Fundamental modeling of wave propagation in temporally relaxing media with applications to cardiac shear wave elastography

Abstract

Shear wave elastography (SWE) might allow non-invasive assessment of cardiac stiffness by relating shear wave propagation speed to material properties. However, after aortic valve closure, when natural shear waves occur in the septal wall, the stiffness of the muscle decreases significantly, and the effects of such temporal variation of medium properties on shear wave propagation have not been investigated yet. The goal of this work is to fundamentally investigate these effects. To this aim, qualitative results were first obtained experimentally using a mechanical setup, and were then combined with quantitative results from finite difference simulations. The results show that the amplitude and period of the waves increase during propagation, proportional to the relaxation of the medium, and that reflected waves can originate from the temporal stiffness variation. These general results, applied to literature data on cardiac stiffness throughout the heart cycle, predict as a major effect a period increase of 20% in waves propagating during a healthy diastolic phase, whereas only a 10% increase would result from the impaired relaxation of an infarcted heart. Therefore, cardiac relaxation can affect the propagation of waves used for SWE measurements and might even provide direct information on the correct relaxation of a heart.