Mathematical modelling of atrial and ventricular pressure-volume dynamics and their change with heart rate

This paper presents mathematical models that can simulate the cardiovascular system of a healthy sheep under normal resting conditions in which the heart rate changes significantly. The models include several new modelling features that are introduced progressively. The contraction of the cardiac chambers is modelled using a time-dependent muscle force with constant elasticity instead of time dependent elasticity. A new hypothesis about the mechanical contraction of the atria generates realistic pressure volume (PV) loops. The inter-ventricular interaction is modelled as well. Additionally, hysteresis is incorporated in the aortic valve to produce an end-systolic reverse (negative) flow. Most of the model parameter values are based on previous literature data while time periods of delay, atrial and ventricular contraction are derived using experimental data from 14 sheep. We provide new relationships between contraction time and delay as a function of heart period. The effects of different aspects of our modelling on the mean cardiac output, stroke volume, ejection time, ejection fraction and PV loops are studied. Model outputs are compared with published experimental results where possible, and are within a wide range of physiological observations.