Ординатура / Офтальмология / Английские материалы / Advances in Understanding Mechanisms and Treatment of Infantile Forms of Nystagmus_Leigh, Devereaux_2008
.pdf
16
Effect of Eye Exercise on Clinical Outcome of Noncompressive Ocular Motor Nerve Palsy
ANUCHIT POONYATHALANG, PISIT PREECHAWAT, AND VITOO JANVIMALUANG
ABSTRACT
Our objective was to study the effect of eye exercise on noncompressive ocular motor nerve palsies in addition to medical treatment. Traditional treatments to reduce diplopia in ocular motor nerve palsies include occlusion, prisms, and botulinum toxin injection. To reduce recovery time, the use of eye movement exercises has been introduced. Patients with ocular motor nerve palsy were randomly instructed to move their eyes back and forth in the directions of paresis 100 times a day. Time from onset of palsy until return of normal visual fusion was recorded and compared between an exercise and a nonexercise group. Eleven patients had cranial third nerve palsy, 12 had sixth nerve palsy, and 1 had both third and sixth nerve palsy. All patients were treated with oral aspirin or other antiplatelet agent. The eye exercise group included 9 patients, and the non–eye exercise group had 15 patients. The eye exercise group had an average recovery time of 3.8 weeks as compared to the 25.5 weeks for the nonexercise group. Patients who performed eye exercises had shorter recovery times from double vision than patients who were only given medical treatment. However, since our sample size was very small, other factors could be responsible for the results, and further studies are warranted.
Patients with extraocular muscle paralysis are often frustrated by double vision and related functional problems. Some patients are also distressed with dizziness
and nausea. Occlusion of one eye, spectacle prisms, and injection of botulinum toxin have been used to reduce diplopia during the recovery period. Usually, occlusion of the paralytic eye is recommended, but without stereopsis patients may encounter difficulties in daily activities. Rehabilitation of extraocular muscle palsy has involved exercises that emphasize maximal ocular motor effort1 or invoking the vestibulo-ocular reflex.2 However, there is little evidence-based support for such rehabilitation programs. In patients with noncompressive ocular motor nerve palsies, complete recovery of eye movement usually occurs within six months, but in patients with severe nerve injury, recovery is more variable.3 Training using the patient’s finger provides strong visual and somatosensory feedback, along with the corollary discharge of the motor command (efference copy), thereby providing a strong cue for the patient to make an appropriate eye movement in the correct direction.4 It has been proposed that eye movement exercise can assist not only in promoting movement on the affected side but also in decreasing hyperactivity on the unaffected side that might contribute to a muscular contracture.5 One goal of such eye movement exercises is to reduce recovery time.
PATIENTS AND METHODS
Twenty-four patients from our outpatient clinic who had double vision at the onset of their illness were recruited from 127 patients complaining of double vision between January 2003 and July 2004. The inclusion criteria were acute onset of diplopia, paralytic eye
136
EFFECT OF EYE EXERCISE ON OCULAR MOTOR NERVE PALSY 137
movement that eventually subsided, normal imaging studies, and no prior treatment with antiplatelet or anticoagulation. All patients presented for their initial visit within two weeks of onset of symptoms.
Patients who failed to recover within one year of the onset of paralysis were excluded from this study. Other exclusion criteria were a history of trauma, orbital accident, tumor, compressive lesion such as aneurysm, autoimmune diseases, chronic disorders such as thyroid-associated ophthalmopathy, myotonic dystrophy, myasthenia gravis, or chronic progressive external ophthalmoplegia. Demographic data such as age; sex; and systemic disorder that may affect the outcome, such as diabetes mellitus, hypertension, or dyslipidemia, were recorded.6
The severity of diplopia was based on the measurement of strabismus in prism diopters. The prism bar was placed in front of the paralytic eye and increased to the point that the subject could see a single target at distance. In individuals who had both horizontal and vertical deviations, we recorded the sum total of both deviations in prism diopters.
Patients were randomly assigned to perform exercises or no exercise. Patients assigned to exercises were instructed to move both eyes back and forth, following one of their fingers as it moved slowly in the plane of paresis, 100 times per day every day. As an example, in the case of cranial sixth nerve palsy, patients had to follow finger motion to extreme left and right, ignoring the limitation of the paretic muscle. At two weeks follow-up, the eye exercise group was rechecked to ensure that the method of exercise was being performed correctly. Patients were reassured about their general prognosis of ischemic ocular motor nerve palsy and the rationale of the exercise. They were encouraged to open both eyes as much as possible while in a safe environment, and to attempt to view binocularly. Ophthalmoplegia was evaluated at study entry, at the end of the two-week session, and every month in both groups.
