June 2016
Volume 57, Issue 7
Open Access
Low Vision  |   June 2016
Clustering of Eye Fixations: A New Oculomotor Determinant of Reading Speed in Maculopathy
Author Affiliations & Notes
  • Aurélie Calabrèse
    Minnesota Laboratory for Low-Vision Research University of Minnesota, Minneapolis, Minnesota, United States
  • Jean-Baptiste Bernard
    Aix Marseille Univ, CNRS, LPC, Marseille, France
  • Géraldine Faure
    Low Vision Clinic, University Hospital of La Timone, Marseille, France
  • Louis Hoffart
    Aix Marseille Univ, APHM, Department of Ophthalmology, University Hospital of La Timone, Marseille, France
  • Eric Castet
    Aix Marseille Univ, CNRS, LPC, Marseille, France
  • Correspondence: Eric Castet, Université Aix Marseille - Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7290, Laboratoire de Psychologie Cognitive 3, place Victor Hugo – case D, 13331 Marseille cedex 3, France; eric.castet@univ-amu.fr
Investigative Ophthalmology & Visual Science June 2016, Vol.57, 3192-3202. doi:10.1167/iovs.16-19318
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      Aurélie Calabrèse, Jean-Baptiste Bernard, Géraldine Faure, Louis Hoffart, Eric Castet; Clustering of Eye Fixations: A New Oculomotor Determinant of Reading Speed in Maculopathy. Invest. Ophthalmol. Vis. Sci. 2016;57(7):3192-3202. doi: 10.1167/iovs.16-19318.

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

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Abstract

Purpose: To describe and quantify a largely unnoticed oculomotor pattern that often occurs when patients with central field loss (CFL) read continuous text: Horizontal distribution of eye fixations dramatically varies across sentences and often reveals clusters. Also to statistically analyze the effect of this new factor on reading speed while controlling for the effect of saccadic amplitude (measured in letters per forward saccade, L/FS), an established oculomotor effect.

Methods: Quantification of nonuniformity of eye fixations (NUF factor) was based on statistical analysis of the curvature of fixation distributions. Linear mixed-effects analyses were performed to predict reading speed from oculomotor factors based on eye movements of 34 AMD and 4 Stargardt patients (better eye decimal acuity from 0.08 to 0.3). Single-line French sentences were read aloud by these patients, who all had a dense scotoma covering the fovea as assessed with MP1 microperimetry.

Results: Nonuniformity of fixations is a strong determinant of reading speed (−0.76 log units; 95% confidence interval [CI] [−0.86, −0.66]). This effect is not confounded with the effect of L/FS. The per sentence proportion of trials with clustering is predicted by the frequency of occurrence of the lowest-frequency word in each sentence.

Conclusions: The NUF factor is a new oculomotor predictor of reading speed. This effect is independent of the effect of L/FS. Reading performance, as well as motivation to read, might be enhanced if new visual aids or automatic text simplification were used to reduce the occurrence of fixation clustering.

Reading is the major visual problem experienced by low-vision patients.1,2 This is especially true for age-related macular degeneration (AMD) patients,3 as deterioration of the macula causes severe central field loss (CFL), thus specifically affecting high-resolution processing.4,5 Reading speed is commonly used as a performance measure of reading in low-vision research.623 
Patients with CFL complain that text reading is very slow (when not impossible) even when text size is increased above peripheral acuity threshold, and many studies have increased our knowledge about the visual factors that are determinants of reading speed.2426 Reading performance is affected not only by visual factors, though. When we read text such as a sentence printed on a sheet of paper, reading consists of a sequence of saccades and fixations, which is referred to as eye-mediated reading,27 so that reading speed is actually mainly determined by the number of fixations and the average fixation duration.28 
Describing the oculomotor patterns observed during eye-mediated reading and understanding their meaning, as well as their link with reading speed, is thus a very important line of research. One striking result, originally described by Bullimore and Bailey,29 has received much attention. The basic finding is the correlation between reading speed and the average size of the horizontal component of forward saccades.2933 The unit used for this latter measure is usually the number of letters per forward saccade (L/FS) as in the original study of Bullimore and Bailey. Letters per forward saccade is assumed to reflect the perceptual span used when reading a sentence, that is, the useful quantity of information processed within each fixation and allowing programming of the next forward saccade's amplitude.34,35 The correlation between reading speed and L/FS is thus interpreted as evidence that slower readers have a smaller perceptual span: This is the shrinking perceptual span hypothesis. This causal hypothesis has been formalized and tested with a mediation model showing that the effect of L/FS on reading speed is fully exerted through the average number of fixations and not through the average fixation duration.28 The major advantage of a mediation analysis over a series of independent regression analyses is the integration of causally linked factors within a single and unified model.3641 
While the relationship between L/FS and reading speed is a positive result that is now well documented, another important relationship between eye movements and reading speed might have been overlooked. Indeed, visual inspection of eye data maps suggests that eye fixations are often not uniformly distributed within sentences. A typical example from one patient of our study is shown in Figure 1A: The two plots show fixation maps for two sentences having highly different horizontal distributions of fixations. In the left plot, a clear-cut cluster of fixations is observed around the last word (“tulipes”) while fixations are uniformly distributed along the horizontal dimension for the first words of the sentence. This is in sharp contrast with the even horizontal distribution observed for another sentence read by the same patient (plot on the right). 
Figure 1
 
