Theoretical analysis of the hemodynamic variables during sustained mechanical alternans: effect of variations in ventricular filling volume.

A comprehensive discrete analysis of the hemodynamic variables during sustained mechanical alternans (SMA) shows that these variables are governed by simple mathematical relations. The analysis shows that the value of the slope created by the two alternating beats on the stroke volume-end diastolic (SV-EDV) plane is gamma = (mu - 1).(1 + beta)/(mu - beta), where mu = SVS/SVW, SVS and SVW denote the strong and weak beats, respectively, in the presence of one contractile state of the beating heart, and the beats associated with the higher and lower contractile states, respectively, in the presence of two alternating contractile states; beta = FVS/FVW, FVS and FVW are the filling volumes following SVS and SVW, respectively. Two separate analyses show that this equation is valid, whether SMA is exhibited in the presence of one or two contractile states, and irrespective of the SV-EDV functional relationship. A criterion based on this slope, in terms of measurable parameters, is described to determine if SMA is caused by variations in EDV and FV. This comprehensive quantitative analysis enables a complete classification of the various types of SMA into subcategories with well-defined features. In particular, this analysis confirms former interesting theoretical consequence that when FV is constant, gamma attains the value of 2, independently of the value of mu or any other factor.