A Mathematical Model of Renal Blood Distribution Coupling TGF, MR and Tubular System

Objective:To investigate the relationship between renal blood distribution and the physiological activities of the kidney. Methods:A mathematical model is developed based on Hagan-Poiseuille law and mass transport, coupling mechanics of myogenic response (MR), tubuloglomerular feedback (TGF) and the tubular system in the renal medulla. The model parameters, including the permeability coefficients, the vascular lumen radius and the solute concentration at the inlet of the tubes, are derived from the experimental results. Simulations of the blood and water flow in the loop of Henel, the collecting duct and vas rectum, are carried out by the model of the tubular system in the renal medulla, based on conservations of water and solutes for transmural transport. Then the tubular model is coupled with MR and TGF mechanics. Results:The results predict the dynamics of renal autoregulation on its blood pressure and flow,and the distributions are 88.5% in the cortex, 10.3% in the medulla, and 1.2% at papilla,respectively. The fluid flow and solute concentrations along the tubules and vasa recta are obtained. Conclusion:The present model could assess renal functions qualitatively and quantitatively and provide a methodological approach for clinical research.