The Spectral Main Sequence of Human Saccades

Harwood, Mark; Mezey, Laura E.; Harris, Christopher M.

doi:10.1523/jneurosci.19-20-09098.1999

Cited by 56 publications

(58 citation statements)

References 17 publications

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“…Eye position trajectories were assumed to be perfect extended extremals-with perfect plant compensation assumed. A cycle was reset by a simulated saccade using a minimum jerk profile [15]. The three-dimensional projection of the reconstructed phase space trajectory, calculated using Matlab's Tstool toolbox [16], shows a similar profile as observed empirically [13] [ Figure 5(c) and (d)].…”

Section: Timing Limitations and Extended Extremalsmentioning

confidence: 85%

A Distal Model of Congenital Nystagmus as Nonlinear Adaptive Oscillations

Harris

Berry

2006

Nonlinear Dyn

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Abstract. Congenital nystagmus (CN) is an incurable pathological spontaneous oscillation of the eyes with an onset in the first few months of life. The pathophysiology of CN is mysterious. There is no consistent neurological abnormality, but the majority of patients have a wide range of unrelated congenital visual abnormalities affecting either the cornea, lens, retina or optic nerve. In this theoretical study, we show that these eye oscillations could develop as an adaptive response to maximize visual contrast with poor foveal function in the infant visuomotor system, at a time of peak neural plasticity. We argue that in a visual system with abnormally poor high spatial frequency sensitivity, image contrast is not only maintained by keeping the image on the fovea (or its remnant) but also by some degree of image motion. Using the calculus of variations, we show that the optimal trade-off between these conflicting goals is to generate oscillatory eye movements with increasing velocity waveforms, as seen in real CN. When we include a stochastic component to the start of each epoch (quick-phase inaccuracy) various observed waveforms (including pseudo-cycloid) emerge as optimal strategies. Using the delay embedding technique, we find a low fractional dimension as reported in real data. We further show that, if a velocity command-based pre-motor circuitry (neural integrator) is harnessed to generate these waveforms, the emergence of a null region is inevitable. We conclude that CN could emerge paradoxically as an 'optimal' adaptive response in the infant visual system during an early critical period. This can explain why CN does not emerge later in life and why CN is so refractory to treatment. It also implies that any therapeutic intervention would need to be very early in life.

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Section: Timing Limitations and Extended Extremalsmentioning

confidence: 85%

A Distal Model of Congenital Nystagmus as Nonlinear Adaptive Oscillations

Harris

Berry

2006

Nonlinear Dyn

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“…We propose that saccades optimize this trade-off at two levels. First, for any given amplitude and duration of movement there is an optimal trajectory, which is given by the minimum variance trajectory (Harris and Wolpert 1998;Harwood et al 1999). We believe this principle is shared by other aimed movements such as arm movements.…”

Section: Discussionmentioning

confidence: 98%

“…We have chosen a third-order linear model because this provides an excellent fit to the trajectories when using the sensitive technique of Fourier analysis (Harwood et al 1999). However, the general symmetrical bell-shaped profile for fast movements is not only insensitive to modest variations in the precise parameters and the order of linear plant models, but is also predicted by non-linear models (Harris and Wolpert 1998).…”

Section: Discussionmentioning

confidence: 99%

“…Instead, we have solved them numerically. For simulations we have used a third-order linear model (n = 3) of the oculomotor plant with time constants 223, 14 and 4 ms (Harwood et al 1999).…”

Section: Europe Pmc Funders Author Manuscriptsmentioning

confidence: 99%

“…In primates this is usually accomplished by fast saccadic eye movements. The high speed of saccades precludes visual feedback, yet saccades have remarkably stereotyped trajectories (Bahill et al 1975;Collewijn et al 1988;Harwood et al 1999). The peak velocity and the duration increase systematically with the amplitude of the movement, and these relationships have been called the 'main sequence' (Bahill et al 1975).…”

Section: Introductionmentioning

confidence: 99%

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The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off

2006

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In primates, it is well known that there is a consistent relationship between the duration, peak velocity and amplitude of saccadic eye movements, known as the 'main sequence'. The reason why such a stereotyped relationship evolved is unknown. We propose that a fundamental constraint on the deployment of foveal vision lies in the motor system that is perturbed by signaldependent noise on the motor command. This noise imposes a compromise between the speed and accuracy of an eye movement. We propose that saccade trajectories have evolved to optimize a trade-off between the accuracy and duration of the movement. Taking a semi-analytical approach we use Pontryagin's minimum principle to show that there is an optimal trajectory for a given amplitude and duration; and that there is an optimal duration for a given amplitude. It follows that the peak velocity is also fixed for a given amplitude. These predictions are in good agreement with observed saccade trajectories and the main sequence. Moreover, this model predicts a small saccadic dead-zone in which it is better to stay eccentric of target than make a saccade onto target. We conclude that the main sequence has evolved as a strategy to optimize the trade-off between accuracy and speed.

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Eye Movements

Enderle

2006

Wiley Encyclopedia of Biomedical Engineering

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A description of eye movements is presented in this chapter. In addition, models of the saccadic system and smooth pursuit system are also presented. Five different types of eye movements exist: saccades, smooth pursuit, vestibular ocular eye movements, optokinetic eye movements, and vergence eye movements. Saccades are a fast eye movement used to acquire a target by placing the image of the target on the fovea. Smooth pursuit is a slow eye movement used to track a target as it moves by keeping the target on the fovea. The vestibular ocular movement is used to keep the eyes on a target during brief head movements. The optokinetic eye movement is a combination of saccadic and slow eye movements that keeps a full‐field image stable on the retina during sustained head rotation. Each of these movements is a conjugate eye movement, that is, movements of both eyes together driven by a common neural source. A vergence movement is a nonconjugate eye movement allowing the eyes to track targets as they come closer or move farther away. The smooth pursuit system allows tracking of a slow‐moving target to maintain its position on the fovea. Models of the smooth pursuit have been developed using systems control theory, all involving a negative feedback control system that includes a time delay, controller, and plant in the forward loop with unity feedback. The oculomotor plant and saccade generator are the basic elements of the saccadic system. The oculomotor plant consists of three muscle pairs and the eyeball. The control of saccades is initiated by the superior colliculus (SC) and terminated by the cerebellar fastigial nucleus (FN), and involves a complex neural circuit in the mid brain. Both of these control models are for horizontal eye movements only.

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The Spectral Main Sequence of Human Saccades

Cited by 56 publications

References 17 publications

A Distal Model of Congenital Nystagmus as Nonlinear Adaptive Oscillations

A Distal Model of Congenital Nystagmus as Nonlinear Adaptive Oscillations

The Main Sequence of Saccades Optimizes Speed-accuracy Trade-off

Eye Movements

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