Examples from our data showing two very different distributions of fixations for the same patient. (A) Eye fixation maps superimposed on sentences: Each circle represents a fixation (circle area is proportional to fixation duration). The left map shows that fixations are densely clustered around the word “tulipes” (a low-frequency word), whereas the right map shows a more homogeneous horizontal distribution of fixations. (B) Corresponding probability density functions as a function of normalized x-coordinates of eye fixations. In the left plot, the circles represent points of the density curve that have a significant curvature as assessed by the feature significance theory.42 This fixation map is therefore labeled as having a nonuniform distribution of fixations (NUF = 1). In contrast, the density curve for the sentence on the right does not have any point with a significant curvature (NUF = 0). Note that the NUF value calculated for a given sentence varies (0 or 1) across patients.
Figure 1
 
Examples from our data showing two very different distributions of fixations for the same patient. (A) Eye fixation maps superimposed on sentences: Each circle represents a fixation (circle area is proportional to fixation duration). The left map shows that fixations are densely clustered around the word “tulipes” (a low-frequency word), whereas the right map shows a more homogeneous horizontal distribution of fixations. (B) Corresponding probability density functions as a function of normalized x-coordinates of eye fixations. In the left plot, the circles represent points of the density curve that have a significant curvature as assessed by the feature significance theory.42 This fixation map is therefore labeled as having a nonuniform distribution of fixations (NUF = 1). In contrast, the density curve for the sentence on the right does not have any point with a significant curvature (NUF = 0). Note that the NUF value calculated for a given sentence varies (0 or 1) across patients.
These informal observations suggested to us that nonuniformity of eye fixations (NUF) might be an important determinant of reading speed. We therefore quantified this NUF42 in order to define a two-level discrete factor that could be a predictor of reading speed. Having found that NUF did have a clear effect on reading speed, one important question appeared to us as crucial: What are the respective roles of the L/FS and NUF factors in the variations of reading speed? Within a statistical regression framework, do these two factors have unique effects on reading speed? One could argue, for instance, that the well-established L/FS effect on reading speed is actually caused by the NUF. Under this hypothesis, a slow reading speed would occur because fixations accumulate in a circumscribed zone: It is this clustering phenomenon that would be responsible for smaller saccade amplitudes (or, more precisely, smaller L/FS values). In other words, the observed smaller L/FS values (associated with a lower reading speed) would not reflect a smaller perceptual span (regularly distributed along a sentence) but rather the presence of many small saccades within a restricted area. However, to anticipate our results, statistical analyses showed that these two oculomotor factors had unique effects on reading speed. 
In sum, the first goal of our work was to describe and quantify the effect of NUF on reading speed. The second goal was to investigate within a statistical regression framework how this new oculomotor effect interacts with the previously established oculomotor L/FS effect. For this purpose, a dataset initially collected and analyzed to investigate the effect of L/FS on reading speed in low-vision patients with CFL was used.28 Establishing that reading speed is determined by the NUF factor, above and beyond the effect of L/FS, should help us complement our theoretical understanding of the processes that are disrupted during eye-mediated reading with CFL. In addition, from a clinical perspective, the finding that patients with CFL often do not have a spatially homogeneous mode of reading should be taken into account to improve electronic visual aids and to develop the use of automatic text simplification.4346 
Methods
Patients
Patients were recruited for the present study over a 1.5-year period from referrals to the Low Vision Clinic at the La Timone Hospital (Marseille, France). The criteria for including patients in the experiments were the following. The patients had a confirmed diagnosis of established AMD or Stargardt disease from an ophthalmologist. They all had bilateral central scotomas and no other significant disease. Those with a history of neurologic disease or cognitive impairment were not included. Microperimetry was performed with a commercially available instrument (MP1; Nidek Technologies, Padova, Italy) on the eye with better acuity. Analyzing the microperimetry results allowed us to select only eyes with a dense scotoma that covered the fovea (maximal display luminance: 127 cd/m2; background luminance: 1.27 cd/m2). This ensured that these eyes relied on eccentric viewing (details of the methods have been described previously).9,10 Microperimetry results showed that all patients had an established preferred retinal locus for fixation tasks. All patients spoke French as their first language. The research was conducted in accordance with the tenets of the Declaration of Helsinki. Informed consent was obtained from all participants before testing. The present analyses are based on the same 38 patients whose results were presented previously.28 
Stimuli
Fourteen meaningful French sentences were sequentially displayed on a 21-inch cathode ray tube monitor (1024 × 768 pixels) driven by a display controller (ViSaGe; Cambridge Research Systems, Cambridge, UK). Viewing distance was 40 cm. Characters were white (92 cd/m2) on a black background (see two examples in Fig. 1, top row). Each sentence was displayed in Times New Roman font over one line in the middle of the screen. This font was chosen in order to replicate as closely as possible the conditions of major prior studies.29,30 The sentences were created using the following constraints. They all had a simple syntactic structure (e.g., “Elle est allée courir”—“She went for a run”). Words could not have more than eight characters, and proper names were excluded. Only the present or perfect tenses were used. Words were chosen to span a large range of frequencies (in occurrences per million): from 19209 (“à”) to 0.14 (“antivol”) (median: 1278). Word frequency was derived from the French lexical database Lexique,47 based on the corpus of texts “Frantext” (487 books published after 1950 constituting a total of 31 million words). All sentences had 18 to 21 characters (mean: 19.6), including spaces. Print size, defined as the vertical angular size of the lowercase letter x (x-height), was three times the acuity threshold for each patient, with acuity measured using the Early Treatment Diabetic Retinopathy Study (ETDRS) chart: That is, x-height was three times the angular vertical size of the ETDRS letters at threshold.21,48 Mean x-height was 2° (min: 0.84, first quartile: 1.3, median: 2.1, third quartile: 2.5, max: 3.1). 
