Figure 1.
a. Overview of the modules and connections. External biases to the system are shown as ovals. (Note that the actual number of cells in V1, extrastriate and parietal modules are more than shown. Typically several hundreds of neurons exist in each layer.) b. The inhibition and biases influencing competition in the extrastriate and parietal modules. These modules are reciprocally connected. Competition within the extrastriate module operates within each feature type at each spatial location. Neurons in the parietal module compete to determine which spatial location wins the competition for attention. Further description is given in the appendix.
Figure 2.
Kernel used to represent lateral connectivity in the extrastriate module.
This kernel is convolved with the outputs of cells in the extrastriate cortex to give lateral inputs to horizontally selective cells. Hence, this kernel gives the weights of lateral inputs from neighbouring cells. The plot shows that inputs are strongest locally and horizontally towards the right, which is toward the intact hemifield in our simulations.
Figure 3.
Visual Search Scanpaths Produced by the Model.
Simulated scanpaths under (a) normal conditions, (b) hemianopic V1 lesion, and (c) hemineglect parietal lesion. No compensatory mechanism has yet been learned; the weight of the compensation bias is zero and the lateral connections in the extrastriate module are not yet present. Axes refer to pixel position in the scene.
Figure 4.
Line Bisection Scanpaths Produced by the Model.
(a–c) Simulated scanpaths during free viewing of a horizontal line stimulus under (a) normal conditions, (b) hemianopic V1 lesion, and (c) hemineglect parietal lesion. (d–f) Simulated scanpaths during a line bisection task under (d) normal conditions, giving an accurate bisection point of 500, which is line centre, (e) hemianopic V1 lesion, giving a bisection point of 705 (18.6° offset, which is an ipsilesional error of 41.4% of line length), (f) hemineglect parietal lesion, giving a bisection point of 645 (13.2° offset, which is an ipsilesional error of 29.3%). The lines are depicted green, black dots are fixations, and dashed lines connect these to indicate the scanpath. Bisection points are shown as red asterisks. Axes refer to pixel position in the scene. The weight of the bisection task bias is 4.5 in these simulations.
Figure 5.
Effects of Spatial Compensatory Bias on Pathological Search Scanpaths.
With the bias applied, the hemianopic scanpath is now able to search the blind hemifield (a). However, this bias fails to increase contralesional scanning in hemineglect (b). Axes refer to pixel position in the scene.
Figure 6.
Line Scanning and Bisection with Spatial Compensation.
(a–b) Hemianopic scanpath under (a) free viewing, where the model can scan the blind hemifield but does not accurately fixate the line and (b) with the line bisection task, where the task bias does bring the scanpath back to the target line, but only the ipsilesional line segment is viewed, and the bisection point is offset to this side (in this example position 697, a 17.9° offset, or ipsilesional error of 39.8% of line length). Hence spatial compensation alone does not reproduce real hemianopic performance for this task. (c) Hemineglect scanpath during a line bisection task. During this task and under free viewing (not shown), the contralesional line segment is severely neglected and the scanpath deviates from the line. The bisection point is shifted to the ipsilesional part of the line (in this example position 587, 7.9° offset, or an ipsilesional error of 17.6% of line length). This spatial bias is, again, ineffective in promoting contralesional scanning in hemineglect. Axes refer to pixel position in the scene.
Figure 7.
Cortical activity in hemianopia with and without extrastriate lateral connections.
a. Acute hemianopia. Shows activity in the retinotopically-arranged horizontally selective extrastriate cells (left) and parietal (right) modules in the absence of lateral connections, at 300 ms post-fixation. Part of the line is represented in the normal hemifield but the blind hemifield is inactive due to lack of V1 inputs, despite the fact the line actually extends across the whole retina at this fixation point. Since only the intact hemifield contains stimulus-related activity in the parietal module, the next location to attract attention will be on the line in this hemifield. This reflects acute hemianopia before any rehabilitation training. Level of activity is given by the coloured bar. b. Hemianopia with perceptual completion. The top row shows activity in the extrastriate module for the cells selective for horizontal orientations, when lateral connections are enabled. Subplots show activity at 60 ms (onset of the stimulus-related response), 70 ms, 80 ms, 90 ms, 300 ms and 350 ms after fixation at the centre of the horizontal line. The bottom row shows the associated activity in the parietal module. Over time, the left of the line becomes most strongly represented and, therefore, will be chosen as the next saccade target. Note that levels of activity become high in extrastriate and parietal cortices for the blind hemifield. Level of activity is given by the coloured bar. c. Hemianopic scanpath with extrastriate lateral connections. The bisection point, which is offset contralesionally to the midpoint (position 455: −4.1° offset, which is a contralesional error of 9.1% of line length), is shown as a red asterisk. In this simulation the bisection task bias weight was 3 and no spatial compensation was involved. Axes refer to pixel position in the scene.
