Ординатура / Офтальмология / Английские материалы / Advances in Understanding Mechanisms and Treatment of Infantile Forms of Nystagmus_Leigh, Devereaux_2008

treatment she noted that she could not see well to the right. She saw her ophthalmologist the next day, and he identified a right visual field disturbance. She was admitted to University Hospitals of Cleveland later the same day. There was no history of visual disturbance, migraine headache, or smoking. She was not taking birth control pills. The only medical problem was asthma. A neurological examination was normal with the exception of a dense right congruous homonymous hemianopsia.

Magnetic resonance (MR) brain scan revealed an acute left occipital lobe ischemic infarct. Magnetic resonance angiography (MRA) revealed a right vertebral artery dissection at the C1 (atlas) level and occlusion of the calcarine branch of the left posterior cerebral artery. Intravenous heparin was started, and the patient was discharged on warfarin.

A follow-up visit 4.5 months after discharge revealed a persistent right homonymous hemianopsia. An MR brain scan revealed a remote left occipital lobe infarct. An MRA was normal with the exception of slight irregularities of the right vertebral artery lumen.

Anticoagulation was stopped and aspirin started. The right homonymous hemianopsia has persisted.

Patient 2

A 26-year-old woman with a 3-week history of nonradiating neck pain following cholecystectomy underwent a series of chiropractic treatments. One week later, over a period of several hours following a manipulation, she had two episodes of vertigo, each lasting between one and two minutes. The next day during a treatment, she developed the following: sudden onset of “dizziness” followed by vertigo, followed by “trouble focusing”/blurring of vision, followed by numbness of all extremities and nausea. She was sent to a hospital emergency room. Past medical history, family history, and social history were unremarkable. She was taking birth control pills.

Evaluation in the hospital emergency room revealed generalized numbness and weakness. On day 2 of her hospitalization she underwent a neurological evaluation, which revealed the following symptoms and signs: drowsiness, dysarthria, dysphagia, vertical nystagmus, quadriparesis—left greater than right, slightly hyperactive deep tendon reflexes with bilateral Hoffman’s signs, and absent Babinski signs. The sensory examination was normal.

MR of the brain revealed evidence of an acute medullary infarct. MRA revealed evidence of an “abnormal” left vertebral artery. It was unclear whether the narrowing was congenital or the result of a dissection. A detailed “stroke in the young” workup failed to uncover any stroke risks.

The patient was evaluated at University Hospitals 2.25 years later. She had persistent mild slurred speech, trouble focusing on objects “when my body is in motion,” intermittent lightheadedness, and persistent mild weakness of the left extremities. A neurological examination revealed upbeat nystagmus, left hemibody dysdiadochokinesis, a broad-based gait, and unsustained left ankle clonus.

DISCUSSION

The vertebral arteries pass through the transverse foramina of the first six vertebra of the highly mobile cervical spine, which permits approximately 160º of head rotation. Approximately 90º of the rotation is the atlas around the axis. Neck manipulation, particularly a combination of rotation and tilting, can stretch the vertebral artery opposite the direction of rotation, producing a shearing force at the level of the atlantoaxial joint and the potential for dissection with resultant occlusion of the lumen, thrombus formation, and embolization.9,17,21,22 Cadaver studies have demonstrated vertebral artery occlusion with head and neck manipulation.21,23 Repeated neck manipulation also may produce subclinical changes in the vertebral arteries.16,19,20 The accumulation effect then may result in a subsequent stroke at a later date.16,19,20 Far less often, carotid artery dissections may occur with neck manipulation secondary to compression of an internal carotid artery against the upper cervical vertebra.9,17,18

Vertebro-basilar and, less commonly, carotid artery distribution vascular events can be the result of nontherapeutic mechanical injury to the neck (Tables 25.1 and 25.2). Therapeutic neck and back manipulation is an ancient art.24,25 The best-known modern iterations, chiropractic and osteopathy, are both 19th-century American Midwestern inventions.26 Chiropractic manipulation is said to work by reducing subluxations that cause nerve root compression. In 1895, Daniel David Palmer, a dry-goods grocer and later a magnetotherapist, was on a quest to discover a unified concept to explain human illness. By chance, Palmer manipulated a “vertebra racked from its normal position” on Harvey Lillard, a janitor claiming deafness for 17 years.25 The deafness reportedly resolved. Palmer subsequently theorized that all disease is the result of interference with the body’s “innate intelligence” by misaligned vertebrae.25 He coined the term “chiropractic” from the Greek cheiro (hand) and praktekas (practice). From this humble beginning, chiropractic has grown into a large, commonly utilized alternative health-care delivery system. The chiropractor uses different manipulations and mobilization techniques.