Patients were asked to report when they first experienced single vision during binocular straight-ahead viewing of the scene. The time from onset of diplopia to normal fusion in central gaze were recorded in both
the exercise and nonexercise groups. A statistical comparison of the difference between subjects with and subjects without exercise intervention was conducted using an unpaired Student’s t-test. Other parameters thought to have the potential to affect the outcome were similarly analyzed. Differences were considered statistically significant at the p < 0.05 level. Patients from both groups were prescribed oral antiplatelet treatment at the first visit. If diplopia did not resolve after one year, management was reevaluated. The study was approved by the institutional ethics committee.
RESULTS
Twenty-four patients (15 men and 9 women) were studied. The mean age of the individuals was 61.4 years (range: 36 to 80 years). The oculomotor nerve was affected in 11 patients, the abducens nerve was affected in 12 patients, and 1 individual had both oculomotor and abducens nerve palsies. The presumed etiology of the extraocular paralysis in this group of patients was ischemia of the peripheral nerve. The group randomly assigned to eye exercises numbered 9 patients, and the non–eye exercise group numbered 15 patients. All patients in the exercise group followed the instruction on eye movement exercise satisfactorily. The mean deviations in exercise group and non-exercise group were 28.5 and 27.0 diopters, respectively. In all of our patients, diplopia resolved spontaneously; no surgical treatment was required for any patient of either group. Statistical analysis of age, sex, type of cranial nerve involvement (cranial nerve 3 or 6), and size of deviation showed no statistical difference between the exercise and non-exercise groups (p value for age was 0.63, for sex was 1.00, for type of cranial nerve was 0.27, for systemic disorder was 0.83, and for size of deviation was 0.32). The average recovery time of single vision in central gaze significantly favored the exercise group over the non-exercise group, with an average recovery time of 3.83 weeks for the exercise group versus 25.47 weeks for the non-exercise group (Student’s t-test; p = 0.0035) (see Table 16.1).
Table 16.1 Numbers and Averages of Variables of Exercise and Non-exercise Groups
Assigned Group |
Number of |
Average Age (y) |
Average |
Number of Cases with |
Average Recovery |
||
|
Cases |
|
Deviation Angle |
|
Systemic Disorder |
Time of Single Vision |
|
|
|
|
(D) |
|
|
|
in Primary Position |
|
|
|
DM |
HT |
Dyslipidemia |
||
|
|
|
|
(wk) |
|||
|
|
|
|
|
|
|
|
Exercise group |
9 |
63.8 |
27 |
9 |
3 |
1 |
3.83 |
Non-exercise group |
15 |
61.4 |
28.54 |
3 |
2 |
1 |
25.47 |
DM, diabetes mellitus; HT, hypertension.
138 GENERAL ASPECTS OF NORMAL AND ABNORMAL GAZE CONTROL
DISCUSSION
In our study, there were 5 patients in the non-exercise group for which the recovery time was more than six months; all of them occluded their paralytic eye most of the time, either with an eye patch or by squeezing their eyelids shut. Even though these patients eventually regained almost full range of eye movement, they had persistent difficulty adjusting to the spatial environment. In the exercise group, 1 patient with case of cranial third nerve palsy initially had difficulty conducting the exercises correctly because of ptosis; after reassurance and training, eye movements showed improvement. A few patients reported that their double vision persisted in the paralytic direction, causing difficulties especially when driving, even though their eye movement range was near complete. In those patients, we found that the speed of the paralytic muscle was slower than of the conjugate muscle. Since single vision was present in central gaze, we advised using larger head movements, in conjunction with a larger car mirror, to permit driving.
The binocular fusion mechanism normally makes it possible to point both eyes at the same visual target.7 Our exercises provide visual, somatosensory, and efference copy signals so that the brain can adapt to the peripheral motor weakness and induce “spread of concomitance.”8 Thus, our eye exercises may have sped up the spread of concomitance, which is part of the natural course of recovery from ocular motor nerve palsy.
