Open Access
Visual Psychophysics and Physiological Optics  |   May 2022
Psychophysical Reverse Correlation Revealed Broader Orientation Tuning and Prolonged Reaction Time in Amblyopia
Author Affiliations & Notes
  • Jinli Zhu
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Xiaowei Ruan
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Cheng Li
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Junli Yuan
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Yan Yang
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Wenhua Zhang
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Hanyi Zhang
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Zuopao Zhuo
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Fang-Fang Yan
    Key Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences, Chaoyang District, Beijing, China
    Department of Psychology, University of Chinese Academy of Sciences, Shijingshan District, Beijing, China
  • Chang-Bing Huang
    Key Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences, Chaoyang District, Beijing, China
    Department of Psychology, University of Chinese Academy of Sciences, Shijingshan District, Beijing, China
  • Fang Hou
    School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou, Zhejiang, China
  • Correspondence: Chang-Bing Huang, Key Laboratory of Behavioral Science, Institute of Psychology, Chinese Academy of Sciences, 16 Lincui Road, Chaoyang District, Beijing 100101, China; huangcb@psych.ac.cn
  • Fang Hou, School of Ophthalmology & Optometry and Eye Hospital, Wenzhou Medical University, 270 Xuanyuan Xi Road, Wenxhou, Zhejiang 325027, China; houf@eye.ac.cn
Investigative Ophthalmology & Visual Science May 2022, Vol.63, 3. doi:https://doi.org/10.1167/iovs.63.5.3
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      Jinli Zhu, Xiaowei Ruan, Cheng Li, Junli Yuan, Yan Yang, Wenhua Zhang, Hanyi Zhang, Zuopao Zhuo, Fang-Fang Yan, Chang-Bing Huang, Fang Hou; Psychophysical Reverse Correlation Revealed Broader Orientation Tuning and Prolonged Reaction Time in Amblyopia. Invest. Ophthalmol. Vis. Sci. 2022;63(5):3. doi: https://doi.org/10.1167/iovs.63.5.3.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose: Neural selectivity of orientation is a fundamental property of visual system. We aim to investigate whether and how the orientation selectivity changes in amblyopia.

Methods: Seventeen patients with amblyopia (27.1 ± 7.1 years) and 18 healthy participants (25.1 ± 2.7 years) took part in this study. They were asked to continuously detect vertical gratings embedded in a stream of randomly oriented gratings. Using a technique of subspace reverse correlation, the orientation-time perceptive field (PF) for the atypical grating detection task was derived for each participant. Detailed comparisons were made between the PFs measured with the amblyopic and healthy eyes.

Results: The PF of the amblyopic eyes showed significant differences in orientation and time domain compared with that of the normal eyes (cluster-based permutation test, ps < 0.05), with broader bandwidth of orientation tuning (31.41 ± 10.59 degrees [mean ± SD] vs. 24.76 ± 6.85 degrees, P = 0.039) and delayed temporal dynamics (483 ± 68 ms vs. 425 ± 58 ms, P = 0.015). None of the altered PF properties correlated with the contrast sensitivity at 1 cycle per degree (c/deg) in amblyopia. No difference in PFs between the dominant and non-dominant eyes in the healthy group was found.

Conclusions: The altered orientation-time PF to the low spatial frequency and high contrast stimuli suggests amblyopes had coarser orientation selectivity and prolonged reaction time. The broader orientation tuning probably reflects the abnormal lateral interaction in the primary visual cortex, whereas the temporal delay might indicate a high level deficit.

Amblyopia, also called lazy eye, is clinically characterized by reduced best-corrected visual acuity without detectable structural or pathological abnormalities.15 It causes not only reduced visual acuity,35 but also a variety of deficits in spatial vision, including deterioration of spatial contrast sensitivity,610 stereoscopic vision,11,12 and contour integration.13,14 Aside from refractive error, it is the most frequent cause of vision loss in infants and children.2 
Amblyopia is not only clinically important but also theoretically intriguing. It is believed to be a visual developmental disease where the abnormal visual experience caused by monocular strabismus, anisometropia, high refractive error, and/or form deprivation1517 disrupted the development of cortical functions during a sensitive period in visual development.1820 Amblyopia has been intensively studied in vision science because it reflects the neural consequences that occur when visual development is disrupted and can provide insights for understanding normal visual processing. 
Neural selectivity of orientation is a fundamental property of the visual system,2124 and is commonly believed to emerge in the primary visual cortex.2529 The neural mechanism that determines the sharpness of the orientation tuning has received lots of attention, because the sharpness of tuning cannot be accounted by the thalamocortical feedforward connections22,24,30,31 and must involve intracortical lateral interactions.26,3235 However, whether and how the sharpness of tuning is affected in amblyopia is still on debate. 
The result from single cell recording suggested that amblyopia induced by nonselective visual blur or eye misalignment did not change the bandwidth of the orientation tuning of the V1 neurons in the cat3638 or in the macaque monkey.39,40 On the other hand, the result from human studies showed that amblyopes exhibited impaired performance in orientation discrimination tasks. For example, patients with amblyopia had greater angular thresholds in discriminating the orientation of a narrowband grating,41,42 of the central grating with a surrounding background grating presented,43 as well as of arrays consisting of randomly positioned Gabors.44 As orientation discrimination involves decoding the population responses of a bank of orientation selective neurons, the increased orientation threshold could have reflected a broader tuning width in patients with amblyopia. Thus, it is difficult to exclude the potential contribution of the sensitivity loss to the abnormal orientation discrimination threshold.39,45,46 With a different approach, Levi, Waugh, and Beard47 measured the contrast threshold elevation of line detection as a function of mask orientation at the optimal spatial frequency in amblyopia. The orientation tuning estimated in the amblyopic eyes was found to be qualitatively similar in some participants but broader in others compared to the control eyes. No definitive conclusion was made. 
Therefore, we attempt to directly probe the orientation tuning properties in both healthy and amblyopic participants with a paradigm of subspace reverse correlation.26,4850 By quantifying how random fluctuations of sensory stimuli influence human behavior, the psychophysical reverse correlation estimates how visual system weights the stimuli to guide behaviors48,50,51 (Fig. 1; see Materials and Methods section for more details). The result of the psychophysical reverse correlation, termed as perceptive field (PF), is the psychophysical analogue of a neuronal receptive field, which depicts the weighting function of the visual system. The PF can provide insights that help understand how the visual system processes visual features.5153 By restricting the stimulus fluctuation in the orientation and time domains, we can derive the orientation-time PF of the observer for the task. 
Figure 1.
 
