Simulation of ultrasound backscatter coefficient measurement using the finite element method

Ultrasound backscatter coefficient (BSC) measurement is a method for assessing tissue morphology that can inform on pathologies such as cancer. The BSC measurement is, however, limited by the accuracy with which the investigator can normalise their results to account for frequency dependent effects of diffraction and attenuation whilst performing such measurements. We propose a simulation-based approach to investigate the potential sources of error in assessing the BSC. Presented is a tool for the 2D Finite Element (FE) simulation mimicking a BSC measurement using the planar reflector substitution method in reduced dimensionality. The results of this are verified against new derivations of BSC equations also in reduced dimensionality. These new derivations allow computation of BSC estimates based on the scattering from a 2D scattering area, a line reference reflector and a theoretical value for the BSC of a 2D distribution of scatterers. This 2D model was designed to generate lightweight simulations that allow rapid investigation of the factors associated with BSC measurement, allowing the investigator to generate large data sets in relatively short time scales. Under the conditions for an incoherent scattering medium, the simulations produced BSC estimates within 6% of the theoretical value calculated from the simulation domain, a result reproduced across a range of source f-numbers. This value of error compares well to both estimated errors from other simulation based approaches and to physical experiments. The mathematical and simulation models described here provide a theoretical and experimental framework for continued investigation into factors affecting the accuracy of BSC measurements.