Table 25.1 Vertebrobasilar Stroke: Nontherapeutic

Mechanical Causes

Head positioning during medical procedures/treatment

•Surgery

•Cervical traction

•Emergency resuscitation

•Perimetry

Exercise

•Yoga

•Calisthenics (neck exercises)

Recreation/sports activities

•Wrestling

•Swimming

•Football

•Archery

•Skiing

“Overhead” activities

•Work

•Stargazing

Other

•Driving (backing up)

•Accidents

•Sleeping (unusual position)

Source: Sherman D, Hart R, Easton J. Abrupt change in head position and cerebral infarction. Stroke. 1981;12:2–6; Frisoni G, Anzola G. Vertebrobasilar ischemia after neck motion. Stroke. 1991;22: 1452–1460; Caplan L. Posterior Circulation Disease: Clinical Findings, Diagnosis and Management. Boston, MA: Blackwell Science; 1996; Brain D. Some unresolved problems of cervical spondylosis. Br Med J. 1963;1:771–777; deKeyer J, Henrollen L, van Langenhove L. Vertebral artery occlusion complicating perimetry. Am J Ophthalmol. 1991;11:516–517. Adapted with permission from Devereaux MW. The neuro-ophthalmologic complications of cervical manipulation. J Neuroophthalmol. 2000;20:236–239.

Which of the manipulation maneuvers is most likely to cause vertebral artery dissection is uncertain.1,27

Neuro-ophthalmologic symptoms and signs may be the most prominent, and sometimes the primary, manifestation of cerebrovascular insult after chiropractic manipulation (Table 25.3). The most common are visual field disturbances secondary to occipital lobe strokes, as in Patient 1.6,8,11,28-31

Does the therapeutic benefit of cervical manipulation justify the complication rate? The first problem in answering this question is that the rate of complication is not fully established. The chiropractic literature suggests that stroke risks may be one in 1 million.

Table 25.2 Therapy-Induced Stroke: Potential

Sources

Chiropractic

Osteopathy

Naturopathy

Allopathic (occasional)

Physical therapy

Kung Fu practitioners

Barbers (India)

Friend/spouse

Self

Source: Sherman D, Hart R, Easton J. Abrupt change in head position and cerebral infarction. Stroke. 1981;12:2–6; Terrett A. Malpractice Avoidance for Chiropractors: Vertebrobasilar Stroke following Manipulations. West Des Moines, IA: National Chiropractic Mutual Insurance Co.; 1996; Caplan L. Posterior Circulation Disease: Clinical Findings, Diagnosis and Management. Boston, MA: Blackwell Science; 1996; Parkin P, Wallis W, Wilson J. Vertebral artery occlusion following manipulation of the neck. N Z Med J. 1978;88:441–443; Murthy J, Naidu K. Aneurysm of the cervical internal carotid artery following chiropractic manipulation. J Neurol Neurosurg Psychiatry. 1988;51:1237–1238.

Other studies suggest one per 100,000, and one study one per 20,000.32,33 A recent publication indicated that the risk of stroke in patients under 45 years of age is increased five times following chiropractic manipulation over age-matched controls.33 A survey conducted among California neurologists uncovered 56 strokes.1 I strongly suspect, based on the literature and personal experience, that a large number of cases go unrecognized, and others are recognized but not reported.

Regarding benefits from cervical manipulation for neck pain and headache, a meta-analysis by Hurwitz et al.34 concluded that “[c]ervical spine manipulation and mobilization probably provides at least some shortterm benefits for some patients with neck pain and headache,” hardly a ringing endorsement of the practice. Barr,35 commenting on this study in an editorial, stated that there are “no convincing data to support manual therapy.”

