Spontaneous Nystagmus Violating the Alexander’s Law: Neural Substrates and Mechanisms

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Disobedience to Alexander’s law is occasionally observed in central nystagmus, but the underlying neural circuit mechanisms are poorly understood. We found a violation of Alexander’s law in one or both directions of lateral gaze in lesions of unilateral lateral medulla affecting the vestibular nucleus. When Alexander’s law is violated, the time constant (Tc) was larger than that in the controls (median [interquartile range, IQR]: 14.4 s [6.4–38.9] vs 9.0 s [IQR 5.5–12.6], p = 0.036) while the Tc did not differ between the groups when Alexander’ law is obeyed (9.6 s [3.6–16.1] vs 9.0 s [5.5–12.6], p = 0.924). To test the study hypothesis that an unstable neural integrator may generate nystagmus violating Alexander's law, we primarily utilized the gaze-holding neural integrator computational model, incorporating lesion-induced changes. With normal integrator function, the false rotational cue generates nystagmus following Alexander’s law. The first lesion, which changes the brainstem neural integrator, and the second lesion, which causes the Purkinje synapse to exert excitatory input, both lead to nystagmus that violates Alexander’s law. We propose that when the neural integrator is unstable with lesions in the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus, nystagmus violates Alexander’s law. Nystagmus Alexander’s law Neural integrator Lateral medullary infarction Cerebellum Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Alexander’s law refer to the phenomenon that spontaneous nystagmus increases during the gaze in the fast-phase direction and decreases during the gaze in the opposite slow-phase direction [ 1 ]. This law applies to most nystagmus from either peripheral or central lesions [ 2 , 3 ]. A few hypotheses have been proposed to explain this behavior, which include adaptive changes in the function of velocity-to-position neural integrator [ 4 , 5 ] and inherent physiological properties of the brainstem nuclei that process information both for the vestibulo-ocular reflex (VOR) and normal gaze holding [ 6 , 7 ]. Previously, spontaneous nystagmus that contravenes the Alexander's law has been described in a patient with upbeat nystagmus associated with Wernicke's encephalopathy [ 8 ]. Although the exact mechanism behind this phenomenon remains uncertain, one plausible explanation is an unstable neural integrator, as suggested by the slow phases of nystagmus with an exponentially increasing velocity [ 8 ]. In this context, we hypothesized that coalescence of unstable neural integrator with direction-fixed spontaneous nystagmus may give rise to violation of the Alexander’s law. This study aimed to define the characteristics and anatomical substrates of spontaneous nystagmus that violates the Alexander’s law, and elucidate the mechanism using quantitative oculographic analyses and a mathematical model of an unstable neural integrator. Materials and Methods Subjects We reviewed the medical records 2,652 patients with posterior circulations stroke (PCS) in the stroke registry at two University Hospitals in South Korea, Pusan National University and Pusan National University Yangsan Hospitals during a 13-year period. We found 17 patients having presented spontaneous horizontal or mixed horizontal and torsional nystagmus that disobeyed the Alexander’s law, i.e., decrease of nystagmus when looking in the direction of fast-phases and/or increase of nystagmus during the gaze in the direction of slow-phases (Video 1). The patients included nine men with the age ranging from 31 to 87 years (mean ± SD = 62 ± 13). For comparison, 20 patients with acute vestibular neuritis (VN, 13 men, 56 ± 10 years) served as a control. The demographic and clinical characteristics of the subjects are summarized in Table 1 . Table 1 Demographic and Clinical Characteristics of the Patients Patients with nystagmus violating Alexander’s law (n = 17) Patients with vestibular neuritis (n = 20) p Male sex, n (%) 9 (53) 13 (65) 0.272 Age, y, mean (SD) 62 (13) 56 (10) 0.149 Lesion side, right, n (%) 9 (53) 14 (70) 0.286 Onset to evaluation, day, median (IQR) 1 (0.5–2.5) 1 (1–1) 0.478 SN, °/s, median (IQR) 3.3 (2.0-7.8) 4.8 (2.5–6.5) 0.557 Abnormal vHITs, n (%) 6 (43) 20 (100) < 0.001 vHITs video head impulse tests, IQR interquartile range, SN spontaneous nystagmus, Tc time constant Clinical and Radiological Evaluation All patients received structured neurological and neuro-otological examination by the authors (J-H.C., K.D.C). Bedside neuro-otological evaluation included 4-item HINTS plus (Head Impulse, Nystagmus, Test of Skew, and acute hearing loss detected by finger rubbing) [ 9 ]. All patients had evaluation within 7 days from symptom onset. Patients received stroke protocol MRIs including axial T2, fluid-attenuated inversion recovery image, DWI, and angiography. Eye Movement Recording and Analyses Eye movements were recorded using three-dimensional video-oculography (VOG, SLVNG, SLMED, Seoul, South Korea) with the patients seated upright. The VOG device was calibrated for horizontal and vertical eye positions using its calibration system with laser projections on the screen at a distance of 1.5m. After calibration, we recorded nystagmus by instructing the patients to look at a target straight-ahead and displaced ± 20° horizontally. The target was present for 20 seconds at each position. We analyzed the nystagmus at three gaze positions: the primary and each eccentric gaze. The horizontal eye position was coded positive when looking in the fast-phase direction of spontaneous nystagmus. The slow-phase velocities (SPVs) of nystagmus were calculated using a MATLAB by differentiating eye positions. An average value of all SPVs was measured at each gaze position by applying a linear regression of the velocity versus position [ 3 , 10 , 11 ]. Then, we measured the slope of SPVs between the primary and eccentric gaze positions to determine an obedience of Alexander’s law. When the slopes of the fast and slow phases were both positive, we defined that the nystagmus obeyed the Alexander’s law. In contrast, we defined that the nystagmus violated the Alexander’s law when at least one of the slopes was negative. We also calculated the time constant (Tc) of nystagmus at each eccentric gaze position as follows [ 2 , 3 , 10 , 11 ]. Tc = ∆E pos /∆E vel ∆E pos : difference of eye position between the two positions ∆E vel : difference of slow-phase velocity between the two positions We also recorded spontaneous nystagmus without visual fixation, and positional nystagmus induced by various positional maneuvers including lying down from sitting, head turning to either side while supine, straight-head hanging, and Dix-Hallpike maneuver to each side. Laboratory Evaluation The VOR during head impulses was quantitatively assessed in 14 patients using a video-based equipment (SLMED, Seoul, Korea) as described previously [ 12 ]. The VOR gain was calculated as the ratio of the area under the entire eye-velocity relative to the area under the entire head-velocity. Reference data were obtained from 31 normal controls. The subjective visual vertical (SVV) tilt was measured in 13 patients by seating them upright in a dark room and asking to align a rod (80 cm long and 0.3 cm wide) vertically. The rod was presented randomly at various angles from the vertical at a distance of 130 cm from the patient’s eyes. The SVV tilt was determined by calculating the average deviation from the earth vertical during five adjustments. The SVV tilt was considered abnormal when it exceeded the normal values obtained from healthy controls (-3.0° to 3.0° in both eyes; a negative value indicates a counterclockwise rotation) [ 12 ]. Statistical Analysis All analyses were performed with SPSS (version 22.0, Chicago, IL, USA). Continuous variables were compared using the t test or Mann–Whitney U test, and nominal variables were compared with the χ2 or Fisher exact tests. The significance level was set at p < 0.05. Results Clinical and Radiological Characteristics During visual fixation, patients had mixed horizontal-torsional-upbeat (n = 11), pure horizontal (n = 4), and mixed horizontal-torsional (n = 2) nystagmus (Table 2 ). The direction of horizontal nystagmus was contralesional in all. Without visual fixation, all patients showed mainly horizontal nystagmus with or without a vertical or torsional component. One patient (Pt 4) showed right and clockwise torsional (from the patient’s perspective) beating nystagmus with an upbeat component that was irregularly interposed by left and counterclockwise torsional beating nystagmus with an upbeat component (aperiodic alternating nystagmus). Table 2 Clinical and Radiological Characteristics of Patients with Spontaneous Nystagmus Violating Alexander’s Law Patients Sex/age Lesion side Involved lesions SN with fixation Waveforms change during horizontal gazes SN without fixation Direction Slow phase waveforms Direction Slow phase waveforms 1 F/82 L LM, CB R C D in slow-phase direction in only right eye R = U C 2 F/74 R LM L C (-) L C 3 M/72 L LM, CB R mixed (D + C) (-) R C 4 F/54 L LM R > U > CW mixed (D + I or D + C) (-) R > U > CW (aPAN) C 5 F/62 L LM R mixed (D + C) (-) R = CW C 6 M/31 R LM L > CCW > U C (-) L > CCW > U C 7 F/63 R LM L > CCW > U C (-) L > CCW > U C 8 F/56 L LM R > CW > U mixed (D or D + I or D + C) (-) R > CW > U C 9 F/87 L LM R > CW C (-) R > CW C 10 F/63 R LM, CB L > U > CCW C (-) L > U > CCW C 11 M/67 R LM, CB CCW > L > U C (-) L > CCW > U C 12 M/66 L LM, CB CW > R > U C mixed (D or D + C) in slow-phase direction R > CW > U C 13 M/61 R LM CCW > L > U C (-) L > U > CCW C 14 F/43 R LM CCW > L > U C (-) L > CCW > U C 15 M/57 R LM CCW > L C (-) L > CCW > U C 16 M/62 L LM R > CW > U C (-) R = U > CW C 17 M/52 R LM L = U > CCW I D in slow-phase direction, C in fast-phase direction L = U > CCW I C constant-velocity, CB cerebellum, CCW counterclockwise, CW clockwise, D decreasing-velocity, F female, I increasing-velocity, L left, LM lateral medulla, M male, aPAN aperiodic alternating nystagmus, R right, SN spontaneous nystagmus, U upbeat Direction-changing apogeotropic and geotropic nystagmus were induced during supine roll test in each patient (Pt 13 and 16, respectively). Seven patients showed ocular ipsipulsion with ipsilesional saccadic hypermetria while 11 had impaired horizontal smooth pursuit in one (n = 4) or both directions (n = 7). Accompanying neurological signs included ataxia (n = 17), sensory changes (n = 11), Horner syndrome (n = 6). dysphagia (n = 5), dysarthria (n = 4), and hoarseness (n = 2). The head impulse VOR gains for the horizontal semicircular canals were abnormal in six patients (6/14, 43%); slightly decreased ipsilesionally (n = 2) or bilaterally (n = 1), and increased contralesionally (n = 2) or bilaterally (n = 1). Most of the patients tested exhibited ipsilesional SVV tilt (13/14, 93%). All patients had an acute infarction involving unilateral lateral medulla, and five showed an additional infarction in the ipsilateral cerebellum (Fig. 1 ). Oculographic Analyses Slow-phase Waveforms of Spontaneous Nystagmus Patients showed various slow-phase waveforms of spontaneous nystagmus