Top row: Reverse correlation in a typical electrophysiological experiment. The white noise images were presented to the animal and the neural spikes were recorded. Via reverse correlation, one can derive the receptive field of a particular neuron. Bottom row: Psychophysical reverse correlation in our experiment. Using reverse correlation, one can derive the weighting function of the visual system in the orientation-time domain for the task.
Figure 1.
 
Top row: Reverse correlation in a typical electrophysiological experiment. The white noise images were presented to the animal and the neural spikes were recorded. Via reverse correlation, one can derive the receptive field of a particular neuron. Bottom row: Psychophysical reverse correlation in our experiment. Using reverse correlation, one can derive the weighting function of the visual system in the orientation-time domain for the task.
In the experiment, we asked participants with amblyopia to watch a randomly orientated grating sequence and, at the same time, to make the response as fast as possible whenever s/he saw a vertical grating. The responses were recorded and used to construct the PF for each participant. By comparing the PFs from amblyopic and normal observers, we hope to answer whether and how the property of orientation tuning is altered in amblyopia. 
Materials and Methods
Participants
Seventeen participants with amblyopia (A1–A17, 27.1 ± 7.1 years, 8 men) and 18 control participants (N1–N18, 25.1 ± 2.7 years, 4 men) took part in the experiments. All participants with amblyopia had been previously diagnosed. At the time of the experiment, all participants had gone through detailed ophthalmologic and optometric examinations performed by the authors (J.Z., C.L., and Y.Y.). All participants, except A2, had astigmatism no more than 1.5 diopters (D), and showed no sign of any pathological abnormality. Participant A2 had congenital cataract and intraocular lens implantation in both eyes. A8 and A15 who had strabismus had surgically corrected the eye alignment. All of the control participants had normal or corrected-to-normal vision (logMAR ≤ 0.0). The contrast sensitivity functions (CSF) of the amblyopes (except A8 and A14) were measured using a Bayesian adaptive procedure, the description of which can be found elsewhere.54 There was one participant in the control group and 11 participants in the amblyopic group who had experiences of psychophysical experiments. See the detailed information of the amblyopic participants in Table A1, Appendix A
All participants were naive to the purpose of the study. They wore the best optical corrections at the test distance during the experiments. Eye dominance was determined with the hole-in-card method for each healthy subject.55 The study adhered to the tenets of the Declaration of Helsinki and was approved by the institutional review board of human subject research of the Eye Hospital, Wenzhou Medical University. Written informed consent was obtained from each subject before the experiment. 
Apparatus
The stimuli were generated using customized program written in MATLAB (The MathWorks Corp., Natick, MA, USA) with Psychtoolbox extension.56 The program was run on an Intel NUC computer (Model: NUC6i7kYK; Intel Corporation, Santa Clara, CA, USA). The stimuli were displayed on a gamma-corrected monitor (ASUS SWIFT PG278QR; Asustek Computer Inc., Taipei, Taiwan). The monitor has been carefully tuned and calibrated so that the typical artifacts associated with liquid crystal displays (LCDs)57,58 were minimalized and had negligible effects on participants’ behavior. The display had a spatial resolution of 2560 × 1440 pixels and a refresh rate of 120 Hz. Each pixel subtended 0.009 degrees at a viewing distance of 1.44 m. The mean luminance was 100.7 cd/m2. The key-pressing responses of subjects were recorded by an RT Box with the temporal resolution less than 26 µs59 that ensured precise collection of response time. A chin/forehead rest was used to minimize head movement during the experiment. Observers viewed the stimuli monocularly with their best correction, if any, in a dark room. The eye not being tested was occluded by an opaque patch. 
Stimuli
The stimulus used for measuring orientation tuning was a sequence of sinusoidal gratings presented at 30 Hz (each grating lasted 33.3 ms). The spatial frequency of the gratings was fixed at 1 cycle per degree (c/deg) and the contrast was 99%. The low spatial frequency and high contrast were used to compensate the sensitivity loss in amblyopia.5,39,45,46 We chose 30 Hz presentation rate because it has been widely validated in previous researches48,50 and the orientation tuning did not depend on temporal frequency.60 The gratings had a circular aperture of 3.0-degree diameter and were presented at the center of the display. The orientation of each grating was chosen randomly from 0, 18, 36, 54, 72, 90, 108, 126, 144, and 162 degrees. The phase of the gratings was chosen from 0, π/2, π, and 3π/2 randomly. The entire grating sequence consisted of 1800 gratings and lasted 60 seconds. The presentation order of the gratings with different orientations and phases was generated such that each orientation and phase combination was displayed for equal (45) times. 
Procedure
Each trial started with the presentation of a black fixation dot (diameter of 0.28 degrees) at the center of the screen. The stimulus presentation began after the participant pressed the “SPACE” key. There was a brief tone signaling the onset of the grating sequence. The participants were asked to monitor the gratings presented at the center of the display and to press the button on the RT Box as fast as possible, whenever they noticed a vertical grating (90 degrees orientation). The time stamp of each key press was recorded. After the 60-second stimulus presentation, the fixation spot displayed again at the center of the screen. There was a total of 30 trials in a test session which lasted 45 minutes. No feedback was provided. The participants could take breaks between trials and press the “SPACE” key to initiate the stimulus presentation of the next trial. 
The dominant eyes of the healthy participants and the amblyopic eyes of the participants with amblyopia were tested. All the participants were given practice trials to make sure they fully understood the task before formal experiment. To rule out the potential bias due to our choice of dominant eyes as the control, we additionally tested the non-dominant eye of the eight (of 18) healthy participants who were able to revisit our laboratory. The CSFs of both eyes of the eight participants were also measured during the revisit. 
Analysis
The PF for the orientation identification task was derived using a technique of subspace reverse correlation in the orientation-time domain.26,4850 The data were analyzed to reflect how the history of gratings in different orientations determined the button presses (Fig. 2a). Specifically, we looked at the grating orientations within 1 second periods (30 gratings) prior to each response (key press). The orientation histogram h(θ) was calculated for each time offset τ (− 30 ≤ τ ≤ −1, in the unit of stimulus frames). The results were averaged across the four phases. By dividing the total number of responses, we obtained the response probability p(θ) of a particular orientation θ at time τ (Fig. 2b). By concatenating p(θ) across all τs, we have the orientation-time PF(θ, τ), which had 330 data points in total, with 11 orientations (the response at orientation of 0 degrees was also been treated as that at orientation of 180 degrees) by 30 temporal delays (Figs. 2b, 2c). 
Figure 2.
 
