Loop analysis of blood pressure/volume homeostasis

by Bruno Burlando, Franco Blanchini, Giulia Giordano

We performed a mathematical analysis of the dynamic control loops regulating the vasomotor tone of vascular smooth muscle, blood volume, and mean arterial pressure, which involve the arginine vasopressin (AVP) system, the atrial natriuretic peptide system (ANP), and the renin-angiotensin-aldosterone system (RAAS). Our loop analysis of the AVP-ANP-RAAS system revealed the concurrent presence of two different regulatory mechanisms, which perform the same qualitative function: one affects blood pressure by regulating vasoconstriction, the other by regulating blood volume. Both the systems are candidate oscillators consisting of the negative-feedback loop of a monotone system: they admit a single equilibrium that can either be stable or give rise to oscillatory instability. Also a subsystem, which includes ANP and AVP stimulation of vascular smooth muscle cells, turns out to be a candidate oscillator composed of a monotone system with multiple negative feedback loops, and we show that its oscillatory potential is higher when the delays along all feedback loops are comparable. Our results give insight into the physiological mechanisms ruling long-term homeostasis of blood hydraulic parameters, which operate based on dynamical loops of interactions.