A levy flight model for ultrasound in skin tissues

Starting from the widely accepted point scattering model, this paper establishes through mathematical developments that ultrasound signals backscattered from skin tissues converge to a Levy Flight random process with non-Gaussian α-stable statistics. In addition, it is shown that this signal statistics imply that scatterers in skin have heavy-tailed power-law cross-sections. Therefore, this paper puts forward that the non-Gaussian nature of signals backscattered from skin arises a case limit, where both the number of scatterers and the variance of their cross-sections tend to infinity. Experimental results supported by excellent goodness-of-fit tests confirm the proposed analytical model. Finally, these fundamental results set the basis for new ultrasound-based skin characterization tools.