(a) An illustration of how the perceptive field is derived. The grating orientations within a 1 second period (30 gratings) prior to each response (key press) were piled together. The orientation histogram h(θ) was calculated for each time offset τ. The histogram was then divided by the total number of responses to get p(θ). The red circles represent timestamps of button presses. (b) The perceptive field PF(θ,  τ) is the concatenation of p(θ) over all τs. (c) The perceptive field PF(θ, τ) as a heatmap.
Figure 2.
 
(a) An illustration of how the perceptive field is derived. The grating orientations within a 1 second period (30 gratings) prior to each response (key press) were piled together. The orientation histogram h(θ) was calculated for each time offset τ. The histogram was then divided by the total number of responses to get p(θ). The red circles represent timestamps of button presses. (b) The perceptive field PF(θ,  τ) is the concatenation of p(θ) over all τs. (c) The perceptive field PF(θ, τ) as a heatmap.
To remove the temporal noise, the raw PF was convolved with a Gaussian window in the time domain to remove the frequency component greater than 10 Hz. To better extract the properties of the PF, a parametric model26 was fitted to the temporally smoothed PF data:  
\begin{equation}{\rm{PF}}\left( {\theta ,\tau } \right) = \alpha \left( \tau \right)E\left( \theta \right) + \ \beta \left( \tau \right)I\left( \theta \right) + \ \gamma \left( \tau \right) + c,\end{equation}
(1)
where E(θ) and I(θ) were the excitation and inhibition component of the orientation tuning curve, respectively; α(τ) and β(τ) controls how the excitation, inhibition tuning components evolve over time, respectively; whereas γ(τ) represented a non-orientation selective global component that evolves in time; whereas c represented the baseline guessing rate of the observer. 
Both E(θ) and I(θ) are described by transformed von Mises distribution26,61:  
\begin{equation}E\left( \theta \right) = \ \frac{{\exp \left( {{\kappa _E}\cos \left( {2\left( {\theta - {\theta _E}} \right)} \right)} \right) - {\rm{exp}}\left( { - {\kappa _E}} \right)}}{{\exp \left( {{\kappa _E}} \right) - {\rm{exp}}\left( { - {\kappa _E}} \right)}},\end{equation}
(2a)
 
\begin{equation}I\left( \theta \right) = \ \frac{{\exp \left( {{\kappa _I}\cos \left( {2\left( {\theta - {\theta _I}} \right)} \right)} \right) - {\rm{exp}}\left( { - {\kappa _I}} \right)}}{{\exp \left( {{\kappa _I}} \right) - {\rm{exp}}\left( { - {\kappa _I}} \right)}},\end{equation}
(2b)
where κE and κI determine the width of the excitation and inhibition tunings, respectively; and θE and θI represent the centers of the two components, separately. Given that the target was vertical grating for every participant, θE and θI were set to 90 degrees for simplicity in our analysis. 
The temporal dynamics α(τ), β(τ), and γ(τ) were described by three skewed Gaussian distributions.26,62 
\begin{equation}\alpha \left( \tau \right) = 2\ {a_0}\phi \left( {\frac{{\tau - {\tau _E}}}{{{\sigma _E}}}} \right){\rm{\Phi }}\left( {{\eta _E}\left( {\frac{{\tau - {\tau _E}}}{{{\sigma _E}}}} \right)} \right),\end{equation}
(3a)
 
\begin{equation}\beta \left( \tau \right) = 2\ {\beta _0}\phi \left( {\frac{{\tau - {\tau _I}}}{{{\sigma _I}}}} \right){\rm{\Phi }}\left( {{\eta _I}\left( {\frac{{\tau - {\tau _I}}}{{{\sigma _I}}}} \right)} \right),\end{equation}
(3b)
 
\begin{equation}\gamma \left( \tau \right) = 2\ {\gamma _0}\phi \left( {\frac{{\tau - {\tau _G}}}{{{\sigma _G}}}} \right){\rm{\Phi }}\left( {{\eta _G}\left( {\frac{{\tau - {\tau _G}}}{{{\sigma _G}}}} \right)} \right),\end{equation}
(3c)
where τE, τI, and τG determine the time corresponding to the peak, valley, and extremum of three components, respectively; σE, σI, and σG determine the widths of the distributions, respectively; ηE, ηI, and ηG determine the skewness of the distributions; a0, β0, and γ0 are scaling factors that control the extrema of the components; φ( ) and Φ( ) are the probability density and cumulative probability density functions of a standard normal distribution, respectively. 
Equation 1 was fit to the smoothed PF(θ, τ) data by maximum likelihood procedure63 to obtain the best fit parameters (κE, κI, τE, τI, τG, σE, σI, σG, ηE, ηI, ηG, a0, β0, γ0, and c) and best fit PF(θ, τ) for each participant. The best-fitted PF was used in the comparison between the two groups. Because Equation 1 provided good fit to the data for all participants (χ2 test, all ps > 0.05), we further calculated the r2 of the model for each participant. 
To compare the orientation-time PF between the two groups, a cluster-based permutation test,64,65 was adopted. The test allowed us to look into the connected regions/areas in the orientation-time domain that differed between the amblyopic and normal groups. It has been proposed to deal with high dimensional data set in recent years, while keeping the family-wise error rate under control, and has been widely used in neuroscience for analyzing the electroencephalogram (EEG) or magnetoencephalography (MEG) data.64,65 
After detecting particular regions in the orientation and time domains that differed significantly between PFs in the amblyopic and healthy groups, we then computed the orientation tuning curve and temporal response curve. The orientation tuning curve was calculated as the average PF(θ, τ) over time τ, weighted by its total squared deviation from uniformity at each τ:  
\begin{equation}{\rm{OT}}\left( \theta \right) = \frac{{\mathop \sum \nolimits_\tau {w_\tau }{\rm{PF}}\left( {\theta ,\tau } \right)}}{{\mathop \sum \nolimits_\tau {w_\tau }}},\end{equation}
(4)
where, \({w_\tau } = \mathop \sum \limits_\theta {( {{\rm{PF}}( {\theta ,\tau } ) - 0.1} )^2}.\) 
The temporal dynamics of PF was examined at two orientations, 90 degrees and 54 and 126 degrees (i.e. PF(90,  τ) and PF(54/126,  τ)). Specifically, we defined the temporal response curve: 
\begin{equation}{\rm{PF}}\left( {90,\tau } \right) = \alpha \left( \tau \right) + \ \beta \left( \tau \right) + \ \gamma \left( \tau \right) + c.\end{equation}
(5)
 
