A New Computational Framework for Superior Image Reconstruction in Limited Data Quantitative Photoacoustic Tomography

癌症是美国第二大死因，仅次于心脏病。预计到2023年，美国将有超过60万人死于癌症。癌症患者死亡率高背后的主要因素之一是癌症的晚期诊断，因为大多数癌症没有出现早期症状。因此，开发快速有效的靶向治疗癌症患者的需求尚未得到满足。为此，生物医学成像是建立癌症临床方案的重要组成部分，有助于获得癌症形成和扩散的重要解剖、结构和功能信息。特别是混合成像方法，它使用耦合波的物理，提供癌组织的定量信息，以指导更好的诊断，分期和治疗计划。其中一种混合成像方法是定量光声断层扫描（QPAT），它使用短脉冲近红外光和超声波传播数据来重建癌组织中的高保真光学特性，如光吸收和散射剖面。然而，一些实际的挑战，如缺乏足够的数据集和组织中声速的不确定性，限制了现有计算方法在定量光声断层扫描中的重建质量。该项目将数学博弈论和统计敏感性分析的理论和计算方法结合在一起，以解决上述挑战，并提供高质量的QPAT重建。因此，它将有助于促进对癌变组织进行精确的有针对性的成像，并改善临床结果，从而有助于实现美国卫生与人类服务部的战略目标之一，即“保障和改善国家和全球健康状况和结果”。此外，该项目将为本科生和研究生提供独特的跨学科研究和培训经验，特别是来自代表性不足的群体，并将促进数学家，统计学家和放射科医生在生物医学成像领域的跨学科合作。本课题的科学目标是建立一类新的精确、快速、稳定和鲁棒的非线性重建方案，以解决QPAT中出现的有限数据混合成像问题。为了实现这一目标，具体的研究目标是：(1)开发一种新的无梯度纳什博弈计算方案，用于光声层析成像中未知声速和光能密度的数据补全和识别；(2)构建一种新的高对比度、高分辨率光学参数重建的无梯度优化方案；(3)利用统计敏感性分析对Nash算法进行稳定化和校正，得到QPAT中稳定的重构方法。计算框架将使用小鼠标本的实时光声数据进行验证。该项目还旨在为有限数据反问题的计算方法提供一种新的范例，与现有的计算框架相比，这种计算方法产生的计算成本低、稳定和优越的重建，因此将有利于有效检测癌症。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Cancer is the second leading cause of death in the USA, behind heart disease. In 2023, over 600,000 cancer deaths are projected to occur in the USA. One of the primary factors behind the high death rate for cancer patients is the late diagnosis of cancer, since most cancers do not present early symptoms. Thus, there is an unmet need to develop fast and effective targeted therapies for treating cancer patients. For this purpose, biomedical imaging is a crucial component for establishing clinical protocols in cancer by helping obtain important anatomical, structural, and functional information of cancer formation and spread. In particular hybrid imaging methods, which use physics of coupled waves, provide quantitative information of cancerous tissues to guide better diagnosis, staging, and treatment planning. One such hybrid imaging method is quantitative photoacoustic tomography (QPAT) that uses short-pulse near infrared light and ultrasound propagation data to reconstruct high-fidelity optical properties, like light absorption and scattering profiles, in cancerous tissues. However, several practical challenges, like lack of adequate datasets and uncertainty of sound speed in tissues, limit the quality of reconstructions with existing computational methods in quantitative photoacoustic tomography. This project brings together a novel combination of theoretical and computational methods in mathematical game theory and statistical sensitivity analysis to tackle the aforementioned challenges and provide high quality reconstructions in QPAT. As a result, it will help facilitate accurate targeted imaging of cancerous tissues and improve clinical outcomes, thereby contributing to one of the strategic goals of USA Heath and Human Services to “Safeguard and Improve National and Global Health Conditions and Outcomes”. Furthermore, this project will provide a unique interdisciplinary research and training experience for undergraduate and graduate students, especially from underrepresented groups, and will facilitate interdisciplinary collaboration between mathematicians, statisticians, and radiologists in the field of biomedical imaging.The scientific goal of this project is to build a new class of accurate, fast, stable and robust non-linear reconstruction schemes for solving limited data hybrid imaging problems arising in QPAT. For achieving this goal, the specific research objectives are to (1) develop a new gradient-free Nash games computational scheme for data completion and identification of unknown sound speed and optical energy density in photoacoustic tomography; (2) build a new gradient-free optimization scheme for reconstruction of optical parameters with high contrast and resolution; and (3) use statistical sensitivity analysis to stabilize and calibrate the Nash algorithm for obtaining a stable reconstruction method in QPAT. The computational framework will be validated using real-time photoacoustic data of mice specimens. The project also aims at providing a new paradigm in computational methods for limited data inverse problems that yields computationally inexpensive, stable and superior reconstructions in comparison to existing computational frameworks, and thus will be beneficial for effective detection of cancers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.