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Subcortical connectivity correlates selectively with attention’s effects on spatial choice bias

Significance Forebrain mechanisms of visuospatial attention have been widely studied. Yet, how the midbrain contributes to attention remains comparatively unknown. Here, we examined the role of the superior colliculus (SC), a vertebrate midbrain structure, in attention. Does the SC control sensitivity to attended information, or enable biasing choices toward attended information, or both? We mapped structural connections of the human SC with neocortical regions and found that the strengths of these connections correlated with, and were strongly predictive of, individuals’ choice bias, but not sensitivity. Taken together with previous animal studies, our results suggest that the human SC may play an evolutionarily conserved role in controlling choice bias during visual attention.

< BICchoice-theory, p<0.001; Fig. S5F) (3). The results suggest that the more parsimonious 2-ADC model was more appropriate, compared to the similarity choice model, for fitting behavioral data in this attention task.

Validating SC-cortex connectivity asymmetries
We performed several control analyses to confirm that SC-cortex connectivity asymmetries were not due to systematic biases in data acquisition, in the tractography pipeline, or with the specific sample of subjects analyzed.
First, we compared our tractography results with well-known established connections of the SC with the neocortex. We observed, overall, strongest connectivity of the SC with the precentral region followed by the superior parietal region ( Fig. S2D; Group 1; connectivity weights: SC-precentral=568.8±114.2, SC-superior parietal=356.5±50.4, p<0.001; with Benjamini-Hochberg correction for multiple comparisons). These results are consistent with existing literature on the strong SC connectivity with the motor cortex (precentral gyrus), as well as with the parietal cortex, both in humans (4), and in non-human primates (5,6). Moreover, our previous analysis showed that, despite showing the strongest connection weights overall, SC-precentral ROI connectivity was not asymmetric (Fig. S2F; p=0.758), indicating that hemispheric asymmetry was not a universal property of all SC-cortex connections.
Second, we tested whether the pattern of systematic leftward asymmetries would be apparent for other cortico-cortical connections also. We quantified connection strengths between the V1 and other cortical regions. In this case, we observed a mixed pattern of asymmetries (Fig. S2G). V1 connectivity with other regions in the insula and with the medial occipital cortex was significantly stronger for the right, as compared to the left, hemisphere (p<0.001, Benjamini-Hochberg correction). In contrast, V1 connectivity with cortical regions, such as the frontal (p=0.007) and cingulate (p<0.001), inferior frontal (p<0.001) and basal ganglia (p=0.01) aROIs was stronger for the left than for the right hemisphere (Benjamini-Hochberg correction; Fig. S2E). Next, we compared the extent of asymmetry in the SC and V1 connectivity. For this, we computed the average normalized asymmetry in SC and V1 connection weights (left-right; normalized by the maximum magnitude of asymmetry) across subjects. We found that asymmetries in SC connectivity were consistently higher than that for V1 (p<0.001, Wilcoxon signed rank test).
Third, we quantified the structural connectivity between frontal and parietal regions in Group 1 and Group 2 participants. In particular, we sought to replicate previously reported connectivity asymmetries in three sub-divisions of the Superior Longitudinal Fasciculus (SLF-I, SLF-II and SLF-III; SI Methods). We quantified connectivity using two methods: (i) connection weights using SIFT2, as for the SC and V1 connections and (ii) fascicle volume (7); details of this quantification are provided in the SI Methods section titled "SLF -ROIs and tractography". The results of this analysis replicated the results of de Schotten et al (7). SLF-I connection strengths showed significant leftward asymmetries (SIFT2 weights: SLF-I: left=110.7±6.7; right= 90.4±6.1; p=0.0012, signed rank test) whereas SLF-II and SLF-III connection strengths showed significant rightward asymmetries (SLF-II: left=29.0±3.4; right= 59.8±5.8; SLF-III: left=38.9±5.0; right= 94.1±6.6; p<0.001), with data pooled across the two groups (Fig. S7A). These trends were also present when we analyzed asymmetries in fascicle volumes, the metric adopted by de Schotten et al (7). Again, we observed significant leftward asymmetries in SLF-I and significant rightward asymmetries in SLF-II and SLF-III (volumes: SLF-I: left=8981.0±551.0; right= 7564.2±543.8, p=0.002; SLF-II: left=3393.9±390.6; right= 6600.6±639, p<0.001; SLF-III: left=4137.8±509.2; right= 9712.2±677.7, p<0.001). Each group of participants, when analyzed separately, showed trends similar to the pooled analysis, but only some of these asymmetries were significant, perhaps due to the fewer subject numbers in each group (Fig. S7B).
Taken together, these results indicate that the significant leftward asymmetry in SC-cortex connection weights was not due to systematic biases in the acquisition or analyses protocols.
Evaluating the stability of sensitivity and bias over time Before testing for the relationship between sensitivity, bias and SC connectivity, we had to first address a key question, in terms of the stability of each of these behavioral metrics over time. For this, we compared average sensitivity and bias and their modulation when the participants performed the task inside the fMRI scanner with data from outside the scanner (SI Methods). We observed strong correlations in sensitivity ( Fig. S1E

