LEAPS-MPS: Deep Quasi-Reversibility Inversion for Source Localization Oncological Problems

脑肿瘤是最致命的癌症之一，影响着全世界数百万人。仅在美国，每年就有成千上万的成人和儿童被诊断为原发性脑肿瘤。对于肿瘤学家、神经学家和其他参与该领域的科学家来说，一个关键的焦点是确定肿瘤的具体解剖起源位置。了解这个位点可能有助于深入了解肿瘤的行为方式，预测它可能引起的症状，以及识别与脑肿瘤高度相关的遗传综合征。因此，这些来源信息对脑癌的早期发现有重要的帮助。本项目研究了一种可靠高效的反演算法——深度拟可逆性法（Deep quasi - reverbility Method， DQRM），可以快速重建原发肿瘤的位置。通过积极让本科生参与研究活动和促进院校之间的合作，该项目将有助于脑肿瘤患者的福祉，并有助于培养熟练的STEM劳动力。该项目以历史悠久的HBCU为基础，从而为扩大参与STEM的研究提供了机会。该项目包括对所提出的DQRM进行数值和理论研究，以解决不同复杂程度的源定位肿瘤学问题。该方法结合了变分拟可逆性（QR）方法和深度学习无网格算法。该设计将计算数学、偏微分方程和机器学习技术结合在一起，以快速提供可靠和准确的准解。一方面，变分QR方法可以克服局部特征、高动态非线性和重建过程固有的指数不稳定性。另一方面，深度学习方法处理维度的诅咒和与数据测量相关的成本。该项目的第一个目标是研究反求解器在处理与肿瘤细胞进化动力学相关的准线性抛物模型中的有效性。第二步是通过结合考虑年龄、大小和空间结构等因素的先进肿瘤生长模型来研究该算法的适用性。理论主题是围绕神经网络逼近器对拟解的收敛性。该项目部分由传统黑人学院和大学卓越研究（HBCU-EiR）项目资助。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。

Brain tumors are among the most fatal cancers, affecting millions of individuals worldwide. In the United States alone, each year thousands of adults and children receive a primary brain tumor diagnosis. A key focus for oncologists, neurologists, and other scientists involved in the field is in determining the specific anatomical origin site of the tumor. Knowing this site might help in gaining insights in how the tumor behaves, in predicting the symptoms it is likely to cause, and in identifying genetic syndromes that have a high association with brain tumors. Therefore, this source information can be an important aid in the early detection of brain cancer. This project studies a reliable and efficient inversion algorithm called Deep Quasi-Reversibility Method (DQRM) that can quickly reconstruct the primary tumor’s location. By actively involving undergraduate students in research activities and fostering collaborations between institutions, the project will contribute to the well-being of individuals affected by brain tumors as well as help to cultivate a skilled STEM workforce. The project is based at a long-established HBCU, thus providing an opportunity to broadening research participating in STEM.The project involves numerical and theoretical studies of the proposed DQRM for solving the source localization oncological question with different levels of complexity. The DQRM is a combination of a variational quasi-reversibility (QR) method and a deep learning mesh-free-based algorithm. The design brings together techniques of computational mathematics, partial differential equations, and machine learning to fast deliver a reliable and accurate quasi-solution. On one hand, the variational QR approach can overcome localized features, highly dynamic nonlinearities, and the inherent exponential instability of the reconstruction process. On the other, the deep learning approach handles the curse of dimensionality and the costs associated with data measurement. The first objective of the project is to study the effectiveness of the inverse solver in tackling the quasi-linear parabolic models associated with the evolutionary dynamics of tumor cells. The second is to investigate the applicability of the algorithm by incorporating an advanced tumor growth model that considers factors such as age, size, and spatial structure. The theoretical theme is centered around the convergence of a neural network approximator towards the quasi-solution.This project is funded in part by the Historically Black Colleges and Universities - Excellence in Research (HBCU-EiR) program.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.