Contribution of multiple scattering to the trabecular bone backscatter - dependence on porosity and frequency

Scattering-based ultrasonic methods potentially enable assessment of microscopic structure of bone. In our previous study we have shown how to account the higher orders of scattering in the backscatter evaluation. Here, the role of multiple scattering in bone backscatter is assessed for the varying bone porosity. The set of integral equations corresponding to the singular Sturm-Liouville equation was solved numerically allowing for the calculation of the field scattered forward and backward in the bone model. The results indicate that for the porosities below 85% the approximation of the first order scattering is not valid for all considered frequencies. The Laue's equations were applied to explain considerable increase of the scattering at some frequencies. It was shown that the deformation of trabecular mesh results in flattening of the scattering peaks.