The role of acoustic nonlinearity in tissue heating behind a rib cage using a high-intensity focused ultrasound phased array

The goal of this study was to investigate theoretically the effects of nonlinear propagation in a high-intensity focused ultrasound (HIFU) field produced by a therapeutic phased array and the resultant heating of tissue behind a rib cage. Three configurations of focusing were simulated: in water, in water with ribs in the beam path and in water with ribs backed by a layer of soft tissue. The Westervelt equation was used to model the nonlinear HIFU field, and a 1 MHz phased array consisting of 254 circular elements was used as a boundary condition to the model. The temperature rise in tissue was modelled using the bioheat equation, and thermally necrosed volumes were calculated using the thermal dose formulation. The shapes of lesions predicted by the modelling were compared with those previously obtained in in vitro experiments at low-power sonications. Intensity levels at the face of the array elements that corresponded to the formation of high-amplitude shock fronts in the focal region were determined as 10 W cm−2 in the free field in water and 40 W cm−2 in the presence of ribs. It was shown that exposures with shocks provided a substantial increase in tissue heating, and its better spatial localization in the main focal region only. The relative effects of overheating ribs and splitting of the focus due to the periodic structure of the ribs were therefore reduced. These results suggest that utilizing nonlinear propagation and shock formation effects can be beneficial for inducing confined HIFU lesions when irradiating through obstructions such as ribs. Design of compact therapeutic arrays to provide maximum power outputs with lower intensity levels at the elements is necessary to achieve shock wave regimes for clinically relevant sonication depths in tissue.