Is the Cortical Deficit in Amblyopia Due to Reduced Cortical Magnification, Loss of Neural Resolution, or Neural Disorganization?

Abstract

The neural basis of amblyopia is a matter of debate. The following possibilities have been suggested: loss of foveal cells, reduced cortical magnification, loss of spatial resolution of foveal cells, and topographical disarray in the cellular map. To resolve this we undertook a population receptive field (pRF) functional magnetic resonance imaging analysis in the central field in humans with moderate-to-severe amblyopia. We measured the relationship between averaged pRF size and retinal eccentricity in retinotopic visual areas. Results showed that cortical magnification is normal in the foveal field of strabismic amblyopes. However, the pRF sizes are enlarged for the amblyopic eye. We speculate that the pRF enlargement reflects loss of cellular resolution or an increased cellular positional disarray within the representation of the amblyopic eye.

Significance statement: The neural basis of amblyopia, a visual deficit affecting 3% of the human population, remains a matter of debate. We undertook the first population receptive field functional magnetic resonance imaging analysis in participants with amblyopia and compared the projections from the amblyopic and fellow normal eye in the visual cortex. The projection from the amblyopic eye was found to have a normal cortical magnification factor, enlarged population receptive field sizes, and topographic disorganization in all early visual areas. This is consistent with an explanation of amblyopia as an immature system with a normal complement of cells whose spatial resolution is reduced and whose topographical map is disordered. This bears upon a number of competing theories for the psychophysical defect and affects future treatment therapies.

Keywords: amblyopia; contrast sensitivity; cortex; fMRI; pRF mapping; retinotopy.

Figure 1.

Effect of different types of neuronal disturbances in pRF and CMF estimation from simulation. pRFs were built and sampled regularly across a cortical surface. Position, shape, and size parameters of area V1 were taken from Harvey and Dumoulin (2011). The pRF is estimated from the total neuronal population within a voxel. Hence the properties of all the individual neurons influence the estimated pRF. Simulations were one-dimensional only. Each neuron was described as one point within the cortex represented by a line, the coordinates set between 0 (center of the fovea) and 100 mm. The relationship between CMF and eccentricity was calculated according to Equation 2 (Harvey and Dumoulin, 2011): CMF (mm/deg) = $\frac{1}{cx+d}$, with c = 0.04 mm⁻¹ and d = 0.07°/mm based on that study. The position of the neuron's receptive field (RFmm) were computed from the integral of 1/CMF: RFmm = $\frac{c}{2}$ · mm² + d · mm, where mm is the linear distance in millimeters from the center of the fovea. The size of the neuron's receptive field (RFsize) was calculated according to Equation 1: Rfsize(°) = a. RFmm + b, with a = 0.15°/° and b = 0.48°, based on that study (Harvey and Dumoulin, 2011). A–C, Top row shows pRF size versus eccentricity. D–F, Bottom shows the CMF, cortical distance versus eccentricity. Left column (A, D) shows the effect of different position scatters of the individual neurons (no scatter in red, 2° in green, and 4° in blue). Increasing RF scatter leads to an increase of pRF size (Zuiderbaan et al., 2012) while CMF is hardly affected. Interestingly, the pRF intercept follows the RF scatter closely. B, E, Middle column, Effect of increasing the individual RF sizes (original size in red, +2° in green, and +4° in blue). An increase of RF size provokes an increase of the pRF sizes across all eccentricities but CMF is not affected. C, F, Right column, Effect of reducing the number of neurons within a voxel by sparsely sampling the RFs (fewer RFs contributing to the signal). A sparse representation of 1 means that all RFs were sampled, a sparse representation of 2 corresponds to sample every other RFs, a sparse representation of four corresponds to sample every four RFs. Decreasing the sampling does not lead to any change either in pRF size or in CMF. In all cases, red lines show the same original scenario.

Figure 2.