Then t-tests were used to determine which parameters that differed in each domain, separately, serving as post hoc tests. 
Results
We first looked at the response frequency (defined as the total number of key presses divided by the total number of the target, 5400) made by the amblyopic and healthy participants in the orientation identification task. There was no significant difference in response frequency between the amblyopic and control groups (0.086 ± 0.051 vs. 0.083 ± 0.041, t(33) = 0.183, P = 0.856). 
The Perceptive Field
The best fit PFs are plotted as the upper and lower heatmaps, respectively, in each participant's panel of Figure 3. The time axis of the perceptive field is negative, relative to the time point of response. The model (Equation 1) provided a good fit to the PF for every participant (χ2 test, all ps > 0.05). The fitting statistics of all participants were listed in Table A2, Appendix A. The PF of most participants showed similar characteristics: reaching maximum response at around -500 ms and becoming generally flat around −100 ms prior to the response. The responsive region had a peak at the target orientation (as expected), where it was excited by the stimuli, and two suppressive valleys at adjacent orientations, where the stimulus was less likely to drive responses. It is worthy to note that the PF of participants A1, A16, or A17 did not show any regularity like other participants with amblyopia (see Fig. 3). The coefficient of determination (r2) of A1, A16, and A17 was significantly smaller than that of the rest of participants (0.329 ± 0.082 vs. 0.780 ± 0.088, t(33) = 8.505, P < 0.001; see Table A2, Appendix A). The data of A1, A16, and A17 were too noisy to reliably derive reasonable PF parameters. Thus, their results were excluded from the rest of the analyses. However, including these three participants will not change our results (Fig. A1, Appendix A). 
Figure 3.
 
The smoothed (upper) and best fitted (lower) perceptive fields of the participants with amblyopia (approximately A1 to A17) and healthy participants (approximately N1 to N18). Difference in color indicates the response probability.
Figure 3.
 
The smoothed (upper) and best fitted (lower) perceptive fields of the participants with amblyopia (approximately A1 to A17) and healthy participants (approximately N1 to N18). Difference in color indicates the response probability.
To investigate the effect of amblyopia on the orientation tuning properties, the best-fit PF of the two groups were compared. The averaged (best fit) PF of the 14 amblyopic eyes (AE) and 18 dominant eyes (NE) of healthy participants are shown in Figures 4a and 4b, respectively, along with the difference between the two (Fig. 4c). As shown in the significance map (Fig. 4d), there were three regions where the PFs of the two groups differed. At the target orientation, from time -345 ms to -103 ms, the PF of the AE was significantly smaller than that of the NE (P = 0.009). At both orientations 54 degrees and 126 degrees, from time -310 ms to -241 ms, the response of the AE was significantly greater than that of the NE (both ps = 0.030). The result indicated that the PF of the AE differed from that of the NE in both orientation and time dimensions. 
Figure 4.
 
(a) The averaged perceptive field of the amblyopic group. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. The different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colored areas indicate where the PFs in the two groups differ, but in different signs, respectively.
Figure 4.
 
(a) The averaged perceptive field of the amblyopic group. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. The different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colored areas indicate where the PFs in the two groups differ, but in different signs, respectively.
The Orientation Tuning
The orientation tuning curves of the two groups had a typical “Mexican hat” shape (Fig. 5a). To compare the shape of the orientation tuning between the two groups, the modulation depth of the response, defined by the difference between the maximum and minimum responses, and the full bandwidth at half difference between the maximum response and the response at orthogonal orientation of the orientation tuning curve were extracted (Fig. 5f). The bandwidth of the AE and NE were 31.41 ± 10.59 degrees and 24.76 ± 6.85 degrees, respectively. The AE had a larger bandwidth than that of the NE (t(30) = 2.155, P = 0.039; Fig. 5b). No difference in the modulation depth between two groups was found (t(30) = 0.997, P = 0.327; Fig. 5c). The correlation between the modulation depth and bandwidth was not significant (r = −0.334, P = 0.243). We also compared the width parameters κE and κI of the excitation and inhibition orientation tuning components (Equation 2) between the two groups. The width parameters κE (t(30) = 2.581, P = 0.015; Fig. 5d) and κI (t(30) = 2.359, p = 0.025, Fig. 5e) of the AE were smaller than those of the NE. The result indicated that the orientation tuning in the AE was broader than that in the NE (see Fig. 5). 
Figure 5.
 
(a) The orientation tuning curves of the amblyopic (red) and the normal eye (blue). (b) The bandwidth of the participants with amblyopia was larger than that of the control participants. (c) No significant difference in the modulation depth was found. (d) Both κE and κI in the amblyopic group were significant smaller than that of the control group. Error bar: ±1 standard error. Asterisks: statistical significance with P < 0.05. (f) Shape analysis of the orientation tuning curve. The parameters used in the analysis are illustrated. The modulation depth of the response is defined by the difference between the maximum and minimum responses. The bandwidth is defined as full bandwidth at half difference between the maximum response and the response at its orthogonal orientation.
Figure 5.
 
(a) The orientation tuning curves of the amblyopic (red) and the normal eye (blue). (b) The bandwidth of the participants with amblyopia was larger than that of the control participants. (c) No significant difference in the modulation depth was found. (d) Both κE and κI in the amblyopic group were significant smaller than that of the control group. Error bar: ±1 standard error. Asterisks: statistical significance with P < 0.05. (f) Shape analysis of the orientation tuning curve. The parameters used in the analysis are illustrated. The modulation depth of the response is defined by the difference between the maximum and minimum responses. The bandwidth is defined as full bandwidth at half difference between the maximum response and the response at its orthogonal orientation.
The Temporal Dynamics
We then examined the dynamics of PF in temporal domain. In Figure 6a, the response at the target orientation (i.e. PF(90,  τ) [temporal PF]), is plotted as a function of time for the two groups. The temporal PF of the AE and NE had a similar bell shape, increasing to the peak and then dropping down to the baseline before response. A one-dimensional cluster-based permutation test was used to compare the temporal dynamics of the PF between the two groups. The response of the AE was significantly lower than that of the NE from -310 ms to -103 ms (cluster-based permutation test, P = 0.001; see Fig. 6a). We also plotted the temporal curve at the most suppressive orientation (i.e. 54/126 degrees) in Figure 6b. The amblyopic eyes showed higher responses from -310 ms to -241 ms (cluster-based permutation test, P = 0.006). The shape parameters of the temporal PF, including the peak of target response (Rpeak), the time corresponds to Rpeak (reaction time [RT]), and the full width of half-height (FWHH) were also compared (Fig. 6g). The AE had a significantly longer RT than the NE (483 ms ± 68 ms vs. 425 ms ± 58 ms, t (30) = 2.588, P = 0.015; Fig. 6c). Neither Rpeak (t(30) = 1.283, P = 0.209; Fig. 6d) nor FWHH (t(30) = 0.183, P = 0.856; Fig. 6e) showed any differences between the two groups. The peak time of the inhibition component (Equation 3b) τI of amblyopia was longer than that of the normal controls (t(30) = 2.245, P = 0.032; Fig. 6f). The results indicated that the main temporal change in the amblyopic PF was due to a general delay instead of the overall shape alternation. 
Figure 6.
 