during visual fixation that included linear- (n = 12), exponentially increasing- (n = 1), and mixed forms (n = 4). The mixed-velocity waveforms mostly comprised an initial decreasing-velocity followed by a constant or increasing-velocity even in a single beat. On elimination of visual fixation, the slow phase of spontaneous nystagmus became linear in 16 patients regardless of the waveforms observed during visual fixation while the slow phase velocity remained increasing in one (Pt 17). In three patients (Pt 1, 12 and 17), the patterns of slow-phases were changed by lateral gazes in a various way (Table 2 ). Patterns Violating the Alexander’s Law Spontaneous nystagmus violated the Alexander’s law during the gazes in both directions (n = 5, 29%) or during the gaze only in one direction (n = 12, 71%) (Table 3 ). Of the five patients with a violation in both directions, one (Pt 4) showed centripetal nystagmus (beating toward the primary position during the gaze in the direction of nystagmus). All five patients showed a negative slope for gaze both in the slow- and fast-phase directions (Table 3 and Fig. 2 A), and the median slopes were − 0.027 (IQR − 0.009 ~ -0.156) and − 0.103 (IQR − 0.032 ~ -0.143), respectively. In these patients, spontaneous nystagmus had a linear- (n = 2, Fig. 2 A) or mixed-velocity (n = 3) slow-phase waveforms. Table 3 Oculographic Analysis of Spontaneous Nystagmus as a Function of Horizontal Eye Positions Patient Slow-phase direction Primary position Fast-phase direction Velocity (mean ± SD, °/s) Slope (°/s/°) Tc (∆E pos /∆E vel , s) Velocity (mean ± SD, °/s) Velocity (mean ± SD, °/s) Slope (°/s/°) Tc (∆E pos /∆E vel , s) Complete violation of AL 1 7.24 ± 2.73 -0.012 83.3 7.00 ± 2.14 3.75 ± 1.80 -0.163 6.2 2 14.21 ± 5.14 -0.279 3.6 8.63 ± 8.21 6.58 ± 1.27 -0.103 9.8 3 2.94 ± 0.80 -0.027 37.7 2.41 ± 1.12 2.00 ± 0.82 -0.021 48.8 4 1.59 ± 0.36 -0.033 30.8 0.94 ± 0.47 -1.52 ± 0.32† -0.123 8.1 5 1.78 ± 0.54 -0.006 166.7 1.66 ± 0.54 0.82 ± 0.37 -0.042 23.8 Partial violation of AL in the slow-phase direction 6 4.90 ± 1.47 -0.024 42.6 4.43 ± 1.32 7.14 ± 1.76 0.136 7.4 Partial violation of AL in the fast-phase direction 7 9.94 ± 2.06 0.085 11.8 11.63 ± 2.29 9.37 ± 2.41 -0.113 8.9 8 1.34 ± 0.23 0.027 37.7 1.87 ± 0.76 0 -0.094 10.7 9 3.20 ± 0.73 0.033 30.8 3.85 ± 0.98 2.46 ± 1.11 -0.070 14.4 10 3.29 ± 0.70 0.060 16.8 4.48 ± 2.00 0 -0.224 4.5 11 7.71 ± 3.46 0.513 2.0 17.96 ± 4.05 8.30 ± 2.44 -0.483 2.1 12 1.36 ± 0.31 0.085 11.8 3.06 ± 0.66 0 -0.153 6.5 13 -2.68 ± 1.29† 0.300 3.3 3.31 ± 1.42 2.66 ± 0.87 -0.033 30.8 14 -2.94 ± 1.15† 0.237 4.2 1.79 ± 0.72 1.15 ± 0.13 -0.032 31.3 15 -1.41 ± 0.43† 0.181 5.5 2.20 ± 0.54 1.76 ± 0.54 -0.022 45.5 16 1.39 ± 0.33 0.073 13.8 2.84 ± 0.62 1.46 ± 0.33 -0.069 14.5 17 5.19 ± 2.64 0.506 2.0 15.30 ± 2.57 9.97 ± 1.93 -0.267 3.8 † Negative value indicates that horizontal nystagmus reverses the direction during eccentric position. AL Alexander’s law, Tc time constant, ∆E pos difference of eye position between the two targets, ∆E ve l difference of slow-phase velocity between the two targets Video legends Video. Patient 1 with infarctions in the left lateral medulla and cerebellum shows spontaneous right-beating nystagmus of which the intensities increase during leftward gaze (slow-phase direction) while decrease during rightward gaze (fast-phase direction). Of the 12 patients with a violation of the Alexander’s law only in one direction of gaze, one showed an increase of nystagmus during the gaze in the opposite direction of nystagmus (Pt 6). In this patient, the slow phase was linear, and the slope was − 0.024 during the gaze in the opposite direction of spontaneous nystagmus (Table 3 and Fig. 2 B). In the remaining 11 patients (Pt 7–17), spontaneous nystagmus decreased when looking in the direction of spontaneous nystagmus with a median slope at -0.094 (IQR − 0.033~ -0.224) (Table 3 and Fig. 2 C). The slow phases were mostly linear (n = 9), but accelerating or mixed in each patient (Fig. 3 ). Comparison of the Time Constant between the Controls (patients with VN) and Patients with Spontaneous Nystagmus Violating the Alexander’s Law In the controls, the spontaneous nystagmus invariably obeyed the Alexander’s law with a positive slope during the lateral gazes in both directions. The median slopes were 0.100 (IQR 0.070 ~ 0.156) during the gaze in the direction of spontaneous nystagmus and 0.099 (IQR 0.063 ~ 0.188) during the gaze in the opposite direction. The median Tc was 9.0 s (IQR 5.5 ~ 12.6 s). In 17 patients with spontaneous nystagmus violating the Alexander’s law, the median Tc was measured at 14.4 s (IQR 6.4 ~ 38.9 s) when the Alexander’s law was violated and at 9.6 s (IQR 3.6 ~ 16.1 s) when the Alexander’s law was obeyed. The median Tc was higher when the Alexander’s was violated than that observed in the controls (14.4 s [IQR 6.4–38.9] vs 9.0 s [IQR 5.5–12.6], p = 0.036), whereas the Tc when the Alexander’s law was obeyed in the patients did not differ from the Tc observed in the controls (9.6 s [IQR 3.6–16.1] vs 9.0 s [IQR 5.5–12.6], p = 0.924) (Fig. 4 ). Modeling Neural Integration Model To test the study hypothesis that an unstable neural integrator can generate nystagmus violating Alexander's law, we primarily utilized the gaze-holding neural integrator model [ 13 ], incorporating lesion-induced changes. Based on the neural activities being proportional to eye position, the burst-tonic neurons within the vestibular nucleus and nucleus prepositus hypoglossi are believed to be the primary neural integrator, converting eye velocity into position information. However, this process is not perfect and is known as 'leakiness,' which might offer advantages in counteracting the accumulation of biological noise. This leakiness was herein modeled as a low-pass filter with a time constant of 2 seconds [ 13 ]. The flocculus and paraflocculus then play an important role in compensating for the leakiness of the brainstem neural integrator. They can be modeled either through positive feedback or negative feedback. In the positive feedback model, the eye position signals generated in the brainstem neural integrator are fed back to the neural integrator itself via the pathway through the cerebellum (Fig. 5 A) [ 2 , 14 ]. Meanwhile, the negative feedback model provides feedback to the vestibular nucleus and uses velocity information based on the difference between predicted and estimated eye velocities (Fig. 5 B) [ 13 ]. The details of each model have been introduced elsewhere [ 13 , 14 ], but herein we adopted the negative feedback model, assumed to be more physiological. Lesion-induced Changes Because the lesions observed for the violation of Alexander’s law were commonly located in the lateral medulla, these lesions could directly affect the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus. Therefore, we set the lesion-induced change such that a hyperexcitable brainstem neural integrator abnormally accumulates neural signals, replacing leakiness, or the cerebellar input exerts a positive, instead of a negative, effect on the vestibular nucleus (site-1 in Fig. 5 B and 5 C). The basis of these changes is as follows: For the direct neural integrator lesions, increased intracellular Ca2 + concentration can cause neuronal hyperexcitability [ 15 ]. For the cerebellar positive feedback, it has been suggested that GABA, the inhibitory neurotransmitter utilized by Purkinje cells, can paradoxically exert an excitatory effect (site-2 in Fig. 5 B and 5 C) [ 16 ]. Lastly, we implemented false constant rotational cues to induce lesion-induced spontaneous nystagmus. Simulation The results show that with normal integrator functions, the false rotational cue generates nystagmus following Alexander’s law (first row in Fig. 5 C). The first lesion, which changes the brainstem neural integrator, and the second lesion, which causes the Purkinje synapse to exert excitatory input, both lead to nystagmus that violates Alexander’s law (second and third rows in Fig. 5 C). This successfully visualizes our hypothesis. Discussion This study demonstrates that violation of the Alexander’s law is an occasional finding in patients with Wallenberg syndrome and an unstable neural integrator would be an underlying mechanism of the phenomenon. We provide evidence to support this hypothesis using a gaze-holding neural integrator model that incorporates lesion-induced changes. An explanation for Alexander’s law is adaptive changes in the velocity-to-position neural integrator to reduce spontaneous vestibular nystagmus during the gaze in the slow-phase direction to bring about improvement of vision [ 2 – 5 , 17 ]. The neural integrator is responsible for holding the eyes in eccentric position by mathematically integrating the eye velocity commands [ 2 , 18 , 19 ]. Impaired gaze holding and resultant gaze-evoked nystagmus (GEN) may be observed in lesions involving the nucleus prepositus hypoglossi (NPH) and medial vestibular nucleus (MVN) that play a crucial role in horizontal neural integration [ 20 – 23 ]. If the neural integrator becomes leaky in patients with direction-fixed vestibular nystagmus, the drift velocity of nystagmus increases during the gaze in the fast-phase direction and decreases during gaze in the slow-phase direction, conforming to the Alexander’s law. When the neural integrator becomes unstable, the eyes drift away from the central position, causing centripetal nystagmus [ 2 , 24 – 28 ]. Theoretically, when an unstable neural integrator is combined with direction-fixed vestibular nystagmus, the drift velocity may increase during the gaze in the slow-phase direction and decrease during the gaze in the fast-phase direction, thereby violating the Alexander’s law. In support of this hypothesis, our patients with Wallenberg syndrome and violation of the Alexander’s law showed that the Tc of nystagmus is increased only during the gaze where the Alexander's law was disobeyed. In addition, some patients exhibited the nystagmus with an accelerating (increasing velocity) slow phase or centripetal nystagmus. Our patients with the violation of Alexander’s law had invariable lesions in the lateral medulla. These lesions could directly affect the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus [ 29 , 30 ]. The neural integration for horizontal eye movements depends on a distributed network of neurons lying in the brainstem and cerebellum [ 2 , 20 – 23 ]. The flocculus and paraflocculus enhance the performance of an inherently leaky neural integrator in the brainstem either through positive or negative feedback [ 14 , 31 – 33 ]. Our gaze-holding neural integrator model, incorporating lesion-induced changes showed that when the neural integrator becomes unstable, nystagmus violates Alexander’s law. Under normal integrator function, the false rotational cue generates nystagmus following Alexander’s law. In contrast, the lesion-induced change such that a hyperexcitable brainstem neural integrator abnormally accumulates neural signals, replacing leakiness, or that the cerebellar input exerts a positive, instead of a negative, effect on the vestibular nucleus, produces nystagmus that violates Alexander’s law. Increased intracellular Ca2 + concentration may cause neuronal hyperexcitability for the direct neural