Optimal Design for Inverse Problems in Biomedical Engineering

生物医学工程中的数学模型，例如血液动力学(血流)的计算模型，通常具有大量的未知参数。这些参数必须通过每个患者单独获得的临床测量来估计。然而，目前还不清楚哪些测量是关于参数的最具信息量的，以及哪些参数与回答给定的临床问题最相关。这个项目将通过概率分析和信息论的最新发展，特别关注生物医学工程中遇到的问题，为这个问题开发一个框架。该项目的主要目标是：1。利用信息论方法开发一个“优化设计”的框架。将框架应用于生物医学工程模型：心肌细胞的离子模型和血流的血流动力学模型。开发的框架及其应用将有助于确定哪些量，例如临床测量的组合，对特定的临床问题最具信息量，例如特定疾病的诊断。

Mathematical models in biomedical engineering, for e.g. computational models of haemodynamics (blood flow), often have a large number of unknown parameters. These parameters must be estimated through clinical measurements acquired individually in each patient. However, it is not clear which measurements are most informative about the parameters and which parameters are most relevant to answer a given clinical question. This project will develop a framework for this problem of 'optimal design' through recent developments in probabilistic analysis and information theory with a particular focus on problems encountered in biomedical engineering. Key aims of the project are:1. To develop a framework for 'optimal design' using information theoretic measures.2. To apply the framework on biomedical engineering models: ionic models for cardiac cells and haemodynamics models for blood flow.The developed framework and its applications will help in determining which quantities, for example a combination of clinical measurements, are most informative about a particular clinical question, for example the diagnosis of a particular disease.