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.

中文翻译：

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经肋HIFU重聚焦方法的要素选择：仿真研究。

对于高强度聚焦超声（HIFU）阵列来说，对肋骨遮挡的器官中的肿瘤进行治疗是一项挑战。肋吸收超声波束的能量，从而引起肋的温度升高，波束变形以及聚焦热沉积受到限制。肋骨所带来的挑战推动了有限功率沉积（LPD）重新聚焦算法的发展，该算法能够限制肋骨上的功率沉积，同时最大化聚焦处的能量沉积，从而实现高效且安全的消融。在本文中，将讨论一种新的迭代式稀疏LPD（ISLPD）方法，该方法可提供与以前开发的方法类似的聚焦加热，同时减少HIFU治疗期间激发的换能器的数量。可以进行流程，例如，通过使用再聚焦技术不再使用的元素，与HIFU处理并行进行成像和运动跟踪。该方法通过使用迭代重新加权的罚矩阵来去除换能器元素，从而通过严厉地惩罚以前具有低激励幅度的元素的使用，在多轮稀疏感应的过程中获得更稀疏的解决方案。半定性松弛（SDR）方法用作将非凸约束松弛为凸形式的方法，并使用一模平方作为零模的凸替代物来引起稀疏性。模拟了聚焦在非均匀介质中目标上的1 MHz球形相控阵，以测试算法的功效。使用有限差分时域传播模型对电波从阵列向目标的传播进行了建模。利用非均质生物热传递方程（BHTE）进行的温度模拟可用于确定目标区域（ROI）内的温度上升曲线。这些仿真结果说明了本文提出的基于优化的方法相对于用于元素选择的光线跟踪（阴影）方法的好处。