SLF connectivity: correlation with behavior
We also assessed if hemispheric asymmetries in SLF connectivity could predict hemifield asymmetries in sensitivity and bias. As with the SC-cortex connectivity analysis, we used a support vector machine-based regression model with leave-one-subject-out cross-validation for predicting individual behavioral asymmetries. None of the SLF divisions' connectivity asymmetries (SLF-I, II or III) correlated with asymmetries in sensitivity or bias (Table S2A); nor were these asymmetries predictive of asymmetries in sensitivity or bias (Table S2B). Nevertheless, SLF-II, but not SLF-I or SLF-III, connectivity asymmetry (MIR-L), predicted reaction time asymmetries significantly (δRT; correlation between observed and predicted asymmetries: r=0.48, p=0.023; Fig. S7C), again, replicating the results of De Schotten et al (7).

Correlation between SC-cortex connectivity and bias modulation: control analysis
We performed an additional control analysis to verify if connectivity-behavior correlations could be attributed to variations in the number of SC voxels across subjects; a higher number of SC voxels for a subject would increase the chances of more streamlines being traced for that subject, and thereby yield higher connectivity weights. We traced SC-cortex streamlines using a uniform number of SC voxels in each region across subjects, selecting a common minimum set that showed the strongest connectivity across aROIs (SI Methods). Even in this case, we continued to observe strong correlations between the weights of these subsets of SC fibers and Δbcc (e.g. SC-Parietal: r=0.470, p=0.027; Fig. S3C), indicating that our results were not confounded by inter-individual differences in the volume of the SC ROI across subjects.

Reaction time correlates of SC-cortex connectivity
We computed average reaction times (RT) for correct trials alone, separately, for the cued and uncued locations (by pooling across hemifields) and for the left and right hemifields (by averaging across cued and uncued conditions). Because of the very low proportion of hits (15%, across n=22 subjects) for the lowest change angle (5°), RT data for this angle was excluded from these analyses. Reaction times were significantly lower at the cued location compared to the uncued location (RT: cued= 651±38 ms, uncued= 815±37 ms, p<0.001; Fig. S1C). On the other hand, average RTs for responses to left and right hemifield changes were not significantly different (left=678±39 ms, right=669±36 ms, p=0.64).
Finally, we correlated hemifield asymmetries in RT with hemispheric asymmetries in SC-cortex connectivity, as well as cue-induced modulation of RT (ΔRT) with average SC-cortex connectivity. Hemifield asymmetries in RT correlated strongly with SC-cortex connectivity asymmetry with the Insula (SC-Insula: r=0.492, p=0.020; Fig. S9B), Lateral Occipital (SC-Lateral Occipital: r=0.458, p=0.032) and Medial Occipital (SC-Medial Occipital: r=0.591, p=0.004), aROIs, with the SC-Medial Occipital correlation surviving multiple comparisons correction. On the other hand, we observed no significant correlations between cue-induced modulation of RT and average connectivity between the SC and any cortical ROI (p>0.05; example correlation with SC-parietal connection strengths shown in Fig. S9B).

Participants
All experiments were conducted according to protocols approved by the Institute Human Ethics Committee, Indian Institute of Science, Bangalore. Informed written consent was obtained from each participant before the study.
A total of n=118 unique participants' data were analyzed for this study. All participants had normal or corrected to normal vision with no known history of neurological disorders. Participants were organized into three groups: Group 1 (dMRI and behavior group): Behavioral data (2-ADC attention task) and diffusion MRI data were acquired from n=22 participants (9 females, all right-handed, age: mean=25.1yrs, std=3.5 yrs). The number of participants was determined with power analysis, based on the correlations between structural connectivity and behavioral metrics (see section on Power analysis).
Group 2 (dMRI group): Diffusion MRI data from the Human Connectome Project (HCP) database were analyzed from n=60 participants (30 females, age: mean=29.5 yrs, std=3.2 yrs). Subjects were chosen based on progressively increasing HCP identifiers until an equal number of male and female subjects, with an equal number of left and right handers of each gender, were identified. We tested and confirmed that there was no significant difference in average absolute handedness across the two subgroups (handedness score, left-handed: mean=-80.5, std=10.70, right-handed: mean=78.33, std=19.54; p=0.599, two-sample t-test).