Visual field maps extracted from pRF positions of a normal subject and an amblyopic participant (threshold of variance explained set at 10% for illustration purpose only). The figure shows posteroinferior views of left and right inflated surfaces. A, B, Maps for polar-angle (left) and eccentricity (right) of a normal subject. A, Maps when the stimulus was seen with the DE only. B, Maps when the stimulus was seen with the nDE only. C, D, Maps for polar angle (left) and eccentricity (right) of an amblyopic subject (subject A8). C, Maps when the stimulus was seen with the FFE only. D, Maps when the stimulus was seen with the AME only. C, D, Global organization of the visual information coming from the AME is consistent. The main difference between the two eyes is that there are fewer voxels that survived thresholding for the AME. The delimitation of the visual areas was based on the position of the upper vertical meridian (UVM; solid black line), lower vertical meridian (LVM; dotted black line), and horizontal meridian (HM, solid white line). The two insets on the top show the color overlays indicating the visual field angle (left) and the eccentricity (right). The visual areas are labeled on the polar-angle maps on A and C. For orientation clarity, the major sulci (outlined in dotted white lines) are labeled on the eccentricity maps (A, C). IPS, Intraparietal sulcus; TOS, transverse occipital sulcus; AOS, anterior occipital sulcus; LOS, lateral occipital sulcus; CaS, calcarine sulcus; OTS, occipitotemporal sulcus; COS, colateral sulcus.

Figure 3.

Comparison of the numbers of voxels with >30% variance explained between the two eyes. For each ROI (V1, V2, V3, V3AB, and V4), we calculated, for DE and nDE in normal subjects, and for AME and FFE in amblyopes, how many voxels had more than 30% of their variance explained by the model, as a percentage of total number of voxels (%DE, %nDE, %AME, and %FFE). The mean and the SEs of the ratios between the two eyes for each ROI are reported in gray for the group of normal subjects (%nDE/%DE) and in red for the group of the amblyopes (%AME/%FFE). The DE and the nDE are very comparable in normals. In AME compared to FFE, fewer voxels have more than 30% of their variance explained. This difference increases from V1 to V4.

Figure 4.

Change of pRF sizes, CMF, and pPI size across eccentricity in V1 voxels of a normal subject and the eight amblyopic participants. A, The pRF sizes increase with eccentricity. B, The CMF decreases with visual field eccentricity for the two eyes. C, The pPI is near constant for the DE and the nDE of normals and for the fellow eye of the amblyopes but decreases with eccentricity in the AME of the amblyopic subjects. The dots and the error bars represent the mean and SD of the binned data. The thick lines represent the best fitting regression line. Black, Data estimated from the DE of a normal. Green, Data from the nDE. Blue, Data from the fixing eye of the amblyopes. Red, Data from the AME.

Figure 5.

Change of pRF size (A), CMF (B), and pPI size (C) across eccentricity in V2 voxels of a normal subject and the eight amblyopic participants. Same configuration as Figure 4.

Figure 6.

Change of pRF size (A), CMF (B), and pPI size (C) across eccentricity in V3 voxels of a normal subject and the eight amblyopic participants. Same configuration as Figure 4.

Figure 7.

Distribution of the AME positions during the recording session. Each red dot corresponds to the median position of the AME relative to the center of the visual stimulus display during the recording of an fMRI volume (duration of 1940 ms). This accounts for saccadic eye movements as well as drifts. The variability of the eye positions was measured as the area of the 95% confidence ellipses (black). A, B, AME positions of subject A1 (A) and A2 (B) during their two fMRI sessions. C, Lack of correlation between the 95% confidence ellipse areas (in the abscissas) and the pRF sizes (FFE, blue; AME, red). Each dot corresponds to an amblyopic participant, the colored dotted lines being the regression lines. D, Lack of correlation between the squint angles and the pRF sizes from the AME. Each dot corresponds to an amblyopic participant, the colored dotted line being the regression line.

Figure 8.

