Modeling Blood Flow Control in the Kidney

The ability of vascular beds to maintain nearly constant blood flow despite large fluctuations in blood pressure is known as blood flow autoregulation. Impaired autoregulation in the kidney is both a symptom of and a contributing factor to the progression of diseases such as hypertension and diabetes. Obtaining a better understanding of renal autoregulation under both physiological and pathological conditions will lead to improved methods for controlling the progression of kidney-related diseases. Mathematical modeling based on experimental observations has become an important tool for investigating and understanding mechanisms of autoregulation and feedback in the kidney and is used here to describe blood flow control in the kidney under healthy and diabetic conditions. The model presented here couples two autoregulation mechanisms to the transport of chloride ions in the kidney, generating new insight into how blood flow in the kidneys of healthy and diabetic patients changes in response to increased blood pressure or impaired regulatory mechanisms.

The mathematical model developed in this study describes the dynamics of blood flow regulation in a single nephron, the functional unit of the kidney. The model includes two primary mechanisms of kidney autoregulation, the myogenic response and tubuloglomerular feedback (TGF), which constrict or dilate the afferent arteriole (vessel that supplies blood to the nephron upstream of the glomerular filtration unit) in response to changes in blood pressure and chloride ion concentration, respectively. The model is composed of two parts: (1) a millimeter-scale blood vessel wall mechanics model describing the nonlinear effects of the myogenic and TGF responses and (2) a molecular-scale mechanistic model of chloride ion transport in the loop of Henle (the salt/fluid reabsorption portion of the nephron downstream of the glomerular filtration unit). The model also accounts for the lag time dynamics associated with communicating the measured chloride concentration at the outlet of the loop of Henle to the smooth muscle cells of the afferent arteriole. Model parameters for physiological and diabetic conditions were taken or estimated from the experimental literature. The resulting system of delay differential equations was solved numerically using the delay differential equation solver DDE23 in MATLAB.

The model was used to study the isolated and combined effects of the myogenic and TGF mechanisms as blood pressure varies. The model predicts stable glomerular filtration rate within a physiological range of perfusion blood pressure (60–180 mmHg). The results indicate that the myogenic response contributes more significantly than the TGF mechanism to the autoregulation of blood flow, and the contribution of TGF to overall autoregulation is significant only within a narrow band of perfusion pressure values near the baseline. The coupled dynamic model predictions of kidney blood flow are consistent with experimental observations [1]‑[5]. Model simulations of renal autoregulation in diabetic patients show a significant 60% increase in kidney blood flow, largely due to simulated impairment of voltage-gated calcium ion channels of the smooth muscle cells in the afferent arteriole that prevent constriction of the vessel. The present model was also used for bifurcation analysis to investigate how changes in key model parameters and system perturbations affect autoregulation dynamics.

References:

[1] LG Navar et al., Kidney Int, 1998, 54:S17-21.

[2] RJ Roman, Am J Physiol, 1986, 251:F57-65.

[3] RJ Roman et al., Am J Physiol, 1985, 248:F199-205.

[4] CM Sorensen et al., Am J Physiol, 2000, 279:R1017-1024.

[5] SJ Van Dijk et al., Kidney Int, 2006, 69:1369-1376.