# Fisher-Rao Regularized Transport Analysis of the Glymphatic System and Waste Drainage

## TL;DR

This paper introduces a Fisher-Rao regularized Lagrangian framework for analyzing the glymphatic system's waste drainage, enabling visualization and differentiation of flow patterns under various conditions, with implications for understanding Alzheimer's disease.

## Contribution

It presents a novel Lagrangian approach using Fisher-Rao regularization for analyzing time-varying flows in the glymphatic system, offering interpretability and visualization advantages over existing methods.

## Key findings

- Successfully captures known glymphatic flows.
- Distinguishes flow patterns under different anesthetics.
- Provides insights into altered waste drainage states.

## Abstract

In this work, a unified representation of all the time-varying dynamics is accomplished with a Lagrangian framework for analyzing Fisher-Rao regularized dynamical optimal mass transport (OMT) derived flows. While formally equivalent to the Eulerian based Schr\"odinger bridge OMT regularization scheme, the Fisher-Rao approach allows a simple and interpretable methodology for studying the flows of interest in the present work. The advantage of the proposed Lagrangian technique is that the time-varying particle trajectories and attributes are displayed in a single visualization. This provides a natural capability to identify and distinguish flows under different conditions. The Lagrangian analysis applied to the glymphatic system (brain waste removal pathway associated with Alzheimer's Disease) successfully captures known flows and distinguishes between flow patterns under two different anesthetics, providing deeper insights into altered states of waste drainage.