Stochastic ray tracing for simulation of high intensity focal ultrasound therapy

Abstract

An algorithm is presented for rapid simulation of high-intensity focused ultrasound (HIFU) fields. Essentially, the method combines ray tracing with Monte Carlo integration to evaluate the Rayleigh-Sommerfeld integral. A large number of computational particles, phonons, are distributed among the elements of a phase-array transducer. The phonons are emitted into random directions and are propagated along trajectories computed with the ray tracing method. As the simulation progresses, an improving stochastic estimate of the acoustic field is obtained. The method can adapt to complicated geometries, and it is well suited to parallelization. The method is verified against reference simulations and pressure measurements from an ex vivo porcine thoracic tissue sample. Results are presented for acceleration with graphics processing units (GPUs). The method is expected to serve in applications, where flexibility and rapid computation time are crucial, in particular clinical HIFU treatment planning.

Computationally Efficient Transcranial Ultrasonic Focusing: Taking Advantage of the High Correlation Length of the Human Skull

“…In this case, the computation time should be less than one minute. Three main categories of numerical acoustic propagation methods have been reported and can be listed in increasing complexity: ray tracing [27], angular spectrum methods [24] and full wave propagation [21,28]. The first two methods provide almost instantaneous results.…”

Improved intercostal HIFU ablation using a phased array transducer based on Fermat's spiral and Voronoi tessellation: A numerical evaluation

“…Within every plane of the modeled tissue stack, the steady‐state pressure field p ( r) was assumed to satisfy the linear wave equation: where is the Laplace operator, and k = ω / c − iα is the complex wave number determined by the angular frequency ω , the celerity c , and the attenuation coefficient α in the respective medium. Therefore, nonlinear wave propagation was not taken into account.…”

“…The steady‐state pressure field was calculated at 1.0 MHz in a reference plane positioned in the oil tank containing the transducer, perpendicular to the beam axis ( mm, = 513 × 513 pixels). For the clinical phased arrays, this pressure field was obtained through the far‐field approximation: where is the pressure induced by element i at the position of pixel j , is the directivity function, is the position vector of the center of element i , and is the position vector of pixel j . The pressure in each pixel j in the reference plane was thus obtained by summation of the pressure contributions from every transducer element i .…”

Development of focus controlling method with transcranial focused ultrasound aided by numerical simulation for noninvasive brain therapy

“…In future work on the method, in order to obtain a higher accuracy method with a short calculation time, the ray-tracing method can replace SR as the method of determining the phase of each element. 33) We will achieve an accurate and rapid method of determining the phase distribution by considering refraction at the interface between water and the skull, as well as the difference in the time of flight between all elements.…”