Recently, eye movement is represented by the axis angle, rotation vector, or quaternions, not by Fick coordinates. The axis angle, rotation vector, and quaternions measure single axis rotation from a chosen reference position to the current eye position. Using the axis angle, rotation vector, or quarternions, we can represent the eye position and eye velocity in the same three-dimensional coordinate. Using the axis angle, rotation vector, or quarternions, we can calculate the axis around which the eye rotates. We can also calculate the angular velocity around the axis. In this review, using the axis angle, rotation vector, or quarternions, we show that the gain of the vestibule-ocular reflex (VOR gain) around the eye rotational axis can be calculated both when lateral semicircular canals are mainly stimulated and when vertical semicircular canals are mainly stimulated. We calculated this VOR gain of patients with horizontal canal-type or posterior semicircular canal-type benign paroxysmal positional vertigo (BPPV). As a result, cupulolithiasis in semicircular canals affected the dynamics of the VOR at 0.1 Hz, but not at higher frequencies, and canalolithiasis in semicircular canals does not change the VOR gain at any frequencies. We also show that we can identity the affected lesion of semicircular canals by calculating the axis of positional nystagmus in BPPV patients. Posterior canal-type BPPV caused positional nystagmus of which the rotational axis was perpendicular to the plane of the posterior semicircular canal or pure torsional axis. Anterior semicircular canal-type BPPV caused positional nystagmus of which the eye rotational axis was perpendicular to the plane of the anterior semicircular canal. BPPV due to the simultaneous involvement of both horizontal and posterior semicircular canals had two rotational axes; at first it was perpendicular to the plane of the posterior semicircular canal, and next, it was perpendicular to the plane of the horizontal semicircular canal.

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Geotropic direction-changing positional nystagmus is considered to be caused by canalolithiasis of the horizontal semicircular canal. However, horizontal nystagmus, which persists without decreasing over time, can not be explained by canalolithiasis. The pathophysiology of the persistent type of geotropic direction-changing positional nystagmus is considered to be a result of light debris cupulolithiasis of the horizontal semicircular canal. In the supine position, permanent horizontal nystagmus toward the intact side is observed. In neutral position 1, with the head turned about 30 degrees to the affected side, the nystagmus decreases and eventually stops. With greater headturn, nystagmus toward the earth lasts for more than one minute. These phenomena are considered to indicate that the cupula is deflected by the buoyancy of attached light debris which is hypodense compared with the endolymph. In the nose-down position, persistent horizontal nystagmus to the affected side is detected. In neutral position 2, with the head turned about 30 degrees to the affected side, the nystagmus stops. To evaluate Ewald's first law, we quantitatively compared horizontal nystagmus in the supine position and that in the nose-down position with the use of video-oculography. The patients were fifteen women and four men with persistent horizontal positional nystagmus toward the ground, ranging in age from 23 to 83 years (average, 59.2 years). They had no evidence of neurologic disease. In fifteen patients (78.9%), the maximum slow phase velocity in the nose-down position was greater than that in the supine position. Therefore, an ampullopetal deviation of the horizontal semicircular canal cupula was considered to bring about stronger nystagmus than an ampullofugal displacement of the cupula.

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In order to study how dorso-ventral and naso-occipital linear accelerations affect the ocular responses induced by inter-aural axis linear accelerations, three-dimensional cyclic modulation of eye positions and velocities during off-vertical axis rotation (OVAR) were analyzed in four rhesus monkeys. The animals were rotated in darkness at 60°/s about an earth horizontal axis while placed in a pitched position relative to the rotation axis, so that the plane in which the gravitational vector rotated around the head was varied while the acceleration applied along the inter-aural axis remained identical across different pitch conditions. The amplitude of the compensatory bias slow phase eye velocity was the largest when the gravitational vector rotated in a plane between the animals' stereotaxic horizontal and presumed utricular planes. The phase of the modulation in yaw (horizontal) slow phase velocity, but not in eye position, tended to lag as the stimulus axis deviated from the normal to the presumed utricular plane. The modulation of roll (torsional) eye position was a function of the interaural acceleration, but the amplitude of modulation of roll slow phase velocity decreased with an increase in the roll bias velocity. Modulation of pitch (vertical) eye position was the largest when the axis of rotation corresponded to the head yaw axis, but modulation of pitch slow phase velocity was the largest during rotation about an axis close to the roll axis. Thus, the time differentiation of the positional modulation did not predict the velocity modulation. It is hypothesized that there are separate pathways for processing cyclic modulations of the eye position and velocity, and that the velocity storage utilizes both utricular and saccular information.