integrator lesions [ 15 ], while for the cerebellar positive feedback, it has been suggested that GABA, the inhibitory neurotransmitter utilized by Purkinje cells, may paradoxically exert an excitatory effect [ 16 ]. Consistent with our results, previous experimental studies also showed that injection of either bicuculline or muscimol into the MVN caused instability of gaze holding, in which the eye drifts away from the central position with increasing-velocity waveforms, implying an unstable neural integrator [ 34 , 35 ]. These effects may be related to inactivation either of neurons within NPH-MVN or the cerebellar projections to them that control the fidelity of neural integration. Patients with a lesion restricted to the vestibular nuclei may show diverse signs of both peripheral vestibulopathy (spontaneous nystagmus, caloric paresis, and positive head impulse tests) and central vestibular dysfunction (GEN) [ 30 , 36 – 38 ]. Our study disclosed that lesions in the area of the vestibular nuclei can lead to diverse patterns of spontaneous nystagmus and its modulation by visual fixation and gaze. These findings may be explained by significant divergence of excitatory projections from the peripheral vestibular structures and brainstem neural integrators, along with inhibitory inputs from the cerebellum (Fig. 6 ) [ 2 , 13 , 29 , 30 ]. Some patients exhibited a mixed pattern of slow-phase velocity of spontaneous nystagmus with a beat-to-beat and intrabeat variability. Even in a single beat, the nystagmus consisted of an initial decelerating and following linear or accelerating slow phases. Similar waveforms have been reported in vertical nystagmus observed in lesions involving the paramedian tract (PMT) [ 39 ] or in patients with ankylosing spondylitis [ 40 ]. According to a mathematical model, these unusual waveforms may occur due to the pulse-step mismatch creating the initially decreasing-velocity waveforms due to leaky neural integrators, and subsequent disruption of the cerebellar feedback for gaze holding through PMT, resulting in unstable neural integrators and nystagmus with an increasing-velocity waveform [ 39 , 40 ]. GEN and superimposed pendular nystagmus observed in patients with multiple sclerosis also imply that the neural integrator can be simultaneously leaky and unstable [ 41 ]. Our patients more frequently showed a violation of the Alexander’s law only in one direction. This indicates that dysfunction of the neural integration depends on gaze direction. Thus, the neural integrators may become unstable in one direction while they become leaky in other directions of gaze [ 42 – 44 ]. Indeed, asymmetrical GEN has been described in patients with unilateral lesions of the NPH or MVN [ 30 , 37 , 38 , 45 ]. In unilateral lesion of the NPH, the neural integration is more severely impaired with a decrease in the Tc of postsaccadic drift after ipsilesional eccentric gaze [ 45 ]. Conclusion Spontaneous nystagmus in patients with Wallenberg’s syndrome can violate Alexander’s law, which permit a differentiation from acute peripheral vestibular syndrome. The violation of the Alexander’s law may be attributed to unstable neural integrator and can be simulated by lesions affecting the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus. Declarations Author contributions J-HC and E-HO analyzed and interpreted the data and wrote the manuscript. H-SK, J-YP, S-ML, S-YC, H-JK, J-YC, J-SK and JOM analyzed and interpreted the data. K-DC designed and conceptualized the study, interpreted the data, and revised the manuscript. All authors reviewed and approved the final version of the manuscript. K-DC is responsible for the overall content as guarantor, and obtained funding. Funding This research was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (NRF-2023R1A2C1004810). Data availability Anonymized data will be shared upon request from any qualified investigator. Conflict of interest Drs. JH Choi, EH Oh, HS Kim, JY Park, SM Lee, SY Choi, HJ Kim, JY Choi, J Otero-Millan, and KD Choi report no disclosures. Dr. JS Kim serves as an Associate Editor of Frontiers in Neuro-otology and on the editorial boards of the Journal of Clinical Neurology, Frontiers in Neuro-ophthalmology, Journal of Neuro-ophthalmology, and Journal of Vestibular Research, and Clinical and Translational Neurology. Ethical approval All the experiments performed in this study followed the tenets of the Declaration of Helsinki. Informed consents were obtained from the participants (including technicians in supplementary video) after the nature and possible consequences of this study had been explained to them. This study was approved by the Institutional Review Board of Pusan National University (2308-031-130) and Pusan National University Yangsan Hospitals (05-2023-180). References Alexander G. Die Ohrenkrankheiten im Kindesalter. In: Handbuch der Kinderheilkunde, edited by Schlossmann A. Leipzig, Germany: Vogel, 1912, pp. 84 – 96. Leigh RJ, Zee DS. The Neurology of Eye Movements. 5th ed. New York: Oxford University Press; 2015. Hegemann S, Straumann D, Bockisch C. Alexander's law in patients with acute vestibular tone asymmetry–evidence for multiple horizontal neural integrators. J Assoc Res Otolaryngol. 2007;8:551–61. Robinson DA, Zee DS, Hain TC, Holmes A, Rosenberg LF. Alexander's law: its behavior and origin in the human vestibulo-ocular reflex. Ann Neurol. 1984;16:714–22. 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Head-shaking nystagmus in lateral medullary infarction: patterns and possible mechanisms. Neurology. 2007;68:1337–44. Lee SU, Park SH, Park JJ, Kim HJ, Han MK, Bae HJ, et al. Dorsal Medullary Infarction: Distinct Syndrome of Isolated Central Vestibulopathy. Stroke. 2015;46:3081–7. Kamath RY, Keller EL. A neurological integrator for the oculomotor control system. Math Biosci. 1976;30:341–52. Glasauer S. Cerebellar contribution to saccades and gaze holding: a modeling approach. Ann N Y Acad Sci. 2003;1004:206–19. Beh SC, Frohman TC, Frohman EM. Cerebellar Control of Eye Movements. J Neuroophthalmol. 2017;37:87–98. Straube A, Kurzan R, Büttner U. Differential effects of bicuculline and muscimol microinjections into the vestibular nuclei on simian eye movements. Exp Brain Res. 1991;86:347–58. Arnold DB, Robinson DA, Leigh RJ. Nystagmus induced by pharmacological inactivation of the brainstem ocular motor integrator in monkey. Vis Res. 1999;39:4286–95. Kim HA, Lee H. Isolated vestibular nucleus infarction mimicking acute peripheral vestibulopathy. Stroke. 2010;41:1558–60. Kim HJ, Lee SH, Park JH, Choi JY, Kim JS. Isolated vestibular nuclear infarction: report of two cases and review of the literature. J Neurol. 2014;261:121–9. Ataç C, Kısabay A, Çetin Akkoç C, Saruhan G, Çelebisoy N. Vestibular nuclear infarction: Case series and review of the literature. J Stroke Cerebrovasc Dis. 2020;29:104937. Tian J, Otero-Millan J, Zee DS, Kheradmand A. Upbeat Nystagmus with an Unusual Velocity-Decreasing and Increasing Waveform: a Sign of Gaze-Holding Dysfunction in the Paramedian Tracts in the Medulla? Cerebellum. 2023;22:148–54. Abel LA, Traccis S, Dell'Osso LF, Ansevin CF. Variable waveforms in downbeat nystagmus imply short-term gain changes. Ann Neurol. 1983;13:616–20. Gupta P, Shaikh AG. Leaky and Unstable Neural Integrator Can Coexist-Paradox Observed in Multiple Sclerosis. J Neuroophthalmol. 2020;40:226–33. Cannon SC, Robinson DA, Shamma S. A proposed neural network for the integrator of the oculomotor system. Biol Cybern. 1983;49:127–36. Crawford JD, Vilis T. Modularity and parallel processing in the oculomotor integrator. Exp Brain Res. 1993;96:443–56. Aksay E, Olasagasti I, Mensh BD, Baker R, Goldman MS, Tank DW. Functional dissection of circuitry in a neural integrator. Nat Neurosci. 2007;10:494–504. Kim SH, Zee DS, du Lac S, Kim HJ, Kim JS. Nucleus prepositus hypoglossi lesions produce a unique ocular motor syndrome. Neurology. 2016;87:2026–33. Additional Declarations No competing interests reported. Supplementary Files video.mp4 Cite Share Download PDF Status: Published Journal Publication published 20 Jan, 2025 Read the published version in The Cerebellum → Version 1 posted Editorial decision: Revision requested 16 Nov, 2024 Reviews received at journal 09 Nov, 2024 Reviews received at journal 01 Oct, 2024 Reviewers agreed at journal 01 Sep, 2024 Reviewers agreed at journal 30 Aug, 2024 Reviewers invited by journal 29 Aug, 2024 Editor assigned by journal 12 Jul, 2024 Submission checks completed at journal 12 Jul, 2024 First submitted to journal 11 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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National University School of Medicine, Pusan National University Yangsan Hospital","correspondingAuthor":false,"prefix":"","firstName":"Eun","middleName":"Hye","lastName":"Oh","suffix":""},{"id":329652218,"identity":"c30f25a3-65e7-4f1f-b631-14f1bf717bce","order_by":2,"name":"Hyun Sung Kim","email":"","orcid":"","institution":"Gyeongsan National University School of Medicine and Gyeongsang National University Changwon Hospital","correspondingAuthor":false,"prefix":"","firstName":"Hyun","middleName":"Sung","lastName":"Kim","suffix":""},{"id":329652221,"identity":"8f8f5a81-37df-4fa5-85af-61c52530462d","order_by":3,"name":"Ji-Yun Park","email":"","orcid":"","institution":"Ulsan University Hospital, University of Ulsan College of Medicine","correspondingAuthor":false,"prefix":"","firstName":"Ji-Yun","middleName":"","lastName":"Park","suffix":""},{"id":329652224,"identity":"9dd0bcf4-48d9-4794-b6d5-4962636d248a","order_by":4,"name":"Suk-Min Lee","email":"","orcid":"","institution":"Pusan National University Hospital, Pusan National University School of Medicine and Biomedical Research Institute","correspondingAuthor":false,"prefix":"","firstName":"Suk-Min","middleName":"","lastName":"Lee","suffix":""},{"id":329652225,"identity":"8ccc74a4-2c62-46dc-ac34-ba14a0fcb210","order_by":5,"name":"Seo Young Choi","email":"","orcid":"","institution":"Pusan National University Hospital, Pusan National University School of Medicine and Biomedical Research Institute","correspondingAuthor":false,"prefix":"","firstName":"Seo","middleName":"Young","lastName":"Choi","suffix":""},{"id":329652226,"identity":"3c7f562e-7cba-4c22-ac0a-005219cae470","order_by":6,"name":"Hyo Jung Kim","email":"","orcid":"","institution":"Seoul National University Bundang Hospital","correspondingAuthor":false,"prefix":"","firstName":"Hyo","middleName":"Jung","lastName":"Kim","suffix":""},{"id":329652228,"identity":"27dd2312-3ea1-4a4f-9435-fbf7b29afbc6","order_by":7,"name":"Jeong-Yoon 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Choi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIie3OsQuCQBTH8dfiJM7vOPBvuBZdwr9FOXASCYSm5lqkWeifcGo+EHKJXAUXp5udnCIKSogIT7eG+w5vePCBH4BO94ch+AYAW31+ppFwNoFiBiF7LttuXcWsKmQLWw/IUYwTakp3mbEmYXXoMjhzoJY/TmyMDGqyJshrcBAMAbapGPYm1yCvyh7hPoHQFxFBLiIHFzvxnKogJJUOyRhPSB1tMDhwk6QKgiWX2N282KrKE3a9Z+NFQYb84apmfROdTqfT/eoBfek62M2Ic4sAAAAASUVORK5CYII=","orcid":"","institution":"Pusan National University Hospital, Pusan National University School of Medicine and Biomedical Research Institute","correspondingAuthor":true,"prefix":"","firstName":"Kwang-Dong","middleName":"","lastName":"Choi","suffix":""}],"badges":[],"createdAt":"2024-07-11 07:40:50","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4722547/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4722547/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s12311-025-01788-0","type":"published","date":"2025-01-20T15:56:56+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":61884952,"identity":"e51f184c-2d55-482b-a19e-de18d06d7461","added_by":"auto","created_at":"2024-08-06 16:20:44","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":719157,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eInvolved lesions in 17 patients with spontaneous nystagmus violating the Alexander’s law.