A theoretical model of neuronal population coding of stimuli with both continuous and discrete dimensions

In a recent study the initial rise of the mutual information between the firing rates of N neurons and a set of p discrete stimuli has been analytically evaluated, under the assumption that neurons fire independently of one another to each stimulus and that each conditional distribution of firing rates is gaussian. Yet real stimuli or behavioural correlates are high-dimensional, with both discrete and continuously varying features.Moreover, the gaussian approximation implies negative firing rates, which is biologically implausible. Here, we generalize the analysis to the case where the stimulus or behavioural correlate has both a discrete and a continuous dimension. In the case of large noise we evaluate the mutual information up to the quadratic approximation as a function of population size. Then we consider a more realistic distribution of firing rates, truncated at zero, and we prove that the resulting correction, with respect to the gaussian firing rates, can be expressed simply as a renormalization of the noise parameter. Finally, we demonstrate the effect of averaging the distribution across the discrete dimension, evaluating the mutual information only with respect to the continuously varying correlate.Comment: 20 pages, 10 figure

Representational capacity of a set of independent neurons

The capacity with which a system of independent neuron-like units represents a given set of stimuli is studied by calculating the mutual information between the stimuli and the neural responses. Both discrete noiseless and continuous noisy neurons are analyzed. In both cases, the information grows monotonically with the number of neurons considered. Under the assumption that neurons are independent, the mutual information rises linearly from zero, and approaches exponentially its maximum value. We find the dependence of the initial slope on the number of stimuli and on the sparseness of the representation.Comment: 19 pages, 6 figures, Phys. Rev. E, vol 63, 11910 - 11924 (2000

Simultaneous recordings of ocular microtremor and microsaccades with a piezoelectric sensor and a video-oculography system

Our eyes are in continuous motion. Even when we attempt to fix our gaze, we produce so called “fixational eye movements”, which include microsaccades, drift, and ocular microtremor (OMT). Microsaccades, the largest and fastest type of fixational eye movement, shift the retinal image from several dozen to several hundred photoreceptors and have equivalent physical characteristics to saccades, only on a smaller scale (Martinez-Conde, Otero-Millan & Macknik, 2013). OMT occurs simultaneously with drift and is the smallest of the fixational eye movements (∼1 photoreceptor width, >0.5 arcmin), with dominant frequencies ranging from 70 Hz to 103 Hz (Martinez-Conde, Macknik & Hubel, 2004). Due to OMT’s small amplitude and high frequency, the most accurate and stringent way to record it is the piezoelectric transduction method. Thus, OMT studies are far rarer than those focusing on microsaccades or drift. Here we conducted simultaneous recordings of OMT and microsaccades with a piezoelectric device and a commercial infrared video tracking system. We set out to determine whether OMT could help to restore perceptually faded targets during attempted fixation, and we also wondered whether the piezoelectric sensor could affect the characteristics of microsaccades. Our results showed that microsaccades, but not OMT, counteracted perceptual fading. We moreover found that the piezoelectric sensor affected microsaccades in a complex way, and that the oculomotor system adjusted to the stress brought on by the sensor by adjusting the magnitudes of microsaccades

The Viscoelastic Properties of Passive Eye Muscle in Primates. III: Force Elicited by Natural Elongations

We have recently shown that in monkey passive extraocular muscles the force induced by a stretch does not depend on the entire length history, but to a great extent is only a function of the last elongation applied. This led us to conclude that Fung's quasi-linear viscoelastic (QLV) model, and more general nonlinear models based on a single convolution integral, cannot faithfully mimic passive eye muscles. Here we present additional data about the mechanical properties of passive eye muscles in deeply anesthetized monkeys. We show that, in addition to the aforementioned failures, previous models also grossly overestimate the force exerted by passive eye muscles during smooth elongations similar to those experienced during normal eye movements. Importantly, we also show that the force exerted by a muscle following an elongation is largely independent of the elongation itself, and it is mostly determined by the final muscle length. These additional findings conclusively rule out the use of classical viscoelastic models to mimic the mechanical properties of passive eye muscles. We describe here a new model that extends previous ones using principles derived from research on thixotropic materials. This model is able to account reasonably well for our data, and could thus be incorporated into models of the eye plant

