Optimal Design for Inverse Problems in Biomedical Engineering

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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.