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

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 Schrödinger 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.

Keywords: Fisher-Rao regularization; Glymphatic system; Optimal mass transport.

Fig. 1.

Eulerian and Lagrangian visualizations of flow dynamics. (A) For each time point, streamlines are computed at a fixed set of initial locations. Color is used to distinguish streamline clusters and time-varying flow behavior is observed by comparing streamlines across time. (B) Alternatively, temporal changes in particle trajectories are encompassed by pathlines and presented in a single image. Time-varying particle attributes associated with the pathlines, such as (C) density and (D) speed, exemplify the simplistic yet informative nature of our unified visualization framework.

Fig. 2.

Comprehensive pathline visualization of 130 minutes of glymphatic transport of DOTA (Gd-Dota) in a rat anesthetized with DEXM+ISO (left) and ISO (right). The pathlines in green are derived from the entire brain and nasal conchae. Both rats exhibit pathlines in the nasal conchae, signifying that Gd-DOTA exited along the olfactory nerves via the cribriform plate to lymphatic vessels in the submucosa of the nasal cavities. Pathlines that follow the middle cerebral artery (MCA) are outlined in red. More pathlines are clearly evident in the rat anesthetized with DEXM+ISO than ISO anesthesia, confirming that GS transport is more efficient during DEXM+ISO anesthesia. Scale bar = 3mm.

Fig. 3.

Speed pathlines over 130 minutes of GS transport distinguishing flow behavior under two anesthetics, DEXM+ISO (top) and ISO (bottom).

Fig. 4.

Speed pathlines into the nasal conchae extracted from the GS speed `connec-tome' and divided up into fast (red) speed lines with speed magnitude > 0055 a.u. and slower (green) speed lines with speed magnitudes in the range of 0:001 – 0:050 a.u. (A, B) ISO anesthetized rats are characterized by rapid efflux of solute into the nasal cavity and (C, D) the vast majority of speed lines in the DEXM+ISO anesthetized rats are slower. (E) Proportion of voxels with fast moving solute. Data are mean ∓ SEM.