The brain lacks lymph vessels and must rely on other mechanisms for clearance of waste products, including amyloid β that may form pathological aggregates if not effectively cleared. It has been proposed that flow of interstitial fluid through the brain's interstitial space provides a mechanism for waste clearance. Here we compute the permeability and simulate pressure-mediated bulk flow through 3D electron microscope (EM) reconstructions of interstitial space. The space was divided into sheets (i.e., space between two parallel membranes) and tunnels (where three or more membranes meet). Simulation results indicate that even for larger extracellular volume fractions than what is reported for sleep and for geometries with a high tunnel volume fraction, the permeability was too low to allow for any substantial bulk flow at physiological hydrostatic pressure gradients. For two different geometries with the same extracellular volume fraction the geometry with the most tunnel volume had 36% higher permeability, but the bulk flow was still insignificant. These simulation results suggest that even large molecule solutes would be more easily cleared from the brain interstitium by diffusion than by bulk flow. Thus, diffusion within the interstitial space combined with advection along vessels is likely to substitute for the lymphatic drainage system in other organs.T ransport of nutrients and waste within the brain's parenchyma is paramount to healthy brain function. Although lymphatic vessels occur within the meninges (1, 2), they are absent from the brain's parenchyma. This raises the question of how waste products are cleared from the brain (3-8). There is an urgent need to resolve this question, given the fact that several neurological disorders are associated with accumulation of toxic debris and molecules in the brain interstitium (9). Most notably, insufficient clearance may contribute to the development of Alzheimer's disease and multiple sclerosis (9, 10).Recently the "glymphatic" hypothesis (10) was launched. This hypothesis holds that the brain is endowed with a waste clearance system driven by bulk flow of fluid through the interstitium, from paraarterial to paravenous spaces, facilitated by astrocytic aquaporin-4 (AQP4). Further, it was proposed that cerebral arterial pulsation (11) and respiration (12) drive paravascular fluid movement and cerebrospinal fluid (CSF)-interstitial fluid (ISF) exchange. Here, bulk flow is defined as the movement of fluid down the pressure gradient, advection is the transport of a substance by bulk flow, and convection is transport by a combination of advection and diffusion.There is strong evidence for paravascular advection (8, 13-15), although the details of influx and efflux pathways and the underlying driving forces are debated (10, 15-17). There are, however, controversies regarding the relative importance of advective versus diffusive transport within the interstitial space (3,5,7,8), and the idea that a hydrostatic pressure gradient can cause an advective flow within the ...

No abstract

We study perfusion by a multiscale model coupling diffusion in the tissue and diffusion along the one-dimensional segments representing the vasculature. We propose a block-diagonal preconditioner for the model equations and demonstrate its robustness by numerical experiments. We compare our model to a macroscale model by [P. Tofts, Modelling in DCE MRI, 2012].