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Adaptive finite element computations of nonlinear elasticity problems

非线性弹性问题的自适应有限元计算

基本信息

批准号：
EP/D503035/1
负责人：
Jonathan Whiteley
金额：
$ 15.72万
依托单位：
University of Oxford
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FD503035%2F1
关键词：
Adaptive finite element computations nonlinear

项目摘要

We propose to use mathematics to help doctors working in hospitals provide better care for two groups of patinets. these groups of patients are women with breast cancer, and patients with heart disease. We begin this summary by describing how mathematics may help provide better care for these groups of patients, and then brifly describe the mathematics we use.Approximately 10% of women in developed countries will develop breast cancer during the course of their lives. A cancerous tumour may be located using one or more clinical imaging techniques from a range of clinical technique, one of these techniques, called magnetic resonance imaging, the woman will be lying on her front. For another technique, called X-ray mammography, the woman will be standing with her breast compressed between two plates. For another technique, called ultrasound, the woman will be lying on her side. The breast will take a very differnt shape for each of these techniques. Should the woman require surgery to remove a tumour, she will lie on her back during surgery and the breast will take yet another shape. This will make hard for the surgeon to locate the tumour in the breast. We intend to use mathematics to help the surgeon locate the tumour.Heart disease is the major cause of death in the western world. The forces needed for a heartbeat are generated by biochemical reactions inside cells in the heart. In a healthy heart the cells will contract at roughly the same time, which enables the efficient pumping of blood around the body. This doesn't always happen in an unhealthy heart. We propose to use mathematics to explain what happens instead.The mathematics we use relates the dformation of the breast or the heart to the forces that are applied. Body organs change shape when a force is applied to them, or when a person changes prosition, e.g. stands up rather than lies down. This change in shape is described by equations that may be solved by programming a computer to use a mathematical algorithm. As body organs can be very complex, a computer may take a long time to solve the problem using these algorithms. The work described in this proposal intends to establish the most suitable algorithm, i.e. the alorithm that will execute on a computer in the shortest time whilst ensuring that the answer is correct.

我们建议使用数学来帮助在医院工作的医生为两组患者提供更好的护理。这些病人包括患乳癌的妇女和患有心脏病的病人。我们开始这个总结描述如何数学可以帮助提供更好的照顾这些群体的病人，然后简要描述我们使用的数学。大约10%的妇女在发达国家将发展乳腺癌在他们的生活过程中。癌性肿瘤可以使用一种或多种临床成像技术来定位，这些技术之一，称为磁共振成像，女性将躺在她的前面。对于另一种技术，称为X射线乳房摄影术，妇女将站在她的乳房压缩在两个板。对于另一种称为超声波的技术，女性将侧卧。乳房将采取一个非常不同的形状为每一个这些技术。如果女性需要手术切除肿瘤，她将在手术期间仰卧，乳房将呈现另一种形状。这将使外科医生很难找到乳房中的肿瘤。我们打算用数学来帮助外科医生确定肿瘤的位置。心脏病是西方世界的主要死因。心跳所需的力量是由心脏细胞内的生化反应产生的。在健康的心脏中，细胞将大致同时收缩，这使得血液能够有效地泵送到身体各处。这并不总是发生在一个不健康的心脏。我们建议使用数学来解释所发生的事情。我们使用的数学将乳房或心脏的变形与所施加的力联系起来。当一个力施加到身体器官上时，或者当一个人改变姿势时，例如站起来而不是躺下时，身体器官会改变形状。这种形状的变化由方程描述，该方程可以通过编程计算机以使用数学算法来求解。由于身体器官可能非常复杂，计算机可能需要很长时间才能使用这些算法解决问题。本提案中描述的工作旨在建立最合适的算法，即在最短时间内在计算机上执行的算法，同时确保答案是正确的。