NSF Award
2451193
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.<br/><br/>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.<br/><br/>This project is funded in part by the Historically Black Colleges and Universities - Excellence in Research (HBCU-EiR) program.<br/><br/>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.
