Divisive Normalization from Wilson-Cowan Dynamics

Divisive Normalization and the Wilson-Cowan equations are influential models of neural interaction and saturation [Carandini and Heeger Nat.Rev.Neurosci. 2012; Wilson and Cowan Kybernetik 1973]. However, they have not been analytically related yet. In this work we show that Divisive Normalization can be obtained from the Wilson-Cowan model. Specifically, assuming that Divisive Normalization is the steady state solution of the Wilson-Cowan differential equation, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson-Cowan kernel but also has a signal-dependent contribution. A standard stability analysis of a Wilson-Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability demonstrates the consistency of our steady state assumption, and is in line with the straightforward use of Divisive Normalization with time-varying stimuli. The proposed theory provides a physiological foundation (a relation to a dynamical network with fixed wiring among neurons) for the functional suggestions that have been done on the need of signal-dependent Divisive Normalization [e.g. in Coen-Cagli et al., PLoS Comp.Biol. 2012]. Moreover, this theory explains the modifications that had to be introduced ad-hoc in Gaussian kernels of Divisive Normalization in [Martinez et al. Front. Neurosci. 2019] to reproduce contrast responses. The proposed relation implies that the Wilson-Cowan dynamics also reproduces visual masking and subjective image distortion metrics, which up to now had been mainly explained via Divisive Normalization. Finally, this relation allows to apply to Divisive Normalization the methods which up to now had been developed for dynamical systems such as Wilson-Cowan networks

Effect of even and odd-order aberrations on the accommodation response.

AIM: To investigate the potential effect that odd and even-order monochromatic aberrations may have on the accommodation response of the human eye. METHODS: Eight healthy subjects with astigmatism below 1 D, best corrected visual acuity 20/20 or better and normal findings in an ophthalmic examination were enrolled. An adaptive optics system was used in order to measure the accommodation response of the subjects' eyes under different conditions: with the natural aberrations being present, and with the odd and even-order aberrations being corrected. Three measurements of accommodation response were monocularly acquired at accommodation demands ranging from 0 to 4 D (0.5 D step). RESULTS: The accommodative lag was greater for the accommodative demands of 1.5, 3, 3.5 and 4 D for the condition in which the even-order aberrations were corrected, in comparison to that obtained for the natural aberrations and corrected odd-order aberrations for the same accommodation demands. No statistically significant differences were found between the accommodation responses under the three conditions. CONCLUSION: The odd and even-order aberrations are not helping the visual system to accommodate, because their partial correction do not affect the accommodation performance

Estimation of the mechanical properties of the eye through the study of its vibrational modes

Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral analysis of the eyeball vibrational modes has not been performed yet. Here we develop a new finite difference method to compute both the spheroidal and, specially, the toroidal eigenfrequencies of the human eye. Using this numerical model, we show that the vibrational eigenfrequencies of the human eye fall in the interval 100 Hz - 10 MHz. We find that compressible vibrational modes may release a trace on high frequency changes of the intraocular pressure, while incompressible normal modes could be registered analyzing the scattering pattern that the motions of the vitreous humour leave on the retina. Existing contact lenses with embebed devices operating at high sampling frequency could be used to register the microfluctuations of the eyeball shape we obtain. We advance that an inverse problem to obtain the mechanical properties of a given eye (e.g., Young's modulus, Poisson ratio) measuring its normal frequencies is doable. These measurements can be done using non-invasive techniques, opening very interesting perspectives to estimate the mechanical properties of eyes in vivo. Future research might relate various ocular pathologies with anomalies in measured vibrational frequencies of the eye.Comment: Published in PLoS ONE as Open Access Research Article. 17 pages, 5 color figure

Assessing the accommodation response after near visual tasks using different handheld electronic devices