\u003c/strong\u003e Diffusion-weighted images show the lesions mostly affecting unilateral lateral medulla. Five patients (patients 1, 3, and 10-12) have additional infarctions in the ipsilesional cerebellum.\u003c/p\u003e","description":"","filename":"figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/a2d1423154dfc16768700f4a.png"},{"id":61885884,"identity":"01377a0c-08bd-46fe-a44c-ddf2ba6b6fcf","added_by":"auto","created_at":"2024-08-06 16:36:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1436909,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe patterns violating the Alexander’s law\u003c/strong\u003e.\u003cstrong\u003e \u003c/strong\u003e(\u003cstrong\u003eA\u003c/strong\u003e) In patient 2, the slow-phase velocities (SPVs) of nystagmus increase when looking in the slow-phase direction while decrease when looking in the fast-phase direction. As a result, both slopes for gazes in the slow- and the fast-phase directions have negative values. The slow-phase waveforms of the nystagmus have a linear velocity during the primary and eccentric gazes (inside the rectangle). (\u003cstrong\u003eB\u003c/strong\u003e) In patient 6, the nystagmus increases during the gaze in both directions. The slow phases are linear (inside the rectangle). (\u003cstrong\u003eC\u003c/strong\u003e) In patient 17, the nystagmus decreases during the gaze in both directions, thus the slope is negative in the fast-phase direction. The slow phase waveforms are variable, showing an increasing-velocity at the primary position, and then changing into a decreasing velocity during the gaze in the slow-phase direction and a constant velocity during the gaze in the fast-phase direction (inside the rectangle).\u003c/p\u003e","description":"","filename":"figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/95b4070839f86b182e6374ae.png"},{"id":61884951,"identity":"2c45566c-5585-468b-9ca1-1f46f5c0e970","added_by":"auto","created_at":"2024-08-06 16:20:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":661782,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe slow-phase waveform of spontaneous nystagmus with a mixed-velocity in patient 8.\u003c/strong\u003eThe slow phase starts with a rapid drift with a deceleration, which is then followed by an acceleration (red asterisks) or constant velocity (green asterisks). Some waveforms show a pure decreasing velocity (blue asterisks).\u003c/p\u003e","description":"","filename":"figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/a60456ab3ded8ef17530c04a.png"},{"id":61885325,"identity":"75303180-4bfe-4a53-8d99-fd4e01714233","added_by":"auto","created_at":"2024-08-06 16:28:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":200333,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of the time constants between patients with spontaneous nystagmus violating the Alexander’s law and vestibular neuritis.\u003c/strong\u003eThe median Tc is higher when the Alexander’s is violated than that observed in the controls (14.4 s [interquartile range, IQR 6.4-38.9] vs 9.0 s [IQR 5.5-12.6]), whereas the Tc when the Alexander’s law is obeyed in the patients does not differ from the Tc observed in the controls (9.6 s [IQR 3.6-16.1] vs 9.0 s [IQR 5.5-12.6]).\u003c/p\u003e\n\u003cp\u003eAL=Alexander’s law, VN=vestibular neuritis\u003c/p\u003e","description":"","filename":"figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/ad34e5f986e3eb130db7923f.png"},{"id":61886414,"identity":"aaa3e3b8-cc96-4d47-b7e3-2825e7e20df0","added_by":"auto","created_at":"2024-08-06 16:44:44","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":770910,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematics of neural integrator models and the result of simulations.\u003c/strong\u003e (\u003cstrong\u003eA\u003c/strong\u003e) In the positive feedback model, the cerebellum compensates for the leakiness of the neural integrator with position information. (\u003cstrong\u003eB\u003c/strong\u003e) The model of negative velocity feedback. The vestibular signals primarily reach the vestibular nucleus (VN). These signals are then sent to the ocular motor nucleus (OMN) via both the direct and the neural integrator pathways, which in turn send signals to the eye plant. The cerebellum receives predicted eye velocity signals using a forward model of the eye plant, as well as desired eye velocity information through primary vestibular afferents. The difference between these signals is sent to the negative feedback pathway. (\u003cstrong\u003eC\u003c/strong\u003e) For the simulation, three changes were made. One is the introduction of a false rotational cue (20 degrees/s clockwise in the yaw axis), simulating lesion-induced vestibular bias. This results in spontaneous nystagmus directed rightward. With normal integrator function, the gaze direction during the quick phase of nystagmus increases eye velocity, while gaze in the opposite direction decreases it. However, lesions at sites 1 and 2 alter the function of the neural integrator, making it unstable. These changes generate spontaneous nystagmus that does not comply with Alexander's law during lateral gaze movements.\u003c/p\u003e","description":"","filename":"figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/3ccf5e33be47eda594c4d4cb.png"},{"id":61884953,"identity":"c3fb4746-859f-4a8b-8393-ca45689df4ba","added_by":"auto","created_at":"2024-08-06 16:20:44","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":682084,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic illustration of the anatomical connections among the VN, NPH, vestibular nerve, and cerebellum.\u003c/strong\u003e The VN receives excitatory projections from the ipsilateral vestibular nerve and contralateral NPH while it receives inhibitory projections from the ipsilateral cerebellum and its contralateral partner via the commissural connections.\u003c/p\u003e\n\u003cp\u003eIV=abducens nucleus, NPH=nucleus prepositus hypoglossi, VN=vestibular nucleus\u003c/p\u003e","description":"","filename":"figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/6915fa27fedbf97896d6dfa5.png"},{"id":74858280,"identity":"e966b627-146f-43df-af9e-bcce686bffa8","added_by":"auto","created_at":"2025-01-27 16:06:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6862460,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/d43f4582-ea07-4493-a184-6e3126658b90.pdf"},{"id":61884958,"identity":"8cb2528c-6ef8-47bf-9db0-ddaca7087e96","added_by":"auto","created_at":"2024-08-06 16:20:44","extension":"mp4","order_by":8,"title":"","display":"","copyAsset":false,"role":"supplement","size":11761431,"visible":true,"origin":"","legend":"","description":"","filename":"video.mp4","url":"https://assets-eu.researchsquare.com/files/rs-4722547/v1/3cfeed8a16e529b1fdde8844.mp4"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spontaneous Nystagmus Violating the Alexander’s Law: Neural Substrates and Mechanisms","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAlexander\u0026rsquo;s law refer to the phenomenon that spontaneous nystagmus increases during the gaze in the fast-phase direction and decreases during the gaze in the opposite slow-phase direction [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. This law applies to most nystagmus from either peripheral or central lesions [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. A few hypotheses have been proposed to explain this behavior, which include adaptive changes in the function of velocity-to-position neural integrator [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] and inherent physiological properties of the brainstem nuclei that process information both for the vestibulo-ocular reflex (VOR) and normal gaze holding [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e \u003cp\u003ePreviously, spontaneous nystagmus that contravenes the Alexander's law has been described in a patient with upbeat nystagmus associated with Wernicke's encephalopathy [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Although the exact mechanism behind this phenomenon remains uncertain, one plausible explanation is an unstable neural integrator, as suggested by the slow phases of nystagmus with an exponentially increasing velocity [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In this context, we hypothesized that coalescence of unstable neural integrator with direction-fixed spontaneous nystagmus may give rise to violation of the Alexander\u0026rsquo;s law.\u003c/p\u003e \u003cp\u003eThis study aimed to define the characteristics and anatomical substrates of spontaneous nystagmus that violates the Alexander\u0026rsquo;s law, and elucidate the mechanism using quantitative oculographic analyses and a mathematical model of an unstable neural integrator.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eSubjects\u003c/h2\u003e \u003cp\u003eWe reviewed the medical records 2,652 patients with posterior circulations stroke (PCS) in the stroke registry at two University Hospitals in South Korea, Pusan National University and Pusan National University Yangsan Hospitals during a 13-year period.\u003c/p\u003e \u003cp\u003eWe found 17 patients having presented spontaneous horizontal or mixed horizontal and torsional nystagmus that disobeyed the Alexander\u0026rsquo;s law, i.e., decrease of nystagmus when looking in the direction of fast-phases and/or increase of nystagmus during the gaze in the direction of slow-phases (Video 1). The patients included nine men with the age ranging from 31 to 87 years (mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u0026thinsp;=\u0026thinsp;62\u0026thinsp;\u0026plusmn;\u0026thinsp;13). For comparison, 20 patients with acute vestibular neuritis (VN, 13 men, 56\u0026thinsp;\u0026plusmn;\u0026thinsp;10 years) served as a control. The demographic and clinical characteristics of the subjects are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eDemographic and Clinical Characteristics of the Patients\u003c/b\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePatients with nystagmus violating Alexander\u0026rsquo;s law (n\u0026thinsp;=\u0026thinsp;17)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePatients with vestibular neuritis (n\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMale sex, n (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9 (53)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13 (65)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.272\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge, y, mean (SD)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e62 (13)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e56 (10)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.149\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLesion side, right, n (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9 (53)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14 (70)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.286\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOnset to evaluation, day, median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1 (0.5\u0026ndash;2.