Extensions of the Immersed Interface Method to Open Tube Interfaces and Hemodynamic Models

Blood flow can be modeled as a fluid-structure interaction problem in which the vessel is represented as an infinitely thin elastic interface that exerts a singular force on the internal and surrounding fluid. The immersed interface method was created to solve this type of immersed boundary problem with second-order accuracy in space and time. However, the interface must be a closed shape, which is not conducive to modeling flow in a vessel.

An extension of the immersed interface method to also solve immersed boundary problems where the interface is shaped like an open tube that transverses the fluid domain is presented. Numerical results indicate that this method converges with second order in both space and time and can sharply capture discontinuities in the fluid solutions.

Additionally, mathematical models for simulating renal blood flow under physiological and pathophysiological conditions are presented.

In particular, models simulating the myogenic response to changes in systolic blood pressure in the afferent arteriole and models simulating

the effect of pericyte contractions on vascular congestion in the descending vasa recta is considered.