Analytical and Computational Approaches for Quantitative Tomography of Tissue

本项目将基于耦合物理逆问题，通过对生物物质的电特性进行成像，开发新的非侵入性定量层析成像方法。该研究有望通过为比现有成像方法更高精度和分辨率的新成像方法提供理论基础，实现对当前医学诊断实践和生物医学研究中使用的数据进行解码的新技术。已知电导率和介电常数的定量分布可以区分良性肿瘤和恶性肿瘤，其可以应用于监测肺的肺功能、胸腔血容量、高热、重症监护中的新生儿的胃肠功能，该项目将促进对数据中信息内容的理解，并产生具有各向异性结构的生物组织的定量图像同时使用最佳数量的测量。该项目的另一个方面是开发稳健的方法，这些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，它将为生物研究提供新的工具，使生物过程的成像在更小的规模。在该项目的过程中，研究生将在跨学科的研究领域进行培训。该项目的研究结果将被整合到一个学生研讨会和一个特殊的主题课程的数学，物理学和工程专业的学生在中央佛罗里达大学。该项目集成了新的进展，在数学分析的非线性逆问题与工程进展传感器设计和数据采集，并旨在改变范式在一些当前的工程实践。该项目的分析部分位于非线性反问题，几何，优化和几何测量理论的交叉点。主要研究者（PI）计划改善物理模型中出现的各向异性最小梯度问题的现有知识，这些问题接近实际工程实践。特别是，PI试图通过采用最小的内部数据来确定生物组织在两张量重建中的各向异性结构。该项目的另一个方面是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。该项目还旨在确定图形或神经网络上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，重建方法将转化为算法，并在模拟数据上进行测试。该奖项反映了NSF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。

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.