Wave Refraction Effects in High Intensity Focused Ultrasound

Abstract

High-Intensity Focused Ultrasound (HIFU) is a promising field of research being developed as an alternative to surgery and radiation therapy for the treatment of tumours. Within this field, many current methods of calculation/simulation use approximations rather than solve the Partial Differential Equation (PDE) directly. We consider the linear acoustic equation with and without damping for a material with spatially varying properties. Our approach used spectral methods to manage the derivatives and solve the PDE. We started from the basics to tune our intuition for the problem. This allowed us to discuss some effects of phenomenological damping and to study the effects of wave reflection and refraction. Further, we were able to use these tools to investigate a possible cause of unexpected heating found clinically. To this end we used spectral numerical methods to solve the equation and applied stochastic analysis to examine the effects of variations in a few of the relevant parameters (sound speeds and the radius of an anomaly) on the outcome. This model highlighted the fact that, due to the reflection and refraction of the ultrasound waves, more heating may occur inside obstacles in the treatment path than previously expected. The stochastic review found that discrepancies in the radius of the obstacle has a much larger impact on the outcome of the HIFU treatment than discrepancies in the parameters for the speed of sound in the various media. Thus more time and resources should be allocated to properly mapping and measuring the size and shape of obstacles in the treatment path as opposed to improving the exactness of the values for the speeds of sound.