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. 2021 Sep 21;49(12):3508–3523. doi: 10.1007/s10439-021-02848-2

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© The Author(s) 2021

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Illustration of the simplified model of the left heart, the circulatory system, and the LVAD. Differential states and the pump speed control u(t) are depicted in red. The cyclic flow is indicated by the arrows. The model consists of five compartments for the left atrium (LA), left ventricle (LV), aorta (A), systemic artery, and venous system, represented with the pressure functions P(t). These variables interact with the flows Q(t) in the LVAD and the aorta, while the AV interaction is modeled by the velocity v(t) and position s(t) of the atrioventricular plane displacement (AVPD). Compliance, resistance and inertance parameters C, R, L are depicted next to the corresponding compartment.