An Intra-Cycle Optimal Control Framework for Ventricular Assist Devices Based on Atrioventricular Plane Displacement Modeling

Clemens Zeile,Jeremi Kaj Mizerski,Rüdiger C Braun-Dullaeus,Alexander Schmeisser,Thomas Rauwolf,Sebastian Sager

doi:10.1007/s10439-021-02848-2

Clemens Zeile, Jeremi Kaj Mizerski + Show 4 more

Open Access

https://doi.org/10.1007/s10439-021-02848-2

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Abstract

A promising treatment for congestive heart failure is the implementation of a left ventricular assist device (LVAD) that works as a mechanical pump. Modern LVADs work with adjustable constant rotor speed and provide therefore continuous blood flow; however, recently undertaken efforts try to mimic pulsatile blood flow by oscillating the pump speed. This work proposes an algorithmic framework to construct and evaluate optimal pump speed policies with respect to generic objectives. We use a model that captures the atrioventricular plane displacement, which is a physiological indicator for heart failure. We employ mathematical optimization to adapt this model to patient specific data and to find optimal pump speed policies with respect to ventricular unloading and aortic valve opening. To this end, we reformulate the cardiovascular dynamics into a switched system and thereby reduce nonlinearities. We consider system switches that stem from varying the constant pump speed and that are state dependent such as valve opening or closing. As a proof of concept study, we personalize the model to a selected patient with respect to ventricular pressure. The model fitting results in a root-mean-square deviation of about 6 mmHg. The optimization that considers aortic valve opening and ventricular unloading results in speed modulation akin to counterpulsation. These in silico findings demonstrate the potential of personalized hemodynamical optimization for the LVAD therapy.

Highlights

Left ventricular assist devices (LVADs) provide mechanical circulatory blood support and have become a well-established and successful therapy for end-stage heart failure patients with estimated more than 5000 implanted pumps annually worldwide.[16,28] The role of the heart assist devices is growing in recent years since there are major improvements in the long term treatment.[36]
Solving the parameter estimation (PE) problem from ‘‘Clinical Data and Model Personalization’’ section resulted in the values pÃ 1⁄4 1⁄2324:2; 0:6; 20:4; 4709; 900; 42; 25; 1:35; 0:5>: The result of the switching distance parameter, i.e. standard deviation (SD) 1⁄4 0:5, is equivalent to an atrioventricular plane displacement (AVPD) of only 10 mm and indicates a reduced ventricular function
We have proposed a novel switched systems algorithm for the optimal control of LVADs that provides the opportunity to calculate optimal constant, pwc, or continuous pump speed profiles

Summary

Introduction

Left ventricular assist devices (LVADs) provide mechanical circulatory blood support and have become a well-established and successful therapy for end-stage heart failure patients with estimated more than 5000 implanted pumps annually worldwide.[16,28] The role of the heart assist devices is growing in recent years since there are major improvements in the long term treatment.[36] Contemporary LVADs implement rotary continuous blood flow and are internally implanted in contrast to pulsatile and extracorporeal pumps, which represent the original LVAD design, but which are bigger, less durable, and more invasive than their continuous flow counterpart.[54]. For further details on the devices, the medical background, therapy planning and prognosis we refer to the reviews.[11,27,32,37]

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