Biomedical Engineering Reference
In-Depth Information
Since the time delay before the resumption of activity in the oculomotor motoneurons
after the pulse phase of a saccade is greater for abducting saccades than with adducting sac-
cades, the incidence of saccades with dynamic overshoot should be greater for abducting
saccades than adducting saccades. This is precisely what is observed in saccadic eye move-
ment recordings; most saccades with dynamic overshoot occur in the abducting direction.
Additionally, because the contralateral TN's firing rate decreases as ipsilateral saccade
amplitude increases, the rate of dynamic overshoot decreases, since fewer saccades have
sufficiently high PIRB magnitudes. This is also what is observed in saccadic eye movement
recordings.
It is possible for a normal saccade to have a small PIRB as long as the onset delay is
small. As the onset delay increases, the PIRB must decrease or a saccade with dynamic or
glissadic overshoot occurs.
13.8.6 Time-Optimal Controller
The general principle for a time-optimal controller for the horizontal saccade system is
that the eyes reach their destination in minimum time that involves over 1,000 neurons.
Each neuron contributes to the neural input to the oculomotor plant. Enderle and Wolfe
[16] described the time-optimal control of saccadic eye movements with a single switch-
time using a linear homeomorphic oculomotor plant for the lateral and medical rectus
muscles. Here, we reexamine the 1987 study using the updated oculomotor plant and a
time-optimal controller constrained by a more realistic pulse-slide-step motoneuron stimu-
lation of the agonist muscle with a pause and step in the motoneuron stimulation of the
antagonist muscle, and physiological constraints.
The time-optimal controller proposed here has a firing rate in individual neurons that is
maximal during the agonist pulse and independent of eye orientation, while the antagonist
muscle is inhibited. We refer to maximal firing in the neuron as the intent of the system,
which, because of biophysical properties of the neuron membrane, slowly decays over time,
as described in Enderle [11]. The type of time-optimal controller described here is more
complex than the one in 1987 due to physiological considerations. The time-optimal control-
ler operates in two modes: one for small saccades and one for large saccades.
The duration of small saccades has been reported as approximately constant [23, 50,
Enderle and Zhou, 2010b], and also as a function of saccade amplitude (e.g., [4]). Estimating
the saccade start and end time is quite difficult because it is contaminated by noise. Enderle
and coworkers have used a Kaiser filter to reduce the impact of noise, which others may not
have implemented, and possibly introduced a difference in results. Moreover, synchrony of
firing will have a greater impact on the start time for small saccades than larger saccades,
since the beginning of the saccades is much more drawn out, making detection more difficult.
In our analysis, a regression fit for the data is carried out in two intervals: one between 3 and
7
, and one for those greater than 7
. Our results indicate an approximately constant duration
for small saccades and a duration that increases with saccade size for large saccades. Other
investigators have used a single interval for the regression fit to a straight line or a nonlinear
function. It is possible that using the technique used here will result in a similar conclusion to
ours. Since we did not analyze saccades less than 3
, judgment on saccade duration in this
interval is delayed and supports future investigation.
