Modeling ventricular contraction with heart rate changes

Recently, a mathematical model of the pumping heart has been proposed describing the heart as a pressure source depending on time, volume and flow. The underlying concept is based on a new two-step paradigm that allows separation between isovolumic (non-ejecting) and ejecting heart properties. The first step describes the ventricular pressure in the isovolumic ventricle. In the following step, the isovolumic description is extended with the ejection effect in order to embrace the pumping heart during actual blood ejection. The description of the isovolumic heart properties plays a crucial role in this paradigm. However, only a single isovolumic model has previously been used restricting the heart rate to 1 Hz. In this paper, a family of models describing the isovolumic contracting ventricle are critically examined. A characterization of what constitutes an optimal model is given and used as a criteria for choosing the optimal model in this family. Moreover, and this is indeed a point, the proposed model in this study is valid for arbitrary heart rates and based on experimental data. The model exhibits all major features of the ejecting heart, including how ventricular pressure and flow vary in time for various heart rates and how stroke volume and cardiac output vary with heart rate. The modeling strategy presented embraces the same steps and demarcations as those suitable for clinical examination whereby new experiments are suggested.