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

该项目开发并实现了最新的“傅立叶延拓交替方向”（FC-AD）高性能算法，用于非线性偏微分方程（PDE），通过与实验和众所周知的近似比较来验证此类求解器，并将所得方法应用于现实的医疗配置。这项工作的一个重要部分将设计策略，以显着扩大高强度聚焦超声（HIFU）（一种新兴的微创治疗，使用聚焦超声波束造成局部破坏的癌症组织）的适用性，并使设计的最佳HIFU治疗肝癌，肾癌和胰腺癌。在HIFU中，超声源声学接触患者的皮肤，在体内产生高振幅的超声场，聚焦（并加热）目标区域-从而导致肿瘤破坏。超声波在一种高度异质的介质中传播-最强烈的是由于骨-从而影响加热，例如，通过大血管的灌注产生加热。最佳的HIFU需要一个治疗计划计算工具，以确保治疗的目标区域和周围组织的影响最小。由于先前的3D PDE求解器更昂贵，因此不可能解决这种复杂的HIFU问题。使用交替方向和快速收敛的傅立叶级数的非周期函数，建议的FC-AD方法提供了第一次高阶无条件稳定的数值一般的3D域的成本，仅线性增长的空间离散化的大小;初步测试已经证明了FC-AD方法的能力，令人满意地解决所考虑的非线性声学问题的类型。这种方法将使研究异质性对场聚焦、热沉积和消融特性的影响成为可能-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、几何建模工具等的进一步发展提供了强大的驱动力。所提出的多学科互动将显著地进一步推动计算科学、非线性波物理和癌症治疗这三个领域的最新技术水平。超声已经是一种成熟的医学成像技术，在诊断和治疗应用中的应用越来越广泛，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可以传递能量或修改组织结构的精度和可靠性都严重依赖于将从这种努力中产生的软件类型，从而提供预测生物介质中超声场传播特性的能力。由此产生的方法将适用于广泛的生物医学超声-使快速仪器原型，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实现关键进展的潜力非常重要。

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.