Reading
Reading was monocular (eye with the better acuity), and an appropriate correction for near vision (Metrovision lenses, Perenchies, France), corresponding to the viewing distance, was added over the distance prescription. The other eye was covered. Patients were asked to read aloud each of the 14 sentences without making errors. If at least one word was read incorrectly, the sentence was judged incorrect and excluded from the analysis: Verbal feedback was given to the patient as to the error. The experimenter triggered the presentation of each sentence by pressing a button and then pressed the same button to indicate that the patient had finished reading the sentence. Eye recording was also dependent on these button presses. Reading time was recorded for each sentence. Reading speed was calculated in “standard-length words” per minute where each six characters counts as one standard-length word.49 
Eye Movement Recording and Analysis
Subjects' gaze location was recorded 500 times per second with an EyeLink II eye tracker (EL II, head-mounted binocular eye tracker; SR Research Ltd., Mississauga, ON, Canada) using the head compensation mode. In this mode, the head is free to move (±30°). However, to reduce the risk of displacing the head-mounted eye tracker, patients were encouraged to maintain their head as motionless as possible. Before each session, a three-point gaze calibration was performed followed by a three-point validation (top left, top right, bottom middle). Calibration and/or validation was repeated until the validation error was smaller than 1° on average and smaller than 1.5° for the worst point. 
Ocular data were extracted offline with the Data Viewer software (SR Research Ltd.) into a file whose rows correspond to successive fixations. Each row contains a set of relevant data such as fixation duration and location, previous and next saccade amplitude (the latter was used to assess the horizontal component of saccades). For EyeLink recordings, the eye-event detection is based on an internal heuristic saccade detector built into the EyeLink tracker program. A saccade is determined by three criteria: velocity, acceleration, and displacement thresholds (in the present study, these were respectively set to 30°/s, 8000°/s2, and 0.1°). A blink is defined as a period of saccade-detector activity with the pupil data missing for three or more samples in a sequence. A fixation event is defined as any period that is not a blink or saccade. 
Then, for each sentence, reading speed (in words per minute, wpm), number of fixations, mean fixation duration (in milliseconds), and mean horizontal component of forward saccades (in letters) were calculated. As recommended previously,50 the latter factor was not calculated as the number of letters (per sentence) divided by the total number of forward saccades: It was an average of saccadic horizontal components (in letters) across all individual forward saccades (the conversion from degrees of visual angle to letters is based on our measurements showing that the ratio between x-height and average interletter spacing is 1 for the Times New Roman font).51 This factor is referred to here as letters per forward saccade (L/FS) to preserve terminology continuity with the initial study.29 Each of these factors was natural log transformed and centered with respect to its mean. 
For each fixation map corresponding to a correctly read sentence, we also quantified the nonuniformity of fixations in the horizontal dimension with a two-level discrete factor (NUF). This was achieved with a statistical theory known as local inferential feature significance for multivariate kernel density estimation.42,52 In this theory, the first step is to calculate a probability density function of fixations for each sentence with kernel density estimation (as shown in the bottom row of Fig. 1). The second step is to estimate whether features such as local extrema are statistically significant at some points of the distribution. Here, we were interested in the curvature of density functions as this feature represents whether a “true” peak is present in the distribution of fixations. These principles are illustrated in Figure 1 with the two fixation maps already discussed. The bottom row shows the probability density functions corresponding to the eye fixation maps displayed in the top row. For each point of the distributions, the feature significance algorithm calculates whether the local curvature at this point is statistically significant: The points with a significant curvature are represented with circle symbols. A distribution containing at least one point with a significant curvature was labeled as nonuniformly distributed: NUF = 1 (as the left distribution in Fig. 1). The reference level of the NUF factor in statistical analyses was zero. 
In summary, for each trial corresponding to a correctly read sentence, the following measures were available for statistical analyses: reading speed (in words per minute), number of fixations, mean fixation duration (in milliseconds), mean horizontal component of forward saccades (L/FS), and the NUF factor (0 or 1). 
Statistical Analyses
Statistical analyses were based on linear mixed-effects models. The advantage of using such models when analyzing multilevel data with repeated measurements has been extensively documented.37,5356 Patients and sentences (referred to as “items” in the psycholinguistic literature) were specified as crossed random factors.57 For each patient, 14 repeated measures of reading speed were obtained with 14 sentences (items), but only trials in which sentences had been correctly read were kept in the analyses (406 trials, cf. number of observations in the Table). The mean number of correctly read sentences per subject was 10.7 (min: 2, first quartile: 8.2, median: 11.5, third quartile: 13, max: 14). The mean proportion of correct trials per item (i.e., across patients) was 0.76 (min: 0.61, first quartile: 0.68, median: 0.76, third quartile: 0.84, max: 0.95). One particularly attractive feature of mixed-effects models when random factors are crossed is that inference about experimental effects and interactions no longer requires separate analyses of variance, one for subjects and one for items,58 but can be carried out within a single coherent framework. Model selection procedures followed standard guidelines on building mixed-effects models.54 The significance of fixed effects in the models was assessed with conditional F-tests using Satterthwaite approximations to degrees of freedom and with 95% confidence intervals.5961 Assumptions underlying the models were visually checked with diagnostic plots of residuals.37,56 
Table
 
