Effects of nonlinear ultrasound propagation on high intensity brain therapy

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Abstract
Purpose: As an ultrasound wave propagates nonlinearly, energy is transferred to higher frequencies where it is more strongly attenuated. Compared to soft tissue, the skull has strongly heterogeneous material parameters. The authors characterize with experiments and establish a numerical method that can describe the effects of the skull on the nonlinear components of ultrasonic wave propagation for application to high intensity focused ultrasound (HIFU) therapy in the brain. The impact of nonlinear acoustic propagation on heat deposition and thermal dose delivery is quantified and compared to linear assumptions by coupling an acoustic simulation with a heating model for brain tissue.Methods: A degassed dessicated human skull was placed in a water tank and insonified at 1 MPa with 7 mm transducer from a custom array designed for HIFU treatment. Two dimensional scans were performed preceding and following propagation through the skull with a calibrated hydrophone. Data from the scan preceding the skull were used as an input to a three dimensional finite difference time domain (FDTD) simulation that calculates the effects of diffraction, density, attenuation with linear dependence on frequency via relaxation mechanisms, and second order nonlinearity. A measured representation of the skull was used to determine the skull's acoustic properties. The validated acoustic model was used to determine the loss due to nonlinear propagation and then coupled to a finite difference simulation of the bioheat equation for two focal configurations at 3 and 7.5 cm from the skull surface.Results: Prior to propagation through the skull, the second harmonic component was 19 dB lower than the fundamental, and the third harmonic component was 37 dB lower. Following the skull, the second harmonic component was 35 dB lower and the third harmonic was 55 dB lower. The simulation is in agreement with the measurements to within 0.5 dB across the considered frequency range and shows good agreement across the two dimensional scan. It is then shown that the volume of treated brain is at least twice as large when assuming nonlinear acoustics.Conclusions: The authors have established a three dimensional FDTD simulation that accurately models the effects of nonlinearity and attenuation for propagation through the skull. Experimental validation shows good agreement across a broad frequency range and spatial extent. The nonlinear thermal dose was over an order of magnitude larger at the focus than the linear thermal dose and the necrotic volume was larger by at least a factor of 2. These results have particular applications to treatment planning.

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