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1 (1\u0026ndash;1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.478\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSN, \u0026deg;/s, median (IQR)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.3 (2.0-7.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.8 (2.5\u0026ndash;6.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.557\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAbnormal vHITs, n (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6 (43)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20 (100)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003evHITs\u003c/em\u003e video head impulse tests, \u003cem\u003eIQR\u003c/em\u003e interquartile range, \u003cem\u003eSN\u003c/em\u003e spontaneous nystagmus, \u003cem\u003eTc\u003c/em\u003e time constant\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eClinical and Radiological Evaluation\u003c/h2\u003e \u003cp\u003eAll patients received structured neurological and neuro-otological examination by the authors (J-H.C., K.D.C). Bedside neuro-otological evaluation included 4-item HINTS plus (Head Impulse, Nystagmus, Test of Skew, and acute hearing loss detected by finger rubbing) [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. All patients had evaluation within 7 days from symptom onset. Patients received stroke protocol MRIs including axial T2, fluid-attenuated inversion recovery image, DWI, and angiography.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eEye Movement Recording and Analyses\u003c/h2\u003e \u003cp\u003eEye movements were recorded using three-dimensional video-oculography (VOG, SLVNG, SLMED, Seoul, South Korea) with the patients seated upright. The VOG device was calibrated for horizontal and vertical eye positions using its calibration system with laser projections on the screen at a distance of 1.5m. After calibration, we recorded nystagmus by instructing the patients to look at a target straight-ahead and displaced \u0026plusmn; 20\u0026deg; horizontally. The target was present for 20 seconds at each position.\u003c/p\u003e \u003cp\u003eWe analyzed the nystagmus at three gaze positions: the primary and each eccentric gaze. The horizontal eye position was coded positive when looking in the fast-phase direction of spontaneous nystagmus. The slow-phase velocities (SPVs) of nystagmus were calculated using a MATLAB by differentiating eye positions. An average value of all SPVs was measured at each gaze position by applying a linear regression of the velocity versus position [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Then, we measured the slope of SPVs between the primary and eccentric gaze positions to determine an obedience of Alexander\u0026rsquo;s law. When the slopes of the fast and slow phases were both positive, we defined that the nystagmus obeyed the Alexander\u0026rsquo;s law. In contrast, we defined that the nystagmus violated the Alexander\u0026rsquo;s law when at least one of the slopes was negative. We also calculated the time constant (Tc) of nystagmus at each eccentric gaze position as follows [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTc = ∆E\u003csub\u003epos\u003c/sub\u003e/∆E\u003csub\u003evel\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e∆E\u003csub\u003epos\u003c/sub\u003e: difference of eye position between the two positions\u003c/p\u003e \u003cp\u003e∆E\u003csub\u003evel\u003c/sub\u003e: difference of slow-phase velocity between the two positions\u003c/p\u003e \u003cp\u003eWe also recorded spontaneous nystagmus without visual fixation, and positional nystagmus induced by various positional maneuvers including lying down from sitting, head turning to either side while supine, straight-head hanging, and Dix-Hallpike maneuver to each side.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eLaboratory Evaluation\u003c/h2\u003e \u003cp\u003eThe VOR during head impulses was quantitatively assessed in 14 patients using a video-based equipment (SLMED, Seoul, Korea) as described previously [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The VOR gain was calculated as the ratio of the area under the entire eye-velocity relative to the area under the entire head-velocity. Reference data were obtained from 31 normal controls. The subjective visual vertical (SVV) tilt was measured in 13 patients by seating them upright in a dark room and asking to align a rod (80 cm long and 0.3 cm wide) vertically. The rod was presented randomly at various angles from the vertical at a distance of 130 cm from the patient\u0026rsquo;s eyes. The SVV tilt was determined by calculating the average deviation from the earth vertical during five adjustments. The SVV tilt was considered abnormal when it exceeded the normal values obtained from healthy controls (-3.0\u0026deg; to 3.0\u0026deg; in both eyes; a negative value indicates a counterclockwise rotation) [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eStatistical Analysis\u003c/h2\u003e \u003cp\u003eAll analyses were performed with SPSS (version 22.0, Chicago, IL, USA). Continuous variables were compared using the t test or Mann\u0026ndash;Whitney U test, and nominal variables were compared with the χ2 or Fisher exact tests. The significance level was set at p\u0026thinsp;\u0026lt;\u0026thinsp;0.05.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eClinical and Radiological Characteristics\u003c/h2\u003e \u003cp\u003eDuring visual fixation, patients had mixed horizontal-torsional-upbeat (n\u0026thinsp;=\u0026thinsp;11), pure horizontal (n\u0026thinsp;=\u0026thinsp;4), and mixed horizontal-torsional (n\u0026thinsp;=\u0026thinsp;2) nystagmus (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The direction of horizontal nystagmus was contralesional in all. Without visual fixation, all patients showed mainly horizontal nystagmus with or without a vertical or torsional component. One patient (Pt 4) showed right and clockwise torsional (from the patient\u0026rsquo;s perspective) beating nystagmus with an upbeat component that was irregularly interposed by left and counterclockwise torsional beating nystagmus with an upbeat component (aperiodic alternating nystagmus).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eClinical and Radiological Characteristics of Patients with Spontaneous Nystagmus Violating Alexander\u0026rsquo;s Law\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePatients\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSex/age\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLesion side\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eInvolved lesions\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eSN with fixation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eWaveforms change during horizontal gazes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eSN without fixation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDirection\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSlow phase waveforms\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eDirection\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eSlow phase waveforms\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM, CB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eD in slow-phase direction in only right eye\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u0026thinsp;=\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM, CB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003emixed (D\u0026thinsp;+\u0026thinsp;C)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003emixed (D\u0026thinsp;+\u0026thinsp;I or D\u0026thinsp;+\u0026thinsp;C)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CW (aPAN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003emixed (D\u0026thinsp;+\u0026thinsp;C)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u0026thinsp;=\u0026thinsp;CW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;CW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003emixed (D or D\u0026thinsp;+\u0026thinsp;I or D\u0026thinsp;+\u0026thinsp;C)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;CW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;CW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;CW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM, CB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM, CB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCCW\u0026thinsp;\u0026gt;\u0026thinsp;L\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM, CB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCW\u0026thinsp;\u0026gt;\u0026thinsp;R\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003emixed (D or D\u0026thinsp;+\u0026thinsp;C) in slow-phase direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;CW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCCW\u0026thinsp;\u0026gt;\u0026thinsp;L\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eF/43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCCW\u0026thinsp;\u0026gt;\u0026thinsp;L\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCCW\u0026thinsp;\u0026gt;\u0026thinsp;L\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eR\u0026thinsp;\u0026gt;\u0026thinsp;CW\u0026thinsp;\u0026gt;\u0026thinsp;U\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(-)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eR\u0026thinsp;=\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eM/52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eL\u0026thinsp;=\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eD in slow-phase direction,\u003c/p\u003e \u003cp\u003eC in fast-phase direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eL\u0026thinsp;=\u0026thinsp;U\u0026thinsp;\u0026gt;\u0026thinsp;CCW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eI\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003e\u003cem\u003eC\u003c/em\u003e constant-velocity, \u003cem\u003eCB\u003c/em\u003e cerebellum, \u003cem\u003eCCW\u003c/em\u003e counterclockwise, \u003cem\u003eCW\u003c/em\u003e clockwise, \u003cem\u003eD\u003c/em\u003e decreasing-velocity, \u003cem\u003eF\u003c/em\u003e female, \u003cem\u003eI\u003c/em\u003e increasing-velocity, \u003cem\u003eL\u003c/em\u003e left, \u003cem\u003eLM\u003c/em\u003e lateral medulla, \u003cem\u003eM\u003c/em\u003e male, \u003cem\u003eaPAN\u003c/em\u003e aperiodic alternating nystagmus, \u003cem\u003eR\u003c/em\u003e right, \u003cem\u003eSN\u003c/em\u003e spontaneous nystagmus, \u003cem\u003eU\u003c/em\u003e upbeat\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eDirection-changing apogeotropic and geotropic nystagmus were induced during supine roll test in each patient (Pt 13 and 16, respectively). Seven patients showed ocular ipsipulsion with ipsilesional saccadic hypermetria while 11 had impaired horizontal smooth pursuit in one (n\u0026thinsp;=\u0026thinsp;4) or both directions (n\u0026thinsp;=\u0026thinsp;7). Accompanying neurological signs included ataxia (n\u0026thinsp;=\u0026thinsp;17), sensory changes (n\u0026thinsp;=\u0026thinsp;11), Horner syndrome (n\u0026thinsp;=\u0026thinsp;6). dysphagia (n\u0026thinsp;=\u0026thinsp;5), dysarthria (n\u0026thinsp;=\u0026thinsp;4), and hoarseness (n\u0026thinsp;=\u0026thinsp;2).