Table 25.3 Neuro-ophthalmologic Complications

of Chiropractic Manipulation

Visual field loss

Horner syndrome

Nystagmus

Abducens palsy

Internuclear ophthalmoplegia

Gaze palsy

Central retinal artery occlusion

Painful ophthalmoplegia

Source: Adapted with permission from Devereaux MW. The neuro-ophthalmologic complications of cervical manipulation. J Neuroophthalmol. 2000;20:236–239.

CONCLUSION

Stroke is a well-described consequence of chiropractic manipulation. Neuro-ophthalmologic disorders may be the primary, and occasionally the sole, manifestation of chiropractic-induced cerebrovascular injury. The frequency of chiropractic-induced stroke is uncertain, but it is probably more common than currently appreciated. Patients presenting with stroke, particularly the relatively young without stroke risk factors and with evidence of vertebral artery dissection on neuroimaging procedures, should be questioned about recent chiropractic manipulation. Patients should be made aware of the lack of established benefit of chiropractic cervical manual therapy and the potential risk of neurological injury from manipulation.

References

1.Lee K, Carlini W, McCormick FG, et al. Neurologic complications following chiropractic manipulation: a survey of California neurologists. Neurology. 1995;45:1213–1215.

2.Pratt-Thomas H, Berger K. Injuries after chiropractic manipulation. JAMA. 1947;133:600–603.

3.Mehalic T, Farhat S. Vertebral artery injury from chiropractic manipulation of the neck. Surg Neurol. 1974;2:125–129.

4.Lyness S, Wagman A. Neurological deficit following cervical manipulation. Surg Neurol. 1974;2: 121–124.

5.Davidson K, Weiford E, Dixon G. Traumatic vertebral artery pseudoaneurysm following chiropractic manipulation. Radiology. 1975;115: 651–652.

6.Kreuger B, Okazaki H. Vertebral-basilar distribution infarction following chiropractic manipulation. Mayo Clin Proc. 1980;55:322–332.

7.Schellhas D, Latchaw R, Wendling L, et al. Vertebrobasilar injuries following cervical manipulation. JAMA. 1980;244:1450–1453.

8.Sherman D, Hart R, Easton J. Abrupt change in head position and cerebral infarction. Stroke. 1981;12:2–6.

9.Hart R, Easton J. Dissections of cervical and cerebral arteries. Neurol Clin. 1983;1:155–182.

10.Frumkin L, Baloh R. Wallenberg’s syndrome following neck manipulation. Neurology. 1990; 40:611–615.

11.Frisoni G, Anzola G. Vertebrobasilar ischemia after neck motion. Stroke. 1991;22:1452–1460.

12.Wang J, Lin JJ, Lin JC, et al. Vertebral artery dissection complicated by cervical manipulation: a case report. Chung Hua / Hsueh Tsa Chih. 1995;55(6): 496–500.

13.Sternbach G, Cohen M, Goldschmid D. Vertebral artery injury presenting with signs of middle cerebral artery occlusion: a case report. Angiology. 1995; 46:843–846.

14.Terrett A, Webb M. Vertebrobasilar accidents (VA) following cervical spine adjustment manipulation.

J Am Chiropractic Assoc. 1982;12:2407.

15.Terrett A. Malpractice Avoidance for Chiropractors: Vertebrobasilar Stroke following Manipulations. West Des Moines, IA: National Chiropractic Mutual Insurance Co.; 1996.

16.Hufnagel A, Hammers A, Schonle P, et al. Stroke following chiropractic manipulation of the cervical spine. J Neurol. 1999;246:683–688.

17.Stringer W, Kelly D. Traumatic dissection of the extracranial internal carotid artery. Neurosurgery. 1980;6:123–130.

18.Peters M, Bohl J, Thomke F, et al. Dissection of the internal carotid artery after chiropractic manipulation of the neck. Neurology. 1995;45: 2284–2286.