Results of the Mixed-Effects Models When Regressing Reading Speed on Nonuniformity of Fixations (Model 1), on Letters per Forward Saccade (Model 2), and on Both Factors With an Interaction Term (Model 3)
Table
 
Results of the Mixed-Effects Models When Regressing Reading Speed on Nonuniformity of Fixations (Model 1), on Letters per Forward Saccade (Model 2), and on Both Factors With an Interaction Term (Model 3)
We used the R system for statistical computing62 along with additional R packages: ggplot2, ggmap, cowplot, plyr, texreg, feature, lme4, and mediation. The package “feature” allowed us to quantify the NUF factor by identifying the distributions of fixations that contained at least one significant curvature.42,52 The packages lme4 and mediation were respectively used for (generalized) linear mixed-effects analyses63 and for mediation analyses with mixed effects.6466 
Results
The first new finding of this study is that the NUF factor is a clear-cut determinant of reading speed. A typical illustrative pattern of the relationships between the NUF factor, spatial fixation distributions, and reading speed is shown in Figure 2 for patient A. Although 13 sentences were correctly read by patient A, only 8 sentences are displayed here to improve visual clarity (the 5 sentences that had intermediate reading speeds were removed). These 8 sentences are represented in the eight columns of the figure and are sorted according to reading speed values in words per minute (shown at the top of each subplot in Fig. 2A). For each of these eight trials, the x-axis shows normalized horizontal location of fixations; the beginning and end of each sentence correspond to 0 and 1, respectively. Each subplot in Figure 2A is similar to a time–space plot allowing a clear visualization of the spatiotemporal pattern of fixations (small solid circles) in the horizontal dimension. The corresponding horizontal distributions of fixations are displayed in Figure 2B with standard histograms and in Figure 2C with continuous probability density functions calculated with kernel density estimation. The points of the density functions that have a significant curvature (based on the feature significance algorithm) are shown in bold; the first three sentences in Figure 2, that is, those with the smallest reading speeds, are classified as nonuniform. 
Figure 2
 
Data from a typical subject (patient A) to illustrate the relationship between the horizontal distribution of fixations, the nonuniformity of fixations factor (NUF), and reading speed (wpm: words per minute). Each column represents data for one sentence correctly read by patient A. The horizontal fixation location has been normalized and is represented on the x-axis (0 and 1 representing the left and right limits of each sentence). (A) Time–space plots showing the location (in the horizontal dimension) of each successive eye fixation (solid circle). (B) Histograms of the spatial distributions of fixations shown in (A). (C) Corresponding probability density functions calculated with kernel density estimation. Solid circles superimposed on these functions represent points with a significant curvature as assessed by the feature significance theory (see Methods). For this patient, only the first three sentences were labeled as nonuniformly distributed. Reading speed (top values in [A]) was used to order the columns.
Figure 2
 
Data from a typical subject (patient A) to illustrate the relationship between the horizontal distribution of fixations, the nonuniformity of fixations factor (NUF), and reading speed (wpm: words per minute). Each column represents data for one sentence correctly read by patient A. The horizontal fixation location has been normalized and is represented on the x-axis (0 and 1 representing the left and right limits of each sentence). (A) Time–space plots showing the location (in the horizontal dimension) of each successive eye fixation (solid circle). (B) Histograms of the spatial distributions of fixations shown in (A). (C) Corresponding probability density functions calculated with kernel density estimation. Solid circles superimposed on these functions represent points with a significant curvature as assessed by the feature significance theory (see Methods). For this patient, only the first three sentences were labeled as nonuniformly distributed. Reading speed (top values in [A]) was used to order the columns.
Note that the feature significance algorithm never reports nonuniformity for readers with an intact central field. The main reason is that fixations are very regularly distributed in normal reading.27 This is so even when some irregularities occur because some words (usually long or low-frequency words) receive two or three fixations (called refixations) due to short-range regressive saccades.67 
Some patients did not show any cluster of fixations; that is, the feature significance algorithm never reported nonuniform patterns for these patients. One example is shown with patient B in Figure 3. Only eight sentences were correctly read by patient B, with a mean reading speed (i.e., across trials) of 26.6 wpm (versus 26.8 for patients' average). These plots illustrate one difficulty we encountered when trying to quantify the NUF factor. Visual inspection of the first three plots on the left (i.e., those with the lowest reading speeds) suggests that some form of fixation clustering occurred. However, we could not find any statistical technique that was able to categorize these three sentences as nonuniform. One possible reason for the difficulty to statistically extract clusters might be related to the pattern of backward saccades that seems specific to each patient (proportions of backward saccades for the eight sentences are 0.62, 0.67, 0.57, 0.50, 0.67, 0.59, 0.59, 0.67). Patient B, in contrast to patient A in Figure 2, seems to make only rarely more than two successive forward saccades even when she reads at her highest rate. It is likely that this regular alternation between short sequences of forward and backward saccades might impede the statistical detection of clusters of fixations. In any case, as shown in the next section, the current quantification of the NUF factor is clear enough to reveal its effect on reading speed. We, however, think that this quantification might be much more efficient if future research could discover more sensitive statistical tools able to extract the clusters investigated in the present study. This challenge could also benefit in the future from sequential analyses of forward and backward saccades. 
Figure 3
 