(a) The temporal dynamics of the perceptive field at the target orientation PF(90, τ). (b) The temporal dynamics of the perceptive field at the lateral orientation PF(54, τ). Note that PF(126, τ) is symmetrical to PF(54, τ). Color red: amblyopic eye; color blue: healthy eye. Transparent areas indicate ±1 standard error. The thick black line indicates the region where the two curves significantly differ. The comparisons of RT (c), Rpeak (d), FWHH (e), and the peak time of the inhibition component (Equation 3b), τI (f) between the two groups. Error bar: ±1 standard deviation. Asterisks: statistical significance. (g) Shape analysis of the temporal response curve PF(90,  τ). The peak of the PF at the target orientation (Rpeak), the time corresponds to Rpeak (RT), and the full width of half-height (FWHH) is illustrated.
Figure 6.
 
(a) The temporal dynamics of the perceptive field at the target orientation PF(90, τ). (b) The temporal dynamics of the perceptive field at the lateral orientation PF(54, τ). Note that PF(126, τ) is symmetrical to PF(54, τ). Color red: amblyopic eye; color blue: healthy eye. Transparent areas indicate ±1 standard error. The thick black line indicates the region where the two curves significantly differ. The comparisons of RT (c), Rpeak (d), FWHH (e), and the peak time of the inhibition component (Equation 3b), τI (f) between the two groups. Error bar: ±1 standard deviation. Asterisks: statistical significance. (g) Shape analysis of the temporal response curve PF(90,  τ). The peak of the PF at the target orientation (Rpeak), the time corresponds to Rpeak (RT), and the full width of half-height (FWHH) is illustrated.
Relationship Between Orientation Tuning and Contrast Sensitivity
To investigate how the PF changes in orientation-time domain related to the spatial vision in amblyopia, we performed correlation analyses. No significant correlation was found between the contrast sensitivity (CS) at spatial frequency (SF) of 1 c/deg (CS values of the amblyopic participants are listed in Table A1, Appendix A) and the bandwidth of the orientation tuning or RT in the amblyopic group (both ps > 0.05; Fig. 7). 
Figure 7.
 
(a) The correlation between the bandwidth of the orientation tuning and the CS at 1 c/deg. (b) The correlation between the RT of the PF and the CS at 1 c/deg.
Figure 7.
 
(a) The correlation between the bandwidth of the orientation tuning and the CS at 1 c/deg. (b) The correlation between the RT of the PF and the CS at 1 c/deg.
Comparing PFs Between the Dominant and Non-Dominant Eyes
To rule out the possibility that the PF difference we found between the AE and NE was due to the choice of the dominant eye as the control eye, we additionally collected the PFs of the non-dominant eyes (NDE) from eight (of 18) normal participants, and compared the PFs between the dominant eye (DE) and NDE of these eight healthy participants. The PFs of the DE and NDE are shown in Figures 8a and 8b, respectively. The paired permutation test showed that there was no significant difference in any region of the PFs between DE and NDE of healthy participants (P > 0.05; Figs. 8c, 8d). Further analysis showed that there was no significant difference in either tuning bandwidth (24.7 ± 6.6 degrees vs. 25.6 ± 7.4 degrees, paired t-test, t(7) = 0.585, P = 0.577) or RT (418 ± 50 ms vs. 439 ± 59 ms, paired t-test, t(7) = 0.905, P = 0.396) between the DE and NDE. 
Figure 8.
 
The average PFs of the DE (a) and NDE (b) of the eight healthy participants. (c) The PF difference of the DE and NDE, and (d) the corresponding significance map. The color cyan indicates regions with P > 0.05.
Figure 8.
 
The average PFs of the DE (a) and NDE (b) of the eight healthy participants. (c) The PF difference of the DE and NDE, and (d) the corresponding significance map. The color cyan indicates regions with P > 0.05.
Discussion
Summary
In this study, we asked participants to continuously detect vertical gratings embedded in a stream of randomly oriented gratings and estimated the orientation-time PF for the vertical grating detection task in the amblyopic and healthy participants using a subspace reverse correlation technique.26,4850 Although no difference in the total response frequency was found between the amblyopic and control participants, the cluster-based permutation test revealed that there were significant differences in the PFs between the amblyopic and healthy eyes in both orientation and time domains. Further analyses showed that the orientation tuning curve in the AE was broader than that in the NE (see Fig. 5). The temporal dynamics of the PF in amblyopia showed a general delay (see Figs. 6a, 6b) instead of the shape change of response dynamics (see Fig. 6e). No difference in PFs between the DE and NDE in the normal group was found (see Fig. 8). 
It has been reported that orientation discrimination sensitivity decreased with stimulus contrast.66,67 Thus, we chose gratings of low spatial frequency and high contrast as our stimulus, aiming to equate the effective contrast of the stimulus in the amblyopic and healthy eyes. Although contrast sensitivity loss is the hallmark of amblyopia, the deficits are much more prominent at high spatial frequencies.6,7,68 In addition, suprathreshold contrast perception of the amblyopic eyes was found to be largely normal.69,70 To further confirm this, we additionally measured the CSFs of both DE and NDE of eight healthy participants, and compared these normal CSFs with those of the 12 amblyopic participants who had valid PF measures. The AE exhibited typical CSF deficits, with significantly reduced area under the CSF (AE vs. DE, t(18) = 4.335, P < 0.001; AE vs. NDE, t(18) = 4.403, P < 0.001; Fig. 9a). However, there was no sensitivity difference at 1 c/deg between the amblyopic and either of the healthy eyes (AE vs. DE, t(18) = 1.290, P = 0.213; AE vs. NDE, t(18) = 1.167, P = 0.258), as expected. 
Figure 9.
 
(a) The contrast sensitivity functions of the 12 amblyopic eyes (red), of the dominant eyes (DE, blue) of the eight normal participants, and of the non-dominant eyes (NDEs; yellow) of the same eight participants. (b) Illustrates the orientation tuning of a V1 neuron involves both the feedforward excitation from the lateral genius nucleus,22 and the intra-cortical lateral inhibition.26,34,35,71 (c) Both excitation and inhibition curves were broader in amblyopia. (d) The temporal response curve PF(90, τ) aligned to the peak. The short vertical bars denote the time participants responded. Shaded areas: ±1 standard error.
Figure 9.
 
