A Multicellular Vascular Model of the Renal Myogenic Response

Modeling the interaction between tubuloglomerular feedback and myogenic mechanisms in the control of glomerular mechanics

Introduction: Mechanical stresses and strains exerted on the glomerular cells have emerged as potentially influential factors in the progression of glomerular disease. Renal autoregulation, the feedback process by which the afferent arteriole changes in diameter in response to changes in blood pressure, is assumed to control glomerular mechanical stresses exerted on the glomerular capillaries. However, it is unclear how the two major mechanisms of renal autoregulation, the afferent arteriole myogenic mechanism and tubuloglomerular feedback (TGF), each contribute to the maintenance of glomerular mechanical homeostasis. Methods: In this study, we made a mathematical model of renal autoregulation and combined this model with an anatomically accurate model of glomerular blood flow and filtration, developed previously by us. We parameterized the renal autoregulation model based on data from previous literature, and we found evidence for an increased myogenic mechanism sensitivity when TGF is operant, as has been reported previously. We examined the mechanical effects of each autoregulatory mechanism (the myogenic, TGF and modified myogenic) by simulating blood flow through the glomerular capillary network with and without each mechanism operant. Results: Our model results indicate that the myogenic mechanism plays a central role in maintaining glomerular mechanical homeostasis, by providing the most protection to the glomerular capillaries. However, at higher perfusion pressures, the modulation of the myogenic mechanism sensitivity by TGF is crucial for the maintenance of glomerular mechanical homeostasis. Overall, a loss of renal autoregulation increases mechanical strain by up to twofold in the capillaries branching off the afferent arteriole. This further corroborates our previous simulation studies, that have identified glomerular capillaries nearest to the afferent arteriole as the most prone to mechanical injury in cases of disturbed glomerular hemodynamics. Discussion: Renal autoregulation is a complex process by which multiple feedback mechanisms interact to control blood flow and filtration in the glomerulus. Importantly, our study indicates that another function of renal autoregulation is control of the mechanical stresses on the glomerular cells, which indicates that loss or inhibition of renal autoregulation may have a mechanical effect that may contribute to glomerular injury in diseases such as hypertension or diabetes. This study highlights the utility of mathematical models in integrating data from previous experimental studies, estimating variables that are difficult to measure experimentally (i.e. mechanical stresses in microvascular networks) and testing hypotheses that are historically difficult or impossible to measure.

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 Pinlet 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 Pinlet = 10.5–21.0 kPa, whereas the one that branched last exhibited a later interval with Pinlet = 13.0–24.0 kPa. In the entire vascular network, in contrast to the Pinlet 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 Pinlet 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 Pinlet 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 PGC 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.