Mathematical Methods for Novel Modalities of Medical Imaging

Kuchen DMS-0604778这位研究人员和他的同事开发了分析和数值两种数学技术，用于获得生物组织的图像。它们集中在最近引入的成像方法中出现的数学问题，这些方法几乎没有数学理论：热声层析成像(TAT)、超声调制光学层析成像(UOT)和声电层析成像(AET)。计算机层析成像已成为医学诊断成像和工业无损检测的主要方法。随着时间的推移，已经开发了许多方法，例如X射线断层扫描(通常的CAT扫描)、磁共振成像、发射断层扫描、光学断层扫描(OT)和电阻抗断层扫描(EIT)，仅举几个例子。它们在不同生物组织之间的对比度、分辨率、设备和程序的成本以及患者的安全性方面都有各自的优缺点。例如，像EIT和OT这样廉价而安全的程序都受到低分辨率的困扰。近年来，出现了旨在克服这些问题的新的成像方法，并具有成为廉价、安全和有效的诊断工具的巨大潜力。它们是热声层析成像(TAT)、超声调制光学层析成像(UOT)和声电层析成像(AET)。它们都组合了不同类型的辐射，以克服仅涉及这些模式中的一种的方法(例如，光学层析成像、超声成像或电阻抗成像)的已知困难，例如，超声成像的低对比度以及光学和电阻抗成像的高不稳定性和低分辨率。在这些方法的发展中，数学问题是最关键的问题之一，因为图像必须通过复杂的数学程序获得，而不是像标准(非断层)X射线成像那样通过直接获取。然而，在所有这些模式中，基本上没有必要的分析和数值工具，或者处于非常早期的发展阶段。因此，研究人员开发了获得生物组织图像的数学分析和数值技术，主要目标是TAT、UOT和AET。该项目帮助开发和实施几种新的、廉价和安全的医学诊断成像方法，用于临床。一些非破坏性工业测试的应用也是可能的。研究生在这个项目中扮演着重要的角色，该项目的一些技术和结果被纳入研究生水平的课程。这为学生在精准科学、医学和生物学交界处的激动人心的当代领域的工作做好准备。

KuchmentDMS-0604778 The investigator and his colleague develop mathematicaltechniques, both analytic and numerical, for obtaining images ofbiological tissues. They concentrate on mathematical issues thatarise in recently introduced imaging methods for which there islittle mathematical theory: Thermoacoustic Tomography (TAT),Ultrasound-Modulated Optical Tomography (UOT), andAcousto-Electric Tomography (AET). Computerized tomography has become a major method of medicaldiagnostic imaging and industrial non-destructive testing. Overtime, many modalities have been developed, such as X-raytomography (usual CAT scan), MRI, Emission Tomography, OpticalTomography (OT) and Electrical Impedance Tomography (EIT), toname only a few. All of them have their advantages anddisadvantages in terms of contrast between different biologicaltissues, resolution, cost of devices and procedures, and safetyof the patient. For instance, cheap and safe procedures like EITand OT are plagued by low resolution. Recent years have broughtnovel methods of imaging that intend to overcome these problemsand have a high potential for becoming cheap, safe and effectivediagnostic tools. These are Thermoacoustic Tomography (TAT),Ultrasound-Modulated Optical Tomography (UOT), andAcousto-Electric Tomography (AET). They all combine differenttypes of radiation to overcome the known difficulties of methodsinvolving only one of these modalities (e.g., optical tomography,ultrasound imaging, or electrical impedance tomography), such as,for example, low contrast of ultrasound imaging and highinstability and low resolution of optical and electricalimpedance imaging. Mathematical issues are among the mostcrucial in development of these methods, because images have tobe obtained by sophisticated mathematical procedures rather thanby direct acquisition as in the standard (non-tomographic) X-rayimaging. However, in all these modalities necessary analytic andnumerical tools are essentially absent or at very early stages ofdevelopment. Thus, the investigators develop mathematicalanalytic and numerical techniques for obtaining images ofbiological tissues, with the primary targets being TAT, UOT, andAET. The project aids development and implementation of severalnew, cheap, and safe methods of medical diagnostic imaging to beused in clinics. Some applications for non-destructiveindustrial testing are also possible. Graduate students play asignificant role in the project, and some of the project'stechniques and results are incorporated into graduate-levelclasses. This prepares students for work in excitingcontemporary areas at the junction of exact sciences and medicineand biology.