Impeller-pump model derived from conservation laws applied to the simulation of the cardiovascular system coupled to heart-assist pumps

Previous numerical models of impeller pumps for ventricular assist devices utilize curve-fitted polynomials to simulate experimentally-obtained pressure difference versus flow rate characteristics of the pumps, with pump rotational speed as a parameter. In this paper the numerical model for the pump pressure difference versus flow rate characteristics is obtained by analytic derivation. The mass, energy and angular momentum conservation laws are applied to the working fluid passing through the impeller geometry and coupled with the turbomachine's velocity diagram. This results in the construction of a pressure difference versus flow rate characteristic for the specific pump geometry, with pump rotational speed as parameter. Overall this model allows modifications of the pump geometry, so that the pump avoids undesirable operating conditions, such as regurgitant flow. The HeartMate III centrifugal pump is used as an example to demonstrate the application of the technique. The parameterised numerical model for HeartMate III derived by this technique is coupled with a numerical model for the human cardiovascular system, and the combination is used to investigate the cardiovascular response under different conditions of impeller pump support. Conditions resulting in regurgitant pump flow, the pump resulting in aortic valve closure and taking over completely the pumping action from the diseased heart, and inner ventricular wall suction at pump inlet are predicted by the model. The simulation results suggest that for normal HeartMate III operation the pump speed should be maintained between 3,100 and 4,500 rpm to avoid regurgitant pump flow and ventricular suction. To obtain optimal overall cardiovascular system plus pump response, the pump operating speed should be 3,800 rpm.