Data from patient B whose distributions were all categorized as uniform (NUF = 0). Characteristics and layout of this figure are the same as in Figure 2.
Figure 3
 
Data from patient B whose distributions were all categorized as uniform (NUF = 0). Characteristics and layout of this figure are the same as in Figure 2.
Comparing the patterns obtained by patients A and B is also interesting if we look at the last fixations presented in the time–space plots of Figures 2A and 3A. For patient A and for some sentences, especially the last three (i.e., those with the highest reading speeds), the last fixations are closer to the beginning of the sentence than to the end. This pattern is scarcer for patient B (only for first sentence). All patients had at least one sentence with this pattern. The occurrence of such “long-range” regressive saccades toward previously read words has often been studied in the field of adult expert reading.68,69 These regressions often occur when the meaning previously selected for an ambiguous word is inconsistent with subsequently read text: They are critical for sentence or passage comprehension. We therefore interpret the few final long-range regressive saccades observed with our patients as a final check of some ambiguous parts of the sentence. 
The effect of the NUF factor on reading speed is clearly visible in a scatter plot where each data point represents a correctly read sentence (Fig. 4). The significance of the NUF factor as a determinant of reading speed is indicated by the first mixed-effects analysis (model 1) presented in the Table. This model contains only the NUF factor as a regressor. The negative slope of the effect shows that reading speed is significantly reduced when NUF increases. In this model, as well as in the others presented in the Table, the standard errors of the estimates (between parentheses), hence the confidence intervals, are very small so that all effects have P values smaller than 0.0001. 
Figure 4
 
Effect of nonuniformity of fixations on reading speed (natural log). Data points represent correctly read sentences and are horizontally jittered to reduce overplotting. Boxes represent median reading speed (middle thick line) and 0.1 and 0.9 deciles.
Figure 4
 
Effect of nonuniformity of fixations on reading speed (natural log). Data points represent correctly read sentences and are horizontally jittered to reduce overplotting. Boxes represent median reading speed (middle thick line) and 0.1 and 0.9 deciles.
Previous evidence that L/FS is a strong determinant of reading speed is confirmed by the second mixed-effects analysis (Table, model 2); this model contains only one regressor, L/FS, when the number of L/FS increases, so does reading speed. Note that the new feature of this confirmation is that we used a mixed-effects analysis (i.e., several repeated measures of L/FS for each patient) whereas previous studies used multiple regression (i.e., one single average value of L/FS for each patient). 
The important new finding is that L/FS and the NUF factor have unique effects on reading speed: When both factors are jointly included in a mixed-effects model (Table, model 3), the factors' estimates remain significant. Note that the two effects (NUF and L/FS) are smaller in model 3 than in models 1 and 2, especially for L/FS. This is a consequence of their shared variance and suggests, as mentioned in the introduction, that a part of the L/FS effect is induced by fixation clustering. 
In sum, although there is some multicollinearity between the two factors suggesting that higher levels of NUF are to some extent associated with smaller L/FS values, both factors have unique effects on reading speed as represented in Figure 5. Finally, model 3 shows that there is no interaction between these two factors (the estimate of the interaction term is not significantly different from zero). 
Figure 5
 
Scatter plot of reading speed as a function of L/FS (natural log transformed and centered). Each data point corresponds to a correctly read sentence. Symbols represent the two levels of the nonuniformity factor: uniform (crosses) or with clustering (squares). Lines represent the fixed effects of L/FS as derived from model 3 for the uniform (dashed) and nonuniform (solid) levels of the NUF factor.
Figure 5
 