19.Sherman M, Smialek J, Zane W. Pathogenesis of vertebral artery occlusion following cervical spine manipulation. Arch Pathol Lab Med. 1987;111:851–853.

20.Hart R. Vertebral artery dissection [editorial]. Neurology. 1988;38:987–989.

21.Caplan L. Posterior Circulation Disease: Clinical Findings, Diagnosis and Management. Boston,

MA: Blackwell Science; 1996.

22. Barton J, Margolis M. Rotational obstruction of the vertebral artery at the atlanto-axial joint. Neurology. 1975;9:117–120.

23.Brown B, Tatlow W. Radiographic studies of the vertebral arteries in cadavers: effects of position and traction on the head. Neuroradiology. 1963;81:80–88.

24.Laban M, Taylor R. Manipulation: an objective analysis of the literature. Orthop Clin. 1992;23: 451–459.

25.Magner G. Chiropractic: The Victims’ Perspective. Amherst, New York: Prometheus Books; 1995.

26.Howell J. The paradox of osteopathy [editorial]. N Engl J Med. 1999;341:1465–1467.

27.Patijn J. Complications of manual medicine: a review of the literature. J Manual Med. 1991;6:89–92.

28.Gittinger J. Occipital infarction following chiropractic cervical manipulation. J Clin Neuroophthalmol. 1986;6:11–13.

29.Donzis P, Factor J. Visual field loss resulting from cervical chiropractic manipulation. Am J Ophthalmol. 1997;123:851–852.

30.Jones M, Waggoner R, Hoyt W. Cerebral polyopia with extrastriate quadrantanopia: report of a case with magnetic resonance documentation of

ABSTRACT

Our objective was to investigate the previously observed hysteresis effects of multiand singlestep vergence on visual acuity in a subject with infantile nystagmus syndrome. Eye movements were measured using a high-speed digital video system during fixation of targets at 0º as targets stepped in from far (F) to near (N: 60 D) and back out (5 or 20 s/presentation), as well as during single steps (1 to 5 s/presentation). Higher values of the eXpanded Nystagmus Acuity Function (NAFX) were achieved at far if the previous near target was fixated for 5 seconds. Single steps between near and far (1 and 3 s/presentation) did not improve the following far NAFX. Double-near shifts (F-N-F-N-F) yielded some improvement in far NAFX values in one of two trials with 3-second presentations. Hysteresis was still present for 5-second presentations of multiple-step targets, whereas the NAFX values were high at almost all near targets for 20second presentations; hysteresis was observed only at far. We found that, for better visual acuity at far, a fixation of ≥5 seconds of a near target is required. The time-dependent improvement of visual acuity during convergence or divergence may reflect the time required by the pulleys to reduce the plant’s responsiveness, allowing better vision.

Subjects with infantile nystagmus syndrome (INS) may exhibit hysteresis during disconjugate vergence

eye movements (i.e., fixation of the same target is associated with a higher eXpanded Nystagmus Acuity Function [NAFX]1 if the subject is diverging rather than converging).2 Hysteresis was found to occur in the central 20º of gaze at all examined vergence angles between far (4.2 diopters [D]) and near (60 D). A peripheral mechanism located either in the muscles or in the pulleys was hypothesized as the cause of hysteresis. It was also suggested that transient fixation of a nearer target, before focusing on the object of interest, might be useful in the daily activities of subjects with INS.

To better understand the mechanism of hysteresis associated with INS, its time course, and possible clinical implications, we designed a simple experiment to assess the visual acuity changes of a subject with INS during both multiand single-step vergence trials.

METHODS

Eye movements were measured using a high-speed digital video system (EyeLink II, SR Research, Mississauga, ON, Canada). The NAFX was used to evaluate the IN waveform’s foveation quality at all fixation points. The subject was seated in a chair with a headrest and a chin stabilizer, far enough from an arc where the far LED (4.2 D) was placed to prevent convergence effects (>1.5 m). At this distance, the LED subtended less than 0.1º of visual angle. A stimulus bar containing eight vergence targets was placed along the subject’s line of sight, at eye level, at different increasing vergence angles (LED 1 = 60 D). The room light could be adjusted from dim to blackout to minimize

extraneous visual stimuli. The experiment consisted of different multiand single-step target trials. Multi-step trials included stepping in from far (4.2 D) to near (60 D) and back out to far, allowing 5 or 20 seconds per target interval, to evaluate the time course of hysteresis. Single-step trials, with the target alternating between the far and near positions, were conducted at short intervals (from 1 to 5 seconds per target) and at long intervals (from 10 to 30 seconds per target).

