Biomedical Engineering Reference
In-Depth Information
Pathmanathan and Whiteley,
2009
; Land et al.,
2012
) where the stress is composed
as a sum of a passive and an active part, the latter determined by the so-called ac-
tive tension, also depending on the electrical activation of the cell. In this paper we
address the feasibility of numerical simulations for the macroscopic coupling using
the active strain approach, and we present in detail an example of the full electrome-
chanical interaction. However, we will not discuss advantages and disadvantages of
the different strategies, rather we refer to Ambrosi and Pezzuto (
2012
) and Rossi et
al. (
2012
) for a thorough comparison.
This paper is organized as follows. In Sect.
14.2
we summarize the main math-
ematical characteristics of the electrical and mechanical problem and we detail the
specific modeling strategy that we adopt. The electromechanical coupling, i.e. the
cell contraction dictated by the electrical signal and the corresponding feedback (the
stretch activated currents) are illustrated in Sect.
14.3
. The computational method is
outlined in Sect.
14.4
where we also present a numerical example, and we close with
a discussion in Sect.
14.5
.
14.2 Mathematical Models for Cardiac Electromechanics
Force balance equations for an elastic continuum medium are employed to describe
large deformations of the myocardium under influence of the fluid pressure, the
surrounding organs and its own contraction. Such framework has to be coupled with
the macroscopic bidomain or monodomain equations accounting for the propagation
of the electric potential and ionic currents.
14.2.1 Models for the Heart Electrophysiology
Starting from the pioneering work of Hodgkin and Huxley (
1952
) on the nerve axon
model, several increasingly sophisticate models have been developed for the prop-
agation of electrical signals in cardiac tissue. Here we separate between models for
cardiac cell electrophysiology, and macroscopic tissue-level models based on con-
tinuum mechanics.
Popular cardiac cellular electrophysiology models include those based on exper-
imental observations on animals (e.g., Luo and Rudy,
1991
) and humans (see, e.g.,
Iyer et al.,
2004
; ten Tusscher et al.,
2004
). Such models address cell excitation in
isolation from the rest of the cardiac function. They essentially include a descrip-
tion of the dynamics of ionic species (mainly potassium, calcium, and sodium) along
with the gating processes of several proteins that are blocked or allowed to transport
ions through the cellular membrane. A drastic decrease of computational cost can be
obtained by using simplified low dimensional models based on phenomenological
descriptions of such mechanisms (Rogers and McCulloch,
1994
; Bueno-Orovio et
al.,
2008
). The price to pay for this simplification, provided that a correct behavior of
