Biomedical Engineering Reference
In-Depth Information
We propose that there is a minimum time period that EBNs can be switched on and off
and that this is a physical constraint of the system. As shown in Figure 13.53c,small
saccades have approximately the same duration of 44 ms, and they do not significantly
change as a function of saccade magnitude. Also note that there is randomness in the
response, where saccades with large pulse magnitudes are matched with shorter dura-
tions, and vice versa. As the saccade size increases for small saccades, we propose that
additional neurons are added to the agonist neural input up to 7
,whereabovethis,all
neurons are engaged.
In our model, we sum the input of all active motoneurons into the firing of a single
neuron. Thus, as the magnitude of the saccades increases, the firing rate of the single
neuron in our model increases up to 7
, after which it is maximal, since all neurons are
firing. Keep in mind, however, that the firing rate of a real neuron is maximal and does
not change as a function of saccade magnitude, as is easily seen in Figure 4 in Robinson
[42] and Figure 2 in Van Gisbergen and coworkers [46]. The overall neural input for the
agonist pulse is given by
7
N
yð
N
ag
i
y
<
N
ag
¼
ð
13
:
59
Þ
7
N
ag
max
y
where
N
(y
T
) is the number of neurons firing for a saccade of y
T
degrees,
N
ag
i
is the contri-
bution from an individual neuron, and
N
ag
max
is the combined input from all neurons.
For small saccades, the commencement of firing of the individual neurons, or synchrony
of firing, has a great impact on the overall neural input, since the period of firing during
the pulse is small (10 ms for the estimate in Figure 13.54b). Randomness in the start time
among the active neurons means that the beginning of the saccade is more drawn out than
if they all started together. For smaller saccades, this may result in an incorrect start time,
which then effects the duration. Any lack of synchrony can cause the overall agonist input
to be smaller; this is a much larger factor for a small saccade than a large saccade, since the
pulse duration is much larger. It is very likely that during a saccade, neurons do not all
commence firing at the same instant. This is seen in Figure 13.54b, where there is a small
slope to the regression fit.
Above 7
, the magnitude of the saccade is dependent on the duration of the agonist pulse
with all neurons firing maximally. The agonist pulse magnitude as shown in Figure 13.54a
is approximately a constant according to the regression fit. The duration of the agonist
pulse increases as a function of saccade magnitude, as shown in Figure 13.54b.
The saccade controller described here is a time-optimal controller that differs from the
one describe by Enderle and Wolfe [16] because of the physiology of the system. Active
neurons during the pulse phase of the saccade all fire maximally. For saccades greater than
7
, this is the same time-optimal controller described earlier by Enderle and Wolfe [16]. For
saccades from 3 to 7
, the system is constrained by a minimum duration of the agonist
pulse; saccade magnitude is dependent on the number of active neurons, all firing maxi-
mally, consistent with physiological evidence. In terms of control, it is far easier to operate
the system for small saccades based on the number of active neurons firing maximally,
rather than adjusting the firing rate for all neurons as a function of saccade magnitude as
proposed by others. Thus, the system described here is still time-optimal based on physio-
logical constraints.