CONCLUSIONS
This preliminary study demonstrated that patients who performed eye exercises had shorter recovery times from double vision than patients who were only given medical treatment. Patient education and eye movement training should be instituted early to decrease possible stiffness of the unaffected extraocular yoke muscle. It is important for the patient, ophthalmologist, and orthoptist to establish realistic goals within a reasonable time frame. Unfortunately, many patients hope for immediate improvement. Reassurance had to be offered to our patients from time to time. Therapy with prisms or botulinum toxin may require consideration.9,10 Since our sample size was small, other factors could possibly be responsible for our results. The goal of our exercises was to facilitate recovery of voluntary eye movement using attempted conjugate
eye movements along with visual and somatosensory feedback. The purpose of treatment of ocular motor nerve palsy should focus not only on restoring function of the paretic muscle but also on reestablishing the fusional mechanism.
ACKNOWLEDGMENT This research was supported by Ramathibodi Foundation.
References
1.Everhard-Halm YS, Koornneef L, Zonneveld FW. Conservative therapy frequently indicated in blow out fractures of the orbit. Ned Tijdschr Geneeskd. 1991; 135(27):1226–1228.
2.Kawahira K, Shimodozono M, Etoh S, Tanaka N. New facilitation exercise using the vestibuloocular reflex for ophthalmoplegia: preliminary report. Clin Rehabil. 2005; 19(6):627–634.
3.Golnik KC, Miller NR. Late recovery of function after oculomotor nerve palsy. Am J Ophthalmology. 1991;111:566–570.
4.Leigh RJ, Zee DS. The properties and neural substrate of eye movements. In: Leigh RJ, ed. The Neurology of Eye Movement. New York, NY: Oxford; 2006:3–19.
5.Gonzalez C, Chen HH, Ahmadi MA. Sherrington innervational surgery in the treatment of chronic sixth nerve paresis. Binocul Vis Strabismus Q. 2005;20(3):159–66.
6.Kobashi R, Ohtsuki H, Hasebe S. Clinical studies of ocular motility disturbances. Part 2. Ischemic ocular motor nerve palsy risk factors. Jpn J Ophthalmol. 1997;41:115–119.
7.Leigh RJ, Zee DS. Diagnosis of nystagmus and saccadic intrusion. In: Leigh RJ, ed. The Neurology of Eye Movement. New York, NY: Oxford; 2006: 475–558.
8.Leigh RJ, Zee DS. Diagnosis of peripheral ocular motor palsies and strabismus. In: Leigh RJ, ed.
The Neurology of Eye Movement. New York, NY: Oxford; 2006:385–474.
9.Scott AB, Kraft SB. Botulinum toxin injection in the management of lateral rectus palsy. Ophthalmology. 1985; 92:676–683.
10.Kubatko-Zielinska T, Krzystkowz KM, Madroszkiewicz A, et al. Principles and results of treatment in acquired oculomotor paresis. Klin Oczna. 1995;97:147–151.
17
Expanding the Original Behavioral Infantile Nystagmus Syndrome Model to Jerk Waveforms and Gaze-angle Variations
ZHONG I. WANG, LOUIS F. DELL’OSSO,
AND JONATHAN B. JACOBS
ABSTRACT
Our objective was to expand the behavioral ocular motor system (OMS) model for infantile nystagmus syndrome (INS) by (a) incorporating jerk and jerk with extended foveation waveforms using a unifying mechanism for both pendular and jerk waveforms and (b) incorporating idiosyncratic variation of INS amplitude with gaze angles. Ocular motor recordings of humans, using infrared reflection, high-speed digital video, and magnetic search coil systems, were used as templates for the computer simulations. All simulations and analyses were performed in MATLAB Simulink environment. Examinations of eye movement data during different states of attention suggested that pendular and jerk INS waveforms came from the same underlying smooth-pursuit-system oscillation. Simulation of unidirectional jerk waveforms required a resettable neural integrator in the pursuit premotor circuitry. Alexander’s law relationships were used to produce desired INS “null” positions and sharpness. At various gaze angles, these Alexander’s law relationships influenced the INS slowphase amplitudes differently, thus mimicking the same gaze-angle effects observed in INS patients. The simulations of a robust behavioral OMS model demonstrated that both pendular and jerk waveforms can be generated by the same pursuitsystem instability. Alexander’s law output effectively modulates the nystagmus variation at different gaze angles.
