Mathematical Methods for Novel Modalities of Medical Imaging

KuchmentDMS-0604778 这位研究者和他的同事开发了分析和数值两种方法来获得生物组织的图像。 他们专注于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（达特），超声调制光学层析成像（UOT）和声电层析成像（AET）。 计算机断层扫描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，已经开发了许多模式，例如X射线断层扫描（通常的CAT扫描），MRI，发射断层扫描，光学断层扫描（OT）和电阻抗断层扫描（EIT），仅举几例。 这些方法在不同生物组织间的对比度、分辨率、设备和程序的成本以及患者的安全性方面各有优缺点。 例如，像EIT和OT这样便宜而安全的程序受到低分辨率的困扰。 近年来出现了新的成像方法，旨在克服这些问题，并有很大的潜力成为廉价，安全和有效的诊断工具。 这些是热声断层扫描（达特），超声调制光学断层扫描（UOT），和声电断层扫描（AET）。 它们都结合了联合收割机不同类型的辐射以克服只涉及这些模态之一的方法的已知困难（例如，光学断层摄影、超声成像或电阻抗断层摄影），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。 数学问题在这些方法的发展中是最关键的，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射线成像那样直接采集。 然而，在所有这些模式中，必要的分析和数值工具基本上是不存在的，或者处于非常早期的发展阶段。 因此，研究人员开发了用于获得生物组织图像的分析和数值技术，主要目标是达特，UOT和AET。 该项目帮助开发和实施了几种新的、廉价的、安全的医学诊断成像方法，以供临床使用。 非破坏性工业测试的一些应用也是可能的。 研究生在该项目中发挥了重要作用，一些项目的技术和成果被纳入研究生课程。 这为学生在精确科学、医学和生物学的交叉点上从事激动人心的当代领域的工作做好了准备。

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.