Numerical Optimal Control of Turbo Dynamic Ventricular Assist Devices

Raffael Amacher,Marianne Daners,Gregor Ochsner,Hendrik Tevaearai,Alois Amstutz,Stijn Vandenberghe,André Plass,Jonas Asprion,Markus Wilhelm

doi:10.3390/bioengineering1010022

Raffael Amacher, Marianne Daners + Show 7 more

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https://doi.org/10.3390/bioengineering1010022

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Abstract

The current paper presents a methodology for the derivation of optimal operating strategies for turbo dynamic ventricular assist devices (tVADs). In current clinical practice, tVADs are typically operated at a constant rotational speed, resulting in a blood flow with a low pulsatility. Recent research in the field has aimed at optimizing the interaction between the tVAD and the cardiovascular system by using predefined periodic speed profiles. In the current paper, we avoid the limitation of using predefined profiles by formulating an optimal-control problem based on a mathematical model of the cardiovascular system and the tVAD. The optimal-control problem is solved numerically, leading to cycle-synchronized speed profiles, which are optimal with respect to an arbitrary objective. Here, an adjustable trade-off between the maximization of the flow through the aortic valve and the minimization of the left-ventricular stroke work is chosen. The optimal solutions perform better than constant-speed or sinusoidal-speed profiles for all cases studied. The analysis of optimized solutions provides insight into the optimized interaction between the tVAD and the cardiovascular system. The numerical approach to the optimization of this interaction represents a powerful tool with applications in research related to tVAD control. Furthermore, patient-specific, optimized VAD actuation strategies can potentially be derived from this approach.

Highlights

Ventricular assist devices (VADs) are mechanical systems aimed at supporting the blood circulation in patients with severe heart failure
We present a methodology that circumvents the limitation of preselecting a certain speed profile by the application of model-based numerical optimization
A sinusoidal speed profile synchronized to the cardiac cycle or a speed profile obtained from the numerical solution of an optimal-control problem (OCP) was applied

Summary

Introduction

Ventricular assist devices (VADs) are mechanical systems aimed at supporting the blood circulation in patients with severe heart failure. After five decades of intensive development, various devices have become increasingly applied, typically as a “bridge to transplantation”, i.e., for patients with no other alternative left [1]. By assisting and, unloading the failing cardiac ventricle, VADs have been shown to contribute to some degree to myocardial recovery [2,3]. Feedback control strategies to physiologically adapt the operation of turbo dynamic VADs (tVADs) to the oxygen demand and to optimize left-ventricular unloading have been subject to continuous research [5,6,7,8,9,10]. A square-wave speed profile was applied by Bearnson et al [11] and Bourque et al [12]

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