Thresholds for nonlinear effects in high- intensity focused ultrasound propagation and tissue heating

For a variety of reasons, including their simplicity and ability to capitalize upon superposition, linear acoustic propagation models are preferable to nonlinear ones in modeling the propagation of high-intensity focused ultrasound (HIFU) beams. However, under certain conditions, nonlinear models are necessary to accurately model the beam propagation and heating. In analyzing the performance of a HIFU system, it is advantageous to know before the analysis whether a linear model suffices. This paper examines the problem of determining the thresholds at which nonlinear effects become important. It is demonstrated that nonlinear interaction has different effects on different physical and derived quantities, such as compressional pressure, rarefactional pressure, intensity, heat rate, temperature rise, and thermal lesion volume. Thresholds are determined as a function of the dimensionless gain, nonlinearity, and absorption parameters. The relative difference between linear and nonlinear predictions is plotted as a series of contours, enabling practitioners to locate their system in parameter space and determine whether nonlinearity significantly affects the quantities of interest.