Biomedical Engineering Reference
In-Depth Information
model are shown in the leftmost column of Fig. 4. After reinterpretation of the
deactivation of the outward 'pacemaker current'
I
K2
of the Bristow-Clark model as an
activation of inward
I
f
[89], the model has four time-dependent (gated) ionic currents
(
I
si
,
I
K
,
I
f
, and
I
Na
) and a relatively large time-independent (non-gated) 'background
current'. The Bristow-Clark model has been updated by Reiner and Antzelevitch
[73], who replaced
I
K2
by an
I
f
current consistent with the data obtained in the first
voltage clamp experiments on small SA node preparations. Further, ''to generate a
biologically accurate action potential'', i.e. an action potential with a realistic shape
and duration,
I
K1
(shown as
I
b,K
in Fig. 4) was increased by 30%,
I
Na
was decreased by
12% and
I
si
was increased by 15%.
A large body of information on the ionic current systems underlying pacemaker
activity had been obtained from voltage clamp experiments on small rabbit SA node
preparations containing §100 cells carried out in the mid 1970s by Irisawa and Noma
(see review by Irisawa et al. [37]). From data obtained in these studies, the first
mathematical model of (multicellular) SA node pacemaker activity was constructed
by Yanagihara et al. [91]. An extension of this model, based on more recent
experimental information on the 'slow inward current' (or 'secondary inward current',
I
si
) was presented by Irisawa and Noma [36]. It has the same five membrane current
components as the Bristow-Clark model:
I
si
,
I
K
,
I
f
,
I
Na
, and
I
b
(Fig. 4). However,
unlike the Bristow-Clark model, the equations for
I
si
,
I
K
, and
I
f
are based on data from
voltage clamp experiments on SA node preparations. The
I
Na
equations were adopted
from the MNT model, whereas the background current was estimated from the
difference between the computed total amplitude of the four gated currents and the
experimental steady-state current-voltage curve. Although the action potentials of the
Bristow-Clark and Irisawa-Noma models are quite similar (Fig. 4a; Table 3), the
underlying ionic currents (Fig. 4c-g) are clearly not. This highlights the different
approaches of either modifying model equations to obtain a particular 'reference
action potential'—an approach that has recently been followed by Lovell et al. [50]—
or incorporating voltage clamp data from SA node preparations with a minimal set of
'adjustable' parameters.
In 1985, DiFrancesco and Noble [14] published a new model of Purkinje fibre
electrical activity that, for the first time, fully incorporated the currents generated by
the electrogenic sodium-calcium exchanger and sodium-potassium pump (
I
NaCa
and
I
NaK
, respectively) and accounted for the variations in intracellular sodium, calcium,
and potassium concentrations. From this model, a model of SA node pacemaker
activity was developed by Noble and Noble [61]. The DiFrancesco-Noble equations
were used “with parameters appropriate to the SA node except where specific
information on the SA node existed that required the equations to be changed”.
Calcium uptake and release by the SR was represented with separate calcium stores
(Fig. 2, top left). The slow inward current was separated into
I
NaCa
and a fast gated
component with calcium-dependent inactivation (
I
Ca
). The equations for
I
f
and
I
K
were
based on voltage clamp experiments on multicellular SA node preparations, whereas
the
I
Na
equations were based on data obtained on Purkinje fibres. The equations for
I
NaCa
and for intracellular calcium storage and release were only partly based on
experimental observations. The conductance of the calcium background current
I
b,Ca
was chosen to give a diastolic free calcium level in the presumed
