Biomedical Engineering Reference
In-Depth Information
including the size (number of cells) of the focus region, the intercellular coupling
among the focus cells, the input resistance of the surrounding quiescent cells, and the
value and spatial orientation of the coupling conductances among the surrounding
cells. Another factor that is less well appreciated is that the focus region itself may be
inhomogeneous both in terms of membrane properties as well as in the distribution of
cellular coupling [7,8]. In this review, we will illustrate some of the experimental and
theoretical studies, which have been done to determine some of the interactions
among these factors.
2 Interactions Among Spontaneously Pacing Cells
When cells with intrinsically different spontaneously pacing rates are electrically
connected, they might be expected to in some way ''synchronize'' their pacing to
form a better current source for activation of surrounding quiescent tissue. A number
of simulation and experimental studies have been done on this phenomenon. We did
some early simulations [13] with the Noma-Irisawa [10] model of spontaneously
pacing SA nodal cells in which we assumed two populations of cells: one with the
normal model properties and another group with increased
L
-type calcium current
(2 ×
I
si
) such that their automaticity was increased. In this case we considered these to
be two aggregates of cells (similar to the chick embryo cell aggregates experimentally
studied later on by Veenstra and DeHaan [19]) with each model aggregate having a
membrane area of 1 mm
2
. As shown in Fig. 1 the resulting cycle length (CL) for low
coupling resistance is the same as if there were a single aggregate with an average
value of 1.5 times the normal
I
si
. However, as the coupling resistance between the
aggregates was increased, the synchronized CL increased toward the value of the
faster aggregate. As the synchronized CL increased there was also a greater delay
between the activation times of the two aggregates and a greater disparity in the
maximum d
V
/d
t
of the upstrokes of the action potentials. The effects of increased
coupling resistance (e.g., fewer gap junctions) can be thought of as converting the
process of consensual synchronization to that of local propagation in which the cells
with greater intrinsic automaticity thus dominate the overall rate. Note also that the
ability of the two aggregates to synchronize was preserved up to a coupling resistance
of 25 Mȍ, even though the surface area of the model aggregate (1 ×10
-2
cm
2
) was
much larger than a single cell. From the approximate membrane surface area of only
20 ×10
-6
cm
2
for single nodal cells, we could extrapolate from these results that a
resistance of up to 12.5 ×10
9
ȍ would allow synchronization of a pair of nodal cells.
This corresponds to an intercellular coupling conductance of ~0.1 nS which could be
produced by a very few gap junction channels.
More recently, we used our ''coupling clamp'' circuit [24] to actually couple
together isolated rabbit SA nodal cells with a defined coupling conductance [20]. In this
technique, we simultaneously record the potential of two cells physically isolated from
each other and use a computer system to calculate what coupling current would exist if
there were a specified coupling conductance (G
c
) and then, updated at short time
intervals (e.g., 25 ȝs), supply this time varying current to one cell and the negative of
this current to the other cell. Our results are shown in the top panel of Fig. 2a.
