User:Katje95/sandbox
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The forward problem of electrocardiology is a computational and mathematical approach to study the electrical activity of the heart through the body surface.[1] The principal aim of this study is to computationally reproduced an electrocardiogram (ECG), which has important clinical relevance to defined cardiac pathologies such as ischemia and infarction, or to test pharmaceutical intervation. Given the important functionalities and the relative small invasiveness of them, the electrocardiography techniques are used quite often as clinical diagnostic tests. Thus, it is natural to proceed to computationally reproduce an ECG, which means to mathematically model the cardiac behaviour inside the body.[1]
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The three main part of a forward model for the ECG are:
- a model for the cardiac electrical activity.
- a model for the diffusion of the electrical potential inside the torso, which represents the extracardiac region.
- some specific heart-torso coupling conditions.[2]
Thus, to obtained an ECG, a mathematical electrical cardiac model must be considered, coupled with a diffusive model in a passive condutctor that describe the electrical propagation inside the torso.[1]
The coupled model is usually a three-dimensional model made of partial differential equations (PDE). Such model is solved considering finite element method (FEM) for the solution's space evolution and semi-implicit numerical schemes for the solution's time evolution. However, the computational costs of such techniques, especially with three dimensional simulations, are quite high. Thus, a simplify model are often considered, solving for example the heart electrical activity separately from the problem on the torso. To provide realistic results, three dimensional anatomically-realistic models of the heart and the torso must be used.[1]
Another possible simplification is a dynamical model made of three ordinary differential equations.[3]