Lagrangian Optimal Mass Transport with Applications to the Glymphatic System
Year: 2019
Type: preprint
Abstract: In this work, a unified representation of all the time-varying dynamics is accomplished with a Lagrangian framework for analyzing regularized dynamical optimal mass transport (OMT) derived flows. Our Lagrangian framework is also applicable to the Fisher-Rao regularization because, as we show, it is equivalent to our regularized dynamical OMT formulation. The advantage of the Lagrangian framework is that the time-varying trajectories and particle attributes are displayed in a single visualization. This provides a natural capability to identify and distinguish flows under different conditions. Applying our Lagrangian analysis to the glymphatic system, we successfully distinguish between flow patterns under two different anesthetics. We should also note that the Fisher-Rao regularization makes direct contact with some of the very nice recent work on entropic regularization for the computation of optimal mass transport as well as the Schrodinger bridge theory. The latter provides a stochastic aspect to the approach described in the present work.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2915536733