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A Personalized Switched Systems Approach for the Optimal Control of Ventricular Assist Devices based on Atrioventricular Plane Displacement

View ORCID ProfileClemens Zeile, Thomas Rauwolf, Alexander Schmeisser, Jeremi Kaj Mizerski, Rüdiger C. Braun-Dullaeus, Sebastian Sager
doi: https://doi.org/10.1101/2020.05.27.119149
Clemens Zeile
1Institute of Mathematical Optimization, Otto-v.-Guericke-Universität, Universitätspl. 2, 39106 Magdeburg, Germany
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  • ORCID record for Clemens Zeile
  • For correspondence: clemens.zeile@ovgu.de
Thomas Rauwolf
3Department of Cardiology, Otto-v.-Guericke-Universität, Leipziger Str. 44, 39120 Magdeburg, Germany
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Alexander Schmeisser
3Department of Cardiology, Otto-v.-Guericke-Universität, Leipziger Str. 44, 39120 Magdeburg, Germany
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Jeremi Kaj Mizerski
1Institute of Mathematical Optimization, Otto-v.-Guericke-Universität, Universitätspl. 2, 39106 Magdeburg, Germany
2Department of Heart Surgery, SPSW im. pap. Jana Pawła II, Aleja Jana Pawła II 10, 22-400 Zamość, Poland
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Rüdiger C. Braun-Dullaeus
3Department of Cardiology, Otto-v.-Guericke-Universität, Leipziger Str. 44, 39120 Magdeburg, Germany
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Sebastian Sager
1Institute of Mathematical Optimization, Otto-v.-Guericke-Universität, Universitätspl. 2, 39106 Magdeburg, Germany
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Abstract

Objective 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.

Methods 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.

Results 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. Optimized constant and piecewise constant rotor speed profiles improve the default initialized solution by 31% and 68% respectively.

Conclusion These in silico findings demon-strate the potential of personalized hemodynamical optimization for the LVAD therapy.

Significance LVADs and their optimal configuration are active research fields. Mathematical optimization enhances our understanding of how LVADs should provide pulsatility.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • C. Zeile (clemens.zeile{at}ovgu.de), J. Mizerski (jeremi.mizerski{at}ovgu.de) and S. Sager (sager{at}ovgu.de) T Rauwolf (thomas.rauwolf{at}med.ovgu.de), A. Schmeisser (alexander.schmeisser{at}med.ovgu.de) and R. C. Braun-Dullaeus (r.braun-dullaeus{at}med.ovgu.de)

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted May 30, 2020.
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A Personalized Switched Systems Approach for the Optimal Control of Ventricular Assist Devices based on Atrioventricular Plane Displacement
Clemens Zeile, Thomas Rauwolf, Alexander Schmeisser, Jeremi Kaj Mizerski, Rüdiger C. Braun-Dullaeus, Sebastian Sager
bioRxiv 2020.05.27.119149; doi: https://doi.org/10.1101/2020.05.27.119149
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A Personalized Switched Systems Approach for the Optimal Control of Ventricular Assist Devices based on Atrioventricular Plane Displacement
Clemens Zeile, Thomas Rauwolf, Alexander Schmeisser, Jeremi Kaj Mizerski, Rüdiger C. Braun-Dullaeus, Sebastian Sager
bioRxiv 2020.05.27.119149; doi: https://doi.org/10.1101/2020.05.27.119149

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