A Nonlinear State-Space Model of a Combined Cardiovascular System and a Rotary Pump

A nonlinear lumped parameter model of the cardiovascular system coupled with a rotary blood pump is presented. The blood pump is a mechanical assist device typically interposed from the left ventricle to the aorta in patients with heart failure. The cardiovascular part of the model (consisting of the left heart atrium and ventricle), and the systemic circulatory system are implemented as an RLC circuit with two diodes. The diodes represent the mitral and aortic valves in the left heart. The cardiovascular model has been validated with clinical data from a patient suffering from cardiomyopathy. The pump model is a first order differential equation relating pressure difference across the pump to flow rate and pump speed. The combined cardiovascular-pump model has been represented as a fifth order nonlinear dynamical system in state space form with pump speed as the control variable. This model was used to simulate the hemodynamic variables to different values of afterload and a linearly increasing (ramp) pump speed. Because of its small dimensionality, the model is suitable for both parameter identification and the application of modern control theory.