Group 3 (2-ADC behavior group):
Behavioral data (2-ADC attention task) was acquired from two studies involving studying the effect of neurostimulation on sensitivity and bias. Data analyzed here were acquired from baseline (sham stimulation) sessions comprising two subgroups: 3a (n=24, 2 females, age: range: 18-28 yrs); and 3b (n=26, 4 females, age: range: 18-27 yrs). These data were combined and analyzed here to measure hemifield asymmetries in sensitivity and bias in an independent group of subjects. Subjects in subgroups 3a and 3b who were common with Group 1 were excluded from analyses; among subjects common to subgroups 3a and 3b, the subgroup in which the subject's data was acquired first (chronologically) was included for analysis. This resulted in a final set of n=34 participants (4 females, age: range: 18-28 yrs).

Task and behavioral analyses
Task. Participants were tested on a two alternative change detection (2-ADC) paradigm (8). Stimulus presentation and data acquisition were programmed with Psychtoolbox and MATLAB 2015b (Natick, MA). Subjects were seated with their head resting on a custom chin rest and with the eyes positioned 60 cm away from a visual display (24" BenQ LCD monitor, 60 Hz refresh rate). Responses were recorded with an RB-840 response box (Cedrus Inc). Subjects were instructed to maintain fixation at a central fixation cross throughout the experiment. Fixation and eye movements were monitored using an infra-red based eyetracker (Gazepoint GP3, 60 Hz sampling rate).
The task began with a gray screen and a prompt for the subject to begin the trial block. After this a fixation cross (0.5° of visual angle) was presented for 200 ms, following which two full contrast Gabor gratings (spatial frequency 1.9 cpd) appeared for 250 ms, one on either side of the fixation cross. The center of each grating was displaced by 5° along the horizontal meridian from the fixation cross and had a diameter of 2.4°. Following this, a spatial cue (directed arrow, 0.5°) appeared above the fixation cross indicating the grating toward which attention should be directed. Following a random delay, chosen from an exponential distribution (300-1100 ms), the screen was blanked briefly (200 ms), and the gratings reappeared. Following reappearance, either one of the two gratings had changed in orientation or neither grating had changed. Subjects were instructed to identify the grating that changed in orientation, or to indicate "no change" if they perceived that neither changed in orientation, by pressing one of three distinct buttons (Fig. S1A).
Training and testing. Each behavioral testing session comprised 10 blocks of 50 trials each. Each block consisted of three trial types: validly cued trials, in which the orientation change occurred at the cued grating, invalidly cued trials, in which the orientation change occurred at the uncued grating, and "no change" trials, in which neither grating changed in orientation. Validly cued changes and invalidly cued changes are referred to, respectively, as "cued" and "uncued" changes, subsequently, and also in the main text. 80% of the trials were change trials and the remaining 20% were no-change trials. Among the change trials, 75% were validly cued and 25% were invalidly cued changes (cue validity: 75%). The cue presentation and change magnitudes were randomized and counterbalanced across locations within and across blocks. The change in grating orientation could occur at one of five values: 5°, 9°, 15°, 26° or 45°.
Subjects participated in a training session one day prior to behavioral testing. Training sessions consisted of 2 blocks with feedback indicating the location of change (cued, uncued or no change) and the correctness of their response, followed by 10 blocks without feedback. In addition, on the behavioral testing day, participants were provided with two additional feedback blocks before the testing session. Data from training sessions and feedback blocks were not included in these analyses.

Response configuration.
To limit the impact of lateralized motoric response biases on these results, we adopted the following strategy: 18/22 Group 1 participants responded with a more complex response key mapping (Fig. S1A), using the "up" and "down" buttons to indicate leftward and rightward changes. Response mappings were counterbalanced such that 50% of the participants responded with an upward button press for a left change and a downward button press for a right change, and the other 50% responded with the converse response mapping. The remaining 4/18 participants responded with a default configuration (Fig. S1A) by pressing either the "left" or the "right" button to indicate a change in the left or right grating, respectively. In each case participants responded with the index finger of their dominant hand. "No-change" responses were always indicated by pressing the central button in the response box (Fig. S1A).
Behavioral testing of Group 1 participants inside the scanner followed the same procedure, except that the stimuli were projected onto a vertical screen whose display was reflected onto a mirror attached to the receiver head-coil. Subjects viewed the stimuli through this display set up, and responded using response key holders, one provided in each hand. The response holder had four keys, three of which were used to indicate appropriate responses. Behavioral testing of Group 3 participants followed a procedure similar to that for Group 1, except for the following differencesthe response time cut-offs were at 1.5s and 1s for subgroups 3a and 3b respectively. Participants in subgroup 3b were tested on change angles 5°, 10°, 15°, 20° and 25°and the time for which the spatial cue was presented was chosen from an exponential distribution between 200-5000 ms. Behavioral testing of Group 4 participants followed the same protocol as Group 1 with the only change being that the participants responded using their non-dominant hand (in this case, left hand). 6/10 participants responded with an upward (downward) button press for a left (right) change. The remaining participants responded with the opposite mapping. As before, "no change" responses were indicated by pressing a central button (Fig. S1A).
Eye-tracking. In all behavioral experiments conducted outside the scanner, participants' fixation was monitored and gaze deviations from the central fixation cross were recorded. Trials in which the fixation deviated by more than 2 degrees to the left or right of the fixation cross or those in which the tracker failed to track the subjects' gaze for more than 100 ms, were rejected. Median rejection rate was 1.7% [0.6-2.7%] (median, 95% confidence interval) across subjects for Group 1, 3.4% [1.4-7.2%] for Group 3a and 3.0% [1.4-5.8%] for Group 3b.
Power analysis. Power analysis for sample size was performed for Group 1 once data from n=10 subjects was collected. Median correlation values were computed between behavioral metrics and SC-cortex connectivity weights to the 11 cortical aROIs (Fig. S2C), as representative of the effect size. Sample sizes were determined based on α=0.05 and β=0.2, corrected for multiple comparisons (Bonferroni correction). This analysis estimated a sample size of n=20. 2 subjects showed outlier values of bias, well removed from the rest of the subjects in the group (Fig. 3D, bottom). We, therefore, acquired data (both behavior and diffusion MRI) from 2 additional subjects for Group 1, for a total of n=22.