(a) The contrast sensitivity functions of the 12 amblyopic eyes (red), of the dominant eyes (DE, blue) of the eight normal participants, and of the non-dominant eyes (NDEs; yellow) of the same eight participants. (b) Illustrates the orientation tuning of a V1 neuron involves both the feedforward excitation from the lateral genius nucleus,22 and the intra-cortical lateral inhibition.26,34,35,71 (c) Both excitation and inhibition curves were broader in amblyopia. (d) The temporal response curve PF(90, τ) aligned to the peak. The short vertical bars denote the time participants responded. Shaded areas: ±1 standard error.
To rule out the possibility that the PF difference we found between the AE and NE was due to the eye dominance, we additionally collected the PFs of the non-dominant eyes from eight (of 18) healthy participants. No significant difference was found in any region of the PFs between the DE and NDE of the eight healthy participants (see Fig. 8). We further compared the bandwidth and RT between the AE and NDE. There was also no significant difference in bandwidth (t(20) = 1.360, P = 0.189; Fig. 10a) or in RT (t(20) = 1.511, P = 0.147; Fig. 10b) between the AE and NDE. After inspection of the individual data of the bandwidth and RT (see Figs. 10a, 10b), we suspect that no statistical difference found between the AE and NDE was probably due to the insufficient sample size (8 NDEs). To overcome this, we used the bootstrap procedure to estimate the standard errors for bandwidth and RT of the AE (n = 14), DE (n = 8), and NDE (n = 8). There were 10,000 bootstrap samples of the bandwidth and RT that were generated for the AE, DE, and NDE, respectively, with the data for DE and NDE were always paired. Figure 10c shows that empirical distributions of the bandwidth samples for the AE, DE, and NDE. The Z test showed that the bandwidth difference between the AE and DE was significant (z = 1.92, P = 0.028). The bandwidth difference between the AE and NDE was marginally significant (z = 1.602, P = 0.055). There was no significant difference in bandwidth between the DE and NDE (z = 0.611, P = 0.27). Similar results for the RT samples can be seen in Figure 10d. There was a significant difference in RT between the AE and DE (z = 2.68, P = 0.004), and between the AE and NDE (z = 1.66, P = 0.048). There was no significant difference in RT between the DE and NDE (z = 0.956, P = 0.17). Thus, the PF difference between the AE and DE we found in the study was not likely due to the choice of the dominant eye as the normal control group. Instead, it should be interpreted as reflecting the difference in orientation processing between the amblyopic and normal visual system. 
Figure 10.
 
The tuning bandwidth (a) and RT of temporal dynamics (b) in the AE (red), DE (blue), and NDE (yellow). Each filled cycle denotes the data of each participant. The black dotted lines connect paired data of the DE and NDE. Error bar: ±1 standard deviation. The empirical distributions of the tuning bandwidth (c) and RT (d) were estimated from 10,000 bootstrap samples. The dashed lines indicate the means of the distributions. Asterisks: Statistical significance for P < 0.05. #: Marginal significance for 0.05 < P < 0.1.
Figure 10.
 
The tuning bandwidth (a) and RT of temporal dynamics (b) in the AE (red), DE (blue), and NDE (yellow). Each filled cycle denotes the data of each participant. The black dotted lines connect paired data of the DE and NDE. Error bar: ±1 standard deviation. The empirical distributions of the tuning bandwidth (c) and RT (d) were estimated from 10,000 bootstrap samples. The dashed lines indicate the means of the distributions. Asterisks: Statistical significance for P < 0.05. #: Marginal significance for 0.05 < P < 0.1.
The Orientation Tuning in Amblyopia
Psychophysical reverse correlation technique has been widely used to probe the early sensory processing in early visual cortex.50,72,73 Especially with the task in which the participant was in control of the viewing duration, psychophysical reverse correlation offers the advantage of unbiased estimation of the sensory kernel.51,74 By using the same paradigm of rapid presentation of gratings in different orientations, Roeber, Wong, and Freeman48 showed that the paradigm could revoke strong cross-orientation suppression, which was tied with the sharpness of neural orientation tuning in visual cortex.32,33 The PF estimated in our study is very similar to that found in the V1 neurons of awake macaques.75 The orientation tuning curve we found had a typical “Mexican hat” shape, similar to that reported in V1 neurons26 as well as in human observers.50 In addition, the bandwidth of the healthy participants found in our experiment was also comparable with that measured in simple cells of macaque striate cortex23 and in human observer.7678 Neurons at higher hierarchy of visual processing likely have larger receptive field79 and broader tuning width.80 As summarized by Cass, Stuit, Bex, and Alais,78 the smallest bandwidth to the 1 c/deg grating reported in the literature was about 24 degrees, which is very close to what we found (26 degrees) here. Therefore, we believe that the orientation aspect of the estimated PF was more likely to reflect the tuning property of the low-level visual processing, and our result provided strong evidence for examining whether and how amblyopia affects orientation tuning in human. 
We found that the orientation tuning in the amblyopic visual system was broader than that in the normal visual system. This is consistent to the result in a previous study, where Huang, Zhou, Liu, et al.43 measured the monocular tilt illusion in patients with amblyopia, and suggested that the abnormal tilt illusion in amblyopia could be explained by a broader orientation tuning. Levi, Waugh, and Beard47 also found that there were some of the amblyopic participants who showed broader orientation tuning. The shape and bandwidth of the orientation tuning estimated in our study are also within the range reported in the study by Levi, Waugh, and Beard.47 
The width of excitation and inhibition tuning, reciprocally related to the parameters κE and κI, were found both wider in amblyopia (see Figs. 5d, 5e). The orientation tuning of a V1 neuron involves both the feedforward information from the lateral genius nucleus,22 and the intra-cortical interaction26,34,35 (see Fig. 9b). Our results might suggest that the geniculocortical feedforward input and intracortical lateral interactions in orientation processing are both affected in amblyopia (see Fig. 9c). There were human studies that demonstrated that the geniculocortical input and lateral interaction were impaired in amblyopia. Using high-resolution functional magnetic resonance imaging (fMRI), Wen, Wang, Zhou, et al.81 found the amblyopic eye exhibited reduced response in the parvocellular layers of the lateral geniculate nucleus and weaker connection to V1. With psychophysical approaches, Polat, Sagi, and Norcia82 and Polat, Ma-Naim, Belkin, and Sagi83 reported that the abnormal spatial interaction in patients with amblyopia suggested the horizontal connections in primary visual cortex were disrupted. 
The Response Dynamics in Amblyopia
Psychophysical reverse correlation could also provide the temporal dynamics of the visual processing. The PF was essentially the histogram of stimulus orientations of all responses at different time (see Fig. 2). The temporal spread of the PF essentially reflected the variability of the RT across trials. There was no difference in FWHH of the temporal response curve, PF(90, τ), between the two groups. When we aligned the peak time of the temporal PFs of the two groups, it is evident that the shape of the temporal PF of the two groups was similar (see Fig. 9d). The result suggests that the RT variability of the AE and NE was comparable. 
The orientation-time PF is information-rich, as it encompasses the entire temporal course from the neural processing delay from the retina to the brain and from the brain to the muscles. The RT of the temporal response curve was more than 400 ms, which is much greater than that of neural responses in V1.26,71,84 Thus, the RT possibly contained a substantial component taken by the processing at downstream visual areas of V1. The AE showed a significantly longer RT than the NE(DE), which is consistent with previous works involving psychophysics8587 or EEG measurement.88 The temporal response curve had a flat region that followed the hump, where the stimulus had no influence on the response (see Fig. 6a, Fig. 9d). This region set the lower limit of the RT which is believed to consist of the time needed to generate the internal representation from the stimulus, and the post-sensory delay that is needed to execute the response.51,89,90 Given that the FWHHs of the temporal response curve in the AE and NE were similar, and that the effective contrast between the AE and NE were equated, we thus speculated that the prolonged RT in amblyopia possibly reflected the post-sensory delay at downstream visual areas of V1. Similar to our finding, Farzin and Norcia87 has also reported that the prolonged RT in amblyopia was independent of visual acuity and suggested the cortical connections to higher brain areas underlying decision and response selection processes were affected by amblyopia. 
Conclusion
In conclusion, using a subspace reverse correlation paradigm with gratings of 1 c/deg and 99% contrast, we found an altered orientation-time PF in amblyopia characterized by a broader tuning width and general temporal delay. Our result suggests that amblyopia may lead to abnormal feedforward geniculocortical input and lateral intracortical connections, and higher level deficit that related to downstream processing. Our study sheds light on the mechanisms underlying the deficits of orientation processing in amblyopia. It also bridges the gap between the findings at single cell and behavioral levels and provides rigorous constraint for models of orientation selectivity. 
Acknowledgments
The authors thank Peng Zhang for helping us with the cluster-based permutation test. We are also grateful to the anonymous reviewers for their constructive suggestions. 
Supported by National Key Research and Development Program of China (2020YFC2003800 to C.B.H.), the National Natural Science Foundation of China (NSFC81600764 to F.H.; NSFC 32071056 and 32100864 to C.B.H.), the Department of Human Resources and Social Security of Zhejiang Province (Qianjiang Talent Project, QJD1803028 to F.H.), Wenzhou Science and Technology Bureau (Y20180710 to X.R.), the Scientific Instrument Developing Project of the Chinese Academy of Sciences (ZDKYYQ20200005 to C.B.H.). 
Disclosure: J. Zhu, None; X. Ruan, None; C. Li, None; J. Yuan, None; Y. Yang, None; W. Zhang, None; H. Zhang, None; Z. Zhuo, None; F.-F. Yan, None; C.-B. Huang, None; F. Hou, None 
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Appendix A
The detailed information of the amblyopic participants is listed in Table A1. The goodness of fit of Equation 1, including χ2 statistics and r2, for each participant is listed in Table A2. When all participants were included, the cluster-based permutation test showed that the differences between the AE and NE were significant (Fig. A1). 
Table A1.
 
