Elements Selection for Transcostal HIFU Refocusing Method: Simulation Study

Treatment of tumors in organs obscured by the ribs is a challenge for high-intensity focused ultrasound (HIFU) array. The ribs absorb the ultrasound beam's energy causing the temperature of the ribs to rise, the beam to be distorted, and the focal heat deposition to be limited. The challenges presented by the ribs motivated the development of the limited power deposition (LPD) refocusing algorithm, which is capable of limiting the power deposition over the ribs while maximizing the energy deposition at the focus, thus achieving an efficient and safe ablation. In this article, a new iterative sparse LPD (ISLPD) approach that provides similar focal heating to previously developed methods while reducing the number of transducers excited during the HIFU treatment is discussed. It will be possible to conduct processes, such as imaging and motion tracking in parallel with the HIFU treatment by using the elements no longer used by the refocusing technique. The approach removes transducer elements by using an iteratively reweighted penalty matrix to achieve a more sparse solution over the course of multiple rounds of sparsity induction by harshly punishing the use of elements that previously had low excitation magnitudes. The semidefinite relaxation (SDR) method is used as a means of relaxing the nonconvex constraints into convex form and induces sparsity using the one-norm squared as a convex surrogate for the zero-norm. A 1-MHz spherical phased-array focused on a target in an inhomogeneous medium is simulated to test the algorithms' efficacy. The propagation of the waves as they travel from the array toward the target was modeled using a finite-difference time-domain propagation model. Temperature simulations that utilized the inhomogeneous bioheat transfer equation (BHTE) were used to determine the temperature rise profile within the region of interest (ROI). These simulation results illustrate the benefits of the optimization-based approach proposed in this article over the ray-tracing (shadowing) method for element selection.