First Mathematical Model Able to Reproduce the Heart Function: Ventricular Numerical Modelling.

In this section is described the first numerical model of the (left or right) ventricle. In this model the ventricular filling and ejection phases are described separately. The contraction and ejection phases are implemented using a modified variable elastance model.

In Eq. 1, P(t) is the instantaneous ventricular pressure, V(t) is the instantaneous ventricular volume and V_{0} is the rest volume at zero pressure. In the left upper panel is plotted the ventricular loop on the pressure-volume plane. ESPVR (EDPVR) is the End Systolic (Diastolic) Pressure Volume Relationship. Ved (Ves) is the end diastolic (systolic) ventricular volume and SV is the stroke volume.

Instantaneous Ventricular Elastance Equation with Variable V_{0}(t).

Equation 2 is based on the hypothesis tht the relation between the ventricular volume and pressure is linear. The ventricular elastace E(t) changes with the contractility state of the myocardium.

Ventricular Filling Phase in the First Ventricular Numerical Model.

Equation 5 reproduces the ventricular filling phase with the EDPVR. Changing the value of the constants (C, D, E, k and j) it is possible to obtain different EDPVR lines that intersect the volume axis in different V_{0} points.

This simple model of the atrial activity is described as a linear capacity characterised by a constat value of compliance and unstressed volume, i.e. the contractile activity of the atrium was neglected.