The ocular motor system (OMS) model for infantile nystagmus syndrome (INS) simulates the responses of individuals with several pendular waveforms (pendular with foveating saccades [Pfs] and pseudopendular with foveating saccades [PPfs]) based on a loss of damping of the normal pursuit-subsystem instability and its interaction with other OMS components. Accurate model simulations during fixation, saccades to known targets (steps, pulses, and pulse-steps), and smooth pursuit (ramps and step-ramps), as well as many emergent properties and unexpected predictions of the model, duplicate the recorded responses of humans with INS, providing strong support for the hypothetical mechanisms in the model.1,2
There are, however, a number of INS features that were not included in the original OMS model. To expand this behavioral model, we intend to incorporate jerk and jerk with extended foveation waveforms by employing a unifying mechanism for both pendular and jerk waveforms. Alexander’s law variation of slow-phase velocity was included in an interim version of the model; its output will be utilized to simulate slow-phase amplitude changes affecting the eXpanded Nystagmus Acuity Function (NAFX) peak,3 or the INS “null.”
METHODS
The ocular motor recordings and observations used for the computer simulation came from approximately 1,000 subjects with INS, who were recorded
139
140 GENERAL ASPECTS OF NORMAL AND ABNORMAL GAZE CONTROL
in our laboratory over 37 years. Eye movements were measured using either an infrared reflection (Eye-Trac 210, Applied Science Laboratories, Bedford, MA), a magnetic scleral search coil (CNC Engineering, Seattle, WA), or a high-speed digital video (EyeLink II, SR Research Ltd., Mississauga, Ontario, Canada) system. Specifications of the recording systems can be found elsewhere.4 All simulations were performed in the MATLAB Simulink (MathWorks, Natick, MA) environment.
RESULTS
Eye movement data with inattention from INS individuals revealed large pendular oscillations underneath the jerk waveforms (Fig. 17.1A). In Figure 17.1B, the foveating fast phase was delayed, and the accelerating slow phase actually decelerated (with a point of inflection) before the fast phase reset the fovea on target. As soon as attention to the target was reestablished (either spontaneously or after verbal prompting by the
experimenter), a foveating fast phase was generated and jerk waveforms reoccurred.
Examination of these data demonstrated that the underlying pendular oscillation had to be reset when each foveating saccade was made. A resettable neural integrator in the pursuit premotor circuitry (PMC+) was necessary to accomplish the resetting. This neural integrator has the same structure as that found in pulse generators,5-7 and is different from the common neural integrator in the final motor pathway. Using the fove- ating-saccade motor command, the oscillation was reset so that the underlying pendular waveform could be restarted. The time delays in both the feedback and feed-forward loops in PMC+ were also reset (i.e., the stored energy had to be dumped). Figures 17.1C–F show simulations of the model under various visual inputs. Jerk waveforms in both directions consistently arrived at the new target positions; despite slight differences in the sizes of each saccade, foveation always occurred (within ±0.5° of the target). The model also responded correctly to step inputs with different directions, onset times, and durations.