m-ADC model description
We employed the m-ADC (multi-Alternative Detection/Change Detection) model (8,9) to estimate participants' perceptual sensitivities and choice biases to different spatial locations. The m-ADC model is a multi-dimensional signal detection model specifically designed to analyze behavior in multi-alternative tasks such as the one described above. Here, we describe the two-dimensional signal detection model for the 2-ADC task used in this study; a general description for a task with any number of alternatives can be found in (8,9). The 2-ADC model specifies a bivariate decision variable Y = (YC, YUC), where each Yi (i = C, UC) denotes sensory evidence for change at the respective location, cued (C) or uncued (UC) (Fig. 1B). Each component of the decision variable is represented along one of two orthogonal axes in a two-dimensional decision space. Signal distributions, corresponding to the "change" event at each spatial location are represented as 2dimensional Gaussians with a non-zero mean and unit variance. The mean of the bivariate Gaussian has a non-zero component along the decision variable axis corresponding to the location of the change event. For example, in Fig. 1B, the red Gaussian (contour) denotes the decision variable distribution for change at the cued location (YC), whereas the blue Gaussian (contour) denotes the decision variable distribution for change at the uncued location (YUC). The noise distribution, corresponding to the "no change" event, is modeled as a 2-dimensional Gaussian with zero-mean and unit variance (Fig. 1B, black Gaussian contour). Change detection sensitivity (d'C or d'UC) at each location is quantified as the difference between the means of the signal and noise distributions along the corresponding axis.
The 2-ADC model specifies that the subject indicates one of three choices -change at the cued location, change at the uncued location, and no change -based on a decision surface comprising three intersecting lines, dividing the decision space into three non-overlapping decision zones, each corresponding to one of the three choices. The decision surface is parametrized by two criteria (cC and cUC), one at each location, and belongs to the family of optimal decision surfaces for distinguishing signal from noise in such multialternative tasks (2,9).
On each trial, the subject makes a decision based on the value of the bivariate decision variable on that trial. Briefly, if a decision variable component exceeds its respective criterion value at one location, but not the other (YC > cC or YUC > cUC, but not both), the subject makes a decision indicating a change at the respective location. If the decision exceeds criterion at no location (YC ≤ cC or YUC ≤ cUC), the subject provides a no-change response. If the decision variables exceed the respective criteria at both locations (YC > cC and YUC > cUC), then the subject indicates a response at the location at which the decision variable exceeds its (respective) criterion by a greater magnitude (YC − cC <> YUC − cUC). Based on this decision rule, the 2-ADC model relates response probabilities to sensitivities and criteria. The proportion of the bivariate Gaussian for each of the three stimulus events -change in the cued grating, in the uncued grating or no change (Fig. 1B, red, blue or black Gaussians) -that lies within each of the three decision zones (Fig. 1B, red, blue or gray shaded regions) governs the conditional probability of that response (or decision) for that stimulus event. The mathematical equations linking conditional response probabilities to d' and criteria are presented in (8) (their equations 3-6). d' and criteria were estimated from the response probabilities in the contingency table with maximum likelihood estimation (9).

