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I was interested to read the report of Janssenet al 1 of a patient with upbeat nystagmus who had had a medial medullary infarct. By contrast with our patient,2 their patient had slow phases with a constant velocity, a “vestibular” type of nystagmus of central origin. As noted by Janssen et al, Hiroseet al 3 have reported on a patient with a medial medullary infarct and upbeat nystagmus; some slow phases were exponential, some of constant velocity.
In the analysis of slow phases it is useful to plot eye velocity against position rather than plot eye position against time. In this representation, the plot of a vestibular type of slow phase with constant velocity is a horizontal straight line. However, when position varies exponentially with time, velocity is a linear function of position:
dx/dt = −kx, x = x0exp(−kt)
The gradient k is the decay constant. A regression line may be fitted and confidence limits for k established. A more detailed analysis4 of the upbeat nystagmus in our patient with a medial medullary infarct confirmed that decay constants were significantly different from zero and therefore not “vestibular”. However, the decay constants for the different slow phases varied and the plot of eye velocity against position seemed to be non-linear (figure). It is not surprising slow phases attributable to “integrator failure” might not be strictly exponential. The model of the perihypoglossal nuclei as a pure integrator rests on the assumption that the statics of the eye (the oculomotor plant) can be modelled by a pure “spring and dashpot”, second order linear differential equation.5 This is an approximation for horizontal movements and a greater approximation for vertical eye movements. It also rests on the assumption that the anatomical connections are more simple than in reality. The variability of decay constants is consistent with the findings of Hiroseet al.3 This may reflect the varying activity of other afferents to the perihypoglossal nuclei. Nevertheless, the approximate linearity of the plots suggest that part of the function of the nucleus intercalatus, the most caudal of the perihypoglossal nuclei, is integration. Perhaps the reason that such a caudal structure may be involved in vertical integration is the need to coordinate vertical head position signals from cervical afferents with integrated head velocity signals from vestibular nuclei.
It would be of interest to know whether velocity–position plots of any of the slow phases of the patient of Janssen et al 1 show a non-zero gradient.
Bronstein et al reply:
We thank Munro for his interest in the patient we reported in this Journal with a low medullary lesion and upbeat nystagmus.1-1 The lesion probably involved the nucleus intercalatus, the lowermost part of the perihypoglossal nucleus, a nucleus thought to perform integration of ocular-motor signals. For the benefit of the general readership of thisJournal we should like to clarify that the integration alluded to is mathematical integration. For instance, eye or head velocity signals arriving at such an integrator emerge as approximations of eye or head position signals. Currently accepted theories of ocular-motor function establish that a lesion to a gaze holding integrator produces nystagmus with slow phase velocity showing exponential decay. By contrast, peripheral vestibular lesions cause nystagmus with linear (constant) slow phase velocity.
The current discussion is centred on the findings in three recently reported patients with lesions probably involving the nucleus intercalatus.1-1-1-3 The patients reported by Munroet al 1-2 and Hiroseet al,1-3 with large medullary lesions, had predominantly exponentially decaying slow phase velocity. Our patient, with a small paramedian lesion, had nystagmus with linearly decaying slow phase velocity.1-1 Following Munro’s suggestion we obtained velocity-position plots of single nystagmic beats and found most of them to be linear (horizontal line on velocity-position plots (figure)). Only about 10%-15% of nystagmic beats showed some degree of exponential decay (velocity-position plots with a non-zero gradient). On this basis, as well as on the presence of tilt (otolith) stimulus sensitivity, we argue that a small nucleus intercalatus lesion presents clinically as a central vestibular nystagmus. Larger lesions may damage additional neuronal circuits involved in ocular-motor integration.1-4