Biomedical Engineering Reference
In-Depth Information
isolated cardiac cells, the extracellular space is grounded to earth (cf. Figs. 1, 2).
Given the required computational power, only simple first-generation cardiac cell
models, with few variables and equations, can be used in large-scale bidomain
simulations. Thus, bidomain simulations do not permit highly detailed studies of
effects of individual ionic currents on cardiac activation. This also holds, to a lesser
extent, for monodomain simulations. Cardiac cell models that are typically used in
large-scale simulations include the simplified ionic models by Fenton and Karma [21]
and Bernus et al. [2].
3 SA Nodal Cell Models
Starting with the model by Yanagihara et al. [91], a number of SA nodal cells has
been developed (Tables 1, 2). The complexity of the models has increased
considerably over the years as new currents have been identified and more
experimental data have become available. Data have been obtained almost exclusively
from experiments on rabbit. Therefore, it is not surprising that, with the exception of
the recently developed mouse SA nodal cell model by Mangoni et al. [54], all SA
nodal models are in effect models of rabbit SA nodal cells. The Hodgkin-Huxley
formalism of channel gating has proven successful in SA nodal cell modelling, with
only one model employing Markov-type channel gating [50].
In this section, an overview of 25 years of SA nodal cell modelling is given,
illustrated with spontaneous electrical activity generated in 12 different SA nodal cell
models that have published since 1980 (Figs. 4, 5, 6; Table 3). Subsets of these
models have previously been compared by Wilders et al. [89], Garny et al. [25], and
Kurata et al. [43]. In the study by Wilders et al. [89], the models by Bristow and Clark
[6], Irisawa and Noble [36], Noble and Noble [61], and Noble et al. [62] were
compared, whereas Garny et al. [25] compared the models by Demir et al. [11],
Dokos et al. [16], and Zhang et al. [93] as well as an updated version of the Noble et
al. [62] model, as incorporated in the commercially available OxSoft Heart 4.X
software package (see paragraph 4.2). In their presentation of a novel SA nodal cell
model, Kurata et al. [43] have compared this model to the models by Wilders et al.
[89], Demir et al. [11], Dokos et al. [16], and Zhang et al. [93].
3.1 SA Nodal Cell Models of the 1980s: Generic Models
Realistic mathematical models of electrical activity of cardiac cells could not be
constructed before electrophysiological techniques allowed measurements of
individual membrane currents. The McAllister-Noble-Tsien Purkinje fibre model
(MNT model [57]) was the first mathematical model of electrical activity of cardiac
cells that was based on experimental data on individual membrane currents. Two
years later, Beeler and Reuter [1] published their widely used mathematical model of
electrical activity of the ventricular myocardial cell, based on the MNT model
(Table 1). Several years later, Bristow and Clark [6] presented a mathematical model
of (multicellular) SA node pacemaker activity that was constructed by modifying the
MNT model. The membrane current components of this Purkinje fibre model were
modified to reproduce a particular SA nodal ''reference transmembrane potential
waveform.'' The action potential and associated ionic currents generated by this
