Contraction and relaxation-induced oscillations of the left ventricle of the heart during the isovolumic phases

A theoretical analysis is presented for the transient dynamical response of the left ventricle of the heart during the isovolumic contraction and relaxation phases of the cardiac cycle. Small oscillations of the left ventricular cavity pressure and wall motion are excited by the initial rates of filling and emptying of the ventricle as well as the rate of change in muscle fiber activation. The analysis applies to the genesis of the first and second heart sounds. The ventricle is modeled as a finite, thick-walled incompressible cylinder having a continuum of imbedded axial and circumferential active muscle fibers, which interacts with a fixed volume of an incompressible, ideal fluid. The solution is obtained using a two-timing asymptotic expansion procedure. The theoretical calculations of left ventricular pressure waveforms compare favorably with published recorded pressure waveforms. The amplitude spectra of computed waveforms contain information concerning the active elastic modulus of the fibers, which is a measure of cardiac contractility.