RESULTS

In the small, multiple-step target trials, the original hysteresis first reported for 5-second intervals was reproduced at all vergence angles (Fig. 26.1A). However, for 20-second intervals, the NAFX values were high during both convergence and divergence at all angles, except for 4.2 D (far) and 7 D, where hysteresis was observed (Fig. 26.1B).

Large, single-step trials between near and far (5 seconds per interval) showed a buildup in the NAFX values measured at far. With shorter intervals (1 and 3 seconds per interval), there was no improvement in the following NAFX at far. Double-near shifts (F-N-F-N-F) with 5-second intervals yielded successively higher NAFX values at both near and far (Fig. 26.2A). With 3-second intervals, some improvement in far NAFX values was seen in one of two trials (Fig. 26.2B). When longer intervals were tested (≈ 30 seconds), each initial increase in NAFX was diminished as fixation was maintained at both near and far (Fig. 26.2C). In particular, hysteresis-induced NAFX improvement started to decay after 10 to 20 seconds for the far targets.

Similarly, initial convergence-induced NAFX improvement at near (60 D) began to diminish within 20 seconds.

DISCUSSION

The damping of IN with convergence is well known and documented by eye movement data.3,4 This effect in both decreasing the intensity of nystagmus and allowing better waveform foveation quality has been attributed to the reduction of plant’s responsiveness (i.e., gain) during convergence. This might be, in turn, due to the repositioning of the muscle pulleys.2,5 IN damping by means of convergence has been shown to take place over a broad range of gaze angles (±20°), with associated improvement in the high-visual-acuity field, based on calculated NAFX values.2

Hysteresis (i.e., system output is dependent on both the current and the previous inputs) was an unexpected finding in different INS subjects performing vergence tasks. However, neither the time course of hysteresis nor closer simulations of daily-life conditions, where this finding may be useful, had been investigated before this preliminary study. The multi-step trials showed that hysteresis is present only at far targets (4.2 D and 7 D) if a 20-second target interval is presented, suggesting that, at central near targets (between 10.3 D and 60 D), the NAFX stays high for presentation intervals greater than 5 seconds.

Our present study also shows that quickly shifting gaze from a far object of interest to a nearer target, even if done repetitively, might increase the NAFX value for the far target only slightly. The records

showed that higher values of NAFX were achieved for fixation of the far target only when the previous near target was presented for at least 5 seconds. In order to substantially improve visual performance in fixating a far target, the near target must be presented for at least 5 seconds, preferably shifting fixation between far and near twice before finally fixating the far target (Fig. 26.2). Therefore, quickly shifting gaze from a road sign to the steering wheel while driving, as previously suggested,2 might not be helpful in increasing visual acuity, unless done twice.

Vergence-induced NAFX improvement, with possible associated hysteresis, starts to diminish after approximately 10 to 20 seconds. Therefore, we suggest it is the act of refixation (converging or diverging) that actually provides the initial improvement in visual function in subjects with INS. This also applies under real-life conditions, even in subjects who use baseout prisms to maximize the INS damping associated with convergence.

The time-dependent improvement of visual acuity during convergence or divergence may reflect the time required by a peripheral mechanism, either at the pulley or the muscle level, to reduce the plant’s responsiveness to nystagmus. The repositioning of the pulleys going from near to far might take place with a higher time-constant profile (slower loss of plant’s stiffness), yielding a transient visual acuity improvement while diverging (hysteresis).

In conclusion, our results help clarify the time course of hysteresis in a subject with INS. Further studies are required to explore the possible occurrence and time course of hysteresis in other forms of nystagmus

that damp with convergence, as well as to better characterize hysteresis at different gaze angles.