\u003c/p\u003e \u003cp\u003eThe head impulse VOR gains for the horizontal semicircular canals were abnormal in six patients (6/14, 43%); slightly decreased ipsilesionally (n\u0026thinsp;=\u0026thinsp;2) or bilaterally (n\u0026thinsp;=\u0026thinsp;1), and increased contralesionally (n\u0026thinsp;=\u0026thinsp;2) or bilaterally (n\u0026thinsp;=\u0026thinsp;1). Most of the patients tested exhibited ipsilesional SVV tilt (13/14, 93%).\u003c/p\u003e \u003cp\u003eAll patients had an acute infarction involving unilateral lateral medulla, and five showed an additional infarction in the ipsilateral cerebellum (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eOculographic Analyses\u003c/h2\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003eSlow-phase Waveforms of Spontaneous Nystagmus\u003c/h2\u003e \u003cp\u003ePatients showed various slow-phase waveforms of spontaneous nystagmus during visual fixation that included linear- (n\u0026thinsp;=\u0026thinsp;12), exponentially increasing- (n\u0026thinsp;=\u0026thinsp;1), and mixed forms (n\u0026thinsp;=\u0026thinsp;4). The mixed-velocity waveforms mostly comprised an initial decreasing-velocity followed by a constant or increasing-velocity even in a single beat. On elimination of visual fixation, the slow phase of spontaneous nystagmus became linear in 16 patients regardless of the waveforms observed during visual fixation while the slow phase velocity remained increasing in one (Pt 17). In three patients (Pt 1, 12 and 17), the patterns of slow-phases were changed by lateral gazes in a various way (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003ePatterns Violating the Alexander\u0026rsquo;s Law\u003c/h2\u003e \u003cp\u003eSpontaneous nystagmus violated the Alexander\u0026rsquo;s law during the gazes in both directions (n\u0026thinsp;=\u0026thinsp;5, 29%) or during the gaze only in one direction (n\u0026thinsp;=\u0026thinsp;12, 71%) (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Of the five patients with a violation in both directions, one (Pt 4) showed centripetal nystagmus (beating toward the primary position during the gaze in the direction of nystagmus). All five patients showed a negative slope for gaze both in the slow- and fast-phase directions (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA), and the median slopes were \u0026minus;\u0026thinsp;0.027 (IQR \u0026minus;\u0026thinsp;0.009 ~ -0.156) and \u0026minus;\u0026thinsp;0.103 (IQR \u0026minus;\u0026thinsp;0.032 ~ -0.143), respectively. In these patients, spontaneous nystagmus had a linear- (n\u0026thinsp;=\u0026thinsp;2, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA) or mixed-velocity (n\u0026thinsp;=\u0026thinsp;3) slow-phase waveforms.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eOculographic Analysis of Spontaneous Nystagmus as a Function of Horizontal Eye Positions\u003c/b\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePatient\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eSlow-phase direction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePrimary position\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c10\" namest=\"c8\"\u003e \u003cp\u003eFast-phase direction\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVelocity\u003c/p\u003e \u003cp\u003e(mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD, \u0026deg;/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSlope\u003c/p\u003e \u003cp\u003e(\u0026deg;/s/\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTc\u003c/p\u003e \u003cp\u003e(∆E\u003csub\u003epos\u003c/sub\u003e/∆E\u003csub\u003evel\u003c/sub\u003e, s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eVelocity\u003c/p\u003e \u003cp\u003e(mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD, \u0026deg;/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eVelocity\u003c/p\u003e \u003cp\u003e(mean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD, \u0026deg;/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eSlope\u003c/p\u003e \u003cp\u003e(\u0026deg;/s/\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eTc\u003c/p\u003e \u003cp\u003e(∆E\u003csub\u003epos\u003c/sub\u003e/∆E\u003csub\u003evel\u003c/sub\u003e, s)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eComplete violation of AL\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.24\u0026thinsp;\u0026plusmn;\u0026thinsp;2.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e83.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.00\u0026thinsp;\u0026plusmn;\u0026thinsp;2.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.75\u0026thinsp;\u0026plusmn;\u0026thinsp;1.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e6.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.21\u0026thinsp;\u0026plusmn;\u0026thinsp;5.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.63\u0026thinsp;\u0026plusmn;\u0026thinsp;8.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6.58\u0026thinsp;\u0026plusmn;\u0026thinsp;1.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e9.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.94\u0026thinsp;\u0026plusmn;\u0026thinsp;0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e37.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.41\u0026thinsp;\u0026plusmn;\u0026thinsp;1.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.00\u0026thinsp;\u0026plusmn;\u0026thinsp;0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e48.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.59\u0026thinsp;\u0026plusmn;\u0026thinsp;0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.94\u0026thinsp;\u0026plusmn;\u0026thinsp;0.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.52\u0026thinsp;\u0026plusmn;\u0026thinsp;0.32\u0026dagger;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.78\u0026thinsp;\u0026plusmn;\u0026thinsp;0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e166.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.66\u0026thinsp;\u0026plusmn;\u0026thinsp;0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.82\u0026thinsp;\u0026plusmn;\u0026thinsp;0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.042\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e23.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePartial violation of AL in the slow-phase direction\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.90\u0026thinsp;\u0026plusmn;\u0026thinsp;1.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e42.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.43\u0026thinsp;\u0026plusmn;\u0026thinsp;1.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e7.14\u0026thinsp;\u0026plusmn;\u0026thinsp;1.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.136\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e7.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"10\" nameend=\"c10\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003ePartial violation of AL in the fast-phase direction\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.94\u0026thinsp;\u0026plusmn;\u0026thinsp;2.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e11.63\u0026thinsp;\u0026plusmn;\u0026thinsp;2.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9.37\u0026thinsp;\u0026plusmn;\u0026thinsp;2.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.113\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e8.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.34\u0026thinsp;\u0026plusmn;\u0026thinsp;0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e37.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.87\u0026thinsp;\u0026plusmn;\u0026thinsp;0.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.094\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e10.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.20\u0026thinsp;\u0026plusmn;\u0026thinsp;0.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.85\u0026thinsp;\u0026plusmn;\u0026thinsp;0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.46\u0026thinsp;\u0026plusmn;\u0026thinsp;1.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e14.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.29\u0026thinsp;\u0026plusmn;\u0026thinsp;0.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e16.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.48\u0026thinsp;\u0026plusmn;\u0026thinsp;2.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.224\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.71\u0026thinsp;\u0026plusmn;\u0026thinsp;3.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.513\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e17.96\u0026thinsp;\u0026plusmn;\u0026thinsp;4.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e8.30\u0026thinsp;\u0026plusmn;\u0026thinsp;2.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.483\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e2.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.36\u0026thinsp;\u0026plusmn;\u0026thinsp;0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.06\u0026thinsp;\u0026plusmn;\u0026thinsp;0.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e6.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.68\u0026thinsp;\u0026plusmn;\u0026thinsp;1.29\u0026dagger;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.31\u0026thinsp;\u0026plusmn;\u0026thinsp;1.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.66\u0026thinsp;\u0026plusmn;\u0026thinsp;0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.033\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e30.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.94\u0026thinsp;\u0026plusmn;\u0026thinsp;1.15\u0026dagger;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.237\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.79\u0026thinsp;\u0026plusmn;\u0026thinsp;0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e31.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.41\u0026thinsp;\u0026plusmn;\u0026thinsp;0.43\u0026dagger;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.181\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.20\u0026thinsp;\u0026plusmn;\u0026thinsp;0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.76\u0026thinsp;\u0026plusmn;\u0026thinsp;0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e45.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.39\u0026thinsp;\u0026plusmn;\u0026thinsp;0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.84\u0026thinsp;\u0026plusmn;\u0026thinsp;0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.46\u0026thinsp;\u0026plusmn;\u0026thinsp;0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.069\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e14.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.19\u0026thinsp;\u0026plusmn;\u0026thinsp;2.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.506\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15.30\u0026thinsp;\u0026plusmn;\u0026thinsp;2.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9.97\u0026thinsp;\u0026plusmn;\u0026thinsp;1.