Unbalanced Regularized Optimal Mass Transport with Applications to Fluid Flows in the Brain

TL;DR

This paper introduces an unbalanced regularized optimal mass transport method that relaxes mass preservation constraints, enabling more flexible modeling of fluid flows in the brain with a detailed numerical solution.

Contribution

It develops an unbalanced rOMT framework and provides a numerical solution for analyzing brain fluid flows, extending prior balanced formulations.

Findings

Effective in modeling brain fluid dynamics.

Handles mass variation in transport processes.

Applicable to dynamic image tracking.

Abstract

As a generalization of the optimal mass transport (OMT) approach of Benamou and Brenier's, the regularized optimal mass transport (rOMT) formulates a transport problem from an initial mass configuration to another with the optimality defined by the total kinetic energy, but subject to an advection-diffusion constraint equation. Both rOMT and the Benamou and Brenier's formulation require the total initial and final masses to be equal; mass is preserved during the entire transport process. However, for many applications, e.g., in dynamic image tracking, this constraint is rarely if ever satisfied. Therefore, we propose to employ an unbalanced version of rOMT to remove this constraint together with a detailed numerical solution procedure and applications to analyzing fluid flows in the brain.