RTI Experiment Simulation assuming Convective and Diffusive Interstitial Transport in the Brain: Concentration over time (and space)

Simulation of interstitial transport in the brain assuming convective and diffusive transport with perivascular efflux routes.  The movie shows the transient concentration of TMA ions in a real-time iontophoresis (RTI) experiment, where a small molecular probe is applied to brain tissue at a known rate and its concentration measured over time a a point 100-200um away, here 150 um.  RTI experiments are used to characterize the properties of interstitial tissue to determine its void volume and tortuosity, 0.18 and 1.85 for the condition shown here.  In this simulation, a model of combined diffusion and convection (superficial velocity=50 um/min) is applied to fit experimental data and range.  (Convection assumes Darcy's Law with a hydraulic conductivity of 2x10^-6 cm² mmHg s^-1 and pressure difference of 2.15 mmHg). The model domain is a cube 750 um on a side with 8 penetrating arterioles and 8 penetrating venules.  The first and third columns from the left are venules and the second and fourth are arterioles, with convective flow from arteriole to venule.  As transport of molecules in the perivascular space is known to be faster than in the interstitium, the concentration is assumed to be c=0 at the vascular walls.  The solute (TMA) must pass through a perivascular wall with lower diffusivity than the interstitium to leave the domain through a vascular wall (D_wall=5%D_interstitium).  Although it is difficult to see in the movie, both the presence of convection and the perivascular efflux routes cause range(variability) in the measured concentration curves for different source and detection point combinations that is consistent with experimental data--see additional posted data.  Computations performed using FEniCS, movie made using Paraview.