Title: Investigation of ultrasonic shock wave propagation and superharmonic field generation in human soft tissues

Authors: Narendra D. Londhe, R.S. Anand

Addresses: Electrical Engineering Department, IIT Roorkee, Roorkee-247667, Uttarakhand, India. ' Electrical Engineering Department, IIT Roorkee, Roorkee-247667, Uttarakhand, India

Abstract: In this paper, two theoretical methods for the description of non-linear ultrasound wave generated from axis symmetric circular source and propagation in soft human tissues has been described. Burgers| equation was used to model the non-linear propagation of single sinusoidal wave with finite amplitude. In the first method for lossless medium, the analytical solution of Burgers| equation has been achieved by using Fubini method in pre-shock region while weak shock theory was applied in post-shock region. In case of lossy medium, the analytical solution of Burgers| equation was achieved by using linear diffusion equation via Hopf-Cole transformation in pre-shock region and Fay|s equation in post-shock region. In the second method, the operator splitting methodology was implemented in which absorption term was solved using Crank Nicholson finite difference (CNFD) method and non-linear term by using analytical method at each step for both lossless and lossy medium. Both the methods were solved using 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 harmonic and superharmonic components variation along the distance of propagation has been studied using both proposed methods and their results have been compared.

Keywords: nonlinear waves; ultrasonic imaging; Burgers| equation; shock formation; soft tissue; ultrasonic shock waves; shock wave propagation; superharmonic field generation; waveform distortion; shock formation; circular piston; lossy tissue medium; lossless tissue medium.

DOI: 10.1504/IJMMNO.2010.035429

International Journal of Mathematical Modelling and Numerical Optimisation, 2010 Vol.1 No.4, pp.316 - 329

Published online: 30 Sep 2010 *

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