A new current-based control model of the combined cardiovascular and Rotary Left Ventricular Assist Device

Rotary Left Ventricular Assist Devices (LVAD) are mechanical pumps implanted in patients with congestive heart failure to assist their heart in pumping the required amount of blood in the circulatory system. Until recently, the combined mathematical model of the LVAD coupled with the left ventricle has assumed the availability of the rotational speed of the pump as the independent control variable. In reality, however, the device is controlled by the pump motor current which, in turn, produces the desired rotational speed of the pump motor. Therefore, the actual implementation of any desired speed controller for the device requires the solution of an inverse problem in order to determine the corresponding motor current that yields the desired pump speed. Recently, it has been observed from in-vivo experiments that an LVAD that is controlled by a motor current with a given profile (constant or ramp-like) has yielded a corresponding pump speed that exhibits a superposition of an oscillatory component which is synchronized with the pulsatility of the heart hemodynamic variables. Because of this, it has become evident that the solution of this inverse problem is extremely difficulty to accomplish. In this paper, we reformulate the existing combined LVAD and left ventricle model in such a way so as to introduce the pump motor current instead of the pump speed as the control variable, hence avoiding the inverse problem altogether. This new model is not only a more realistic representation of the LVAD control variable but also is much more practical in that it allows for the derivation of a controller directly in terms of the pump motor current rather than indirectly in terms of its rotational speed. Validation of this model and the challenges involved in using it when designing a feedback controller for the LVAD are also discussed.