The ventricular-arterial coupling system can be mathematically modeled using eigenwave modes of the arterial system to understand the matching of natural frequencies with heart rate.
This eigenmode model extends arterial wave analysis; leaves open whether natural frequency matching with heart rate improves clinical outcomes.
In response to harmonic forces generated by the heart, the arterial system executes strong coupled distributed oscillatory motions. These oscillations are described by a pressure-area wave equation, which is solvable subject to appropriate Sturm–Liouville boundary conditions. The response pressure can be represented as a sum of stationary waves which are the eigenmodes of the whole arterial system. Natural frequencies of the system are related to the eigenvalues and the phase velocity. Matching of these natural frequencies with heart rate or its harmonics is important in ventricular-arterial coupling. Transfer functions for the pressure can be constructed from the corresponding eigenfunctions.
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Wang et al. (2008) studied this question.
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