A model study of instability of the inverse problem in electrocardiography
| Autor: | Ilias Iakovidis, Clyde F. Martin |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Statistics and Probability
General Immunology and Microbiology Applied Mathematics Models Cardiovascular Geometry General Medicine Inverse problem Regularization (mathematics) General Biochemistry Genetics and Molecular Biology Symmetry (physics) Closed and exact differential forms Spherical model Electrocardiography Distribution (mathematics) Modeling and Simulation Humans A priori and a posteriori Applied mathematics Uniqueness General Agricultural and Biological Sciences Mathematics |
| Zdroj: | Mathematical Biosciences. 107:127-148 |
| ISSN: | 0025-5564 |
| DOI: | 10.1016/0025-5564(91)90075-t |
| Popis: | The inverse problem in electrocardiography is studied analytically using a concentric spheres model with no symmetry assumptions on the potential distribution. The mathematical formulation is presented, and existence and uniqueness of the solution are briefly discussed. Solution to the inverse problem is inherently very unstable. The magnitude of this instability is demonstrated using the derived analytical inverse solution for the spherical model. Regularization methods used to date are based on a regularization parameter that does not relate to any measurable physiological parameters. This paper presents a regularization method that is based on a parameter in the form of an a priori bound on the L2 norm of the inverse solution. Such a bound can be obtained from the theoretical estimates based on the measured values of the body surface potentials together with experimental knowledge about the magnitudes of the epicardial potentials. Based on the presented regularization, an exact form of the regularized solution and estimates of its accuracy are derived. |
| Databáze: | OpenAIRE |
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