A proposed microscopic elastic wave theory for ultrasonic backscatter from myocardial tissue

The physical structures responsible for ultrasonic scattering from myocardial tissue have not yet been conclusively defined. It is hypothesized in this paper that the backscatter from myocardium is primarily due to inhomogeneities approximately the size of the myocytes. In particular, it is proposed that the acoustic contrast responsible for the scattering is that between the extracellular collagen network that surrounds each myocyte (or myocyte bundle) and the rest of the tissue (the myocytes' intracellular contents). To test this hypothesis, a simple elastic wave scattering model for myocardium was developed. An elementary scatterer is modeled as an ellipsoidal shell, having the material properties of wet collagen, imbedded in a host medium having the average properties of myocardium. The first Born approximation to elastic scattering is used to calculate the frequency-dependent scattering from a single scatterer. To scale up from a single scatterer to a distribution of scatterers, it is assumed that the power received at the transducer is simply the sum of the power scattered in the direction of the transducer by each individual scatterer located in the active volume of the beam (an independent-scatterer approximation). Calculations are restricted to the backscattering direction (pulse-echo), although the theory can accommodate pitch-catch scattering at all angles. With the aid of a computer program, the acoustic backscatter coefficient is calculated using the Born formalism and then measurement effects (frequency-dependent beam width and attenuation correction factors) are incorporated to arrive at calculated integrated (frequency-averaged) backscatter. Both the backscatter coefficient and integrated backscatter are calculated for angles of incidence that range from parallel to the long axis of the scatterer to perpendicular to this fiber direction. For the low MHz frequencies typically used in clinical echocardiography, the calculated absolute magnitude of the acoustic backscatter coefficient lies within a range from 0.0001 to 0.001 cm-1 sr-1. For selected fiber geometries, the anisotropy in integrated backscatter as the angle of incidence is varied with respect to the fiber orientation is about 10 dB. The predicted frequency dependence of the acoustic backscatter coefficient is calculated to be about f3.9 in the low MHz frequency range. These calculated results are reasonably consistent with published experimental measurements and provide a successful preliminary test of the hypothesis.