title: Optimal-mass-transfer-based estimation of glymphatic transport in living brain.
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 para-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) approach3to derive 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.
authors.affiliation: Dept. of Computer Sciences and Applied Mathematics/Statistics, Stony Brook University, Stony Brook, New York 11790.
authors.forename: Vadim
authors.initials: V
authors.lastname: Ratner
authors.affiliation: Dept. of Computer Sciences and Applied Mathematics/Statistics, Stony Brook University, Stony Brook, New York 11790.
authors.forename: Liangjia
authors.initials: L
authors.lastname: Zhu
authors.affiliation: Dept. of Computer Sciences and Applied Mathematics/Statistics, Stony Brook University, Stony Brook, New York 11790.
authors.forename: Ivan
authors.initials: I
authors.lastname: Kolesov
authors.affiliation: School of Medicine, Rochester University, NY.
authors.forename: Maiken
authors.initials: M
authors.lastname: Nedergaard
authors.affiliation: Dept. of Anesthesiology, Stony Brook University Hospital, Stony Brook, NY, 11790.
authors.forename: Helene
authors.initials: H
authors.lastname: Benveniste
authors.affiliation: Dept. of Computer Sciences and Applied Mathematics/Statistics, Stony Brook University, Stony Brook, New York 11790.
authors.forename: Allen
authors.initials: A
authors.lastname: Tannenbaum
keywords: Monge Kantorovich problem; cerebrospinal fluid flow in brain; diffusion equation; diffusion tensor estimation; inverse problem; liquid flow modeling; optical flow; optimal mass transport