Nonlinear control of a hybrid pneumo-hydraulic mock circuit of the cardiovascular system

Abstract

Hybrid cardiovascular mock circuits (HMC), designed for dynamic testing of Ventricular Assist Devices (VAD), offer physiologic accuracy by sequestering model complexity in silico and ease of construction by reducing number of model elements in vitro. Despite superior response time and precision, pneumatic actuation is avoided in HMCs due to nonlinear dynamics and noise. We tested the hypothesis that a HMC consisting of a variable elastance-driven numerical cardiovascular circuit (CVS) coupled to a pneumo-hydraulic physical circuit can be controlled without linearizing system dynamics. Reference left ventricular and aortic pressures were generated in silico in a seventh-order electrical analogue of the CVS and transmitted via an electro-hydraulic interface to the physical circuit. There, they were tracked in in vitro preload and afterload pneumo-hydraulic reservoirs, respectively. The nonlinear pneumatic dynamics in the reservoirs was controlled using the Lyapunov stability criterion. A centrifugal pump, the speed (i.e., flow) of which was adjusted manually or using PID control, was interposed between the reservoirs and mimicked the VAD under evaluation. The flow of a recirculating gear pump was controlled by an integral backstepping method to equalize reservoir fluid volumes by rejecting pressure and flow disturbances. Sensor noise was reduced with discrete-time Kalman filtering. Our results showed that normal, failing, and assisted cardiovascular physiologies simulated in silico were commensurate with clinical data obtained from subjects with similar pathologies. The numerical pressure references were tracked with high accuracy at the physical VAD terminals. Reservoir volumes remained stable at various combinations of heart rate, pressure, and VAD flow for prolonged durations with negligible steady-state error. The HMC described here offers a stable performance testing platform for VAD prototypes.