Vibrations of the Semilunar Valve Modeled by an Elastic Stretched Membrane in a Fluid

Аннотация

A modified model for the operation of the semilunar valve is proposed, which makes it possible to estimate the spectrum of acoustic oscillations that occur as it closes. The authors have analyzed closing of the pulmonary valve cusps under a drop in pressure in the pulmonary artery and the right ventricle. Filling of the semilunar valve cusps with blood was taken into account, which leads to an increase in its closing time. This time increases in proportion to the square root of the increase in mass. The second part of the article considers elastic vibrations of a valve that is already closed. The vibrations involve both the cusps and walls of the pulmonary artery, as well as the surrounding fluid. The simplest model of this complex oscillatory system can be an elastic stretched membrane immersed in a fluid and excited by a pulsed force action from the side of the closing valve cusps. It is demonstrated that the second heart sound, heard during auscultation, is a train of damped oscillations, the ultimate duration of which is controlled by the hydraulic resistance of the vibrating cusps. Both the closing process and excited vibrations are nonlinear and multimode. The spectrum and duration of vibrations depend on their amplitude and tension of the valves. The average vibration frequency decreases with time. These results can be useful both for understanding the physical features of the process and for developing new diagnostic methods. In particular, increased pressure in the pulmonary artery can be diagnosed by increasing the frequency and decay time of vibrations in the pulmonary component of the second heart sound.