Numerical Modeling and Simulation of Blood Flow in a Rat Kidney: Coupling of the Myogenic Response and the Vascular Structure

A numerical simulation was carried out to investigate the blood flow behavior (i.e., flow rate and pressure) and coupling of a renal vascular network and the myogenic response to various conditions. A vascular segment and an entire kidney vascular network were modeled by assuming one single vessel as a straight pipe whose diameter was determined by Murray's law. The myogenic response was tested on individual AA (afferent artery)-GC (glomerular capillaries)-EA (efferent artery) systems, thereby regulating blood flow throughout the vascular network. Blood flow in the vascular structure was calculated by network analysis based on Hagen-Poiseuille's law to various boundary conditions. Simulation results demonstrated that, in the vascular segment, the inlet pressure P-inlet and the vascular structure act together on the myogenic response of each individual AA-GC-EA subsystem, such that the early-branching subsystems in the vascular network reached the well regulated state first, with an interval of the inlet as P-inlet = 10.5-21.0 kPa, whereas the one that branched last exhibited a later interval with P-inlet = 13.0-24.0 kPa. In the entire vascular network, in contrast to the P-inlet interval (13.0-20.0 kPa) of the unified well-regulated state for all AA-GC-EA subsystems of the symmetric model, the asymmetric model exhibited the differences among subsystems with P-inlet ranging from 12.0-17.0 to 16.0-20.0 kPa, eventually achieving a well-regulated state of 13.0-18.5 kPa for the entire kidney. Furthermore, when P-inlet continued to rise (e.g., 21.0 kPa) beyond the vasoconstriction range of the myogenic response, high glomerular pressure was also related to vascular structure, where P(GC )of early-branching subsystems was 9.0 kPa and of late-branching one was 7.5 kPa. These findings demonstrate how the myogenic response regulates renal blood flow in vascular network system that comprises a large number of vessel elements.

Automated summary

A numerical simulation was conducted to study the blood flow behavior and the coupling of a renal vascular network and the myogenic response. The results showed that the myogenic response can regulate blood flow in the vascular network, with the early-branching subsystems reaching the regulated state first and the late-branching subsystems reaching it later. The asymmetric model exhibited differences among subsystems.