Cerebrospinal Fluid and Interstitial Fluid Motion via the Glymphatic Pathway Modelled by Optimal Mass Transport

Abstract

It was recently shown that the brain-wide cerebrospinal fluid (CSF) and interstitial fluid exchange system designated the glymphatic pathway plays a key role in removing waste products from the brain, similarly to the lymphatic system in other body organs1,2. It is therefore important to study the flow patterns of glymphatic transport through the live brain in order to better understand its functionality in normal and pathological states. Unlike blood, the CSF does not flow rapidly through a network of dedicated vessels, but rather through peri-vascular channels and brain parenchyma in a slower time-domain, and thus conventional fMRI or other blood-flow sensitive MRI sequences do not provide much useful information about the desired flow patterns. We have accordingly analyzed a series of MRI images, taken at different times, of the brain of a live rat, which was injected with a paramagnetic tracer into the CSF via the lumbar intrathecal space of the spine. Our goal is twofold: (a) find glymphatic (tracer) flow directions in the live rodent brain; and (b) provide a model of a (healthy) brain that will allow the prediction of tracer concentrations given initial conditions. We model the liquid flow through the brain by the diffusion equation. We then use the Optimal Mass Transfer (OMT) approach3 to model the glymphatic flow vector field, and estimate the diffusion tensors by analyzing the (changes in the) flow. Simulations show that the resulting model successfully reproduces the dominant features of the experimental data.