Nonlinear mechanics of the heart's swinging during pericardial effusion.

When excessive fluid accumulates in the pericardial space, the heart, suspended by the great vessels, is then free to swing as a pendulum. The swinging may occur at either the same frequency as the heart rate (1:1 oscillation) or at half the heart rate (2:1 oscillation), the latter frequency often arising during cardiac tamponade. We show that these two frequencies of oscillation may be explained by the nonlinearity of Newton's equation of motion as applied to the heart. Terms in the equation correspond to gravitational and buoyancy forces, forces due to ejection of blood into the great vessels, and damping forces. A transition between the 1:1 and 2:1 swinging is found to occur when particular parameters of the model are changed, notably when there is an increase of heart rate. This finding is compatible with previous clinical reports.