Scatter plot of reading speed as a function of L/FS (natural log transformed and centered). Each data point corresponds to a correctly read sentence. Symbols represent the two levels of the nonuniformity factor: uniform (crosses) or with clustering (squares). Lines represent the fixed effects of L/FS as derived from model 3 for the uniform (dashed) and nonuniform (solid) levels of the NUF factor.
We also analyzed our data with the two-mediator model presented in a previous analysis of the effects of oculomotor patterns on reading speed.28 The basic questions that can be answered with such a model aim at understanding whether the effects of any factor on reading speed are mediated through the average number of fixations, through the average fixation duration, or through a mixture of both. We first show that the total effect of the NUF factor on reading speed is mediated by both factors, with a highly predominant causal role for the average number of fixations (when controlling for the effects of L/FS). The proportion of the total effect that is mediated by the average number of fixations has an estimate of 0.89 (95% confidence interval [CI]: [0.84, 0.96]). The proportion of the total effect that is mediated by the average fixation duration has an estimate of 0.05 (95% CI: [0.02, 0.09]). In other words, when nonuniformity increases, a small but significant part of its effect on reading speed is exerted through an increase in average fixation duration (which itself induces a decrease in reading speed). We also reproduced the results reported previously showing how the effect of L/FS on reading speed is fully mediated through the number of fixations.28 What is new in the present analysis is that the effect of the new NUF factor is controlled for. As previously described, the proportion of the total effect of L/FS that is mediated by the number of fixations is close to 1 with an estimate of 1.02 (95% CI: [0.87, 1.19]). The proportion of the total effect that is mediated by the average fixation duration has an estimate of −0.008 (95% CI: [−0.14, 0.08]). 
We finally looked for factors that might predict the NUF factor at the patient level or at the sentence level. We first wondered whether the proportion of nonuniform sentences (as quantified by the NUF factor) for each patient could be related to the fixation instability measured during a fixation task.7072 Fixation instability was assessed with eye fixation data collected with MP1 microperimetry while patients had to fixate a central cross for 30 seconds (in three successive sessions). Bivariate contour ellipse area (BCEA) in squared degrees was calculated from these data for each patient. The proportion of nonuniform trials for each patient was regressed on BCEA with a generalized linear mixed-effects model, but the effect was not significant (estimate 0.57; SE: 0.33; P: 0.08). Similarly, none of the other clinical factors collected for each patient was a significant predictor of the per patient proportion (i.e., across sentences) of nonuniform trials. 
While we did not find any patient-specific predictor of the NUF factor, we found a sentence-specific predictor. For each of the 14 sentences, the word with the lowest frequency of occurrence was selected. This resulted in 14 sentence-specific frequency values (referred to below as lowest frequency) that were used as a continuous predictor of the per sentence proportion (i.e., across patients) of fixation clusters. The per sentence proportion of nonuniform trials was regressed on lowest frequency with a generalized linear mixed-effects model. The effect of lowest frequency was found to be significant (estimate −0.044; SE: 0.016; P: 0.007; 95% CI: [−0.08, −0.01]). These results indicate that the probability of finding a fixation cluster within a sentence increases when the frequency of the lowest-frequency word in this sentence decreases. This is illustrated by two typical examples in Figure 1, where the lowest-frequency word (“tulipes”, tulips) in the sentence on the left has a low frequency of 2.4. In contrast, the lowest frequency observed in the sentence on the right is 58.3 (for the word “payer,” to pay). 
Discussion
The present study describes and quantifies an oculomotor pattern that seems to have been overlooked in previous studies of eye-mediated reading with patients having lost their central vision. When this pattern occurs in a sentence, eye fixations have a nonuniform distribution in the horizontal dimension: Typically, fixations are evenly distributed along the whole sentence except for a small portion where they are densely clustered (note that character size was 3× acuity threshold for each patient). First, we show how the presence/absence of the NUF can be quantified with a statistical theory whose principle is to test for the presence of local modes in a continuous probability density function.42,52 Based on this quantification, a discrete two-level factor (the NUF factor) can then be used to categorize each sentence. Mixed-effects analyses show that the NUF factor is an important determinant of reading speed. Most importantly, this effect acts jointly with another previously described oculomotor factor: the number of L/FS. We find that these two factors have unique effects on reading speed, thus suggesting that they reflect different underlying processes. 
The positive L/FS effect on reading speed is usually interpreted as reflecting the role of the perceptual span in reading and has been extensively discussed elsewhere.2830 The perceptual span represents the spatial extent of useful information that is used both to process information within each fixation and to program the next saccade.27,73 The idea is thus that quick readers are able to extract within-fixation information from a larger horizontal area than slow readers. This hypothesis about the role of the perceptual span in eye-mediated reading is paralleled by the role of the visual span when reading is performed with static eyes in the rapid serial visual presentation (RSVP) paradigm.7480 It is important to note that the visual span and the perceptual span are two constructs that must be distinguished.73,81,82 For instance, O'Regan82 calls visual span “what can be seen without making use of lexical knowledge and contextual constraints,” which is the case, for instance, when measuring the visual span with the trigram method,77 and perceptual span “what can be perceived by additionally making use of them” (p. 502). The latter case clearly corresponds to meaningful sentence reading, as in the present work, where higher-level linguistic factors, such as lexical inference or predictability, can take place. Many studies have shown that the perceptual span differs in several ways from the visual span; for instance, it is dynamic (it can change from fixation to fixation), of wider extent, and asymmetric (larger to the right).83 Another important difference is that the perceptual span is attentionally constrained during eye-mediated reading.8487 This is suggested, for instance, by the reduction of the perceptual span when foveal processing difficulty increases. One important goal for future research is to investigate and clarify the relationship between visual span and perceptual span especially in the context of low-vision reading. While there is no doubt that larger visual spans are correlated with faster eccentric reading speeds,7480 it is still not known how visual span variations affect oculomotor behavior, notably L/FS values (which reflect perceptual span), during eye-mediated reading. 
Investigation of the factors that might be determinants of the NUF suggests that patient-specific factors are less likely than sentence-specific factors to predict the NUF factor. Concerning patient-specific characteristics, we checked whether fixation clusters might be due to fixational instability. It has indeed been shown that fixational instability, as measured in a fixation task,70 is significantly associated with eye-mediated reading speed,71 although the effect is not systematic.32 However, we did not find a significant association between patients' fixational instability and per patient proportion of trials with fixation clustering. This suggests that the challenge in identifying some difficult words, as reflected by NUF, is more dependent on psycholinguistic characteristics related to words or sentences than on oculomotor factors. More generally, we could not find any patient-specific clinical factor able to predict his/her proportion of trials with fixation clustering. 
However, our results provided evidence for an influence of sentence-specific factors on the NUF factor. We had hypothesized that significant fixation clusters might be partly induced by some words whose frequency of occurrence is relatively low, as lexical access is slower for low-frequency words in peripheral vision.88 Generalized linear mixed-effects analysis did indicate that the frequency value of the word with the lowest frequency in a sentence is significantly associated with the NUF factor: A frequency decrease of the lowest-frequency word in a sentence increases the probability of observing fixation clustering. Future research with more complex sentences than in our study should determine whether other factors, such as words' predictability and length or syntactic complexity, also influence the occurrence of NUF. 
