Biomedical Engineering Reference
In-Depth Information
Fig. 4.12.
First lead of ECGs for a simulation with several beats. Comparison between the full
order model (full line) and the POD reduced order model (dotted line)
on the snapshots obtained from the first heart beat. In Fig. 4.13 (top) we see, as
expected, that the first beats perfectly match. Fig. 4.13 (bottom) shows that, at the
eleventh beat, the ECGs are still very close. Hence, the POD reduced-order model
seems to be reliable to compute long time simulations with variable heart rates. It
offers therefore an interesting option to compute efficiently restitution curves.
4.7 Conclusions
In this overview, various aspects of the modelling of cardiac electrophysiology were
considered: mathematical analysis, numerical simulation and numerical analysis.
The main goal was to present a strategy to compute 12-lead ECGs with a model
fully based on PDEs and ODEs and depending on a moderate number of parame-
ters. The results turned out to be satisfactory in physiological conditions, and for
some pathologies. It is nevertheless clear that many aspects could be improved. For
example, the atria should be included to get P-waves; His bundle and Purkinje fibres
could be explicitly modelled; ionic models could be based on physiological models
instead of phenomenological ones. But it is worth keeping in mind that these im-
provements would come with many additional parameters and would require data
that are extremely difficult to obtain clinically.
The ECG simulator presented in this chapter has already been used in various ap-
plications: optimization of pacing sites [20], ECG reconstruction from electrograms
