Modeling the instantaneous pressure-volume relationship in the left ventricle

Pressure-volume loops are a common modeling tool of the cardiovascular system. They are very useful because they characterize the global function of the cardiac pump and can also be analyzed by considering the various phases of the cardiac cycle and marking each point of a cycle with the corresponding time. When several loops are considered, the points corresponding to the same time t in each loop can be joined to define a curve named isochrone. In this work, we are interested in models of the instantaneous pressure-volume relationship, i.e. isochrone models. More precisely, we concentrate on the 6 models considered by Lankhaar et al. [1] and we propose a critical analysis of the work of these authors and suggest some improvement of their procedure.
[1] Lankhaar J.W. et al. Annals of Biomedical Engineering,
Volume 37, Number 9, 1710-1726, 2009.