The ventricular-arterial coupling system can be analyzed by the eigenwave modes of the whole arterial system

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.