Journal
IEEE TRANSACTIONS ON MEDICAL IMAGING
Volume 33, Issue 4, Pages 902-912Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TMI.2014.2297952
Keywords
Activation time imaging; biomedical imaging; biomedical signal processing; convex relaxation; electrocardiography (ECG); inverse problems
Categories
Funding
- National Center for Research Resources from the National Institutes of Health [5P41RR012553-14]
- National Institute of General Medical Sciences from the National Institutes of Health [8 P41 GM103545-14]
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Noninvasive imaging of cardiac electrical function has begun to move towards clinical adoption. Here, we consider one common formulation of the problem, in which the goal is to estimate the spatial distribution of electrical activation times during a cardiac cycle. We address the challenge of understanding the robustness and uncertainty of solutions to this formulation. This formulation poses a nonconvex, nonlinear least squares optimization problem. We show that it can be relaxed to be convex, at the cost of some degree of physiological realism of the solution set, and that this relaxation can be used as a framework to study model inaccuracy and solution uncertainty. We present two examples, one using data from a healthy human subject and the other synthesized with the ECGSIM software package. In the first case, we consider uncertainty in the initial guess and regularization parameter. In the second case, we mimic the presence of an ischemic zone in the heart in a way which violates a model assumption. We show that the convex relaxation allows understanding of spatial distribution of parameter sensitivity in the first case, and identification of model violation in the second.
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