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Nonlinear mechanics of the heart's swinging during pericardial effusion
1Department of Medicine, Beth Israel Hospital, Boston, Massachusetts.
Insights
The heart
Area of Science:
- Cardiovascular dynamics
- Biophysics
- Nonlinear mechanics
Background:
- Excess pericardial fluid can cause the heart to swing like a pendulum.
- This swinging can occur at 1:1 or 2:1 frequencies relative to heart rate.
- 2:1 oscillation is often observed in cardiac tamponade.
Purpose of the Study:
- To explain the dual frequencies of heart swinging using Newton's equation of motion.
- To investigate the transition between 1:1 and 2:1 oscillation frequencies.
- To correlate model findings with clinical observations of cardiac tamponade.
Main Methods:
- Applied nonlinear Newton's equation of motion to the heart's pendulum-like motion.
- Incorporated terms for gravitational, buoyancy, blood ejection, and damping forces.
- Analyzed model parameters to identify conditions causing frequency transitions.
Main Results:
- Nonlinearity of Newton's equation explains 1:1 and 2:1 heart swinging frequencies.
- Model predicts a transition between 1:1 and 2:1 oscillations.
- Increased heart rate is a key parameter influencing this transition.
Conclusions:
- The nonlinear dynamics of the heart can account for observed pendulum-like swinging frequencies.
- Model findings support clinical observations linking heart rate changes to oscillation patterns in conditions like cardiac tamponade.
- This biophysical model provides a framework for understanding heart motion under fluid accumulation.
Abstract:
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.