A variable time step self-consistent mean field DSMC model for three-dimensional environments.

A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier-Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman-Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to

Elimination of substances from the brain parenchyma: efflux via perivascular pathways and via the blood-brain barrier.

This review considers efflux of substances from brain parenchyma quantified as values of clearances (CL, stated in µL g-1 min-1). Total clearance of a substance is the sum of clearance values for all available routes including perivascular pathways and the blood-brain barrier. Perivascular efflux contributes to the clearance of all water-soluble substances. Substances leaving via the perivascular routes may enter cerebrospinal fluid (CSF) or lymph. These routes are also involved in entry to the parenchyma from CSF. However, evidence demonstrating net fluid flow inwards along arteries and then outwards along veins (the glymphatic hypothesis) is still lacking. CLperivascular, that via perivascular routes, has been measured by following the fate of exogenously applied labelled tracer amounts of sucrose, inulin or serum albumin, which are not metabolized or eliminated across the blood-brain barrier. With these substances values of total CL ≅ 1 have been measured. Substances that are eliminated at least partly by other routes, i.e. across the blood-brain barrier, have higher total CL values. Substances crossing the blood-brain barrier may do so by passive, non-specific means with CLblood-brain barrier values ranging from  1000 for water and CO2. CLblood-brain barrier values for many small solutes are predictable from their oil/water partition and molecular weight. Transporters specific for glucose, lactate and many polar substrates facilitate efflux across the blood-brain barrier producing CLblood-brain barrier values > 50. The principal route for movement of Na+ and Cl- ions across the blood-brain barrier is probably paracellular through tight junctions between the brain endothelial cells producing CLblood-brain barrier values ~ 1. There are large fluxes of amino acids into and out of the brain across the blood-brain barrier but only small net fluxes have been observed suggesting substantial reuse of essential amino acids and α-ketoacids within the brain. Amyloid-β efflux, which is measurably faster than efflux of inulin, is primarily across the blood-brain barrier. Amyloid-β also leaves the brain parenchyma via perivascular efflux and this may be important as the route by which amyloid-β reaches arterial walls resulting in cerebral amyloid angiopathy