Biomedical Engineering Reference
In-Depth Information
tection and interpretation of the morphology of the usual electrocardiograms (ECG)
at a few points on the body surface or from the evolution of body surface maps (see
[135, 136, 160] for a survey). The information content of ECGs and body maps is
limited, due to the strong signal attenuation and smoothing associated with current
conduction from heart to thorax; thus it is a difficult task to detect from these signals
detailed information on pathological heart states. The scientific ground of Electrocar-
diology is the so called
Forward Problem of Electrocardiology
, that studies the bio-
electric cardiac sources and conducting media in order to derive the potential field.
Of considerable interest are also the so called
Inverse Problems of Electrocardiog-
raphy
in terms of potentials or cardiac sources (see e.g. the reviews [54, 96, 112]).
In this paper, we will focus on the modelling and simulation techniques for describ-
ing the bioelectrical activity in the myocardium at the macroscopic level which are
the basic tools for the formulation of the Forward and Inverse Problems in terms of
cardiac sources.
In the past few decades, experimental electrophysiology has been increasingly
supported by the mathematical and numerical models of computational electro-
cardiology. These models provide essential quantitative tools to integrate the in-
creasing knowledge of bioelectrochemical phenomena occurring at several time and
space scales, from microscopic models of ionic channels and currents in the cellular
membrane, to macroscopic models of anisotropic cardiac tissue and organ, see e.g.
[17, 18, 30, 63, 96, 113, 133, 160]. These coupled multiscale models are then vali-
dated by comparing simulated results with experimental
in vitro
and
in vivo
data. At
the next step, these electrophysiological models need to be coupled and integrated
with mechanical model of tissue deformation, hemodynamical models of cardiac
blood flow and, more in general, of the cardiovascular system. This complex integra-
tive effort is the current focus of several research projects, such as the EC sponsored
Virtual Physiological Human (VPH) Initiative, see [63]. Ultimately, the integration
of these models should provide new tools enabling the biomedical community to
link genetic and proteomic databases to anatomy and functions at the cellular, tissue
and organ levels.
In the rest of this paper, we investigate the main mathematical models of the car-
diac bioelectric activity in Sect. 2, covering ionic membrane models, cardiac cell
arrangements, the Bidomain model, together with the main theoretical results on
their mathematical analysis. We also introduce the approximate Eikonal and Mon-
odomain models. In Sect. 3 we review some numerical methods for discretizing the
Monodomain and Bidomain models in space and time, and build a parallel Bidomain
solver based on a multilevel Schwarz preconditioned conjugate gradient method. In
Sect. 4 we report some numerical results illustrating the parallel scalability of the
resulting Bidomain solver. In Sect. 5 we apply the solver to three-dimensional Bido-
main simulations of anode make mechanisms of cardiac excitation generated by a
unipolar extracellular pulse.
