Dynamic modeling of variable speed left ventricular assist devices coupled to the cardiovascular system.

Background: Most of the modeling of the Left Ventricular Assist Devices (LVADs) coupled with the cardiovascular system is based on the assumption of constant rotational speed. Compared with the traditional inertial model, the validated hysteresis model can take into account the unsteady characteristics of LVADs, but it fails to work under the condition of variable speed modulation.

Method: This study takes into consideration the impact of speed variations on the unsteady hysteresis effects. The time constant in the hysteresis model is treated as a time-varying parameter, thereby developing a new model applicable to variable speed modulation. Under sinusoidal speed modulation at various phases, a comparative analysis was undertaken among the steady-state model, inertial model, and the new model. Transient Computational Fluid Dynamics (CFD) simulations and existing experimental results are used for validation.

Results: The new model provides a more accurate method for the predicting the characteristics of LVAD in the coupled model under varying pump speeds, and exhibits higher linearity in the work done by the left ventricle and the blood pump, and $R^2=0.9998$, which is aligning closely with the experimental results. This enhancement renders it applicable for proactive control predictions and passive control validations.