Psychophysical parameter estimation
Raw data. Participants' responses were organized into 3x3 stimulus-response contingency tables (Fig. S1B, right). Rows of each table indicate the location of change and columns indicate the location of response; no-change events and responses are indicated in the last row and column, respectively. Each contingency table comprises five response types: hits, misses, false alarms, misidentifications and correct rejections. Because five angles of orientation change were tested, the contingency table contained 22 independent observations (2 hit rates and 2 misidentification rates per angle and two false alarm rates on no change trials).
Parameter estimation. Using the participants' response contingencies, we estimated sensitivities (d') and criteria (c), separately for leftward cued and rightward cued trials, using the m-ADC model, via a maximum likelihood estimation approach (8). d' values were estimated individually for each orientation change angle whereas criteria were estimated as a single value across all change angles, with the reasonable assumption that subjects could not anticipate the angle of the upcoming orientation change (8). We then averaged the d' value across all change angles for each condition. Therefore, we estimated four values of each parameter (d' and c), one for each hemifield and one for each cue condition (cued and uncued), for the 2-ADC task. In addition, we quantified bias using the choice criterion measure (bcc=c-d'/2) for each of these four conditions. This measure of bias quantifies, the deviation of the criterion from the equal likelihood point of signal and noise densities along the decision axis (bcc); a more detailed description of these signal detection metrics are provided in (8). The goodness of fit of the model was assessed using a randomization test based on the chi-squared statistic. A low p-value (p<0.05) indicates that the model fit deviated significantly from the observations (Fig. S1B, left).
Quantifying hemifield asymmetries, and modulation by endogenous cueing. We quantified asymmetries in the baseline (average) values of the sensitivity, bias and reaction time parameters across the visual hemifields as follows: Baseline psychophysical parameters were computed as the averages of their values across the cued and uncued conditions for each visual hemifield, separately. A difference of these average values across the left and right hemifield locations quantified the visual hemifield asymmetry for each parameter. We denote the hemifield asymmetries with the lower case Greek letter δ (e.g. δd' = ½(d'Left Cued + d'Left Uncued ) − ½(d'Right Cued + d'Right Uncued )). On the other hand, we computed the attentional modulation as the difference between the values of these parameters across the cued and uncued conditions, averaged across the hemifield locations. We denote the attentional modulation values with the upper case Greek letter Δ (e.g. Test-retest reliability of psychophysical parameters across sessions. All participants also performed the 2-ADC task while undergoing a functional MRI scan. 18 (out of 22) participants were scanned within 16 days of behavioral testing outside the scanner (median interval: 4 days; 5 th -95 th percentile: [1,15]). The remaining 4 (out of 22) participants were scanned before behavioral testing (median interval: 142 days; range 22-206 days). Three participants reported discomfort during the fMRI scan and were unable to complete the task; therefore, data from 19/22 subjects was considered for test-retest reliability analysis. The fMRI task was identical to the one used in behavioral testing except for the specific orientation change angles that were tested: 6 angles of cued grating change (3, 6, 15 ,24, 39 and 45 degrees) and 4 angles of uncued grating change (6,15, 24 and 39 degrees). Consistency (test-retest reliability) in psychophysical parameters across the fMRI and behavioral testing sessions was assessed by computing correlations of sensitivity and bias inside and outside the scanner; correlations were computed both in terms of parameter values in each hemifield, as well as the modulation of the parameter values by endogenous cueing.

