational burden and slow model simulations. To overcome this barrier, we propose Tau-BNO, a Brain Neural Operator surrogate framework for rapidly approximating NTM dynamics that captures both intra-regional reaction kinetics and inter-regional network transport. Tau-BNO combines a function operator that encodes kinetic parameters with a query operator that preserves initial state information, while approximating anisotropic transport through a spectral kernel that retains directionality. Empirical evaluations demonstrate high predictive accuracy ($R^2\approx$ 0.98) across diverse biophysical regimes and an 89\% performance improvement over state-of-the-art sequence models like Transformers and Mamba, which lack inherent structural priors. By reducing simulation time from hours to seconds, we show that the surrogate model is capable of producing new insights and generating new hypotheses. This framework is readily extensible to a broader class of connectome-based biophysical models, showcasing the transformative value of deep learning surrogates to accelerate analysis of large-scale, computationally intensive dynamical systems.

Figures (9)

• Figure 1: Tau-Brain Neural Operator (Tau-BNO) Architecture.a. Input consists of initial tau concentration fields derived from experimentally defined mouse injection sites, together with sampled aggregation and fragmentation rate parameters ($\lambda_f, \lambda_\gamma, \lambda_\delta, \lambda_\epsilon, \lambda_\mu$). b. A Query Operator encodes regional initial tau concentrations, and a Function Operator encodes kinetic parameters; their interaction is passed through a Directed Graph Operator defined on the structural connectome to model asymmetric inter-regional transport. c. A learnable projector generates tau spatiotemporal dynamics across all 426 brain regions.
• Figure 2: Brain network representations for tau transport modeling.a. Original directed MCA connectome encoding region-to-region tau transport pathways. b--d. Three derived undirected proximity networks capturing complementary topological features: b. first-order symmetric network preserving global connectivity structure; c. second-order indegree network emphasizing convergent (afferent) connectivity; d. second-order outdegree network emphasizing divergent (efferent) connectivity. Edge brightness indicates connection strength. Together, these representations enable graph neural networks to recover directional transport dynamics from symmetrized adjacency matrices.
• Figure 3: Performance comparison of Tau-BNO with 11 benchmarking models.a. Quantitative evaluation (RMSE, MAE) across six general-purpose architectures, highlighting the limitations of standard predictive models for PDE-governed tau transport. b. Comparison among five neural operator variants, showing Tau-BNO's superiority within the operator learning family. c. Training dynamics of Tau-BNO over 1000 epochs, showing log-scale RMSE and stable convergence behavior. d. Temporal evolution of absolute prediction error for Tau-BNO and three representative neural operators, illustrating sustained accuracy across the full trajectory.
• Figure 4: Ablation analysis of Tau-BNO architecture. Performance comparison for modular (FO, QO, DGO) and kernel (Fourier, differential) ablations.
• Figure 5: Spatiotemporal prediction accuracy across diverse physiological regimes. Brain heatmaps of relative prediction error for Tau-BNO and three neural operator baselines under three representative biophysical regimes. Parameters $[\lambda_f, \lambda_\gamma, \lambda_\delta, \lambda_\epsilon, \lambda_\mu]$ denote tau production rate, aggregate rate, anterograde transport velocity, retrograde transport velocity, and uptake release rate, respectively. a. Transport-only regime ($\lambda_f=0$): $[0.0, 8\times10^{-3}, 100, 100, 1.20]$. b. High anterograde regime (anterograde dominant transport): $[9\times10^{-4}, 4.8\times10^{-3}, 80.6, 22.6, 0.47]$. c. High retrograde regime (elevated production, strong retrograde transport): $[9.8\times10^{-3}, 4.2\times10^{-3}, 58.6, 92.5, 0.51]$. Color scale denotes relative error magnitude. Across regimes, Tau-BNO exhibits consistently lower error than competing models.

Theorems & Definitions (1)

• Lemma 1: Differential kernel