We described a pupillometry-based method which showed capable to assess biases in covert spatial attention in controls, participants with neglect, and visual field deficits in participants with hemianopia. In participants with left-sided neglect (an attentional deficit), the pupil responded stronger to the luminance on the right side of the visual display as compared to the left, indicating a rightward bias in automatic, covert attention. A similar pattern was observed for visual field deficits (a sensory deficit): the pupil responded stronger to the intact rather than defective parts of the visual field. This supports the central hypotheses at very large effect size. As in Strauch, Romein, et al. (2022), bar width (full hemifields, peripheral bars) showed no effect on the difference in pupil light response.
In all individuals with left-sided neglect, pupil responses indicated a rightward bias. However, the strength of this bias varied between participants with neglect, and two of the five participants with neglect had scores descriptively similar to controls. Neglect severity measured in clinical tasks (cancellation, line bisection) during a later, more chronic phase did not link to the degree of bias observed in our pupillometry based measurements. This could suggest that the pupil picked up on the automatic attentional bias present in earlier post-stroke phases, but with increasing awareness and increasingly learned coping mechanisms, behavioral and covert attentional biases diverged. 
Averaged measures for horizontal bias per participant and pupil bias against classical neuropsychological tests. Top: Difference between the pupil size change in trials with white/black and black/white stimuli, averaged across both blocks (full hemifields, peripheral bars), per participant (averaged difference across period 550e2450 ms). Values close to the horizontal 0-point reflect unbiased pupil responses, negative values (to the left) indicate a leftward bias, i.e., stronger pupil responses to the luminance of the left side of the screen, and positive values (to the right) indicate a rightward bias, i.e., stronger pupil responses to the luminance of the right side of the screen. Groups are denoted by colors and schematic drawings of visual/attentional field defects (green: controls; blue: neglect; orange: hemianopia left; red: hemianopia right; black: quadrants and other visual field deficits); vertical dashed lines denote medians for controls and participants with neglect. Labels denote individual participants as given in the tables and supplementary material Bottom: scores on neuropsychological tests per participant with neglect scattered against assessed pupil bias. Left: Total number of targets omitted in the star cancellation task during the more acute phase after stroke (see Table 2 for the number of days poststroke at the moment of assessment). A higher number of omissions indicates more neglect. All remaining scores were assessed on the same day, or shortly previous to it (i.e., Catherine Bergego Scale; CBS). Second left: Total number of targets omitted in the star cancellation task at the day of the test session, i.e., in a later phase. Second right: Endpoint weightings bias taken from the line bisection task. Positive values indicate a leftward attention bias, negative values a rightward attention bias. Right: Total score on the CBS. For all participants, at least 7 items of the CBS were scored. The total score was computed by multiplying the average of the scored items by 10. Higher scores reflect more neglect behavior in daily life, as observed by the occupational therapist.
For all five participants with neglect, including those two for whom the pupillometry-based bias was in the range of healthy controls, practitioners observed neglect behaviour in daily life as assessed with the Catherine Bergego Scale. One may argue that the pupillometric estimate proposed here therefore carries little value, as the Catherine Bergego Scale is considered a highly sensitive measures for effects of neglect on daily life (Azouvi et al., 1996). However, the high sensitivity comes with a low specificity, and a low precision in assessing individual subprocesses of attention. First, the low specificity of the Catherine Bergego Scale might have led to some behaviour observed by practitioners being misdiagnosed as neglect. Determining whether observed behaviour is specifically related to neglect or due to, for instance, apraxia or a severe primary sensory or motor deficit is difficult (Azouvi et al., 1996; Menon & Korner-Bitensky, 2004). This is why standardized neuropsychological tests are designed to assess cognitive functions in isolation. Of course, not knowing what exactly caused a specific behaviour is also the case for standardized tests (i.e., the problem of task impurity), but most likely even more so for observed behaviour in a more complex and dynamic context. Thus, other factors than a bias in lateralized attention might as well have influenced ratings on the Catherine Bergego Scale. Speculatively, this might explain the results of participant N5, who did not show neglect on the star cancellation task (not even in the acute phase) but for whom points were assigned on the Catherine Bergego Scale. Second, the pupil bias score measures a specific aspect of neglect, namely a “default” lateralized covert attention bias. For some individuals, neglect might only show in situations with higher attentional demands (e.g., when dual-tasking is required) or in which there is competition between (relevant) ipsilesional and contralesional information. The latter might underlie the results of participant N1, whose pupil bias score was comparable to most severe biases in healthy controls, but who omitted 8 left targets on the star cancellation task, in which ipsilesional stimuli are present.
Whilst data of five participants warrants further replication, our findings raise the question whether covert attentional biases present chronically persistent. In line with this notion, recent auditory-based ERP measures as a proxy for attention showed no improvement of automatic attentional biases in left-sided neglect after rehabilitation treatment, despite improvement on classical neuropsychological tests (Hildebrandt, Notbohm, Duning, & Schweser, 2023). If follow-up research confirms that the automatic attention bias in participants with neglect indeed does not resolve, this would have substantial implications for understanding the recovery of neglect. Generally, it is thought that recovery of the impairment itselferestoration of the underlying attentional systemetakes place within the first threemonths post-stroke (Durfee & Hillis, 2023; Kerkhoff & Schenk, 2012; Nijboer et al., 2013). After this initial period, recovery is thought to be mainly driven by compensatory strategies. The results from the current study, however, lead to the hypothesis that already in the first three months, other processes (e.g., top-down attention) become involved for the compensation for the automatic attention bias (Hildebrandt et al., 2023), which itself may never recover.