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e3.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u0026dagger; Negative value indicates that horizontal nystagmus reverses the direction during eccentric position.\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cem\u003eAL\u003c/em\u003e Alexander\u0026rsquo;s law, \u003cem\u003eTc\u003c/em\u003e time constant, \u003cem\u003e∆E\u003c/em\u003e\u003csub\u003e\u003cem\u003epos\u003c/em\u003e\u003c/sub\u003e difference of eye position between the two targets, \u003cem\u003e∆E\u003c/em\u003e\u003csub\u003e\u003cem\u003eve\u003c/em\u003el\u003c/sub\u003e difference of slow-phase velocity between the two targets\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cb\u003eVideo legends\u003c/b\u003e\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cb\u003eVideo.\u003c/b\u003e Patient 1 with infarctions in the left lateral medulla and cerebellum shows spontaneous right-beating nystagmus of which the intensities increase during leftward gaze (slow-phase direction) while decrease during rightward gaze (fast-phase direction).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOf the 12 patients with a violation of the Alexander\u0026rsquo;s law only in one direction of gaze, one showed an increase of nystagmus during the gaze in the opposite direction of nystagmus (Pt 6). In this patient, the slow phase was linear, and the slope was \u0026minus;\u0026thinsp;0.024 during the gaze in the opposite direction of spontaneous nystagmus (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB). In the remaining 11 patients (Pt 7\u0026ndash;17), spontaneous nystagmus decreased when looking in the direction of spontaneous nystagmus with a median slope at -0.094 (IQR \u0026minus;\u0026thinsp;0.033~ -0.224) (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC). The slow phases were mostly linear (n\u0026thinsp;=\u0026thinsp;9), but accelerating or mixed in each patient (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eComparison of the Time Constant between the Controls (patients with VN) and Patients with Spontaneous Nystagmus Violating the Alexander\u0026rsquo;s Law\u003c/b\u003e \u003c/p\u003e \u003cp\u003eIn the controls, the spontaneous nystagmus invariably obeyed the Alexander\u0026rsquo;s law with a positive slope during the lateral gazes in both directions. The median slopes were 0.100 (IQR 0.070\u0026thinsp;~\u0026thinsp;0.156) during the gaze in the direction of spontaneous nystagmus and 0.099 (IQR 0.063\u0026thinsp;~\u0026thinsp;0.188) during the gaze in the opposite direction. The median Tc was 9.0 s (IQR 5.5\u0026thinsp;~\u0026thinsp;12.6 s).\u003c/p\u003e \u003cp\u003eIn 17 patients with spontaneous nystagmus violating the Alexander\u0026rsquo;s law, the median Tc was measured at 14.4 s (IQR 6.4\u0026thinsp;~\u0026thinsp;38.9 s) when the Alexander\u0026rsquo;s law was violated and at 9.6 s (IQR 3.6\u0026thinsp;~\u0026thinsp;16.1 s) when the Alexander\u0026rsquo;s law was obeyed. The median Tc was higher when the Alexander\u0026rsquo;s was violated than that observed in the controls (14.4 s [IQR 6.4\u0026ndash;38.9] vs 9.0 s [IQR 5.5\u0026ndash;12.6], \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.036), whereas the Tc when the Alexander\u0026rsquo;s law was obeyed in the patients did not differ from the Tc observed in the controls (9.6 s [IQR 3.6\u0026ndash;16.1] vs 9.0 s [IQR 5.5\u0026ndash;12.6], \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.924) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eModeling\u003c/h2\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003eNeural Integration Model\u003c/h2\u003e \u003cp\u003eTo test the study hypothesis that an unstable neural integrator can generate nystagmus violating Alexander's law, we primarily utilized the gaze-holding neural integrator model [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], incorporating lesion-induced changes. Based on the neural activities being proportional to eye position, the burst-tonic neurons within the vestibular nucleus and nucleus prepositus hypoglossi are believed to be the primary neural integrator, converting eye velocity into position information. However, this process is not perfect and is known as 'leakiness,' which might offer advantages in counteracting the accumulation of biological noise. This leakiness was herein modeled as a low-pass filter with a time constant of 2 seconds [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The flocculus and paraflocculus then play an important role in compensating for the leakiness of the brainstem neural integrator. They can be modeled either through positive feedback or negative feedback. In the positive feedback model, the eye position signals generated in the brainstem neural integrator are fed back to the neural integrator itself via the pathway through the cerebellum (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA) [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Meanwhile, the negative feedback model provides feedback to the vestibular nucleus and uses velocity information based on the difference between predicted and estimated eye velocities (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB) [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. The details of each model have been introduced elsewhere [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], but herein we adopted the negative feedback model, assumed to be more physiological.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eLesion-induced Changes\u003c/h2\u003e \u003cp\u003eBecause the lesions observed for the violation of Alexander\u0026rsquo;s law were commonly located in the lateral medulla, these lesions could directly affect the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus. Therefore, we set the lesion-induced change such that a hyperexcitable brainstem neural integrator abnormally accumulates neural signals, replacing leakiness, or the cerebellar input exerts a positive, instead of a negative, effect on the vestibular nucleus (site-1 in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC). The basis of these changes is as follows: For the direct neural integrator lesions, increased intracellular Ca2\u0026thinsp;+\u0026thinsp;concentration can cause neuronal hyperexcitability [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. For the cerebellar positive feedback, it has been suggested that GABA, the inhibitory neurotransmitter utilized by Purkinje cells, can paradoxically exert an excitatory effect (site-2 in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Lastly, we implemented false constant rotational cues to induce lesion-induced spontaneous nystagmus.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eSimulation\u003c/h2\u003e \u003cp\u003eThe results show that with normal integrator functions, the false rotational cue generates nystagmus following Alexander\u0026rsquo;s law (first row in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC). The first lesion, which changes the brainstem neural integrator, and the second lesion, which causes the Purkinje synapse to exert excitatory input, both lead to nystagmus that violates Alexander\u0026rsquo;s law (second and third rows in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC). This successfully visualizes our hypothesis.\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study demonstrates that violation of the Alexander\u0026rsquo;s law is an occasional finding in patients with Wallenberg syndrome and an unstable neural integrator would be an underlying mechanism of the phenomenon. We provide evidence to support this hypothesis using a gaze-holding neural integrator model that incorporates lesion-induced changes.\u003c/p\u003e \u003cp\u003eAn explanation for Alexander\u0026rsquo;s law is adaptive changes in the velocity-to-position neural integrator to reduce spontaneous vestibular nystagmus during the gaze in the slow-phase direction to bring about improvement of vision [\u003cspan additionalcitationids=\"CR3 CR4\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The neural integrator is responsible for holding the eyes in eccentric position by mathematically integrating the eye velocity commands [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Impaired gaze holding and resultant gaze-evoked nystagmus (GEN) may be observed in lesions involving the nucleus prepositus hypoglossi (NPH) and medial vestibular nucleus (MVN) that play a crucial role in horizontal neural integration [\u003cspan additionalcitationids=\"CR21 CR22\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. If the neural integrator becomes leaky in patients with direction-fixed vestibular nystagmus, the drift velocity of nystagmus increases during the gaze in the fast-phase direction and decreases during gaze in the slow-phase direction, conforming to the Alexander\u0026rsquo;s law.\u003c/p\u003e \u003cp\u003eWhen the neural integrator becomes unstable, the eyes drift away from the central position, causing centripetal nystagmus [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan additionalcitationids=\"CR25 CR26 CR27\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Theoretically, when an unstable neural integrator is combined with direction-fixed vestibular nystagmus, the drift velocity may increase during the gaze in the slow-phase direction and decrease during the gaze in the fast-phase direction, thereby violating the Alexander\u0026rsquo;s law. In support of this hypothesis, our patients with Wallenberg syndrome and violation of the Alexander\u0026rsquo;s law showed that the Tc of nystagmus is increased only during the gaze where the Alexander's law was disobeyed. In addition, some patients exhibited the nystagmus with an accelerating (increasing velocity) slow phase or centripetal nystagmus. Our patients with the violation of Alexander\u0026rsquo;s law had invariable lesions in the lateral medulla. These lesions could directly affect the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. The neural integration for horizontal eye movements depends on a distributed network of neurons lying in the brainstem and cerebellum [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan additionalcitationids=\"CR21 CR22\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. The flocculus and paraflocculus enhance the performance of an inherently leaky neural integrator in the brainstem either through positive or negative feedback [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Our gaze-holding neural integrator model, incorporating lesion-induced changes showed that when the neural integrator becomes unstable, nystagmus violates Alexander\u0026rsquo;s law. Under normal integrator function, the false rotational cue generates nystagmus following Alexander\u0026rsquo;s law. In contrast, the lesion-induced change such that a hyperexcitable brainstem neural integrator abnormally accumulates neural signals, replacing leakiness, or that the cerebellar input exerts a positive, instead of a negative, effect on the vestibular nucleus, produces nystagmus that violates Alexander\u0026rsquo;s law. Increased intracellular Ca2\u0026thinsp;+\u0026thinsp;concentration may cause neuronal hyperexcitability for the direct neural integrator lesions [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], while for the cerebellar positive feedback, it has been suggested that GABA, the inhibitory neurotransmitter utilized by Purkinje cells, may paradoxically exert an excitatory effect [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Consistent with our results, previous experimental studies also showed that injection of either bicuculline or muscimol into the MVN caused instability of gaze holding, in which the eye drifts away from the central position with increasing-velocity waveforms, implying an unstable neural integrator [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. These effects may be related to inactivation either of neurons within NPH-MVN or the cerebellar projections to them that control the fidelity of neural integration.