ABSTRACT Purpose: To assess the accommodation response after short reading periods using a tablet and a smartphone as well as determine potential differences in the accommodation response at various stimulus vergences using a Hartmann- Shack aberrometer. Methods: Eighteen healthy subjects with astigmatism of less than 1 D, corrected visual acuity of 20/20 or better, and normal findings in an ophthalmic examination were enrolled. Accommodation responses were obtained under three different conditions: accommodation system of the eye relaxed and visually stressed with a tablet and an smartphone for 10 min, at a distance of 0.25 m from the subject's eyes. Three measurements of accommodation response were monocularly acquired at stimulus vergences ranging from 0 to 4 D (1-D step). Results: No statistically significant differences were found in the accommodation responses among the conditions. A moderate but gradually increasing root mean square, coma-like aberration was found for every condition. Conversely, the spherical aberration decreased as stimulus vergences increased. These outcomes were identified in comparison to the one-to-one ideal accommodation response, implying that a certain lag value was present in all stimulus vergences different from 0 D. Conclusions: The results support the hypothesis that the difference between the ideal and real accommodation responses is mainly attributed to parameters associated with the accommodation process, such as the near visual acuity, depth of focus, pupil diameter, and wavefront aberrations. The wavefront aberrations were dependent on the 3-mm pupil size selected in this study. The accommoda tion response was not dependent on the electronic device employed in each condition, and it was mainly associated with young age and level of amplitude of accommodation of the subjects

Accommodative Stimulus-Response Curve with Emoji Symbols

Purpose. To evaluate the static measurement of the accommodative stimulus-response curve with emoji symbols. Methods. The accommodative stimulus-response curve was measured in 18 subjects using a Hartmann-Shack sensor to obtain the objective accommodative response from the Zernike defocus term. Measurements were acquired at different accommodative demands, from 0 to 3 D with a step of 0.5 D. Detailed and nondetailed emoji targets were used with two different sizes, corresponding to the two most common visual angles used in smartphones. Results. A regression analysis was performed to fit the mean results obtained for each target. The determination coefficient was R2≥0.988 for all targets. For the detailed targets, the slopes for the averaged stimulus-response curve were 0.65 and 0.66 for the bigger and smaller sizes, respectively. For the nondetailed targets, the slopes were 0.60 and 0.58 for the bigger and smaller sizes, respectively. p values for these slopes were statistically significant for the two types of targets (p<0.01). Conclusions. Our results reveal that the replacement of a word or several words by detailed or nondetailed emoji symbols seems not to provoke a different accommodative response in normal subjects and under standard viewing conditions in the use of smartphones

Objective assessment of the effect of pupil size upon the power distribution of multifocal contact lenses.

AIM: To analytically assess the effect of pupil size upon the refractive power distributions of different designs of multifocal contact lenses. METHODS: Two multifocal contact lenses of center-near design and one multifocal contact lens of center-distance design were used in this study. Their power profiles were measured using the NIMO TR1504 device (LAMBDA-X, Belgium). Based on their power profiles, the power distribution was assessed as a function of pupil size. For the high addition lenses, the resulting refractive power as a function of viewing distance (far, intermediate, and near) and pupil size was also analyzed. RESULTS: The power distribution of the lenses was affected by pupil size differently. One of the lenses showed a significant spread in refractive power distribution, from about -3 D to 0 D. Generally, the power distribution of the lenses expanded as the pupil diameter became greater. The surface of the lens dedicated for each distance varied substantially with the design of the lens. CONCLUSION: In an experimental basis, our results show how the lenses power distribution is affected by the pupil size and underlined the necessity of careful evaluation of the patient's visual needs and the optical properties of a multifocal contact lens for achieving the optimal visual outcome

Amplitude, Latency, and Peak Velocity in Accommodation and Disaccommodation Dynamics.