A
|
20 |
|
|
|
Inattention |
|
|
|
|
15 |
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
(˚) |
10 |
|
|
|
|
|
|
|
5 |
JRef |
|
JLef |
|
|
|
|
|
position |
|
|
|
|
|
|||
0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Eye |
5 |
|
|
|
|
|
|
|
10 |
|
|
|
|
|
|
|
|
|
15 |
Alternating direction Jef |
|
|
|
|||
|
20 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
|
|
|||||||
C |
|
|
|
|
E |
|
|
|
|
|
1.5 |
|
|
|
|
0.5 |
JR |
|
|
(˚) |
|
|
|
(˚) |
0 |
|
|
||
|
|
|
|
|
|
|
|||
position |
1 |
|
|
|
position |
0.5 |
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
0.5 |
|
|
|
|
1 |
|
|
|
Eye |
0 |
|
|
|
Eye |
1.5 |
|
|
|
|
JL |
|
2 |
|
|
|
|||
0.5 |
|
|
|
|
|
|
|||
|
|
|
|
2.5 |
|
|
|
||
|
0 |
0.5 |
1 |
1.5 |
|
0 |
0.5 |
1 |
1.5 |
|
|
|
Time (s) |
|
|
|
|
Time (s) |
|
B |
|
Time (s) |
D |
|
|
|
|
|
F |
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
20 |
JR |
|
|
|
|
|
|
|
|
|
15 |
|
|
|
|
|
|
15 |
JR |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
(˚) |
0 |
|
|
|
|
|
(˚) |
|
|
|
|
|
|
|
|
10 |
|
|
|
|
|
|
|
10 |
|
|
|
|
|
|||
positionEye (˚) |
|
|
Eyeposition |
|
JL |
|
|
|
|
Eyeposition |
|
|
|
|
|
||
10 |
|
|
5 |
|
|
|
|
|
|
|
|
|
|
|
|||
|
5 |
|
|
|
|
|
|
|
|
|
5 |
|
|
|
|
|
|
|
0 |
|
Inattention |
|
|
|
|
|
|
|
|
JR |
|
|
|
|
|
|
5 |
|
P |
|
10 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|||
|
|
Verbal |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
prompting |
|
15 |
|
|
|
|
|
|
|
|
|
|
|
|
|
15 |
|
|
|
0 |
1 |
2 |
3 |
4 |
5 |
|
0 |
1 |
2 |
3 |
4 |
5 |
|
20 |
|
|
|
|
|
Time (s) |
|
|
|
|
|
Time (s) |
|
|
||
15 |
16 |
17 |
18 |
19 |
20 |
21 |
Time (s)
Figure 17.1 (A) Fixation data from a patient with alternating-direction jerk with extended foveation (Jef) waveforms showing a large underlying pendular oscillation when inattention suppresses the fast phases.
(B) Fixation data from a patient with jerk right (JR) waveforms showing a delayed foveating fast phase and a decelerating slow phase before the fast phase resets the oscillation (by verbal prompting). (C) Model output of jerk left (JL) fixation. (D) Model responses with −15° step input. (E) Model output of jerk right (JR) fixation.
(F) Model responses with 15° step input. In (D) and (F), dashed lines indicate fovea (±0.5° around the target position).
EXPANDED INS MODEL 141
Alexander’s law describes the increase in the amplitude of nystagmus as the eye is moved in the direction of the fast phase in vestibular nystagmus and fusion maldevelopment nystagmus syndrome (FMNS). The Alexander’s law functional block in the internal monitor of the OMS model is based on a tonic imbalance signal modulated by efference copy of the eye position signal. In a previous simulation, gaze-angle effects in FMNS (i.e., foveating and defoveating fast-phase alternation) waveforms were guided by Alexander’s law input.8 For FMNS patients, the two Alexander’s law lines (one for fixation by each eye) operate independently of each other, with only one (depending on the fixating eye) determining the gaze-angle variation. In INS, we hypothesize that both Alexander’s law relationships operate together. This same imbalance, produced by improper calibration of the vestibular system, may also be the underlying reason for INS gaze-angle variation. Figure 17.2A demonstrates the gaze-angle variation model position output, corresponding to the “null” in Figure 17.2B (the NAFX peak in 17.2C) at 10°. Figure 17.2B shows how the two linear functions act simultaneously, with their intersection establishing the “null” position and the slopes of the curves controlling the broadness of the “null.” The modulation was produced by a variable gain in the PMC+ block.
DISCUSSION
When the first version of the OMS model was completed in 2003,2 it simulated the most complex INS waveforms (Pfs, PP, and PPfs) and the behavioral responses consistent with INS data. It demonstrated that our hypothesis for the generation of P, Pfs, PP, and PPfs could be realized by a functionally normal OMS. We have now demonstrated that, without adding a separate mechanism for jerk waveforms to the prior OMS model, and in agreement with observations and accurate eye movement recordings on inattention and waveform transition, the model can simulate pendular and jerk waveforms and behavioral responses from the same underlying mechanism. This supports the hypothesis that most pendular and jerk INS waveforms are due to a loss of pursuit-system damping.
