A quantitative systems physiology model of renal function and blood pressure regulation: Model description

Abstract

Renal function plays a central role in cardiovascular, kidney, and multiple other diseases, and many existing and novel therapies act through renal mechanisms. Even with decades of accumulated knowledge of renal physiology, pathophysiology, and pharmacology, the dynamics of renal function remain difficult to understand and predict, often resulting in unexpected or counterintuitive therapy responses. Quantitative systems pharmacology modeling of renal function integrates this accumulated knowledge into a quantitative framework, allowing evaluation of competing hypotheses, identification of knowledge gaps, and generation of new experimentally testable hypotheses. Here we present a model of renal physiology and control mechanisms involved in maintaining sodium and water homeostasis. This model represents the core renal physiological processes involved in many research questions in drug development. The model runs in R and the code is made available. In a companion article, we present a case study using the model to explore mechanisms and pharmacology of salt-sensitive hypertension.

Figure 1

Schematic representation of the model. Top left: The renal vasculature is modeled by a single preafferent resistance vessel flowing into N parallel nephrons. Bottom left: Sodium and water filtration through the glomerulus is modeled according to Starling's law. Sodium and water are reabsorbed at different fractional rates in the PT, LoH, DCT, and CNT/CD, and sodium and water excretion rates are determined from unabsorbed sodium and water. Top right: Sodium and water excretion feed into the cardiovascular portion of the model, where the balance between excretion and intake determines extracellular fluid volume, plasma sodium concentration, and ultimately cardiac output and MAP. Na concentration and MAP feed back into the renal model (left), closing the loop. Bottom right: Regulatory feedback mechanisms include the RAAS, TGF, myogenic autoregulation, RIHP regulation of tubular Na+ reabsorption, vasopressin regulation of tubular water reabsorption, and local blood flow autoregulation. Variables that provide functional links between the model components are shown in red. Variables that are sensed and drive feedback mechanisms are shown in green.

Figure 2

Impact of choice of controller gains for proportional‐integral feedback controllers on the response of cardiac output (a) and Na concentration (b) to a perturbation (step increase in Na intake). Gains were chosen so that these variables quickly returned to steady state without oscillations (yellow lines).