Time-varying elastance models (TVEMs) are often used for simulation studies of the cardiovascular system with a left ventricular assist device (LVAD). Because these models are computationally expensive, they cannot be used for long-term simulation studies. In addition, their equilibria are periodic solutions, which prevent the extraction of a linear time-invariant model that could be used e.g. for the design of a physiological controller. In the current paper, we present a new type of model to overcome these problems: the mean-value model (MVM). The MVM captures the behavior of the cardiovascular system by representative mean values that do not change within the cardiac cycle. For this purpose, each time-varying element is manually converted to its mean-value counterpart. We compare the derived MVM to a similar TVEM in two simulation experiments. In both cases, the MVM is able to fully capture the inter-cycle dynamics of the TVEM. We hope that the new MVM will become a useful tool for researchers working on physiological control algorithms. This paper provides a plant model that enables for the first time the use of tools from classical control theory in the field of physiological LVAD control.
Keywords: Linear time-invariant model; Model-based controller design; Physiological control; Time-varying elastance model.