Diffusion MRI and tractography
Diffusion MRI acquisition and pre-processing. Structural and diffusion MRI (dMRI) scans were acquired on a Siemens Skyra, 3T scanner with a 32-channel head-coil, at the HealthCare Global Hospital, Bangalore. For each subject, a T1-weighted MPRAGE structural scan was acquired prior to the diffusion scan (1 mm spatial resolution; TE=2.32 ms, TR=2300 ms, FoV=240 mm, flip angle=8°, 256 voxel matrix size, parallel acquisition technique (PAT) with in-plane acceleration factor 2 (GRAPPA)). Diffusion MRI acquisition followed previously published dMRI scan protocols (10). A single diffusion scan was acquired along 64 non-collinear directions with a b-value of 1000 s/mm 2 (2 mm isotropic voxels, TE=90 ms, TR=8900 ms, FoV=256 mm, 128 voxel matrix size, 68 transversal slices with interleaved slice acquisition; parallel acquisition technique (PAT) with inplane acceleration factor 2 (GRAPPA), phase encoding direction: anterior to posterior). Two nondiffusion weighted images (b=0 s/mm 2 ) were acquired, one at the beginning and one at the end of each scan, respectively. Pre-processing of dMRI images followed standard protocols (10). Briefly, the T1 image was first manually aligned to each subject's AC-PC coordinates. Following this, scans were pre-processed to correct for participants' head motion, eddy current related distortions were corrected using a rigid-body alignment algorithm, and subsequently aligned to the AC-PC aligned T1 image using diffusion MRI software package, as part of the Vistasoft suite (https://github.com/vistalab/vistasoft/).
Delineating the SC and other cortical and subcortical ROIs. The AC-PC aligned T1 image was used to perform a subject-wise cortical parcellation based on the Desikan-Killiany cortical atlas in FreeSurfer (11) comprising 34 regions on each hemisphere. FreeSurfer uses a manually-labelled training dataset as a template to label each neuroanatomical region on a cortical surface model in conjunction with standard neuroanatomical convention; these template regions are shown in Fig.  S6A. Each gray-matter region of interest (ROI) on this atlas was smoothed with a 3 mm Gaussian kernel to incorporate adjoining white-matter voxels, to facilitate tractography. These ROIs were combined into coarser, aggregate regions (aROIs), based on anatomical proximity (Fig. S2C); this was done to limit the number of corrections for multiple comparisons necessary when examining brain-behavior correlations.
In addition to these cortical ROIs, the subcortical superior colliculus (SC) was manually delineated with the T1-weighted image of each subject. The SC is readily identified on the tectal plate, based on visual inspection of established anatomical landmarks (12). In the dorso-ventral axis, labelling began with the topmost axial slice of the SC, beginning with, but not including the ambient cistern (cisterna ambiens). The ventral extent included axial slices up to, but not including, the plane of the inferior colliculus. In the antero-posterior axis, all coronal slices with gray matter up to, but not including the cerebral aqueduct at the anterior end and the ambient cistern in the posterior end, were included in the ROI. In the medio-lateral axis, all sagittal slices, delimited by the ambient cistern in either hemisphere were included. Across subjects, this resulted in an SC ROI that spanned 4-6 axial, 15-17 sagittal and 6-8 coronal slices (slice thickness, 1 mm). A group-averaged map of the SC ROI across subjects is shown in Fig. S6B. The substantia nigra (SN) and subthalamic nucleus (STN) were identified using the ATAG atlas (13); these ROIs were transformed from MNI space to subject's native anatomical coordinates. The caudate nucleus ROI was also identified with FreeSurfer (11).
To facilitate inspection of these ROIs and the replication of these results, we have deposited all of the cortical and sub-cortical ROIs delineated for every Group 1 subject, into an online repository (https://dx.doi.org/10.6084/m9.figshare.8082245).
Whole-brain, probabilistic tractography. For analysis of Group 1 participants' data, we employed the following approach. For each subject anatomically-constrained probabilistic tractography (14) was performed with the MRtrix3 software package (15). First, a five-tissue-type segmentation comprising (i) cortical gray matter, (ii) subcortical gray matter, (iii) white matter, (iv) cerebrospinal fluid and (v) other pathological tissues was performed. Next, a Constrained Spherical Deconvolution (CSD) algorithm was used to estimate the voxelwise Fiber Orientation Distributions (FOD), setting the maximum harmonic order for the output FODs to 8 (lmax = 8). Lastly, wholebrain tractography was performed using the gray matter-white matter interface voxels as a seed: a total of 500,000 streamlines were generated for each subject. The maximum length cut-off and fractional anisotropy threshold were set to their default values (200 mm and 0.1, respectively).
For analysis of Group 2 participants, from the HCP database, we used already pre-processed diffusion MRI scans (16). Tractography followed a standard pipeline (MRtrix3), appropriate for multi-shell dMRI scans. First, a 5-tissue type segmentation was performed on the AC-PC aligned T1 weighted image for every subject. Next, multi-shell, multi-tissue CSD was used to generate the voxelwise FODs. Finally, whole-brain tractography (500,000 streamlines) was performed using the gray matter-white matter interface as seed. A maximum length cut-off and fractional anisotropy threshold were set to values recommended for HCP data (250 mm and 0.06, respectively).
Targeted tractography through the superior colliculus. To track fascicles connecting the SC and cortical ROIs, probabilistic targeted tractography was performed in three stages: first by seeding from the SC to trace streamlines to the cortex, then seeding from the cortex to trace streamlines to the SC, and finally combining these to form a union set of streamlines. This 3-stage procedure is elaborated next.