The aim of this work was to ascertain whether there are differences in amplitude, latency, and peak velocity of accommodation and disaccommodation responses when different analysis strategies are used to compute them, such as fitting different functions to the responses or for smoothing them prior to computing the parameters. Accommodation and disaccommodation responses from four subjects to pulse changes in demand were recorded by means of aberrometry. Three different strategies were followed to analyze such responses: fitting an exponential function to the experimental data; fitting a Boltzmann sigmoid function to the data; and smoothing the data. Amplitude, latency, and peak velocity of the responses were extracted. Significant differences were found between the peak velocity in accommodation computed by fitting an exponential function and smoothing the experimental data (mean difference 2.36 D/s). Regarding disaccommodation, significant differences were found between latency and peak velocity, calculated with the two same strategies (mean difference of 0.15 s and -3.56 D/s, resp.). The strategy used to analyze accommodation and disaccommodation responses seems to affect the parameters that describe accommodation and disaccommodation dynamics. These results highlight the importance of choosing the most adequate analysis strategy in each individual to obtain the parameters that characterize accommodation and disaccommodation dynamics

Evaluation of the iridocorneal angle with accommodation using optical coherence tomography.

The changes in the iridocorneal angle structure during accommodation are assessed by means of anterior segment optical coherence tomography. Thirteen right eyes were included in the study. The device used for the measurement was the Visante®omni system. The stimuli were set up at different vergences (0.0 D, -1.5 D, and -3.0 D). The angle opening distance 500 and 750, the trabecular iris space area 500 and 750, and the scleral spur angle parameters were assessed at the nasal and temporal regions. The results in the iridotrabecular angle comparing the three accommodative states of the eye did not yield any statistically significant difference at nasal or temporal angle sections. In light of our results and in the conditions of our study, the structures of the iridocorneal angle are not significantly changed with accommodation

Comparison of the influence of corneo-scleral and scleral lenses on ocular surface and tear film metrics in a presbyopic population

PURPOSE: To assess and compare the effect of the corneo-scleral lenses (C-ScL) and scleral lenses (ScL) on tear film parameters and central corneal thickness (CCT) in healthy presbyopic subjects. METHODS: Thirty subjects wore two contact lenses (CLs), randomly assigned, of neutral power, but of different diameters, 12.7mm (C-ScL) and 18mm (ScL) and being equal in the others parameters: material (HS100) and centre thickness (0.29mm). At baseline, 20min after insertion and at 8h, the tear meniscus area (TMA) and CCT was measured (with optical coherence tomography) as well as tear osmolarity. RESULTS: TMA revealed statistical differences for both lenses at 20min (p<0.001), and also at 8h (p=0.003), being greater for the C-ScL. CCT showed statistical differences for both lenses at 20min (p=0.002), and also at 8h (p=0.001), being lower for the C-ScL. Osmolarity did not reveal statistical differences at 20min (p=0.29), while it was statistically different at 8h (p=0.03), being lower for the C-ScL. CONCLUSIONS: C-ScL lead to a lesser reduction in the TMA and a lower induced hypoxic stress than the ScL. Osmolarity levels remained within normal values across the day with no clinical difference between lenses. Both designs can represent a good optical platform for correcting presbyopia as well as protecting the ocular surface by vaulting the cornea

Effect of Phenylephrine on the Accommodative System.

Accommodation is controlled by the action of the ciliary muscle and mediated primarily by parasympathetic input through postganglionic fibers that originate from neurons in the ciliary and pterygopalatine ganglia. During accommodation the pupil constricts to increase the depth of focus of the eye and improve retinal image quality. Researchers have traditionally faced the challenge of measuring the accommodative properties of the eye through a small pupil and thus have relied on pharmacological agents to dilate the pupil. Achieving pupil dilation (mydriasis) without affecting the accommodative ability of the eye (cycloplegia) could be useful in many clinical and research contexts. Phenylephrine hydrochloride (PHCl) is a sympathomimetic agent that is used clinically to dilate the pupil. Nevertheless, first investigations suggested some loss of functional accommodation in the human eye after PHCl instillation. Subsequent studies, based on different measurement procedures, obtained contradictory conclusions, causing therefore an unexpected controversy that has been spread almost to the present days. This manuscript reviews and summarizes the main research studies that have been performed to analyze the effect of PHCl on the accommodative system and provides clear conclusions that could help clinicians know the real effects of PHCl on the accommodative system of the human eye