Characteristics of the Amblyopica Participants
Table A1.
 
Characteristics of the Amblyopica Participants
Table A2.
 
Goodness of Fit of the Model for All Participants
Table A2.
 
Goodness of Fit of the Model for All Participants
Figure A1.
 
(a) The averaged perceptive field of all 17 amblyopic participants. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. Different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colors indicate where the PFs in the two groups differ, but in different signs, respectively.
Figure A1.
 
(a) The averaged perceptive field of all 17 amblyopic participants. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. Different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colors indicate where the PFs in the two groups differ, but in different signs, respectively.
Figure 1.
 
Top row: Reverse correlation in a typical electrophysiological experiment. The white noise images were presented to the animal and the neural spikes were recorded. Via reverse correlation, one can derive the receptive field of a particular neuron. Bottom row: Psychophysical reverse correlation in our experiment. Using reverse correlation, one can derive the weighting function of the visual system in the orientation-time domain for the task.
Figure 1.
 
Top row: Reverse correlation in a typical electrophysiological experiment. The white noise images were presented to the animal and the neural spikes were recorded. Via reverse correlation, one can derive the receptive field of a particular neuron. Bottom row: Psychophysical reverse correlation in our experiment. Using reverse correlation, one can derive the weighting function of the visual system in the orientation-time domain for the task.
Figure 2.
 
(a) An illustration of how the perceptive field is derived. The grating orientations within a 1 second period (30 gratings) prior to each response (key press) were piled together. The orientation histogram h(θ) was calculated for each time offset τ. The histogram was then divided by the total number of responses to get p(θ). The red circles represent timestamps of button presses. (b) The perceptive field PF(θ,  τ) is the concatenation of p(θ) over all τs. (c) The perceptive field PF(θ, τ) as a heatmap.
Figure 2.
 
(a) An illustration of how the perceptive field is derived. The grating orientations within a 1 second period (30 gratings) prior to each response (key press) were piled together. The orientation histogram h(θ) was calculated for each time offset τ. The histogram was then divided by the total number of responses to get p(θ). The red circles represent timestamps of button presses. (b) The perceptive field PF(θ,  τ) is the concatenation of p(θ) over all τs. (c) The perceptive field PF(θ, τ) as a heatmap.
Figure 3.
 
The smoothed (upper) and best fitted (lower) perceptive fields of the participants with amblyopia (approximately A1 to A17) and healthy participants (approximately N1 to N18). Difference in color indicates the response probability.
Figure 3.
 
The smoothed (upper) and best fitted (lower) perceptive fields of the participants with amblyopia (approximately A1 to A17) and healthy participants (approximately N1 to N18). Difference in color indicates the response probability.
Figure 4.
 
(a) The averaged perceptive field of the amblyopic group. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. The different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colored areas indicate where the PFs in the two groups differ, but in different signs, respectively.
Figure 4.
 
(a) The averaged perceptive field of the amblyopic group. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. The different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colored areas indicate where the PFs in the two groups differ, but in different signs, respectively.
Figure 5.
 
