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

Abstract

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.

Micro to macro scale analysis of the intact human renal arterial tree with Synchrotron Tomography

“…Previously, computational models of mammalian renal blood flow have been derived from quantitative analysis of micro-CT images of the intact rat kidney vasculature [20][21][22] until now, it is not been possible to assess how these analyses compare to the human organ. We therefore compared our human kidney HiP-CT data with those derived from micro-CT data of rat, 5 relating normalised vessel metrics from each species at corresponding generations of the renal arterial network.…”

A Mathematical Model of Blood Loss during Renal Resection

“…Several existing works have contributed to the understanding of renal haemodynamics and blood flow autoregulation [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37], as well as stenosis in human or animal kidney models. For example, Sgouralis and Layton [38], Postnov et al [39], Cury et al [40], and Deng and Tsubota [41,42] offered key insights into healthy renal haemodynamics using various numerical modelling approaches. Specifically, Postnov et al [39] used a probability-based topological approach to develop a mathematical model of a kidney arterial network.…”