Modeling arteriolar flow and mass transport using the immersed boundary method

Flow in arterioles is determined by a number of interacting factors, includ ing perfusion pressure, neural stimulation, vasoactive substances, the intr insic contractility of arteriolar walls, and wall shear stress. We have dev eloped a two-dimensional model of arteriolar fluid flow and mass transport. The model includes a phenomenological representation of the myogenic respo nse of the arteriolar wall, in which an increase in perfusion pressure stim ulates vasoconstriction. The model also includes the release, advection, di ffusion, degradation, and dilatory action of nitric oxide (NO), a potent, b ut short-lived, vasodilatory agent. Parameters for the model were taken pri marily from the experimental literature of the rat renal afferent arteriole , Solutions to the incompressible Navier-Stokes equations were approximated by means of a splitting that used upwind differencing for the inertial ter m and a spectral method for the viscous term and incompressibility conditio n, The immersed boundary method was used to include the forces arising from the arteriolar walls. The advection of NO was computed by means of a high- order flux-corrected transport scheme; the diffusion of NO was computed by a spectral solver. Simulations demonstrated the efficacy of the numerical m ethods employed, and grid refinement studies confirmed anticipated first-or der temporal convergence and demonstrated second-order spatial convergence in key quantities. By providing information about the effective width of th e immersed boundary and sheer stress magnitude near that boundary, the grid refinement studies indicate the degree of spatial refinement required for quantitatively reliable simulations. Owing to the dominating effect of NO a dvection, relative to degradation and diffusion, simulations indicate that NO has the capacity to produce dilation along the entire length of the arte riole. (C) 1998 Academic Press.