Liver Backscatter and the Hepatic Vasculature’s Autocorrelation Function

Abstract

Ultrasound imaging of the liver is an everyday, worldwide clinical tool. The echoes are produced by inhomogeneities within the interrogated tissue, but what are the mathematical properties of these scatterers? In theory, the spatial correlation function and the backscatter coefficient are linked by a Fourier transform relationship, however direct measures of these are relatively rare. Under the hypothesis that the fractal branching vasculature and fluid channels are the predominant source of scattering in normal tissues, we compare theory and experimental measures of the autocorrelation function, the frequency dependence of scattering, and fractal dimension estimates from high contrast 3D micro-CT data sets of rat livers. The results demonstrate a fractal dimension of approximately 2.2 with corresponding power law estimates of autocorrelation and ultrasound scattering. These results support a general framework for the analysis of ultrasound scattering from soft tissues.

Keywords

• scattering
• backscatter
• ultrasound
• tissue
• medical ultrasound
• fractal vasculature
• tissue characterization