Modeling mechanical alternans in the beating heart: advantages of a systems-oriented approach

A model employing an original discrete method is proposed to explain mechanical alternans in the beating heart. This is compared with analysis using the difference-equation method, which has been utilized in some other areas of science and found to better represent the cardiac beat-to-beat behavior. The model shows the critical role of a slope with an exact value of 2 in the functional dependence between stroke volume (SV) and the end-diastolic volume (EDV). The implications of this model with respect to the factors causing sustained mechanical alternans (SMA) in the heart are shown. A criterion for determining whether SMA is caused by variations in EDV is described. However, this possibility is ruled out on the basis of experimental findings. It is further shown that SMA caused primarily by alterations in the contractile state leads to secondary variations in EDV. In this case the model predicts that the mean slope of SV as a function of EDV, as determined by the two alternating beats, has a value of 2 and is independent of the SV-EDV relation. This prediction concerning the relationship between SV and EDV is confirmed by available experimental data. The implications and advantages of the modeling approaches are explored.