ACKNOWLEDGMENTS This research was supported by the Department of Veterans Affairs Merit Review (Dr. Dell’Osso) and the OASI Institute for Research and Care on Mental Retardation and Brain Aging, Troina, Italy (Dr. Serra).

References

1.Dell’Osso LF, Jacobs JB. An expanded nystagmus acuity function: intraand intersubject prediction of best-corrected visual acuity. Doc Ophthalmol. 2002;104:249–276.

2.Serra A, Dell’Osso LF, Jacobs JB, Burnstine RA. Combined gaze-angle and vergence variation in infantile nystagmus: two therapies that improve the high-visual acuity field and methods to measure it.

Invest Ophthalmol Vis Sci. 2006;47:2451–2460.

3.Dell’Osso LF. A Dual-Mode Model for the Normal Eye Tracking System and the System with Nystagmus [dissertation]. University of Wyoming: Laramie; 1968.

4.Dell’Osso LF, Gauthier G, Liberman G, Stark L. Eye movement recordings as a diagnostic tool in a case of congenital nystagmus. Am J Optom Arch Am Acad Optom. 1972;49:3–13.

5.Demer JL, Miller JM, Poukens V, Vinters HV, Glasgow BJ. Evidence for fibromuscular pulleys of the recti extraocular muscles. Invest Ophthalmol Vis Sci. 1995;36:1125–1136.

ABSTRACT

Insights into the pathogenesis of certain ocular oscillations are provided by determining whether eye or head movements can perturb or “reset” the nystagmus, causing a phase shift. When the oscillations are varying slowly, this poses few problems. However, when the oscillations vary rapidly in amplitude, frequency, or phase, it is often difficult to determine whether the perturbation has phaseshifted the nystagmus. The ocular oscillations of oculopalatal tremor (OPT) are a good example of a rapidly varying oscillation. Here, we describe a technique for applying complex wavelet analysis to determine whether OPT ocular oscillations are perturbed by head rotations. By selecting two nystagmus cycles prior to a head rotation and shifting them by twice the period to predict what the nystagmus would have been without the perturbation, we were able to compare this prediction with the two cycles that actually followed the rotation. The phase difference between the cycles before and after head rotation was determined by wavelet coherence analysis. We found that head perturbations caused significant (p < 0.05) rates of change of phase shift in both patients that we studied. Thus, this may be a useful technique for testing hypotheses about the pathogenesis of biological oscillations.

Oscillations are commonly encountered in biological signals. Studying the properties of oscillations often provides insights about their physiological mechanism, and may also aid understanding of the pathogen-

esis of abnormal oscillations. Important properties of the oscillations include amplitude, phase, and frequency, which are easily visualized with a power spectrum. If the oscillations are pure sinusoidal or combinations of a few sinusoidal waves, these properties are relatively easy to determine by using the traditional Fourier transformation. However, almost all biological signals (for example, from cardiac and skeletal muscle and from brain) have nonperiodic properties, and their frequency components vary with the time, which makes the traditional Fourier analysis impractical for analyzing the waveform’s properties. Short-term Fourier analysis can be used to analyze different frequency components at different times, but it cannot reach high resolution in both frequency and time domains.

An alternative approach is wavelet analysis, performed with a wavelet transform (WT). Localized in both time and frequency domains, WT provides detailed information about frequency components at different times, without sacrificing resolution for either frequency or time.1 The WT has good time and poor frequency resolution at high frequencies, and good frequency and poor time resolution at low frequencies, which enables users to separate close frequency components in the low-frequency region and different waveforms on the time axis in the high-frequency region.

An example of oscillations with aperiodic properties occurs as a feature of the clinical syndrome of oculopalatal tremor (OPT).2,3 This disorder is characterized by the slow development of oscillations of the eyes (nystagmus), palate, and other branchial muscles, typically at 2 to 4 Hz. OPT develops months after some

brainstem strokes, in association with hypertrophic degeneration of the inferior olivary nucleus (IO). A recent model has been presented to account for the ocular oscillations of OPT.4 The model has two main features: (1) a pulsatile oscillator at about 2 Hz, created by abnormal electrotonic coupling between cell bodies in the IO; and (2) quasipendular oscillations generated by a learned response from the cerebellum due to the pulsatile IO input. One prediction of this model is that rapid head rotations could “reset” the ocular nystagmus, because the vestibular nuclei project to both IO and vestibulocerebellum. By reset, we mean that the amplitude (energy) of the oscillations will not be changed, but their phase will be changed, by the head movements. Thus, the model predicts that the phase of the waveform will change after the head perturbation, but the energy of the waveform will not.