(a) The orientation tuning curves of the amblyopic (red) and the normal eye (blue). (b) The bandwidth of the participants with amblyopia was larger than that of the control participants. (c) No significant difference in the modulation depth was found. (d) Both κE and κI in the amblyopic group were significant smaller than that of the control group. Error bar: ±1 standard error. Asterisks: statistical significance with P < 0.05. (f) Shape analysis of the orientation tuning curve. The parameters used in the analysis are illustrated. The modulation depth of the response is defined by the difference between the maximum and minimum responses. The bandwidth is defined as full bandwidth at half difference between the maximum response and the response at its orthogonal orientation.
Figure 5.
 
(a) The orientation tuning curves of the amblyopic (red) and the normal eye (blue). (b) The bandwidth of the participants with amblyopia was larger than that of the control participants. (c) No significant difference in the modulation depth was found. (d) Both κE and κI in the amblyopic group were significant smaller than that of the control group. Error bar: ±1 standard error. Asterisks: statistical significance with P < 0.05. (f) Shape analysis of the orientation tuning curve. The parameters used in the analysis are illustrated. The modulation depth of the response is defined by the difference between the maximum and minimum responses. The bandwidth is defined as full bandwidth at half difference between the maximum response and the response at its orthogonal orientation.
Figure 6.
 
(a) The temporal dynamics of the perceptive field at the target orientation PF(90, τ). (b) The temporal dynamics of the perceptive field at the lateral orientation PF(54, τ). Note that PF(126, τ) is symmetrical to PF(54, τ). Color red: amblyopic eye; color blue: healthy eye. Transparent areas indicate ±1 standard error. The thick black line indicates the region where the two curves significantly differ. The comparisons of RT (c), Rpeak (d), FWHH (e), and the peak time of the inhibition component (Equation 3b), τI (f) between the two groups. Error bar: ±1 standard deviation. Asterisks: statistical significance. (g) Shape analysis of the temporal response curve PF(90,  τ). The peak of the PF at the target orientation (Rpeak), the time corresponds to Rpeak (RT), and the full width of half-height (FWHH) is illustrated.
Figure 6.
 
(a) The temporal dynamics of the perceptive field at the target orientation PF(90, τ). (b) The temporal dynamics of the perceptive field at the lateral orientation PF(54, τ). Note that PF(126, τ) is symmetrical to PF(54, τ). Color red: amblyopic eye; color blue: healthy eye. Transparent areas indicate ±1 standard error. The thick black line indicates the region where the two curves significantly differ. The comparisons of RT (c), Rpeak (d), FWHH (e), and the peak time of the inhibition component (Equation 3b), τI (f) between the two groups. Error bar: ±1 standard deviation. Asterisks: statistical significance. (g) Shape analysis of the temporal response curve PF(90,  τ). The peak of the PF at the target orientation (Rpeak), the time corresponds to Rpeak (RT), and the full width of half-height (FWHH) is illustrated.
Figure 7.
 
(a) The correlation between the bandwidth of the orientation tuning and the CS at 1 c/deg. (b) The correlation between the RT of the PF and the CS at 1 c/deg.
Figure 7.
 
(a) The correlation between the bandwidth of the orientation tuning and the CS at 1 c/deg. (b) The correlation between the RT of the PF and the CS at 1 c/deg.
Figure 8.
 
The average PFs of the DE (a) and NDE (b) of the eight healthy participants. (c) The PF difference of the DE and NDE, and (d) the corresponding significance map. The color cyan indicates regions with P > 0.05.
Figure 8.
 
The average PFs of the DE (a) and NDE (b) of the eight healthy participants. (c) The PF difference of the DE and NDE, and (d) the corresponding significance map. The color cyan indicates regions with P > 0.05.
Figure 9.
 
(a) The contrast sensitivity functions of the 12 amblyopic eyes (red), of the dominant eyes (DE, blue) of the eight normal participants, and of the non-dominant eyes (NDEs; yellow) of the same eight participants. (b) Illustrates the orientation tuning of a V1 neuron involves both the feedforward excitation from the lateral genius nucleus,22 and the intra-cortical lateral inhibition.26,34,35,71 (c) Both excitation and inhibition curves were broader in amblyopia. (d) The temporal response curve PF(90, τ) aligned to the peak. The short vertical bars denote the time participants responded. Shaded areas: ±1 standard error.
Figure 9.
 
(a) The contrast sensitivity functions of the 12 amblyopic eyes (red), of the dominant eyes (DE, blue) of the eight normal participants, and of the non-dominant eyes (NDEs; yellow) of the same eight participants. (b) Illustrates the orientation tuning of a V1 neuron involves both the feedforward excitation from the lateral genius nucleus,22 and the intra-cortical lateral inhibition.26,34,35,71 (c) Both excitation and inhibition curves were broader in amblyopia. (d) The temporal response curve PF(90, τ) aligned to the peak. The short vertical bars denote the time participants responded. Shaded areas: ±1 standard error.
Figure 10.
 
The tuning bandwidth (a) and RT of temporal dynamics (b) in the AE (red), DE (blue), and NDE (yellow). Each filled cycle denotes the data of each participant. The black dotted lines connect paired data of the DE and NDE. Error bar: ±1 standard deviation. The empirical distributions of the tuning bandwidth (c) and RT (d) were estimated from 10,000 bootstrap samples. The dashed lines indicate the means of the distributions. Asterisks: Statistical significance for P < 0.05. #: Marginal significance for 0.05 < P < 0.1.
Figure 10.
 
The tuning bandwidth (a) and RT of temporal dynamics (b) in the AE (red), DE (blue), and NDE (yellow). Each filled cycle denotes the data of each participant. The black dotted lines connect paired data of the DE and NDE. Error bar: ±1 standard deviation. The empirical distributions of the tuning bandwidth (c) and RT (d) were estimated from 10,000 bootstrap samples. The dashed lines indicate the means of the distributions. Asterisks: Statistical significance for P < 0.05. #: Marginal significance for 0.05 < P < 0.1.
Figure A1.
 
(a) The averaged perceptive field of all 17 amblyopic participants. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. Different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colors indicate where the PFs in the two groups differ, but in different signs, respectively.
Figure A1.
 
(a) The averaged perceptive field of all 17 amblyopic participants. (b) The averaged perceptive field of the control group. (c) The PF difference between the two groups b and a. Different color represents the value of response probability. (d) The statistical significance of each point of the PF difference based on the cluster-based permutation test. The color cyan indicates regions with P > 0.05. The red and blue colors indicate where the PFs in the two groups differ, but in different signs, respectively.
Table A1.
 
Characteristics of the Amblyopica Participants
Table A1.
 
Characteristics of the Amblyopica Participants
Table A2.
 
Goodness of Fit of the Model for All Participants
Table A2.
 
Goodness of Fit of the Model for All Participants
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