Nonlinear Heart Model Predicts the Range of Heart Rates for Electrical Alternans in Pericardial Effusion
Report ID: TR-365-92Author: Widman, Lawrence / Sacks, Elisha
Date: 1992-02-00
Pages: 14
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Abstract:
We analyze Rigney and Goldberger's [8] two mathematical models of the heart's rocking during pericardial effusion. Both models examine the torques due to the outflow of blood from the heart. The first assumes that the duration of systole varies linearly with heart rate, whereas the second assumes that it does not vary with heart rate. The analysis predicts the motion of the heart for heart rates between 50 and 200 and for a range of initial positions and velocities. The first model predicts that the heart rocks once every other beat (exhibits electrical alternans) at heart rates between 88 and 119 and rocks once per beat otherwise, and explains the appearance and disappearance of alternans mathematically. The results agree within 5% with the published clinical data, which shows alternans at heart rates between 90 and 124. The second model predicts the same qualitative behavior, but with alternans occurring solely at heart rates between 105 and 116. We describe an analysis program for ordinary differential equations that analyzed the models quickly and automatically.