| name | branched-optimal-transport-brain-mapping |
| description | Branched optimal transport framework for inferring stimulus-to-reaction propagation architectures in brain networks. Uses anisotropic branched OT where concavity of flux cost promotes aggregation and branching. Activation: branched optimal transport, stimulus reaction brain mapping, ramified transport brain, brain propagation architecture, optimal transport neuroscience. |
Branched Optimal Transport for Brain Mapping
Variational framework for inferring stimulus-to-reaction routing architectures in the brain using anisotropic branched optimal transport, treating the transport network itself as unknown rather than fixed.
Metadata
- Source: arXiv:2603.19751
- Authors: Cristian Mendico
- Published: 2026-03-20
- Categories: math.OC, q-bio.NC, q-bio.QM
Core Methodology
Key Innovation
Traditional brain state transition models control trajectories on a fixed network substrate. This work inverts the problem: the transport network itself is the inferred object, modeled as a graph/current connecting a stimulation source measure to a reaction target measure.
Technical Framework
-
Anisotropic Branched OT Formulation
- Model as variational problem: find optimal current (graph) connecting source measure μ (stimulation) to target measure ν (reaction)
- Flux cost function is concave → promotes aggregation and branching
- Support of optimal current defines stimulus-to-reaction routing architecture
-
Existence Theory
- Proved existence of minimizers in both discrete and continuous formulations
- Discrete: finite graph with edge currents
- Continuous: measure-theoretic formulation on manifold
-
Hybrid Stochastic Extension
- Combines ramified transport with path-space KL control cost
- Induced graph dynamics incorporate stochasticity
- Provides probabilistic interpretation of routing uncertainty
Mathematical Structure
minimize: ∫ c(θ) d|J|(θ) + KL(Path || Reference)
subject to: div(J) = ν - μ (continuity equation)
where: J = optimal current, c = concave flux cost
Applications
- Inferring brain reaction maps from stimulation experiments
- Mapping neural propagation pathways without pre-defined connectivity
- TMS/tDCS stimulation response prediction
- Understanding brain network plasticity through optimal routing
Implementation Guide
Prerequisites
- Optimal transport library (POT, geomloss)
- Graph optimization tools
- Numerical PDE solvers for continuous formulation
Step-by-Step
- Define source measure μ (stimulation region) and target measure ν (reaction region)
- Choose concave flux cost function c(θ) (e.g., θ^α, α < 1)
- Solve discrete branched OT on candidate graph
- Validate with continuous formulation via level-set methods
- Extend to stochastic version with KL control cost for uncertainty quantification
Pitfalls
- Concave optimization is non-convex → multiple local minima possible
- Discrete approximation may miss fine-scale branching structure
- Stochastic extension adds computational complexity
- Requires careful regularization for numerical stability
Related Skills
- optimal-transport-brain
- brain-network-controllability
- brain-stimulation-dynamics-state
- adaptive-flow-routing-brain-networks