Figure 8.
Failed Perceptual Completion in hemineglect with extrastriate lateral connections.
a. Cortical activity at 300 ms post-fixation is shown in the extrastriate (left panel) and parietal (middle panel) modules when the parietal module has a step-function lesion. Activity for the entire line is present in the extrastriate cortex and the contralesional part of the line is reinforced by compensation through lateral connections. However, this increased extrastriate activity fails to activate a parietal representation of the contralesional line and, hence, this is neglected. If the parietal module is lesioned in a gradient fashion instead (right panel), the increased extrastriate activity does result in some activity in the damaged parietal area but this is insufficient to win the competition for attention. Level of activity is given by the coloured bar. b. Scanpath with parietal lesion (step-function lesion) and extrastriate lateral connections. The bisection point, which is offset into the ipsilesional half of the line (position 685∶16.8° offset, or an ipsilesional error of 37.4% of line length), is shown as a red asterisk. In this simulation the bisection bias weight was 5. Axes refer to pixel position in the scene.
Figure 9.
Example Scanpaths Showing the Effect of Lesion Condition and Bisection Task Bias on Line Scanning & Bisection.
Each sub-plot shows the position of scanpath fixations (black dots) and point of line bisection (red asterisk) under various healthy and lesion conditions when the bisection bias weight was systematically raised, being set to the following values in order left to right: 3, 4, 4.5, 5. Axes refer to pixel position in the scene. a. Intact model. Raising the weight of the bisection task bias has the effect of concentrating the scanpath at the line centre. Bisection was consistently at line centre, position 500 (zero error). b. V1 lesion model. Raising the weight of the bisection task bias causes more fixations to be clustered around the location, offset contralesionally to line centre, which will later become the bisection point. As the task bias weight increases, less fixations are placed at the contralesional line end, but this is still where the majority of fixations are made. Bisection points were always contralesionally offset, in these simulations, from left to right, being: 455 (−4.1° offset, 9.1% of line length error), 468 (−2.9° offset, 6.5% error), 488 (−1.1° offset, 2.4% error), 482 (−1.6° offset, 3.6% error). c. Parietal lesion model using a step-function. If the weight of the bisection task bias is weak, the scanpath does not stay on the line. Bisection points were always highly ipsilesionally offset, in these simulations, from left to right, being: 688 (17.1° offset, 38.0% of line length error), 680 (16.4° offset, 36.4% error), 674 (15.8° offset, 35.2% error), 681 (16.5° offset, 36.6% error). d. Parietal lesion model using a gradient. Bisection points again were highly ipsilesionally offset, in these simulations, from left to right, being: 611 (10.1° offset, 22.4% of line length error), 669 (15.4° offset, 34.1% error), 652 (13.8° offset, 30.7% error), 644 (13.1° offset, 29.1% error).
Figure 10.
Fixation Density Plots from Multiple Scanpath Simulations.
This shows the effect of lesion condition and bisection task bias on line scanning & bisection. Results come from 10 independent scanpath simulations for each condition. The density of fixations at each horizontal position across the scene is plotted in 1° bins. Note that, in order to clearly show each plot, sub-figures are plotted to the scale dictated by the Y axis maximum and this varies between plots. The control condition is shown in row (a), V1 lesion in row (b), parietal step-function lesion model in row (c) and parietal gradient lesion model in row (d). As in figure 9, the bisection bias was systematically increased here such that it is set to 3 in the leftmost column, 4 in the second column, 4.5 in the third and 5 in the final column. Fixations that landed more than 1° away from the line in the vertical direction are excluded. This only affected parietal lesion simulations where fixations were eliminated when they went off the line towards the edge of the scene. The number of simulations in which this occurred is given in table 1.
Table 1.
Comparison of bisection errors under different lesion conditions whilst varying the weight of the bisection bias.