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The dolls' eyes manoeuvre in head tilt in roll (DM), recognised as one of the otolith function tests from Bárány's era in 1906 and treated as a classic test in the roll plane which yields ocular counter-rolling (OCR), was investigated in normal subjects. The DM is a simple, safe, and sound test but has not yet become quantitative. Recently, we devised a new three-dimensional eye movement image analysis technique using a commercialised infrared CCD camera, a personal computer, and public domain software. Image analysis was performed automatically using the public domain software NIH Image.
As the result of the DM, OCRs in particular torsional components of eye movements, of which analysis was performed by NIH Image, were performed by seven healthy normal subjects sampled among fifty normal subjects.
Six subjects were able to perform smooth OCRs under our critical instruction, except one subject wearing soft contact lens. They all reported no perception disorder and experienced had no sickness during the DM.
In a future study, we would like to apply the DM to patients with Meniere's disease (MD). The histopathological feature of MD is defined as endolymphatic hydrops (EH) and EH initially involves the whole inner ear system. If possible, to detect EH in the inner ear organs, we would like to investigate whether or not there is any abnormality of OCRs in MD patients. The DM can be useful to detect such abnormalities, non-invasively.

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A case of persistent primitive trigeminal artery with vertigo as the initial symptom is reported. The case was a 41-year-old female. Since 2002, the patient had repeated episodes of vertigo. In 2004, the patient experienced a loss of consciousness. No lesion causing dizziness was found by CT scan of the brain, MRI of the brain, ECG, brain wave examination, and a balance function test at the Department of Otolaryngology. Persistent primitive trigeminal artery and vertebrobasilar hypoplasia were suspected by MRA and the diagnosis was confirmed by angiography. It is advisable to consider MRA and angiography for vertigo or dizziness of unknown cause.

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Cogan's syndrome is primarily diagnosed based on subsequent episodes of an inflammatory eye disease and rapidly progressive, usually sequential bilateral loss of audiovestibular function. Since there are still no specific tests for the syndrome, it is difficult to diagnose Cogan's syndrome in the early stage before the emergence of both eye and audiovestiubular symptoms. We present a case of a 34-year-old woman who complained of vertigo and bilateral hearing loss. Magnetic resonance imaging (MRI) of the inner ear was performed before the emergence of keratitis. MRI on the 23rd day after onset of hearing loss revealed a slightly high intensity on TI-weighted images in the right vestibule, which showed profound hearing loss. On the 54th day after onset, high signal intensity was noted in the right cochlea, the vestibule, and lateral semicircular canal on Tl-weighted images, but no enhancement. The high signal intensity disappeared seven months after onset, but there was no defect of inner ear signs on the T2-weighted images. A high signal of the inner ear on T1-weighted images is not a specific sign of MRI in Cogan's syndrome, since it is sometimes encountered in the inner ear of labyrinthitis, bleeding in patients with leukemia, and intralabyrinthine schwanoma. However, MRI could be a possible method for the early diagnosis of Cogan's syndrome because this finding might be recognized before the onset of eye symptoms.

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We studied caloric responses of the unaffected side of patients with vestibular neuritis (VN). Six patients with VN, who underwent sequential caloric tests, were enrolled in this study. In all 6 subjects, the maximum slow phase eye velocity of caloric nystagmus on the unaffected side to ice water was smaller at the earlier stage after the vertigo attack (within one month after the attack) than that at the later stage. This phenomenon might be associated with the suppression of contralateral vestibular nuclei, which would be a part of vestibular compensation. We should take into consideration that caloric responses on the unaffected side could be altered according to the stage of the disease.

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