The behavioral output of the OMS model at different gaze angles demonstrated the effectiveness of using Alexander’s law input to simulate the variation of IN waveforms across the whole visual field. The Alexander’s law imbalance (possibly asymmetrical) produced by improper calibration of the vestibular system may have caused the INS gaze-angle variation. The Alexander’s law effects on INS amplitude will be used in future versions of the model to control the
A
|
40 |
|
|
|
|
|
|
|
|
|
30 |
PPfs |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
20 |
|
|
|
|
|
|
|
|
(˚) |
10 |
|
|
|
|
|
|
|
|
Eyeposition |
10 |
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
|
20 |
|
|
|
|
|
|
|
|
|
30 |
|
|
|
|
|
|
|
|
|
40 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |
3.5 |
4 |
|
0 |
Time (s)
B
(˚) |
|
12 |
|
|
|
|
|
|
|
amplitude |
|
10 |
|
|
|
8 |
|
|
|
|
6 |
|
|
|
-phase |
|
|
|
|
|
4 |
|
|
|
|
2 |
|
|
|
Slow |
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
40 |
20 |
0 |
20 |
40 |
Gaze angle (˚)
C
|
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
0.8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
NAFX |
|
|
|
0.6 |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
0.4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
0.2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
||
40 |
20 |
0 |
20 |
40 |
|||||
Gaze angle (˚)
Figure 17.2 Model output of PPfs waveform (A) with a “null” at 10° and increased slow-phase amplitude to either side of the null. The intersection and slopes of the two Alexander’s law lines (B) correspond to the position and sharpness of the null, as seen in (A). The peak position and sharpness of the eXpanded Nystagmus Acuity Function (NAFX) curve (C) correspond to those of the null as shown in (A) and (B).
142 GENERAL ASPECTS OF NORMAL AND ABNORMAL GAZE CONTROL
idiosyncratic transitions between pendular and jerk waveforms. The effects of inattention on INS waveforms will also be incorporated into the model, through the same modulating gain in the PMC+ circuit.
These improvements in the OMS model add another step to the implementation of a complete and idiosyncratic OMS model that can simulate normal as well as pathological (e.g., INS) behaviors.
ACKNOWLEDGMENTS This research was supported by the Department of Veterans Affairs Merit Review.
References
1.Jacobs JB. An Ocular Motor System Model that Simulates Congenital Nystagmus, Including Braking and Foveating Saccades [dissertation]. Cleveland: Case Western Reserve University; 2001.
2.Jacobs JB, Dell’Osso LF. Congenital nystagmus: hypothesis for its genesis and complex waveforms within a behavioral ocular motor system model. JOV. 2004;4(7):604–625.
3.Dell’Osso LF, Jacobs JB. An expanded nystagmus acuity function: intraand intersubject prediction of best-corrected visual acuity. Doc Ophthalmol. 2002;104:249–276.
4.Wang Z, Dell’Osso LF, Zhang Z, Leigh RJ, Jacobs JB. Tenotomy does not affect saccadic velocities: support for the “small-signal” gain hypothesis. Vision Res. 2006;46:2259–2267.
5.Abel LA, Dell’Osso LF, Daroff RB. Analog model for gaze-evoked nystagmus. IEEE Trans Biomed Engng. 1978;BME(25):71–75.
6.Abel LA, Dell’Osso LF, Schmidt D, Daroff RB. Myasthenia gravis: analogue computer model. Exp Neurol. 1980;68:378–389.
7.Kustov AA, Robinson DL. Modified saccades evoked by stimulation of the Macaque superior colliculus account for properties of the resettable integrator. J Neurophysiol. 1995;73: 1724–1728.
8.Dell’Osso LF, Jacobs JB. A normal ocular motor system model that simulates the dual-mode fast phases of latent/manifest latent nystagmus. Biological Cybernetics. 2001;85:459–471.
18
Extension of the eXpanded Nystagmus Acuity Function to Vertical and Multiplanar Data
JONATHAN B. JACOBS AND LOUIS F. DELL’OSSO
ABSTRACT
Our objective was to update and extend the functionality of the eXpanded Nystagmus Acuity Function (NAFX), allowing for its application to biplanar nystagmus and improving its predictive value in clinical evaluations. The original NAFX was based on foveation times taken from a “tau surface,” an array with values calculated for each combination of position and velocity limits of a “foveation window.” For the updated NAFX, we replaced the empirical surface with a mathematically defined surface that matched the original, but without the idiosynchratic irregularities caused by the waveforms of the subjects used for its calculation. For biplanar data, we have investigated combining horizontal and vertical eye movement data into a single radial vector. Age-related relationships were incorporated for more accurate individual visual acuities. Using the same uniplanar patient data, we verified that the updated NAFX yielded results equivalent to those of the original NAFX for the foveation window limits we tested. For biplanar data, the NAFX values were also comparable to those from uniplanar data of the same magnitude. The new version of the NAFX allows greater accuracy in predicting visual acuity for subjects of all ages, for both uniplanar and, eventually, biplanar nystagmus. This will allow researchers and clinicians to select the best therapies for a wider range of nystagmus patients.