It is still an open question whether patients use a single preferred retinal locus (PRL) or multiple PRLs during a reading task.89,90 What consequences would the use of multiple PRLs entail regarding our ability to measure fixation clusters? The most extreme consequence would occur if a difficult word was processed by alternating between a left and a right reading PRL. In this case, the data would show two clusters of fixations separated by a distance of about the horizontal extent of the scotoma. In less extreme cases, a single cluster would be reported by the eye tracker. For instance, if a horizontal PRL (say to the left) was used most of the time and a vertical PRL was used every time a difficult word was encountered, horizontal coordinates of fixations would still be clustered within one single region. The same would happen if vertical and horizontal PRLs were, respectively, used for the “easy” and “difficult” parts of the text. In sum, even if patients use multiple PRLs, any difficulty associated with the identification of a single word is still detectable from eye fixation data either as a single cluster or as two clusters. Consequently, fixation clustering, as measured by the eye tracker and as reported in the present work, will always reveal that reading was difficult in at least one restricted part of the sentence. However, note that the use of multiple PRLs will introduce uncertainty about the relative location (within the sentence) of the word that induced clustering of fixations. This is why we did not find it reliable to report analyses relating the clusters' locations to locations of words. 
The effect of the NUF factor on reading speed, whatever its theoretical determinants, should have important clinical consequences mainly for the design of new visual aids or new techniques of text simplification. Indeed, the dependence of NUF on sentence-specific factors suggests that transforming the sentences that are difficult to read might reduce NUF. Two kinds of transformations could be explored. Firstly, the NUF effect could be taken into account for the design of new dynamic visual aids implemented in electronic vision enhancement systems (EVES).4346 Our general suggestion is that EVES should allow patients to flexibly adapt the degree of magnification, or some other kind of vision enhancement, at any time and with a user-friendly interface. For instance, the knob allowing patients to change the degree of magnification in closed circuit television (CCTV) readers should be made much more accessible than it is in many current models. Thus patients could use a relatively low magnification level (usually the level prescribed by their ophthalmologist or optometrist) when they feel that their reading is relatively fluent. In this case, using a magnification level that is as small as possible is advantageous because it preserves the global layout of the text, which is helpful for page navigation.91 However, when patients feel that their reading flow is stopped because a particular word cannot be identified, they should be given the opportunity to transiently increase the magnification level. However, this level should not be maintained once the word has been identified because this level would be more detrimental for page navigation than the previously used magnification level. Our main point here is that it is not possible to determine in advance what magnification levels will be required in order to identify some difficult words. For instance, the word “lilies” in a proportional font might be very difficult to identify because crowding is very high due to the small distances between the letters l and i.92 In this case, it is likely that identification of the word would imply somehow a letter-by-letter reading strategy requiring a magnification level much higher than the average level required for the most usual words. If such CCTV systems with flexible zooming systems become available, we believe that future research should investigate whether patients would benefit from training procedures that encourage the use of different zooming levels during eye-mediated reading. In sum, concerning the future of innovative visual aids, our results advocate for the development of new adaptive systems that would allow a moment-to-moment adaptation of the vision enhancement characteristics as a function of the current difficulty experienced by the patient (Aguilar C, et al. IOVS 2014;55:ARVO E-Abstract 3006). Ideally, eye movements would be monitored during eye-mediated reading, and online detection of a cluster of fixations would trigger some adapted vision enhancement, or at least some proposals about possible ways of reacting. If such systems were operational, they would probably help minimize the occurrence of fixation clusters so that eye-mediated reading speed would be faster and more constant both within sentences and across sentences. 
Secondly, the NUF effect might also be counteracted by using automatic text simplification.93,94 Text simplification is the process of reducing the linguistic complexity of a text while still retaining the original information. There is clear evidence from studies using manually simplified text that reading comprehension can be improved for readers with poor literacy (second-language learners, persons with deafness, aphasia, dyslexia), for instance, by substituting easier-to-read words for difficult ones. In contrast, studies along these lines for low-vision patients are scarce.95 However, we believe that text simplification should be highly helpful to improve reading performance in these patients. Specifically, it seems very likely that fixation clusters such as those observed in our study would be prevented if low-frequency words were replaced by high-frequency synonyms. Similarly, future research should establish whether substituting for long words or words with many orthographic neighbors would fruitfully reduce NUF. More generally, our proposal seems timely and realistic because of recent progress in automatic text simplification, which has only recently become an established research field based on developments in linguistics and computer science. Our proposal is also interesting as it does not suffer from the frequently expressed concern that text simplification can impede language acquisition by denying learners the opportunity to learn the natural forms of language: Obviously, this is not an issue for AMD patients (i.e., the majority of patients with CFL) because of their age. Automatic text simplification could be used in different ways. As an assistive technology, it could be implemented within EVES by text digitalization (optical character recognition) followed by text simplification; or it could be used when low-vision patients want to read text on a Web site. Finally, it could be employed to produce printed material specifically designed for low-vision patients. 
In conclusion, the present study describes a new explanatory variable (NUF) that significantly alters reading speed in conjunction with an already established oculomotor factor, L/FS. Reading speed is dramatically reduced when a small portion of a sentence, presumably a word, is very difficult to identify, and thus induces a very high density of the horizontal coordinates of eye fixations. The important point is that low-vision patients who read some sentences with very slow reading speed because of fixation nonuniformity can also read other sentences without producing any fixation clusters and with much higher speeds (up to approximately 10× higher). Although the present data are not sufficient to fully assess the theoretical reasons underlying this variability, they suggest that sentence-related characteristics (such as the presence of a low-frequency word) are part of the explanation. In any case, the present findings should foster the development of new techniques for EVES and/or the use of automatic text simplification in order to reduce fixation clustering. Although clusters of fixations do not systematically occur in all sentences, their psychological effects are highly detrimental because they stop the reading flow, which we believe is one major reason patients are discouraged from reading. 
Acknowledgments
The authors thank Bernard Ridings, head of the Department of Ophthalmology, and Frédéric Chouraqui, head of the Low Vision Clinic, for their constant support. We also thank Nuria Gala for discussions about recent advances in the field of automatic text simplification, which might be fruitfully applied to facilitate reading of low-vision patients. 
Supported by a French Ministry of Research and Technology Grant (AC) and a BDI (Bourse de Doctorat pour Ingénieurs) Grant from the Centre National de la Recherche Scientifique (J-BB). 
Disclosure: A. Calabrèse, None; J.-B. Bernard, None; G. Faure, None; L. Hoffart, None; E. Castet, None 
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Figure 1
 
