Optimization of transcostal phased-array refocusing using sparse semidefinite relaxation method

Treating tumors in organs shadowed by the ribs is a challenge for high intensity focused ultrasound (HIFU). The ribs absorb energy from the ultrasound beams causing their temperature to rise, while also distorting the beams, and limiting the target heat deposition. Accordingly, it is necessary to devise focusing methods that address the difficulties presented by the ribs. In this paper, a new approach that reduces total power deposition on the region of interest (ROI) by removing transducer elements is introduced. The method builds on the limited power deposition (LPD) method, which took advantage of the semidefinite relaxation (SDR) method to relax nonconvex constraints into convex form. The method introduced in this paper induces sparsity using the one-norm squared. The results of using this method to focus a 1-MHz spherical phased array on a target in an inhomogeneous medium are presented and compared to the ray tracing (shadowing) approach [1]. A finite-difference time domain propagation model was used to model the wave propagation to the target. Temperature simulations that utilized the inhomogeneous bioheat transfer equation (BHTE) illustrate the advantages of the induced sparsity LPD method. Together, these simulation results illustrate the advantages of using optimization based on sparsity inducing techniques over the shadowing approach.