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Multimodal branched transport infers anatomically aligned brain reaction maps

Cristian Mendico

Abstract

How external stimulation is transformed into distributed reaction patterns remains unresolved at the level of propagation architecture. Existing large-scale control models quantify transition costs on prescribed networks but do not infer the routing map itself from source and target activity. Here we combine task-related blood-oxygen-level-dependent responses, source-reconstructed electrophysiology and tractography-derived anisotropy to estimate stimulation and reaction measures, define an anatomical transport cost, and infer a branched propagation architecture by variational optimisation. Unlike standard transport formulations, branched transport favours aggregation of signal into shared neural highways before redistribution. We further attach a stochastic graph-induced dynamics to the inferred map and quantify the trade-off between geometric efficiency and dynamical controllability. We show that multimodal data generate anatomically aligned brain reaction maps, that anisotropic costs qualitatively reshape routing backbones relative to isotropic baselines, and that hybrid geometric--dynamical optimisation reveals non-trivial rank reversals across branching regimes.

Multimodal branched transport infers anatomically aligned brain reaction maps

Abstract

How external stimulation is transformed into distributed reaction patterns remains unresolved at the level of propagation architecture. Existing large-scale control models quantify transition costs on prescribed networks but do not infer the routing map itself from source and target activity. Here we combine task-related blood-oxygen-level-dependent responses, source-reconstructed electrophysiology and tractography-derived anisotropy to estimate stimulation and reaction measures, define an anatomical transport cost, and infer a branched propagation architecture by variational optimisation. Unlike standard transport formulations, branched transport favours aggregation of signal into shared neural highways before redistribution. We further attach a stochastic graph-induced dynamics to the inferred map and quantify the trade-off between geometric efficiency and dynamical controllability. We show that multimodal data generate anatomically aligned brain reaction maps, that anisotropic costs qualitatively reshape routing backbones relative to isotropic baselines, and that hybrid geometric--dynamical optimisation reveals non-trivial rank reversals across branching regimes.
Paper Structure (34 sections, 23 equations, 11 figures, 2 tables)

This paper contains 34 sections, 23 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Discussion
  4. Methods
  5. Data availability
  6. Code availability
  7. Competing interests

Figures (11)

  • Figure 1: Task-evoked fMRI BOLD pipeline. Simulated blood-oxygen-level-dependent data analysed with a general linear model. Left, stimulus and reaction regressors after convolution with the haemodynamic response. Top right, representative blood-oxygen-level-dependent signals in selected regions of interest. Bottom left, region-wise contrast statistics showing strong task selectivity. Bottom right, blood-oxygen-level-dependent functional connectivity. This figure defines the fMRI component of the source and target estimation step.
  • Figure 2: Source-reconstructed EEG/MEG pipeline. Top left, trial-averaged source-space ERP waveforms showing early stimulus-locked and later reaction-locked components. Top right, source map at $\sim 100$ ms. Bottom left, source map at $\sim 350$ ms. Bottom right, region-wise electrophysiological activity scores for the stimulation and reaction windows. This figure provides the temporally resolved component of the source and target estimation step.
  • Figure 3: Multimodal fusion and probability measures. Top row, normalised fMRI scores, normalised EEG/MEG scores, and fused source and target measures. Bottom left, supply--demand vector $b(v)=\mu_{\mathrm{stim}}^{+}-\mu_{\mathrm{react}}^{-}$. Bottom middle, sensitivity of $\mu_{\mathrm{stim}}^{+}$ to the fusion weight. Bottom right, agreement between blood-oxygen-level-dependent and electrophysiological regional scores. This figure defines the balanced source and target measures used in the branched transport problem.
  • Figure 4: Diffusion-informed anisotropic transport geometry. Left, synthetic fractional-anisotropy map across regions of interest. Middle, diffusion tensor ellipses and principal diffusion axes. Right, anisotropic arc costs on the candidate graph, showing strong directional heterogeneity. This figure defines the tractography-informed transport cost used in the anisotropic optimisation.
  • Figure 5: Data-driven branched optimal transport infers the brain reaction map. (a) Fused $\mu_{\mathrm{stim}}^{+}$. (b) Fused $\mu_{\mathrm{react}}^{-}$. (c) Fractional-anisotropy map and principal diffusion axes. (d) Isotropic branched transport solution. (e) Anisotropic branched transport solution. (f) Edgewise flux comparison between isotropic and anisotropic models. The anisotropic model yields a routing backbone that is qualitatively distinct from the isotropic baseline and more strongly aligned with anatomical directional priors.
  • ...and 6 more figures