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Spatio-Temporal Optimization Approaches to the Transmembrane Potential Based Inverse Problem of ECG

Spatio-Temporal Optimization Approaches to the Transmembrane Potential Based Inverse Problem of ECG
chair:Inverse problem of ECG
type:Masterarbeit
tutor:

Dipl.-Math. Danila Potyagaylo, Dipl.-Ing. Walther Schulze

person in charge:

Elisanda Gil Cortés

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Motivation
The goal of ECG imaging is the reconstruction of cardiac electrical sources from the BSPM (body surface potential maps). The tool could have a great clinical potential by providing a cardiologist the quantitative information about the heart condition, thereby enabling pre-interventional planning and facilitating the intervention procedures themselves.

With the knowledge about model geometry, a linear relationship between heart sources and BSPM can be established. The problem is however severely ill-posed, i.e. it is very sensitive to the measurement and modeling errors. Therefore a special mathematical technique, called regularization, should be applied in order to get a stable solution.
Inverse_problem_2012-11-15
Tasks
In the project new physiologically based approaches to the problem will be developed. In order to overcome the smoothness of a standard Tikhonov solution binary and ternary optimization techniques will be tested for extrasystoles and ischemia regions identification. Furthermore a new spatio-temporal function template of transmembrane voltages will be constructed: at each time step the corresponding functional will be minimized, thus delivering maximum-likelihood estimates for the unknown parameters.

Requirements

  • programming skills in C++, MATLAB
  • linear algebra, analysis
  • some knowledge about optimization and/or cardiac physiology would be a plus