Ultrasound Shock Wave Propagation and Generation of Harmonics in Biological Tissues

In this paper, two theoretical methods for the description of nonlinear ultrasound wave generated from axis symmetric circular source and propagation in soft human tissues is described. Burgers’ equation has been used to model the nonlinear propagation of single sinusoidal wave of finite amplitude. In the first method, the analytical solution of Burgers’ equation was achieved by using Fubini method in preshock region while weak shock theory applied in postshock region for lossless medium. In case of lossy medium, the analytical solution of Burgers’ equation is achieved by using linear diffusion equation via Hopf-Cole transformation in preshock region and Fay’s equation in postshock region. In the second method the operator splitting methodology is implemented in which absorption term is solved using Crank Nicholson Finite Difference (CNFD) method in time and nonlinear term by using analytical method at each step for both lossless and lossy medium. Both the methods are solved in MATLAB. The results have been shown for waveform distortion and shock formation radiated by circular piston source for lossless and lossy tissue mediums. The analytical study of fundamental, second and third harmonic components variation along the distance of propagation has been done using both proposed methods and has been compared.