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Modeling arteriolar flow and mass transport using the immersed boundary method. (English) Zbl 0936.76062

Summary: The authors develop a two-dimensional model of arteriolar fluid flow and mass transport. The model includes a phenomenological representation of the myogenic response of the arteriolar wall, in which an increase in perfusion pressure stimulates vasoconstriction. The model also includes the release, advection, diffusion, degradation, and dilatory action of nitric oxide (NO), a potent, but short-lived, vasodilatory agent. Parameters for the model are taken primarily from the experimental literature of the rat renal afferent arteriole.
They approximate solutions to the incompressible Navier-Stokes equations by means of a splitting that used upwind differencing for the inertial term and a spectral method for the viscous term and incompressibility condition. The immersed boundary method is used to include the forces arising from the arteriolar walls. The advection of NO is computed by means of a high-order flux-corrected transport scheme; the diffusion of NO is computed by a spectral solver. Simulations demonstrate the efficiency of the numerical methods employed.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76Z05 Physiological flows
76D05 Navier-Stokes equations for incompressible viscous fluids
92C10 Biomechanics
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