CDI-Type II: Collaborative Research - Simulation of ultrasonic-wave propagation with application to cancer therapy.

该项目开发并实现了非线性偏微分方程（PDE）的最新“傅立叶延拓交替方向”（FC-AD）高性能算法，通过与实验和已知近似的比较验证了这些解算器，并将所得方法应用于实际的医疗配置。研究的一个重要部分是设计策略，以显著扩大高强度聚焦超声（HIFU）的适用性（一种新兴的微创治疗方法，使用聚焦超声束引起癌症组织的局部破坏），并设计出肝癌、肾癌和胰腺癌的最佳HIFU治疗方法。在HIFU中，超声源与患者皮肤接触，在体内产生高振幅超声场，聚焦（并加热）目标区域，从而导致肿瘤破坏。超声波在高度不均匀的介质中传播——由于骨骼的原因，这种传播最强烈——从而影响加热，例如，通过大血管的灌注产生的加热。最佳HIFU需要一个治疗计划计算工具，以确保治疗目标区域和对周围组织的影响最小。由于以前的3D PDE求解器更昂贵，因此不可能解决如此复杂的HIFU问题。利用交替方向和非周期函数的快速收敛傅立叶级数，提出的FC-AD方法首次为一般三维域提供了高阶无条件稳定数值，其代价仅随空间离散化的大小线性增长；初步试验表明，FC-AD方法能够令人满意地解决所考虑的非线性声学问题的类型。这种方法将使研究非均质性对场聚焦、热沉积和烧蚀性能的影响成为可能，从而实现高度优化的HIFU治疗。相关的几何/计算需求为我们的求解器、几何建模工具等的额外开发提供了强大的推动力。提议的多学科互动将进一步显著地在所有三个领域的艺术状态：计算科学，非线性波物理和癌症治疗。该项目的更广泛意义：超声已经是一种完善的医学成像技术，它在诊断和治疗方面的应用越来越广泛，从肿瘤检测到肾结石破坏，再到靶向药物输送。超声图像的准确性，以及超声传递能量或改变组织结构的精度和可靠性，都主要取决于这种努力所产生的软件类型，这种软件提供了预测超声场在生物介质中的传播特性的能力。由此产生的方法将适用于广泛的生物医学超声-实现快速仪器原型，治疗计划和超声安全评估。虽然工作计划的重点是基于hifu的癌症治疗建模，但在多种治疗和诊断应用中影响关键进展的潜力是非常重要的。

The project develops and implements recent "Fourier continuation alternating direction" (FC-AD) high-performance algorithms for nonlinear Partial Differential Equations (PDE), validates such solvers via comparisons with experiments and well-known approximations, and applies the resulting methodology to realistic medical configurations. A significant portion of the effort will design strategies to expand significantly the applicability of High-Intensity-Focused-Ultrasound (HIFU) (an emerging minimally invasive therapy that uses focused ultrasound beams to cause localized destruction of cancer tissue), and to enable design of optimal HIFU therapies for liver, kidney, and pancreatic cancers. In HIFU, an ultrasound source acoustically contacts the patient's skin to produce a high-amplitude ultrasonic field within the body that focuses on (and heats) a target region---thus leading to tumor destruction. The ultrasound propagates within a medium that is highly heterogeneous---most strongly so due to bone---thus affecting heating, which arises, for example, through perfusion by large blood vessels. Optimal HIFU requires a treatment-planning computational tool, which ensures treatment of the targeted zone and minimal impact on the surrounding tissue. Because previous 3D PDE solvers are more expensive, solution of such complex HIFU problems has not been possible. Using alternating directions and a rapidly convergent Fourier series for non-periodic functions, the proposed FC-AD method has provided for the first time high-order unconditionally stable numerics for general 3D domains at a cost that grows only linearly with the size of the spatial discretization; preliminary tests have demonstrated the capability of the FC-AD method to address satisfactorily the types of nonlinear acoustic problems under consideration. This approach will make possible the study of the effect of heterogeneity on field focusing, heat deposition, and ablation properties - enabling highly optimized HIFU treatment. The associated geometric/computational demands provide a powerful driving force for additional developments of our solvers, geometry modeling tools, etc. The proposed multi-disciplinary interactions will further significantly the state of the art in all three fields: computational science, nonlinear wave physics, and cancer therapy.Broader Significance of the Project: Already a well-established technique for medical imaging, ultrasound is seeing widening use in diagnostic and therapeutic applications ranging from tumor detection, to kidney stone destruction, to targeted drug delivery. Both the accuracy of ultrasound images, and the precision and reliability with which ultrasound can deliver energy or modify the structure of tissue, depend critically on the type of software that will result from this effort, providing a capability to predict the propagation properties of ultrasonic fields in biological media. The resulting methodology will be applicable across the broad spectrum of biomedical ultrasonics - enabling rapid instrument prototyping, treatment planning, and ultrasound safety assessment. Although the work plan is focused on the modeling of HIFU-based cancer treatment, the potential for effecting key advances in multiple therapeutic and diagnostic applications is very significant.