Fixed point analysis of nystagmus

Theodorou, Maria; Clement, Richard A.

doi:10.1016/j.jneumeth.2006.09.025

Cited by 11 publications

(12 citation statements)

References 22 publications

(36 reference statements)

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“…Some of these estimates will be clearly spurious because they do not lie close to the diagonal of the delay space and can thus be discarded. A histogram of the frequency of the remaining estimates will peak at the actual locations of any fixed points (So et al 1997;Theodorou and Clement 2007).…”

Section: Local Linear Analysismentioning

confidence: 99%

“…To summarise, first the fixed points were identified, then the dimensionality of the fixed points was estimated, and finally, the eigenvalues and eigenvectors of the equilibrium were calculated from a least squares estimate of the linear map. Full details of our methods of local linear analysis can be found in previous publications (Abadi et al 1997;Akman et al 2006;Theodorou and Clement 2007).…”

Section: Local Linear Analysismentioning

confidence: 99%

“…Previous applications of local linear analysis to nystagmus used the position signal rather than the reconstructed neural signal (Abadi et al 1997;Akman et al 2006;Theodorou and Clement 2007). The advantage of using the neural signal is that it facilitates the interpretation of the time constants of the local linear model by removing the neural dynamics associated with the muscle plant (Van Opstal et al 1985).…”

Section: Validity Of Estimated Time Constantsmentioning

confidence: 99%

“…Close to an equilibrium the eye velocity is low, corresponding physiologically to a foveation period (Akman et al 2006). State space analysis of congenital nystagmus data based on the eye position signal has shown that even during steady fixation there can be more than one equilibrium state (Theodorou and Clement 2007). Where there are multiple equilibria these represent alternative potential foveation directions, one of which is aligned with the target and thus corresponds to fixation.…”

Section: Introductionmentioning

confidence: 99%

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Components of the neural signal underlying congenital nystagmus

et al. 2012

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Congenital nystagmus is an involuntary bilateral horizontal oscillation of the eyes that develops soon after birth. In this study, the time constants of each of the components of the neural signal underlying congenital nystagmus were obtained by time series analysis and interpreted by comparison with those of the normal oculomotor system. In the neighbourhood of the fixation position, the system generating the neural signal is approximately linear with 3 degrees of freedom. The shortest time constant was in the range of 7-9 ms and corresponds to a normal saccadic burst signal. The other stable time constant was in the range of 22-70 ms and corresponds to the slide signal. The final time constant characterises the unidentified neural mechanism underlying the unstable drift component of the oscillation cycle and ranges between 31 and 32 ms across waveforms. The characterisation of this unstable time constant poses a challenge for the modelling of both the normal and abnormal oculomotor control system. We tentatively identify the unstable component with the eye position signal supplied to the superior colliculus in the normal eye movement system and explore some of the implications of this hypothesis.

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Section: Local Linear Analysismentioning

confidence: 99%

Section: Local Linear Analysismentioning

confidence: 99%

Section: Validity Of Estimated Time Constantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Components of the neural signal underlying congenital nystagmus

et al. 2012

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“…To calculate the nystagmus acuity function for nystagmus patients, a series of parameters, such as foveation duration,3–6 foveation eye positions,5–10 mean velocity of nystagmus slow phase,11 and a combination of foveation eye positions and eye velocities12–14 have been used. Dynamic system analysis,15 fixed point analysis16 and wavelet spectrum17 18 have also been used for nystagmus acuity evaluation. A well-known method in the field of nystagmus research is the expanded nystagmus acuity function (NAFX).…”

Section: Introductionmentioning

confidence: 99%

A new algorithm for automated nystagmus acuity function analysis

Tai

Hertle²,

Bilonick³

et al. 2010

British Journal of Ophthalmology

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Slow–fast control of eye movements: an instance of Zeeman’s model for an action

Clement

Akman

2020

Biol Cybern

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The rapid eye movements (saccades) used to transfer gaze between targets are examples of an action. The behaviour of saccades matches that of the slow–fast model of actions originally proposed by Zeeman. Here, we extend Zeeman’s model by incorporating an accumulator that represents the increase in certainty of the presence of a target, together with an integrator that converts a velocity command to a position command. The saccadic behaviour of several foveate species, including human, rhesus monkey and mouse, is replicated by the augmented model. Predictions of the linear stability of the saccadic system close to equilibrium are made, and it is shown that these could be tested by applying state-space reconstruction techniques to neurophysiological recordings. Moreover, each model equation describes behaviour that can be matched to specific classes of neurons found throughout the oculomotor system, and the implication of the model is that build-up, burst and omnipause neurons are found throughout the oculomotor pathway because they constitute the simplest circuit that can produce the motor commands required to specify the trajectories of motor actions.

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Fixed point analysis of nystagmus

Cited by 11 publications

References 22 publications

Components of the neural signal underlying congenital nystagmus

Components of the neural signal underlying congenital nystagmus

A new algorithm for automated nystagmus acuity function analysis

Slow–fast control of eye movements: an instance of Zeeman’s model for an action

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