Hypothetical membrane mechanisms in essential tremor

This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Saccadic Eye Movement Abnormalities in Children with Epilepsy

Childhood onset epilepsy is associated with disrupted developmental integration of sensorimotor and cognitive functions that contribute to persistent neurobehavioural comorbidities. The role of epilepsy and its treatment on the development of functional integration of motor and cognitive domains is unclear. Oculomotor tasks can probe neurophysiological and neurocognitive mechanisms vulnerable to developmental disruptions by epilepsy-related factors. The study involved 26 patients and 48 typically developing children aged 8–18 years old who performed a prosaccade and an antisaccade task. Analyses compared medicated chronic epilepsy patients and unmedicated controlled epilepsy patients to healthy control children on saccade latency, accuracy and dynamics, errors and correction rate, and express saccades. Patients with medicated chronic epilepsy had impaired and more variable processing speed, reduced accuracy, increased peak velocity and a greater number of inhibitory errors, younger unmedicated patients also showed deficits in error monitoring. Deficits were related to reported behavioural problems in patients. Epilepsy factors were significant predictors of oculomotor functions. An earlier age at onset predicted reduced latency of prosaccades and increased express saccades, and the typical relationship between express saccades and inhibitory errors was absent in chronic patients, indicating a persistent reduction in tonic cortical inhibition and aberrant cortical connectivity. In contrast, onset in later childhood predicted altered antisaccade dynamics indicating disrupted neurotransmission in frontoparietal and oculomotor networks with greater demand on inhibitory control. The observed saccadic abnormalities are consistent with a dysmaturation of subcortical-cortical functional connectivity and aberrant neurotransmission. Eye movements could be used to monitor the impact of epilepsy on neurocognitive development and help assess the risk for poor neurobehavioural outcomes

Modeling the Triggering of Saccades, Microsaccades, and Saccadic Intrusions

When we explore a static visual scene, our eyes move in a sequence of fast eye movements called saccades, which are separated by fixation periods of relative eye stability. Based on uncertain sensory and cognitive inputs, the oculomotor system must decide, at every moment, whether to initiate a saccade or to remain in the fixation state. Even when we attempt to maintain our gaze on a small spot, small saccades, called microsaccades, intrude on fixation once or twice per second. Because microsaccades occur at the boundary of the decision to maintain fixation versus starting a saccade, they offer a unique opportunity to study the mechanisms that control saccadic triggering. Abnormal saccadic intrusions can occur during attempted fixation in patients with neurodegenerative disorders. We have implemented a model of the triggering mechanism of saccades, based on known anatomy and physiology, that successfully simulates the generation of saccades of any size-including microsaccades in healthy observers, and the saccadic intrusions that interrupt attempted fixation in parkinsonian patients. The model suggests that noisy neuronal activity in the superior colliculus controls the state of a mutually inhibitory network in the brain stem formed by burst neurons and omnipause neurons. When the neuronal activity is centered at the rostral pole, the system remains at a state of fixation. When activity is perturbed away from this center, a saccade is triggered. This perturbation can be produced either by the intent to move one's gaze or by random fluctuations in activity.National Science FoundationVoRSUNY DownstateOphthalmologyNeurologyPhysiology and PharmacologyLaboratory of Translational NeuroscienceN/

A competitive integration model of exogenous and endogenous eye movements

We present a model of the eye movement system in which the programming of an eye movement is the result of the competitive integration of information in the superior colliculi (SC). This brain area receives input from occipital cortex, the frontal eye fields, and the dorsolateral prefrontal cortex, on the basis of which it computes the location of the next saccadic target. Two critical assumptions in the model are that cortical inputs are not only excitatory, but can also inhibit saccades to specific locations, and that the SC continue to influence the trajectory of a saccade while it is being executed. With these assumptions, we account for many neurophysiological and behavioral findings from eye movement research. Interactions within the saccade map are shown to account for effects of distractors on saccadic reaction time (SRT) and saccade trajectory, including the global effect and oculomotor capture. In addition, the model accounts for express saccades, the gap effect, saccadic reaction times for antisaccades, and recorded responses from neurons in the SC and frontal eye fields in these tasks. © The Author(s) 2010