\u003c/p\u003e \u003cp\u003ePatients with a lesion restricted to the vestibular nuclei may show diverse signs of both peripheral vestibulopathy (spontaneous nystagmus, caloric paresis, and positive head impulse tests) and central vestibular dysfunction (GEN) [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. Our study disclosed that lesions in the area of the vestibular nuclei can lead to diverse patterns of spontaneous nystagmus and its modulation by visual fixation and gaze. These findings may be explained by significant divergence of excitatory projections from the peripheral vestibular structures and brainstem neural integrators, along with inhibitory inputs from the cerebellum (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSome patients exhibited a mixed pattern of slow-phase velocity of spontaneous nystagmus with a beat-to-beat and intrabeat variability. Even in a single beat, the nystagmus consisted of an initial decelerating and following linear or accelerating slow phases. Similar waveforms have been reported in vertical nystagmus observed in lesions involving the paramedian tract (PMT) [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] or in patients with ankylosing spondylitis [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. According to a mathematical model, these unusual waveforms may occur due to the pulse-step mismatch creating the initially decreasing-velocity waveforms due to leaky neural integrators, and subsequent disruption of the cerebellar feedback for gaze holding through PMT, resulting in unstable neural integrators and nystagmus with an increasing-velocity waveform [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. GEN and superimposed pendular nystagmus observed in patients with multiple sclerosis also imply that the neural integrator can be simultaneously leaky and unstable [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOur patients more frequently showed a violation of the Alexander\u0026rsquo;s law only in one direction. This indicates that dysfunction of the neural integration depends on gaze direction. Thus, the neural integrators may become unstable in one direction while they become leaky in other directions of gaze [\u003cspan additionalcitationids=\"CR43\" citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. Indeed, asymmetrical GEN has been described in patients with unilateral lesions of the NPH or MVN [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. In unilateral lesion of the NPH, the neural integration is more severely impaired with a decrease in the Tc of postsaccadic drift after ipsilesional eccentric gaze [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eSpontaneous nystagmus in patients with Wallenberg\u0026rsquo;s syndrome can violate Alexander\u0026rsquo;s law, which permit a differentiation from acute peripheral vestibular syndrome. The violation of the Alexander\u0026rsquo;s law may be attributed to unstable neural integrator and can be simulated by lesions affecting the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAuthor contributions\u0026nbsp;J-HC and E-HO analyzed and interpreted the data and wrote the manuscript. H-SK, J-YP, S-ML, S-YC, H-JK, J-YC, J-SK and JOM\u0026nbsp;analyzed and interpreted the data. K-DC designed and conceptualized the study, interpreted the data, and revised the manuscript. All authors reviewed and approved the final version of the manuscript. K-DC is responsible for the overall content as guarantor, and obtained funding.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u0026nbsp;\u003c/strong\u003eThis research was\u0026nbsp;supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (NRF-2023R1A2C1004810).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u0026nbsp;\u003c/strong\u003eAnonymized data will be shared upon request from any qualified investigator.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e Drs. JH Choi, EH Oh, HS Kim, JY Park, SM Lee, SY Choi, HJ Kim, JY Choi, J Otero-Millan, and KD Choi report no disclosures. Dr. JS Kim serves as an Associate Editor of Frontiers in Neuro-otology and on the editorial boards of the Journal of Clinical Neurology, Frontiers in Neuro-ophthalmology, Journal of Neuro-ophthalmology, and Journal of Vestibular Research, and Clinical and Translational Neurology.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical approval\u003c/strong\u003eAll the experiments performed in this study followed the tenets of the Declaration of Helsinki. Informed consents were obtained from the participants (including technicians in supplementary video) after the nature and possible consequences of this study had been explained to them. This study was approved by the Institutional Review Board of Pusan National University (2308-031-130) and Pusan National University Yangsan Hospitals (05-2023-180).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAlexander G. Die Ohrenkrankheiten im Kindesalter. 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J Neurophysiol. 2008;100:3105\u0026ndash;16.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGodaux E, Cheron G. The hypothesis of the uniqueness of the oculomotor neural integrator: direct experimental evidence in the cat. J Physiol. 1996;492:517\u0026ndash;27.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eArnold DB, Robinson DA. The oculomotor integrator: testing of a neural network model. Exp Brain Res. 1997;113:57\u0026ndash;74.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDale A, Cullen KE. The nucleus prepositus predominantly outputs eye movement-related information during passive and active self-motion. J Neurophysiol. 2013;109:1900\u0026ndash;11.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcConville K, Tomlinson RD, King WM, Paige G, Na EQ. Eye position signals in the vestibular nuclei: consequences for models of integrator function. 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Neurology. 2016;87:2026\u0026ndash;33.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-cerebellum","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cere","sideBox":"Learn more about [The Cerebellum](http://link.springer.com/journal/12311)","snPcode":"12311","submissionUrl":"https://submission.nature.com/new-submission/12311/3","title":"The Cerebellum","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Nystagmus, Alexander’s law, Neural integrator, Lateral medullary infarction, Cerebellum","lastPublishedDoi":"10.21203/rs.3.rs-4722547/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4722547/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAlexander's law states that spontaneous nystagmus increases when looking in the direction of fast-phase and decreases during gaze in slow-phase direction. Disobedience to Alexander\u0026rsquo;s law is occasionally observed in central nystagmus, but the underlying neural circuit mechanisms are poorly understood. We found a violation of Alexander\u0026rsquo;s law in one or both directions of lateral gaze in lesions of unilateral lateral medulla affecting the vestibular nucleus. When Alexander\u0026rsquo;s law is violated, the time constant (Tc) was larger than that in the controls (median [interquartile range, IQR]: 14.4 s [6.4\u0026ndash;38.9] vs 9.0 s [IQR 5.5\u0026ndash;12.6], \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.036) while the Tc did not differ between the groups when Alexander\u0026rsquo; law is obeyed (9.6 s [3.6\u0026ndash;16.1] vs 9.0 s [5.5\u0026ndash;12.6], \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.924). To test the study hypothesis that an unstable neural integrator may generate nystagmus violating Alexander's law, we primarily utilized the gaze-holding neural integrator computational model, incorporating lesion-induced changes. With normal integrator function, the false rotational cue generates nystagmus following Alexander\u0026rsquo;s law. The first lesion, which changes the brainstem neural integrator, and the second lesion, which causes the Purkinje synapse to exert excitatory input, both lead to nystagmus that violates Alexander\u0026rsquo;s law. We propose that when the neural integrator is unstable with lesions in the brainstem neural integrator itself or the neural synapse between Purkinje cells and the brainstem vestibular nucleus, nystagmus violates Alexander\u0026rsquo;s law.\u003c/p\u003e","manuscriptTitle":"Spontaneous Nystagmus Violating the Alexander’s Law: Neural Substrates and Mechanisms","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-06 16:20:39","doi":"10.21203/rs.3.rs-4722547/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-11-16T15:58:16+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-11-09T19:53:12+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-10-01T22:02:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"336363175010503514947221840165019473121","date":"2024-09-01T16:58:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"326252747131952995478554121780324689832","date":"2024-08-30T04:41:46+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-08-30T00:58:53+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-12T04:47:13+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-12T04:46:44+00:00","index":"","fulltext":""},{"type":"submitted","content":"The Cerebellum","date":"2024-07-11T07:39:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-cerebellum","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"cere","sideBox":"Learn more about [The Cerebellum](http://link.springer.com/journal/12311)","snPcode":"12311","submissionUrl":"https://submission.nature.com/new-submission/12311/3","title":"The Cerebellum","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"271ad117-9f21-4b24-9407-868009a3cfe0","owner":[],"postedDate":"August 6th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-01-27T15:59:04+00:00","versionOfRecord":{"articleIdentity":"rs-4722547","link":"https://doi.org/10.1007/s12311-025-01788-0","journal":{"identity":"the-cerebellum","isVorOnly":false,"title":"The Cerebellum"},"publishedOn":"2025-01-20 15:56:56","publishedOnDateReadable":"January 20th, 2025"},"versionCreatedAt":"2024-08-06 16:20:39","video":"","vorDoi":"10.1007/s12311-025-01788-0","vorDoiUrl":"https://doi.org/10.1007/s12311-025-01788-0","workflowStages":[]},"version":"v1","identity":"rs-4722547","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4722547","identity":"rs-4722547","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}