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 ...

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We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology.In the accompanying paper [1], we analyze the proposed method and prove optimal order convergence and stability.

Intrathecal delivery is a procedure involving the release of therapeutic agents into the cerebrospinal fluid (CSF) hrough a catheter. It holds promise for treating high-impact central nervous system pathologies, for which systemic administration routes are ineffective. In this study we introduce a numerical model able to simultaneously account for solute transport in the fluid and in the spinal cord. Using a Discontinuous Galerkin method and a three-dimensional patient-specific geometry, we studied the effect of catheter position and angle on local spinal cord drug concentration. We considered twenty cardiac cycles to limit the computational cost of our approach, which resolves the physics both in space and time. We used clinically representative data for the drug injection speed and dose rate, and scaled drug diffusion/penetration properties to obtain observable effects during the considered simulation time. Based on our limited set of working parameters, lateral injection perpendicular to the cord turned out to be more effective than other configurations. Even if the adopted scaling does not allow for a direct clinical translation (a wider parametric assessment of the importance of CSF flow, geometry and diffusion properties is needed), it did not weaken our numerical approach, which can be used to systematically investigate multiple catheter, geometry and fluid/tissue properties configurations, thus paving the way for therapy control.