Biases were found to be comparable in strength for participants with damages to sensory (hemianopia) and attentional (neglect) systems. Together with previous findings (Binda et al., 2013; Binda & Murray, 2015; Haab, 1886; Kardon et al., 1991; Maeda et al., 2017; Math^ot et al., 2013; Naber et al., 2011, 2018; Portengen et al., 2021; Skorkovsk_a et al., 2009; Strauch, Wang, et al., 2022), this supports the notion that the pupil light response is not solely reflexive, but heavily modulated by attention and thus cortical processing. Such cortical influences hereby must pass the parietal areas damaged in neglect and with it the attentional system and more frontal areas, likely via the frontal eye fields, to affect the brainstem circuit around the superior colliculus that brings about related modulations in pupil size (Strauch, Wang, et al., 2022; Wang & Munoz, 2018).
Furthermore, previous studies have shown that hemianopia and neglect share anatomical substrates. For example, damage to the optic tracks, linking the lateral geniculate nucleus to the primary visual cortex, could cause hemianopia but is also related to visuospatial neglect (Toba et al., 2020). All participants with neglect had no reported concurrent diagnosis of visual field deficits by the hospital and rehabilitation center, still, we did not obtain information on how this was tested. Possibly undiagnosed visual field deficits could thus have contributed to biased pupil light responses in a subset of participants with neglect.
Importantly, participants with visual field deficits versus those with neglect were not comparable regarding time postinjury, which argues for caution when comparing these groups.
The here introduced method might hold the key to solve a number of longstanding theoretical and applied challenges that neglect continues to pose, which are discussed in the following. On a fundamental level, pupillometry has the potential to uncover the extent to which neglect arises from attentional competition between stimuli or from an inherent bias in spatial attention towards the right (Husain, 2019; Karnath, 2015). To this end, an additional condition featuring a single stimulus on either the left or right side of the intermediate gray display could be incorporated. If pupil light responses were similar for presentation on the right and on the left, this would be in favor of a competition accounteas position would be irrelevant in isolation. If, however, pupil light responses were substantially stronger for the stimulus presented on the right than on the left, this would argue for a default bias to the right, independent of interference from the left. Responses falling between these two extremes would support an integrated view of both accounts and indicate the extent to which neglect is shaped by attentional competition versus default attentional biases.
Adding dual tasks to increase attentional demands has been shown to reveal hidden biases in many neuropsychological tasks that might otherwise go undetected in chronic stages (e.g., Bonato, Priftis, Marenzi, Umilt_a, & Zorzi, 2010; Robertson & Frasca, 1991; Russell, Malhotra, & Husain, 2004). But is mental effort interfering with the interhemispheric balance of dorsal networks (Paladini et al., 2020), directly on the level of the spatial attentional system (Corbetta & Shulman, 2011; Kinsbourne, 1993), or is effort interfering with (highly automatized, yet effortful) compensation strategies instead (Villarreal et al., 2022)? If the account of persistently unaltered pupillometric biases was correct, pupillometric biases should present also without the induction of efforteany further enhancement with effort would argue for an effect of effort on spatial attention in turn. If, however, biases would not enhance, then this would suggest that effort interferes only on the level of executive control needed for compensatory strategies.
Besides these fundamental questions, the here presented method could be useful to dissociate between subtypes of neglect. We propose that, for instance, connected black/white or white/black stimuli that are positioned on both hemifields should go in hand with a much stronger pupillometric bias in allocentric than in egocentric neglect, although, as for the other predictions made in this section above, this remains to be tested. In combination with the aforementioned manipulations this could adequately address the individual, here clustered as a participant with neglect. Neglect is a heterogenous syndrome with a plethora of potential subtypes and possibly different underlying neural substrates and attentional mechanisms at play.
Successful clinical use of the here presented method for diagnosis as an enhancement to existing diagnostic tools will critically depend on iterative improvements to be made for increased feasibility/usability with patients and practitioners as stakeholders. This could be achieved by using gaze-contingent displays, allowing participants to blink, and using eye trackers that are robust to noise. Hereby, a sweet spot in the trade-off between diagnostic properties, cost effectiveness, and burden put on the participants must be found-these considerations could for instance concern the number of trials or the length of stimulus presentation. Furthermore, a study with a large sample size is needed, preferably including participants with left- and right-brain damage following stroke, with and without neglect as determined based upon existing measures to assess reliability, validity, sensitivity, and specificity. This should then also result in a threshold bias score that divides patients with neglect from those without. The estimation of the pupil bias per participant could ideally be determined flexibly, for instance by either reaching a predefined Bayes factor for a null effect or a clear bias, respectively, and then stopping the assessment. 
To conclude, our objective, rapid pupillometry-based method allows to directly assess the core deficit of neglect, namely the ipsilesional (covert) attentional bias in absence of any task beyond simple fixation. Participants with deficits in vision, a sensory function, showed almost similarly biased pupil responses as participants with deficits in attentional function. Our initial data further reveals that covert attention is persistently altered in participants with neglect, even weeks or months after stroke. We expect insights into mechanisms of spatial attention, subtypes of neglect, recovery over time, or the effectiveness and working principles of therapies. This method should next be evaluated on larger scale for the clinical diagnosis of neglect, especially in a more chronic phase post-stroke because of its potential robustness to compensation.