METHODS

We studied 2 patients (aged 46 and 57 years) with OPT syndrome. Each of them wore search coils on the forehead and both eyes while sitting in a 2-meter cube magnetic field. We measured gaze angles (eye in space) of each eye using the magnetic search coil technique, as previously described.5 Scleral search coils were precalibrated on a protractor device prior to placement in the subject’s eyes. Zero eye position was determined as each subject viewed a central visual target (laser spot projected onto a tangent screen at a distance of 125 cm) with each eye in turn. Coil signals were lowpass filtered (0 to 150 Hz) prior to digitization at 500 Hz. During each experiment, subjects were asked to fixate the central visual target for 15 to 30 seconds. After that, the investigator manually applied impulsive head rotations to the subjects approximately every 5 seconds for 30 seconds.

We analyzed the spectrum information of the signal before and after the head perturbation to evaluate the change in energy. In order to get the characteristic spectrum of the resting nystagmus, we chose the fixation period of each trial and picked out a series of saccade-free eye movements (using a criterion of eye velocity less than 40 deg/s). After resampling these movements, we obtained a total of 100 1-second slices, which allowed us to estimate the spectrum and confidence interval. Since the number of slices was large (100), it was possible to use a normal distribution to obtain the confidence interval. We then calculated the spectrum in a series of 1-second slices after the head was perturbed and compared their spectrum with that of the nystagmus during fixation with the head stationary.

The easiest way to measure the phase shift of these ocular oscillations is to compare the waveform with its own shifted version. The OPT oscillations usually

cycle around a fixed frequency within a period, so by shifting the OPT waveform on the time axis by a few cycles, we can predict the phase of the waveform if it was not perturbed. (Testing during the fixation period showed the phase changes between original waveform and shifted waveform are relatively small within a unit time period.) Thus we shifted the ocular oscillation by two cycles and compared its phase with that of its unshifted version before and after the head perturbation.

We also calculated the rate of change of the phase shift, which is the derivative of the phase difference between the shifted OPT oscillation and its unshifted version during the head perturbation. Since wavelet coherence analysis results in two-dimensional data (time and frequency) and the OPT oscillations lie within a certain range of frequencies, we needed to take a circular mean on the frequency axis to create one-dimensional data before we could perform the derivative operation. As we observed, the OPT oscillations have their major frequency components at 1 to 4 Hz, corresponding to period of 0.25 to 1.0 second. A circular mean is defined as:

n

am = atan(X,Y) with X = ∑cos(ai ) and

i=1

Y= ∑sin(ai )

i=1n

where am is the circular mean of ai (i = 1 to n). The circular mean is used here to calculate the mean of trigonometric angles.

RESULTS

After analyzing the eye movement with the wavelet decomposition and reconstruction package in MATLAB (MathWorks, Natick, MA), we found that the energy of OPT oscillation only resides from level 6 to level 8 of the wavelet decomposition, corresponding to a frequency range of approximately 1 to 4 Hz (Note: there is a simple mapping from wavelet level to frequency range). The energy that resides in levels 9–12 corresponds to the lower frequency components in the waveform, and the residual energy is of high frequency and lower amplitude and can be ignored as noise. Thus our analysis focused on the spectrum of levels 6–8 of the wavelet analysis. A comparison of the energy of resting nystagmus versus that of OPT nystagmus after the head perturbation is shown in Figure 27.1. The solid line and the horizontal bars show the resting nystagmus’s mean, upper, and lower 95% confidence interval. The dashed line is the mean of the OPT oscillations after head perturbations. Within levels 7 and 8, the dashed line is within the confidence interval of the