In the first stage, the SC was used as a seed region and 10 million whole-brain streamlines were generated. Next, we selected only those streamlines whose one terminus lay in the SC and the other terminus lay in a cortical ROI. Streamlines traversing the corpus callosum were discarded from each fascicle, using a callosal exclusion ROI (11). Next, we removed streamlines that traversed the brainstem by creating a second exclusion ROI comprising the entire brainstem, as well as brainstem slices in the axial plane of the SC and one additional slice below it. Finally, for each streamline bundle, we identified and removed outlier streamlines. This was done by first identifying the mean path (core) of the bundle, followed by computing the Mahalanobis distance of each streamline from the mean path. Streamlines that lay more than two standard deviations from the core (in terms of the Mahalanobis distance distribution) were discarded. This produced 68 fascicles (streamline bundles), seeded from the SC, connecting the SC to each of the 34 cortical ROIs in each hemisphere (SC→Cortex). In the second stage, the cortical voxel termini of the fascicles identified above were used as seed voxels to track streamlines back to the SC. To ensure unbiased seeding across ROIs and hemispheres, we selected a uniform number of seeds in each ROI, selecting those closest to the centroid of the voxel termini in each region up to the maximum number of voxels connecting the SC to each of the 68 regions. A total of 500 million seeds were employed across the cortex for tracing streamlines. As before, only those streamlines whose one terminus lay in the SC and the other terminus in one of the cortical regions were selected for further analysis. Callosal and brainstem streamlines were removed, and outlier removal was performed. This resulted in 68 fascicles connecting the SC with the cortex, but now seeded from the cortex to the SC (Cortex→SC). Finally, the 68 SC→Cortex and Cortex→SC streamlines were then concatenated to form a single, final fascicle that connected the SC to the respective cortical ROIs. This yielded 68 fascicles connecting the SC with the cortex.
To facilitate inspection of these tracts we have created a 3D model of the SC ROI based on the individually delineated anatomical ROIs ( Fig. 2A). Superimposed on this 3D model we show the entire collection of SC-cortex fibers that were mapped for each subject. Snapshots of this 3D model for a representative subject are shown in Fig. 2A (bottom panel). The 3D model with SC fibers -for every subject in Group 1 has been deposited into an online repository (https://dx.doi.org/10.6084/m9.figshare.8082245). Readers can download and visualize these images from the database, and clear instructions are provided in a Readme file that permit visualizing individual subjects' SC-cortex tracts.
Estimating SC connection weights. Next, we estimated the connection weights for each of these fascicles. For this, fascicles were combined with the whole-brain connectome of 500,000 streamlines, and a spherical deconvolution-informed filtering algorithm (SIFT2; (17)) was applied to the combined connectome. Briefly, SIFT2 is a connectome filtering algorithm that computes weights associated with each streamline, which are representative of the mean cross-sectional area of each streamline. The connectivity strength between SC and each cortical ROI was then computed as the sum of the individual weights of the constituent streamlines in the corresponding fascicle, connecting the SC with the respective ROI. Structural connectivity strength between the SC and any aROI (Fig. S2C) was determined by aggregating all of the fascicle weights connecting the SC to the sub-regions of the respective aROI.
Voxelwise distribution of weights ( Fig. 2A, surface maps) were generated as follows: First we normalized the SC-cortex connectivity weights by their sum for each subject. These weights were then averaged across subjects. The average weights were log-transformed, z-scored and thresholded at a value of 1.0 for surface rendering as a binary map ( Fig. 2A, red).
For the HCP data, targeted tractography and connection strength estimation was performed with an identical approach. Overall, SC-cortex connection weights for the HCP participants were weaker than connection weights in the first group of participants (p<0.001, two-sample t-test), a difference that could arise from, among other factors, to differences in scanner hardware, data acquisition protocols, as well as differences in participant demographics. Surface maps for the HCP dataset were generated in the same way as described above (Fig. 2A, cyan).
SIFT2 weights between every pair of ROIs for each subject in Groups 1 and 2 have also been deposited into the aforementioned online repository as an Excel sheet, for ready inspection and to facilitate reproducing these results (10.6084/m9.figshare.8082245).
Quantifying connectivity with the V1 and basal ganglia. A pre-defined V1 ROI as defined by FreeSurfer's anatomical parcellation was used for all connectivity analyses. Connectivity with the V1 was quantified using an identical procedure as described in the section "Targeted tractography through the superior colliculus". The only difference was that we employed fewer (2 million) seeds for tracking streamlines between the V1 and the cortical ROIs because streamline tracking between cortical regions was comparatively faster and yielded more streamlines, than streamline-tracking between the SC and the cortex. For tracking streamlines with the basal ganglia, the sub-thalamic nucleus (STN) and the substantia nigra (SN) ROIs were combined to form a STN+SN composite ROI. Next, a union ROI comprising the SC and STN+SN was seeded for targeted tractography with 500,000 streamlines. Following tractography, only those streamlines whose termini lay in the SC and STN+SN were retained. Streamlines were further pruned by removing callosal streamlines and outliers as described previously. Similarly, the caudate nucleus was delineated using subcortical segmentation obtained with FreeSurfer (11). Targeted tractography was performed by seeding the SC-caudate union ROI, generating 500,000 streamlines, followed by pruning and outlier removal. In each case, as before, strength of connectivity was quantified with SIFT2 weights.

