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Bridging the Gap between Discrete and Continuous Partial Differential Equations in Medical imaging

弥合医学成像中离散和连续偏微分方程之间的差距

基本信息

批准号：
2204618
负责人：
Erkki Somersalo
金额：
$ 30万
依托单位：
Case Western Reserve University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-08-01 至 2025-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204618&HistoricalAwards=false
关键词：
Bridging Gap between Discrete Continuous

项目摘要

In non-invasive or minimally invasive medical imaging, the goal is to form an image of internal structures of the human body based on measurements performed outside of the body without harming the patient. While the visible part of medical imaging comprising the imaging devices is based on engineering and physics, the image formation and retrieval of pertinent information relies on sophisticated mathematical models and efficient computational methods. This project will address two specific imaging problems, breast cancer screening and stroke detection and classification. Breast cancer screening by mammography is a standard process. However, it is known that, in particular, when the breast tissue is dense, which is the case in 10-40 percent of US women, the risk that a radiologist misses a cancerous lesion is significant. The project will investigate a novel computational idea of using mammography images at different pressure levels and comparing the tissue displacements to estimate the elastic properties of the tissue that are known to be affected by certain cancer types that often remain undetected. Another medical imaging problem addressed in this project is stroke classification by a portable and inexpensive electrical impedance tomography device. It is known that the prognosis of ischemic stroke depends heavily on how early the therapy can be initiated. About 15 percent of stroke patients who made it to the hospital in time were diagnosed with a brain hemorrhage. The therapy meant for ischemic stroke patients would be fatal. A portable classification method suitable for an ambulance could be crucial for diagnosis to save many lives in an emergency. The idea is not new, but the mathematical and computational problems continue to be challenging. This project will focus on the computational challenges in the problems described above and in other mathematically similar problems that cover medical imaging. The results will also be useful in non-destructive material evaluation and geophysics, including other application areas. The project will also include a strong educational component through the involvement of graduate students who will work on their doctoral dissertations on topics central to the project. The project will address mathematical and computational questions associated with the inverse problems of distributed parameters in the Bayesian computational framework, a general methodology that integrates the data with other information about the unknown that may be available. Distributed parameters such as electric conductivity of the brain tissue, or elastic properties of the breast tissue, are typically represented by coefficient functions of partial differential equations (PDEs) that relate these properties to the measurements corresponding to boundary values or samples of the corresponding solution. In order to handle the mathematical model numerically, a discretization of the model is necessary. The discretization of a continuous model for computing the numerical solution is an approximation of the exact model. Therefore, it introduces a discrepancy between the ideal and computational models. These problems are sensitive to any perturbation of the data. Thus even a small modeling error may have disastrous effects on the algorithms if not properly addressed. Therefore, controlling the modeling error in inverse problems will be crucial and challenging. In the approach proposed in this research project, discretization of the continuous model will be based on an underlying metric, coupled with the unknown through a hierarchical Bayesian model. The underlying discretization metric itself will be modeled as an unknown, and its estimation will be part of the inverse problem. The two selected medical imaging applications will serve as outstanding test problems for the methodology, and because of their importance, they will justify the theoretical effort of the project.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.

在非侵入性或微侵入性医学成像中，目标是在不伤害患者的情况下，基于体外测量形成人体内部结构的图像。虽然包括成像设备的医学成像的可视部分是基于工程和物理的，但图像形成和相关信息的检索依赖于复杂的数学模型和高效的计算方法。该项目将解决两个具体的成像问题，乳腺癌筛查和中风检测和分类。乳房X光检查是乳腺癌筛查的标准程序。然而，众所周知，尤其是当乳房组织致密时，放射科医生漏掉癌症病变的风险是很大的，这是10%-40%的美国女性的情况。该项目将研究一种新的计算想法，即使用不同压力水平下的乳房X光检查图像，并比较组织位移，以估计已知受某些癌症类型影响的组织的弹性性质，这些癌症类型通常仍未被发现。这个项目中解决的另一个医学成像问题是通过便携式和廉价的电阻抗断层扫描设备对中风进行分类。众所周知，缺血性卒中的预后在很大程度上取决于多早开始治疗。在及时赶到医院的中风患者中，约有15%被诊断为脑出血。这种针对缺血性中风患者的疗法将是致命的。一种适合救护车的便携式分类方法可能对紧急情况下的诊断至关重要，以挽救许多人的生命。这个想法并不新鲜，但数学和计算问题仍然具有挑战性。这个项目将集中在上述问题和其他涉及医学成像的数学类似问题中的计算挑战。研究结果还将对无损材料评价和地球物理，包括其他应用领域有所帮助。该项目还将包括一个强有力的教育部分，通过研究生的参与，他们将就该项目的核心主题撰写博士论文。该项目将在贝叶斯计算框架中处理与分布参数反问题有关的数学和计算问题，贝叶斯计算框架是一种将数据与其他可能获得的未知信息相结合的一般方法。诸如脑组织的电导率或乳房组织的弹性属性的分布参数通常由偏微分方程(PDE)的系数函数来表示，该偏微分方程(PDE)的系数函数将这些属性与对应于相应解的边界值或样本的测量值相关联。为了对数学模型进行数值处理，需要对模型进行离散化。计算数值解的连续模型的离散化是对精确模型的近似。因此，它在理想模型和计算模型之间引入了差异。这些问题对数据的任何扰动都很敏感。因此，如果处理不当，即使是一个很小的建模错误也可能对算法产生灾难性的影响。因此，控制反问题中的建模误差将是至关重要和具有挑战性的。在本研究项目中提出的方法中，连续模型的离散化将基于底层度量，并通过分层贝叶斯模型与未知相结合。基本的离散化度量本身将被建模为未知的，其估计将是逆问题的一部分。这两个选定的医学成像应用程序将作为该方法的突出测试问题，由于它们的重要性，它们将证明该项目的理论努力是合理的。该奖项反映了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。

项目成果

期刊论文数量（5）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

A spatially distributed model of brain metabolism highlights the role of diffusion in brain energy metabolism

DOI：
10.1016/j.jtbi.2023.111567
发表时间：
2023-07-18
期刊：
JOURNAL OF THEORETICAL BIOLOGY
影响因子：
2
作者：
Idumah，Gideon;Somersalo，Erkki;Calvetti，Daniela
通讯作者：
Calvetti，Daniela

On the fast track: Rapid construction of stellar stream paths

快车道上：快速构建恒星流路径

DOI：
10.1093/mnras/stad1166
发表时间：
2023
期刊：
Monthly Notices of the Royal Astronomical Society
影响因子：
4.8
作者：
Starkman, Nathaniel;Bovy, Jo;Webb, Jeremy J;Calvetti, Daniela;Somersalo, Erkki
通讯作者：
Somersalo, Erkki

Bayesian hierarchical dictionary learning