Biomedical Engineering Reference
In-Depth Information
R-model (cellular adaptation), and we will show particular parameter variations
from which differences in their behaviors will emerge.
4.3. Relationship Between Episode Duration and Inter-Episode Interval
Can we trigger the network before synaptic strength (or firing threshold, if
we consider the R-model) has fully recovered? We can answer this question di-
rectly by looking at Figure 4B. At any time during the inter-episode interval
(while the system is tracking the lower branch of the S-curve), if we transiently
"stimulate" the network so that activity increases above the threshold, the phase
point will move to the high state, initiating an episode. However, the episode
will start from a lower value of
s
than a spontaneous episode, therefore the sys-
tem will track a shorter segment of the upper branch before reaching the left
knee and falling back to the low state (whatever the value of
s
for which we
triggered an episode, the critical value of
s
at which the episode terminates is
always the same). Therefore, the triggered episode is shorter than a spontaneous
episode. More precisely, the longer we wait to artificially trigger an episode, the
longer the episode is, as illustrated in Figure 6A,B.
This model prediction is testable experimentally. Indeed, we have shown
that it is possible to trigger episodes by stimulating sensory nerves afferent to
the spinal cord, and that the duration of the stimulated episodes increases with
the interval between the triggered episode and the end of the previous (sponta-
neous) episode, as shown in Figure 6C,D (37). In other words, the longer we let
the network excitability recover, the longer the triggered episode is. This sug-
gests that in the experimental preparation, as in the model, there is a critical
value of network excitability for which all triggered episodes terminate.
In Figure 6D we have also plotted the durations of spontaneous episodes
(gray dots) against the recovery interval that just preceded the episodes. Al-
though their range is different, the relationship is the same as for stimulated epi-
sodes, suggesting again that all episodes (spontaneous or triggered) terminate at
a fixed level of network excitability. To confirm this finding we have also
looked at the relationship between episode duration and the
following
interval
and found no correlation (37). This lack of correlation suggests that there is no
"memory" of the system's state once an episode is terminated, supporting our
finding that all episodes terminate at a fixed level of network excitability.
Figure 6D shows that spontaneous episodes occur after various intervals.
Unlike our simple model, episodes therefore can start at various levels of net-
work excitability. Episode initiation is a stochastic event. Although a higher
level of excitability means a higher probability of triggering an episode, the
network needs a triggering event in order for an episode to start, and this is
where randomness is introduced. On the other hand, as our data suggest, all epi-
sodes terminate at the same value of network excitability; episode termination is
