A 3-Dimentional Framework for Studying the Effects of Structural and Physical Properties of the Renal Outer Medulla on Urine Concentrating Mechanism

Abstract

Background: Many theories and mathematical simulations have been proposed concerning urine concentrating mechanism (UCM). Due to significant effect of the tubule and vessel architecture in concentrating mechanism, the numerical analysis of UCM through a 3-Dimensional structure might be the answer to find a better consistency between the experimental and theoretical results. Methods: In this paper we have investigated the effects of structural characteristics of the tubules and vessels on the urine concentrating mechanism in the outer medulla (OM) by developing a simple three-dimensional mathematical model. This model is a framework to attain a converged numerical solution for the momentum and species transport equations along with their stiff and coupled boundary conditions based on standard expressions for trans-tubular solutes and water transports on tubule’s membrane. Results: The model structure and the number of the involved tubules have been assumed to be as simple as possible. The effects of slip boundary condition on membrane, Darcy permeability and solute’s diffusivity of the intermediate media on UCM have been studied. It has been shown that this approach can simply simulate preferential interactions and tubule’s confinement by radial diffusion coefficients. Conclusions: All in all, the feasibility of the idea of completely 3-D modeling by employing the concept of diffusion coefficient and Darcy permeability has been explored and validated.