Analytical and Computational Approaches for Quantitative Tomography of Tissue

该项目将基于耦合物理反问题，通过成像生物物质的电特性来开发新的非侵入性定量层析成像方法。这项研究有望为当前医疗诊断实践和生物医学研究中使用的数据解码提供新的技术，为比现有方法更高精度和分辨率的新成像方法提供理论基础。电导率和介电常数的定量分布可以区分良、恶性肿瘤，可用于监测肺功能、胸血容量、体温升高、重症监护新生儿的胃肠功能等。本项目将加深对数据中信息内容的理解，并使用最佳测量次数来生成具有各向异性结构的生物组织的定量图像。该项目的另一个方面是开发稳健的方法，产生与对比度最佳的频率相对应的生物结构的定量图像。因此，它将通过在较小范围内对生物过程进行成像，为生物学研究提供新的工具。在项目过程中，研究生将接受跨学科研究领域的培训。该项目的发现将被整合到中央佛罗里达大学的学生研讨会和数学、物理和工程专业的一门特别主题课程中。该项目将非线性逆问题的数学分析的新进展与传感器设计和数据采集的工程进步相结合，旨在改变当前一些工程实践中的范式。该项目的分析部分位于非线性反问题、几何、最优化和几何测量理论的交叉点。首席调查员(PI)计划改进物理模型中出现的各向异性最小梯度问题的现有知识，使其更接近实际工程实践。特别是，PI试图通过使用最小内部数据来确定在双张量重建中生物组织的各向异性结构。这个项目的另一个方面是试图通过将麦克斯韦电磁学的非线性逆问题技术与磁自旋共振的量子模型相结合，在射频下产生复杂生物结构的定量图像。该项目还旨在通过图形或神经网络来确定具有无限极限对比度的材料中的电导率分布。根据分析结果，重建方法将被翻译成算法并在模拟数据上进行测试。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project will develop new non-invasive quantitative tomographic methods by imaging the electrical properties of biological matter, based on coupled physics inverse problems. The research holds promise to enable new technologies for decoding data used in current medical diagnostic practices and biomedical research by providing the theoretical basis for new imaging methods of higher accuracy and resolution than existing ones. The quantitative distribution of electrical conductivity and permittivity is known to distinguish a benign tumor from a malignant one, it can apply to monitor the pulmonary function of the lung, the thoracic blood volume, hyperthermia, the gastrointestinal function in newborns in intensive care, etc. This project will advance the understanding of information content in the data and produce quantitative images of biological tissues with anisotropic structures while using an optimal number of measurements. Another facet of this project is the development of robust methods which produce quantitative images of biological structure corresponding to frequencies where contrast is optimal. As a consequence, it will provide new tools in biological research by enabling imaging of biological processes at a smaller scale. During the course of the project, graduate students will be trained in an interdisciplinary area of research. The project's findings will be integrated in a student seminar and a special topics course for Mathematics, Physics, and Engineering students at the University of Central Florida.The project integrates novel advances in the mathematical analysis of nonlinear inverse problems with engineering advances in sensor design and data acquisition and aims to shift the paradigm in some of the current engineering practices. The analytical component of the project lies at the intersection of nonlinear Inverse Problems, Geometry, Optimization, and Geometric Measure theory. The principal investigator (PI) plans to improve the current knowledge of the anisotropic least gradient problems arising in physical models which are close to the actual engineering practices. In particular, the PI seeks to determine the anisotropic structure of biological tissue in reconstruction of two-tensors by employing minimal interior data. Another facet of this project seeks to produce quantitative images of the complex biological structure at radio frequencies by coupling the nonlinear inverse problem techniques for Maxwell electromagnetics with the quantum model of resonance of the magnetic spin. The project also aims to determine the electric conductivity distribution in materials with infinite limiting contrast on graphs or neural networks. Based on the analytical findings, the reconstruction methods will be translated in algorithms and tested on simulated data.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.