Imaging the ultrasonic coefficient of nonlinearity: The impact of speed of sound variations

Imaging the acoustical coefficient of nonlinearity, β, is of interest in a number of healthcare interventional applications. For cardiac ablation therapy, detecting the protective fibrofatty layer between the atrial wall and the esophagus would provide risk assessment with respect to esophageal injury. The coefficient of nonlinearity β is an important feature that can be used for discriminating between tissues. Starting from a 1D inhomogeneous generalized lossy nonlinear Westervelt equation, we derived an analytical solution for β, which is then further adapted to work in echo mode. By considering the ratio between the harmonic and fundamental fields, the influence of spatial variations in backscatter coefficient and spatial absorption variations are mitigated. By testing the method on simulations that range from a 1D plane wave excitation with inhomogeneous nonlinearity and absorption, to a 3D linear array scan that also considers inhomogeneities in speed of sound, we show that the designed algorithm is able to estimate the coefficient of nonlinearity, and that the tissue types of interest are well discriminable. The proposed imaging method provides a new approach to β estimation, not requiring a special measurement setup or transducer, that seems particularly promising for in vivo imaging.