Object-oriented Modeling of Renal Autoregulation for a Cardiovascular System

Renal autoregulation maintains blood flow over a wide range of perfusion pressures despite pronounced nonlinear vessel mechanics and neurogenic influences. In lumped-parameter cardiovascular models, vascular beds are commonly represented by linear resistive elements, which are insufficient to reproduce characteristic pressure–flow relationships, critical closing pressure, and dynamic myogenic responses. In this work, a nonlinear representation of the renal vascular resistance is proposed based on an extended MOSFET-inspired circuit analogy. The model allows pressure-dependent conductance, flow limitation at low pressures, and systematic shifts of the pressure–flow characteristic under varying sympathetic activation. This approach enables a compact yet expressive description of arteriolar behavior within an electrical equivalent circuit framework. To emulate renal autoregulation, a phenomenological control concept is introduced that combines two complementary mechanisms acting on different time scales. A fast pressure-driven component represents the myogenic response to changes in perfusion pressure, while a slow adaptive component integrates flow error and aggregates the net effect of metabolic, renal, and humoral regulation. Physiological actuator dynamics are enforced using first-order dynamics, rate limiting, and saturation with anti-windup protection. Simulation results demonstrate that the proposed model reproduces key features of renal autoregulation, including a transient flow overshoot following pressure perturbations, subsequent active flow reduction, and restoration of renal blood flow toward a reference level over time. Static pressure–flow characteristics further exhibit an extended autoregulatory plateau and a pressure-dependent critical closing pressure. The presented approach provides a computationally efficient and physiologically interpretable extension of lumped-parameter cardiovascular models and is well suited for system-level simulations of renal hemodynamics.