ECG Modelling and Simulation
Meaningful computer based simulations of the electrocardiogram ( ECG), linking models of the electrical activity of the heart to ECG signals, are a necessary step towards the development of cardiac models from clinical ECG data.
An ECG simulator is, in addition, a valuable tool for building a virtual data base of pathological conditions, to test and train medical devices but also to improve the knowledge on the clinical significance of some ECG signals.
The heart-torso mathematical model is based on partial differential equations : a reaction diffusion system in the heart (called bidomain model) and the Laplace equation in the torso. These equations are coupled on the heart-torso interface to obtain the ECG model. The bidomain model it self is coupled to a dynamic system governing the electrical activation of the cell membrane. The drug acts directely on the ion channels conductance, we model the drug action by modifiyng the mathematical formulation of ion channels conductances (see papers bellow for more details about modelling).
The mathematical models are then solved folowing different numerical schemes: in space we use finite element methods and in time we use semi-implicit schemes based on Backward differentiation formula.
Examples of Simulation Results
Full details about the following simulations including mathematical models numerical schemes anatomical geometries simulation softwares could be found in the papers below.
Control case
In this video (right) we show the spread of the electrical wave inside the heart and in the body. The change in the color explains the change of the electrical potential magnitude. The ECG is measured on the standard 9 electrodes psitions. In this movie (left), we show the first lead of the ECG which is the difference between the left and the right arm electrical potentials.
hERG block case
We studied the effect of compounds that act on sodium potassium and L-type calcium ion channels.
Here is an example of a hERG block simulation. This simulation is supposed to show the effect of 10 nMol of the compound “Dofetilide” on the ECG.
Details about simulation could be found in these papers:
- N. Zemzemi, B. Rodriguez. Effects of L-type calcium channel and human ether-a-go-go related gene blockers on the electrical activity of the human heart: a simulation study. EP-Europace, Oxford University Press, 2014.
- Nejib Zemzemi; Miguel Oscar Bernabeu; Javier Saiz Rodriguez; Jonathan Cooper; Pras Pathmanathan; Gary Mirams; Joe Pitt-Francis; Rodriguez Blanca. Computational assessment of drug-induced effects on the electrocardiogram: from ion channel to body surface potentials. British Journal of Pharmacology, Wiley-Blackwell, 2013.
- Nejib Zemzemi; Javier Saiz Rodriguez; Rodriguez Blanca. Role of L-type Calcium in Modulating Pro-Arrhythmic Effects of Dofetilide in Human. Computing in Cardiology, Sep 2012, Krakow, Poland.
- N Zemzemi, MO Bernabeu, J Saiz, B Rodríguez. Simulating drug-induced effects on the heart: from ion channel to body surface electrocardiogram. Functional Imaging and Modeling of the Heart, 2011.