Page 46 - Artificial Intelligence for Computational Modeling of the Heart

16 Chapter 1 Multi-scale models of the heart for patient-specific simulations

events, although with limited spatial accuracy due to the intrin-
sic smoothing and volume averaging effect of surface measure-
ments (as compared for instance to invasive surface mapping of
the heart). Furthermore, noninvasive electrocardiographic imag-
ing aims at using BSPM to compute epicardial potentials by solv-
ing the inverse elegrophysiology problem [95–97]. By focusing on
the reconstruction of epicardial potentials, this approach has the
advantage of potentially leveraging the proven effectiveness of
epicardial surface mapping techniques for the localization of car-
diac electrical events; however, accurate reconstruction can be
challenging in real clinical scenarios [98].

Bidomain modeling of the coupled heart-body system
Body surface potentials (BSP) can be directly modeled by ex-
tending the tissue-level electrophysiology model with a compo-
nent representing the body as an electrically conductive medium.
In this case, the heart is electrically coupled with the surround-
ing tissue in the torso. Therefore, the modeling hypotheses lead-
ing to the definition of the monodomain model are not adequate,
since by ignoring the extra-cellular compartment the model can-
not account for electrical coupling with other tissues. The bido-
main model has thus been the modeling framework of choice for
BSP simulations. By recalling the definition of the transmembrane
potential as v = φ i − φ e , with φ i and φ e representing the intra- and
extracellular potential respectively, the bidomain model reads:

∂v

χ C m + J ion =∇ · R i ∇v + J stim ,
∂t (1.10)
∂v

χ C m + J ion =−∇ · R e ∇v + J stim ,
∂t
with the same meaning of the symbols in Eqs. (1.5)–(1.7)and
where R i and R e represent the intra- and extracellular electrical
conductivity tensors, respectively. In this case, the boundary con-
ditions express the absence of current flow from the intracellular
compartment to the surrounding tissue (the torso): R i ∇φ i · n = 0,
where n is the epicardial surface normal. Current balance is guar-
anteed at the interface between the extracellular compartment
and the torso:
(R e ∇φ e ) · n =−(R o ∇φ o ) · n, (1.11)
where R o and φ o are the conductivity tensor and electrical poten-
tial in the torso. Finally, the torso can be modeled as a passive
electrical medium, for which the spatial distribution of the poten-
tial is described by Laplace’s equation:

∇· R o ∇φ o = 0. (1.12)