The mathematical rules governing the hemodynamic variables during mechanical alternans in the beating heart

Discrete methods compatible with the discrete features of the beating heart are used to attain a quantitative understanding of the transient response due to a perturbation and sustained mechanical alternans (SMA) in the beating heart. A first-order difference equation describes the SV (stroke volume) response resulting from the Frank-Starling mechanism. It is shown that the value of γ, the slope of the SV-EDV (end diastolic volume) curve, determines the type of response obtained as a result of perturbation. When the effect of opening aortic pressure (p) is also considered, SV response is determined by a second-order difference equation. It is shown that the hemodynamic variables during SMA are governed by a simple mathematical relation, independent of its primary cause and the SV-EDV functional relationship. A criterion for the determination of the causative factor of SMA, in terms of measurable parameters, is described