SLF -ROIs and tractography.
To track the three divisions of the Superior Longitudinal Fasciculus (SLF), we selected frontal and parietal ROIs from the Desikan-Killiany atlas (18) that corresponded closely with the regions selected by de Schotten et al (7), as follows: In each hemisphere, we chose the superior and inferior parietal ROIs to constitute the parietal terminus for the SLFs. We chose the superior frontal and rostral middle frontal ROIs as the frontal termini for SLF I and II, respectively. For SLF III, we chose the inferior frontal aROI (Fig. S2C) as the frontal terminus. For each SLF division, we first created a union ROI combining the frontal and parietal termini regions. Next, we performed targeted tractography, tracing 50,000 fibers through this union ROI. We then extracted only those fibers whose one end lay in the frontal and the other end in the parietal region. As described above, we cleaned fiber bundles by removing callosal and outlier fibers. Finally, we combined these clean bundles with a whole brain connectome comprising 500,000 fibers and quantified connection weights for the combined connectome with SIFT2 (17): Connection strength for each SLF tract was quantified as the sum of strengths of the individual streamlines making up the tract. To obtain the volume of each tract we multiplied the SIFT2 weight (indicative of crosssection area (17)) of each streamline with its length and summed these values across all streamlines for each tract.

Structure-behavior relationships
Prediction analysis. To predict asymmetries in behavioral metrics based on asymmetries in structural connectivity, we fit a regression model with the behavioral asymmetries as the response variable and connectivity asymmetries as predictors. Connectivity asymmetries were quantified with a modulation index: MIR-L = (wR-wL) / (wR+ wL); where w denotes the SIFT2 weight of a fascicle connecting the SC with the left or right hemispheric cortical ROI (denoted by subscripts L and R, respectively). This was done to selectively quantify asymmetries and remove the contribution of inter-individual variability in the individual fascicle connection strength. Predictions were carried out using regression based on support vector machines, with a linear kernel. We employed a leaveone-out cross-validation approach: the model was trained with data from all but one of the participants and the behavioral score of the left-out participant was predicted using her/his structural connectivity weights and the regression coefficients obtained from the trained model (Fig.  3B).
For predicting δbcc and δd' using SC connectivity asymmetry, we used the MIR-L of the SC-cortical connections (34 fascicles) along with the SC-caudate and SC-STN+SN connections (36 predictors in total) using a linear kernel with the box constraint (BC) and ε-margin set to default values of the "fitrsvm" command in MATLAB (BC=1). Predictions using V1 connectivity were carried out in a similar manner. Connections that contributed strongly to these predictions were identified by thresholding the magnitude of the normalized regression coefficients at 0.5.
Attentional modulation predictions using average SC and V1 connectivity were carried out in a similar manner, except using a polynomial kernel of order 2. Prediction analyses and parameter selection were performed in the same manner as with the asymmetry predictions. As before, connections that contributed strongly to these predictions were identified by thresholding the magnitude of the normalized regression coefficients at 0.5.
For predicting δbcc and δd' and δRT using SLF connectivity asymmetry, we used the MIR-L of the SLF connection weights using a polynomial kernel of degree 3, with the box constraint (BC) and εmargin set to default values, as before; other kernels (linear or polynomial of lower orders) failed to yield any significant predictions. Attentional modulation predictions with average SLF connectivity were carried out in a similar manner, with the same hyperparameters.
Statistical tests. For tests of significance difference between baseline psychophysical quantities (d', bcc) and attentional modulation of these quantities (Δd', Δbcc), between hemifields, we employed a non-parametric Wilcoxon signed rank test. All correlations were computed using robust correlations (19). In particular, we report values of "bend-correlation", a technique robust to univariate outliers. Significant p-values in all figures are reported with asterisks with the following convention: * -p<0.05, ** -p<0.01, *** -p<0.001. Unless indicated otherwise, correction for multiple comparisons for all tests of significance was performed with the Benjamini-Hochberg correction.

Fig. S1. Hemifield asymmetries in replicate cohort and test-retest reliability of behavioral metrics.
A. Response mapping for the 2-ADC paradigm. Subjects respond to a left change with a top button press and a right change with a bottom button press. The response mapping was counterbalanced such that half the subjects responded to a left change with a top button press and the other half with the bottom button press. 4/22 subjects responded with a left button press for a left change and right button press for a right change. "No change" responses were always indicated by a central button press. B. (Left) Test for goodness of fit of the m-ADC model. Histogram showing the distribution of the p-value (x-axis) corresponding to a randomization test based on the chi-squared statistic is shown for when the subject performed the task inside the fMRI scanner (red) and outside     Table S1. B. Montage depicting the anatomical location of the superior colliculus ROI (group average map) on the axial plane in Group 1 participants' data (n=22). Color scale indicates overlap of SC voxels across subjects.     A. Table showing the correlation between connectivity asymmetry in the three SLF sub-divisions (rows) and asymmetries in sensitivity (first column) and choice bias (second column). B. Table  showing the correlation between observed and predicted asymmetries in sensitivity (first column) and choice bias (second column), as predicted using connectivity asymmetry in the three SLF subdivisions (rows).