A Nonlinear Model for Flow Estimation and Control in a Percutaneous Heart Assist System

A percutaneous ventricular assist device (pVAD) is an external heart assist system that bypasses blood from left atrium, right atrium, or femoral vein, and returns it to femoral artery to support patients who suffer from acute heart failure. The system typically consists of a blood pump (the VAD), a venous or atrial drainage cannula, and an arterial perfusion cannula. Because the device usually allows cardiologists the freedom of choosing the arterial cannula size and configuration based on a patient´s body size, it is extremely difficult but important to predict the amount of blood flow the device can provide to the patient before the device is implanted and is up and running. In this paper, the pVAD system is modeled as a nonlinear electric circuit, including a speed dependent voltage source and current dependent resistors to simulate the pressure- flow relationship in the cannulae. The model structure is developed based upon the theory of fluid flow in pipes and the model parameters are identified by least-squares fit of the model to the experimental data. The blood flow rate provided by the system is determined by solving a quadratic equation whose coefficients are determined based on the sizes and configurations of the arterial cannulae. The model was tested on the tandem heart pVAD (Cardiac Assist Inc., Pittsburgh, PA) and was shown to be able to predict the flow rates accurately with error indices for all test conditions less than 6%, when comparing the predicted flow rates from the model with the experimental data. Also, computer simulation of the pVAD system with a cardiovascular model showed that the accuracy of the model in estimating the flow rate is robust regardless of the interaction between the device and the cardiovascular system. In addition to being able to estimate the flow given the sizes of the cannulae, this model can also be used to control the pump speed to achieve a desired flow for a given cannula configuration.