The original eXpanded Nystagmus Acuity Function (NAFX),1 which was based on the Nystagmus Acuity Function (NAF),2 is a mathematically derived relationship that relates visual acuity to the attempts at foveation that occur within nystagmus waveforms, based on the duration and cycle-to-cycle stability of these foveation periods. In the original function, the foveation window was defined as the times at which the target was within ±0.5° of the fovea and not moving faster than ±4.0 deg/s with respect to it. However, there are many patients who could not meet these criteria, so their nystagmus could not be analyzed by the NAF, prompting the development of the NAFX, which allows for larger foveation windows (up to ±6° by ±10 deg/s) by varying τ, the foveation duration constant. The collection of τ for all combinations of position and velocity limits is called the “tau surface,” and is shown in Figure 18.1A. While the shape does, in general, appear to be regular, there are obvious irregularities in the surface, most notably along the lower position values (left side of Fig. 18.1A). This was a consequence of some of the data that were used to generate the original surface: the “pseudopendular with foveating saccades” (PPfs) waveform has two saccades per cycle,3 and as the position limit was increased, the slow phase following the braking saccade was included in the calculation, inadvertently increasing the measured foveation time.
As originally developed, the NAFX was applied only to nystagmus that occurred within one plane, as most infantile nystagmus is predominantly horizontal. However, there is no reason why the algorithm cannot be used to evaluate data in the vertical plane as well.
143
144 GENERAL ASPECTS OF NORMAL AND ABNORMAL GAZE CONTROL
Figure 18.1 The original tau surface (A) generated from multiple data sets from an individual with infantile nystagmus syndrome and used in the software for the first version of the eXpanded Nystagmus Acuity Function (NAFX). Note the unevenness of the surface caused by both fitting the data and the small size of the nystagmus signal from this subject. (B) The revised tau surface. (C) The difference between the revised and original tau surfaces, plotted as a percentage difference. The flat surface is a zero plane, shown for reference. (D) The results of 40 analyses comparing the NAFX using the original tau surface versus the revised tau surface. The 45° line represents perfect equality.
Furthermore, we propose that the NAFX should be suitable for analysis of multiplanar nystagmus waveforms as one operation, by first combining the separate horizontal and vertical components into a radial vector.
Finally, as the NAFX is intended for use by clinicians as well as researchers, it must have a userfriendly interface while retaining the ability to allow deeper investigation of the data being analyzed.
METHODS
Rather than discarding the existing flawed tau surface and calculating a replacement using new data, we elected to reconstruct it by modifying its outlying values. To do this, we took each curve of fixed
velocity at each position limit and performed a double exponential fit (using the MATLAB curve-fitting toolbox [MathWorks, Natick, MA]) of the form a × exp (b × x) + c × exp (d × x) to the non-outlier points, with the resulting curves having r2 values of no less than 0.95. We defined the “velocity= 4 deg/s” border to be a constant, τ = 33.3 milliseconds, the original value from the NAF, and in close agreement with the fit of the tau surface data. We also defined the “position = 6°” line to be linear with the endpoints set by the fit to the endpoint of the “velocity = 10 deg/s” curve and the 33.3 milliseconds from the aforementioned 4 deg/s border and applied small shifts to align the previously fitted curves to this border. Finally, we fit all the original points along the “position = 0.5°” border with a simple polynomial, yielding an r2 value of 0.98 (Fig.18.1B).
EXTENSION OF NAFX TO VERTICAL AND MULTIPLANAR DATA 145
Figure 18.2 (top panel) Combining horizontal (top) and vertical (middle) eye movement data to create a radial nystagmus waveform (bottom). The dashed lines at ±0.5° represent the foveal extent. (bottom panel) The result of 22 biplanar eXpanded Nystagmus Acuity Function (NAFX) analyses compared to analyses of the individual uniplanar components. In most, but not all, cases, the radial NAFX is less than that of both individual components, as expected.