Change of pRF sizes across eccentricity in V1 voxels of the amblyopic participant A4. The figure illustrates how the unsteady fixation of the AME can affect the estimation of pRF sizes. The effect on the AME data can be seen by comparing the purple and the red lines. The configuration is very similar to that of Figure 4A, but the data were combined every 0.5° of eccentricity. The dots and error bars represent the mean and SD of the binned data. The line is the best fitting regression line. The purple open dots and dotted line represent the data from the AME without correction for eye movements. The red closed dots and thick line represent the data from the AME after correction, which mainly produced an overall reduction of the error bars. The data from the FFE are shown in black and blue. The black open dots and dotted line represent the data from the FFE without correction for eye movements. The blue closed dots and thick line represent the data from the FFE after correction using not the FFE's movements but the AME's movements instead. The eye-movement deficit produces an overall increase of variability (increase size of error bars) and also an increase of the pRF sizes close to the fovea (as predicted by the simulation; Fig. 1, left). This increase is nonetheless not large enough to explain the difference of pRF sizes between the AME and the FFE.

Figure 9.

Summary of the group data. A, Change of pRF sizes. B, Change of CMF. C, Change of pPI with respect of visual field eccentricity. Grouped data from normal eye (DE and nDE were combined) are shown in black, FFE in blue, and AME data in red. The top row summarizes the data from V1, the middle row the data from V2, and the bottom row the data from V3. The dots and error bars are respectively the mean and SEs of the binned points between subjects. The solid lines represent the best fitting functions and the colored areas reflect the 95% confidence intervals of these fits (after bootstrapping and refitting).

Figure 10.

pRF differences between visual areas and measures of the cc-pRF sizes of V2 and V3 from V1. A, Normal eyes (black). B, FFEs (blue). C, AMEs (red). The top row shows that pRF size differences of V2 and V3 compared with those of V1 increase up the visual pathway and increase in slope up the hierarchy too for the eyes of the normal subjects and for the fixing eye of the amblyopes but not for the AME of the amblyopes. The bottom row shows the cc-pRFs. cc-pRF sizes of V2 and V3 do not vary with eccentricity for the eyes of normal subjects and for the fixing eye of the amblyopes but decreases in the AME. Lines were fit to bins, and the bins were bootstrapped and fits repeated to give 95% confidence intervals (colored areas).

Figure 11.

Comparison of the distribution of the pRFs between the data for two eyes in V1, V2, and V3 voxels. The first two rows show the distribution of pRFs in the visual field, estimated from voxels in V1 of one normal subject (black and gray) and one amblyopic subject (A8, in blue and red). A, For each voxel (with a >30% variance explained for both eyes) the position of its pRFs in a polar plot of the normal participant. The black line represents the shift between the position from DE to nDE. The light gray dots represent the position of the pRFs of the nDE. B, The correlation between the azimuth coordinates between the two eyes. C, Correlation between the elevation coordinates. D, Relationship between the eccentricity of the pRFs of the nDE and the difference in eccentricity between the two eyes. A–D show how similar the pRFs positions are between the two eyes in normals. E, For each voxel (with a >30% variance explained for both eyes) the position of its pRFs in a polar plot of one amblyopic participant. The blue line represents the shift between the position from FFE to AME. The red dots represent the positions from the AME. F, The correlation between the azimuth coordinates between the two eyes. G, The correlation between the elevation coordinates. H, Relationship between the eccentricity of the pRFs of the AME and the difference in eccentricity between the two eyes. E–H, The pRF positions were highly correlated in amblyopic subjects. The corresponding correlation values were reported in I–K (respectively, azimuth, elevation coordinates, and eccentricity) for V1, V2, and V3. There was more variability in the azimuth position between the two eyes in the amblyopes, and that the variability increases along the visual pathway from V1 to V3. K shows that the pRFs tend to be more eccentric in AMEs and that this tendency increases with eccentricity but not with visual hierarchy.