Biomedical Engineering Reference
In-Depth Information
sustained components (
I
to
and
I
sus
, respectively) [47], albeit with some debate on the
latter [85]. It should be noted that
I
st
,
I
to
and
I
sus
are not consistently found in
experiments on SA nodal cells.
Furthermore, as reviewed by Boyett et al. [4], a correlation between current density
and cell size (membrane capacitance) was reported for several ionic currents in
addition to a correlation between action potential shape and cell size, with higher
densities and more pronounced action potentials in larger, presumably peripheral
cells. Thus, Zhang et al. [93] developed models of 'central' and 'peripheral' SA nodal
cells that differ in cell size (20 vs. 65 pF) and current densities, resulting in distinct
'central' and 'peripheral' action potential shapes (two leftmost columns of Fig. 6
1
).
The peripheral cell beats at a high rate (6.2 Hz) and its upstroke, with a maximum
upstroke velocity of 83 V/s (Table 3), is driven by sodium current rather than L-type
calcium current.
I
Ks
,
I
to
, and
I
sus
, but not
I
st
, have been incorporated into the Zhang et
al. [93] models. The models have pump and exchanger currents, but no provisions are
made for changes in ion concentrations: these are all set to constant values. In
particular, [Ca
2+
]
i
is fixed at 100 nM (Fig. 6b). The models have been extended with
equations for intracellular calcium handling and sustained inward current by Boyett et
al. [5], but thus far these extended models have not been widely used. Another
extension of the Zhang et al. models is the incorporation of equations for
I
K,ACh
and
the modulation of
I
f
and
I
Ca,L
by ACh [94].
Building on previous models [11, 16, 89, 93], Kurata et al. [43] formulated an
improved model of a primary SA nodal pacemaker cell. The model includes
I
st
, new
formulations for voltage and calcium dependent inactivation kinetics of
I
Ca,L
, new
expressions for activation kinetics of
I
Kr
(see also [44]), revised kinetic formulas for
I
to
and
I
sus
, and new formulations for voltage-and concentration-dependent kinetics of
I
NaK
. Furthermore, the intracellular volume is not only separated into an SR volume,
with calcium buffering through calsequestrin, and a myoplasmic volume, with
calcium buffering through calmodulin and troponin, but the myoplasm also has a
restricted subsarcolemmal space as a diffusion barrier for calcium ions. Unlike some
of the earlier models, the Kurata et al. model does not include
I
Na
,
I
b,Ca
, and
I
p,Ca
: these
three currents were assumed to be negligible. As in the models by Zhang et al. [93],
I
Ks
is relatively small (Fig. 6d) and has little effect on normal pacemaker activity, as
demonstrated by the <1 ms change in cycle length upon complete block of
I
Ks
(data
not shown). The model includes
I
K,ACh
, which constitutes the current that appears in
Fig. 6h as
I
b,K
. The Kurata et al. model was modified by Maltsev et al. [53] to include
a phenomenological representation of spontaneous calcium release during diastolic
depolarization to assess the functional importance of this calcium release, which
could accelerate diastolic depolarization through
I
NaCa
.
Matsuoka et al. [55] developed the 'Kyoto model', which is a compound model
that can both simulate a ventricular cell and an SA node cell, and includes a
contraction model that allows the calculation of sarcomere shortening. The SA node
model, which was further examined in an accompanying paper by Sarai et al. [75],
1
As set out in detail by Garny et al. [26], the model equations listed in the paper by Zhang et al.
[93] do not match the simulation results presented in the same paper. The action potentials
and current traces shown in Fig. 6 have been obtained with the correct equations, which are
listed by Garny et al. as the '0D capable' version of the models [26].
