Data-driven discovery of sparse dynamical model of cardiovascular system for model predictive control.

Cardiovascular diseases remain the leading cause of death globally. In recent years, vagal nerve stimulation (VNS) has shown promising results in the treatment of a number of cardiovascular diseases. In this approach, mild electrical pulses are sent to the brain via the vagus nerve. This open-loop neurostimulation, however, leads to various side effects due to physiological and inter-patient variability and therefore a closed-loop delivery strategy of electrical pulses that accounts for this variability is desired. In this context, we envision data-driven sparse dynamical model parameterized by patient-specific data as appropriate for use in closed loop controller design. In this work, we build a dynamical model for mean arterial pressure and heart rate using the method sparse identification of nonlinear dynamics (SINDy). As a proxy for real datasets or measurements from a patient, we simulate a mechanistic model from the literature and then discover a data-driven model for predicting mean arterial pressure and heart rate in response to neural stimulus. This discovered model is then used to design a controller to be implemented in closed-loop via model predictive control. We observe that this data-driven model is interpretable, consistent with experiments, provides insights on the sensitivity of different stimulation locations and simplifies the formulation of the optimal control problem. Noting the set-point tracking performance of this closed-loop model-based controller that uses this discovered model, we conclude that the model is adequate in capturing the dynamics of a highly nonlinear cardiovascular system for the purpose of optimal predictive controller design.