Investigation of ultrasonic shock wave propagation and superharmonic field generation in human soft tissues (Q614199)

Summary: Two theoretical methods for the description of nonlinear ultrasound waves generated from an axis symmetric circular source and propagation in soft human tissues has been described. Burgers' equation was used to model the nonlinear propagation of single sinusoidal waves with finite amplitude. In the first method for a lossless medium, the analytical solution of Burgers' equation has been achieved by using the Fubini method in pre-shock region while weak shock theory was applied in the post-shock region. In case of a lossy medium, the analytical solution of Burgers' equation was achieved by using linear diffusion equations via a Hopf-Cole transformation in the pre-shock region and Fay's equation in the post-shock region. In the second method, the operator splitting methodology was implemented in which the absorption term was solved using the Crank Nicholson finite difference (CNFD) method and a nonlinear term by using an analytical method at each step for both the lossless and the lossy medium. Both the methods were solved using MATLAB. The results have been shown for waveform distortion and shock formation radiated by a circular piston source for lossless and lossy tissue mediums. The analytical study of fundamental, second harmonic and superharmonic components variation along the distance of propagation has been studied using both proposed methods and their results have been compared.