  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.
