Page 40 - Artificial Intelligence for Computational Modeling of the Heart

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

or myocardium tissues [64,65]. These models reproduce the ob-
served shape of the action potential and how it changes under the
effect of external conditions, without focusing on the underlying
ionic phenomena. Hence, they provide a simplified representa-
tion of the dynamics of the cell, which limits their ability to cap-
ture changes in the electrophysiology due to microscopic effects,
for instance as a result of the action of pharmacological agents.
On the other hand, these models are typically controlled by a lim-
ited number of model parameters, which makes them computa-
tionally efficient. Moreover, the parameters are typically directly
related to the shape of the action potential or ECG measurements,
which enables effective parameter estimation strategies from clin-
ically available data.
Biophysical models simulate the ionic interactions across the
cell membrane and the biological phenomena underlying ion
channels [13,67–69]. They are largely based on direct measure-
ments of electrical signals in animal models, which hinders their
direct translation to human studies. Recently, models aiming at
describing the specific cellular dynamics of human cardiac my-
ocytes have been introduced, although limited by the scarce avail-
ability of data for model validation and calibration [70]. They aim
at reproducing the electrical activity of the cell with high fidelity, at
the expense of increased number of parameters: this makes them
typically more computationally intensive than phenomenologi-
cal models. Parameter estimation is also more difficult, as some
quantities needed for model calibration may not be directly ob-
servable in non-invasive experiments.

An example: the Mitchell–Schaeffer model
The model proposed by Mitchell and Schaeffer (M-S) [71] al-
lows capturing normal electrophysiology as well as tissue-level
pathologies like cardiac dyssynchrony and minor to mild arrhyth-
mias
dv
= J in (v,h) + J out (v) + J stim (t). (1.1)
dt
There are two unknowns in the model: the trans-membrane
potential, or voltage v(t), and a gating variable h(t),which mod-
els the state of the ion channels (opened / closed) that control
the inward and outward currents across the cell membrane. The
M-S model can therefore be seen as a “lumped” simplification of
more complex, ionic models. According to Eq. (1.1), the tempo-
ral change of trans-membrane potential equals to the combined
effect of the inward current, outward current, and stimulation cur-