Collaborative research: Mathematics of emerging imaging methods in medicine and homeland security

合作研究：医学和国土安全中新兴成像方法的数学

• 批准号: 1211463
• 负责人: Peter Kuchment
• 金额: $ 41.58万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1211463&HistoricalAwards=false
• 关键词: Collaborative; research; Mathematics; emerging; imaging; Collaborative; research; Mathematics; emerging; imaging

Computerized tomography plays a central role in biomedical imaging. Tomography techniques are also extensively used for industrial non-destructive testing, in geology and geophysics, astronomy, and in other areas. Lately, they have found important applications in homeland security. Over the last decades, several modalities have been developed and have became standard. Such are, for instance, the traditional X-ray CT scan, SPECT, MRI, Optical-, Ultrasound-, and Electrical Impedance Tomography, to name a few. However, such tasks as detection of small cancerous tumors in soft tissues or finding a small amount of nuclear material in a large container still present a significant challenge. In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have been emerging. By combining two or three different types of waves (or physical fields) these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information - at a lesser cost and with less health hazard to a patient. As a rule, the images in these modalities are obtained by complex mathematical procedures, rather than through direct acquisition. The corresponding mathematics is, mostly, at very early stages of development. Thus, the first part of the project addresses the central mathematical and numerical issues in several of the novel hybrid techniques, based on combinations of magnetic, electric, acoustic, and optical waves, and the general mathematical issues common to all of these techniques. The second part of the projects is directed toward the improvement of the known methods and development of new tomographic techniques for homeland security problems. In particular, we will focus on the detection techniques for illicit weapons-grade nuclear materials in cargo, to be used at border crossings and harbors. In the third part these techniques will be used to resolve some outstanding problems in Synthetic Aperture Radar applications, radio tomography, ultrasound reflectometry, and other areas.The goal of the project is to develop new techniques of medical imaging, as well as efficient methods of detecting illicit nuclear materials at border crossings and in harbors. The project will have a significant impact on the development and implementation of several new sensitive, inexpensive, and safe methods of biomedical imaging, efficient techniques of nuclear threat detection in homeland security, with applications in several other areas of imaging and non-destructive industrial testing (e.g., synthetic aperture radar). The results will be disseminated through publications in high quality research journals, presentations at national and international conferences, and series of lectures at various venues. Graduate students will play a significant role in the project, which will prepare them for work in the exciting area at the junction of exact sciences, medicine, biology, and homeland security. Parts of the study resulted from the project will be delivered in graduate level classes, lecture series at national and international schools and conferences, and in two monographs.

计算机断层扫描在生物医学成像中起着核心作用。 断层扫描技术还广泛用于地质和地球物理学，天文学和其他领域的工业非破坏性测试。最近，他们发现了国土安全部的重要应用。在过去的几十年中，已经开发出几种方式并成为标准的。例如，这就是传统的X射线CT扫描，SPECT，MRI，光学，超声和电阻抗断层扫描，仅举几例。但是，诸如检测软组织中小癌性肿瘤或在大容器中发现少量核材料的任务仍然带来重大挑战。 近年来，革命性的“混合”或“多物理学”的医学成像方法已出现。通过结合两种或三种不同类型的波（或物理领域），这些方法克服了经典层析成像技术的局限性，并提供原本无法使用的，潜在的挽救生命的诊断信息 - 成本较小，对患者的健康危害较小。通常，这些方式中的图像是通过复杂的数学程序而不是直接获取来获得的。相应的数学主要是发展的早期阶段。因此，该项目的第一部分基于磁性，电气，声波和光波的组合以及所有这些技术共有的一般数学问题，解决了几种新型混合技术中的中心数学和数值问题。 项目的第二部分是针对改善已知方法，并开发用于国土安全问题的新层析成像技术。特别是，我们将专注于在过境点和港口使用的非法武器级核材料的检测技术。在第三部分中，这些技术将用于解决合成孔径应用，无线电断层扫描，超声反射仪和其他领域的一些杰出问题。该项目的目的是开发医学成像的新技术，以及检测在过境点和港口中的非法核材料的有效方法。该项目将对在国土安全部的生物医学成像，有效的核威胁检测技术，有效的核威胁检测技术的开发和实施产生重大影响，并在其他几个成像和非破坏性工业测试领域中进行了应用（例如，合成射雷尔）。 结果将通过高质量研究期刊的出版物，国家和国际会议的演讲以及各个场所的一系列讲座来传播。研究生将在该项目中发挥重要作用，这将使他们在精确的科学，医学，生物学和国土安全部的令人兴奋的领域工作做好准备。该项目的部分研究将在研究生级课程，国立和国际学校和会议的讲座系列以及两篇专着。