Examples from our data showing two very different distributions of fixations for the same patient. (A) Eye fixation maps superimposed on sentences: Each circle represents a fixation (circle area is proportional to fixation duration). The left map shows that fixations are densely clustered around the word “tulipes” (a low-frequency word), whereas the right map shows a more homogeneous horizontal distribution of fixations. (B) Corresponding probability density functions as a function of normalized x-coordinates of eye fixations. In the left plot, the circles represent points of the density curve that have a significant curvature as assessed by the feature significance theory.42 This fixation map is therefore labeled as having a nonuniform distribution of fixations (NUF = 1). In contrast, the density curve for the sentence on the right does not have any point with a significant curvature (NUF = 0). Note that the NUF value calculated for a given sentence varies (0 or 1) across patients.
Figure 1
 
Examples from our data showing two very different distributions of fixations for the same patient. (A) Eye fixation maps superimposed on sentences: Each circle represents a fixation (circle area is proportional to fixation duration). The left map shows that fixations are densely clustered around the word “tulipes” (a low-frequency word), whereas the right map shows a more homogeneous horizontal distribution of fixations. (B) Corresponding probability density functions as a function of normalized x-coordinates of eye fixations. In the left plot, the circles represent points of the density curve that have a significant curvature as assessed by the feature significance theory.42 This fixation map is therefore labeled as having a nonuniform distribution of fixations (NUF = 1). In contrast, the density curve for the sentence on the right does not have any point with a significant curvature (NUF = 0). Note that the NUF value calculated for a given sentence varies (0 or 1) across patients.
Figure 2
 
Data from a typical subject (patient A) to illustrate the relationship between the horizontal distribution of fixations, the nonuniformity of fixations factor (NUF), and reading speed (wpm: words per minute). Each column represents data for one sentence correctly read by patient A. The horizontal fixation location has been normalized and is represented on the x-axis (0 and 1 representing the left and right limits of each sentence). (A) Time–space plots showing the location (in the horizontal dimension) of each successive eye fixation (solid circle). (B) Histograms of the spatial distributions of fixations shown in (A). (C) Corresponding probability density functions calculated with kernel density estimation. Solid circles superimposed on these functions represent points with a significant curvature as assessed by the feature significance theory (see Methods). For this patient, only the first three sentences were labeled as nonuniformly distributed. Reading speed (top values in [A]) was used to order the columns.
Figure 2
 
Data from a typical subject (patient A) to illustrate the relationship between the horizontal distribution of fixations, the nonuniformity of fixations factor (NUF), and reading speed (wpm: words per minute). Each column represents data for one sentence correctly read by patient A. The horizontal fixation location has been normalized and is represented on the x-axis (0 and 1 representing the left and right limits of each sentence). (A) Time–space plots showing the location (in the horizontal dimension) of each successive eye fixation (solid circle). (B) Histograms of the spatial distributions of fixations shown in (A). (C) Corresponding probability density functions calculated with kernel density estimation. Solid circles superimposed on these functions represent points with a significant curvature as assessed by the feature significance theory (see Methods). For this patient, only the first three sentences were labeled as nonuniformly distributed. Reading speed (top values in [A]) was used to order the columns.
Figure 3
 
Data from patient B whose distributions were all categorized as uniform (NUF = 0). Characteristics and layout of this figure are the same as in Figure 2.
Figure 3
 
Data from patient B whose distributions were all categorized as uniform (NUF = 0). Characteristics and layout of this figure are the same as in Figure 2.
Figure 4
 
Effect of nonuniformity of fixations on reading speed (natural log). Data points represent correctly read sentences and are horizontally jittered to reduce overplotting. Boxes represent median reading speed (middle thick line) and 0.1 and 0.9 deciles.
Figure 4
 
Effect of nonuniformity of fixations on reading speed (natural log). Data points represent correctly read sentences and are horizontally jittered to reduce overplotting. Boxes represent median reading speed (middle thick line) and 0.1 and 0.9 deciles.
Figure 5
 
Scatter plot of reading speed as a function of L/FS (natural log transformed and centered). Each data point corresponds to a correctly read sentence. Symbols represent the two levels of the nonuniformity factor: uniform (crosses) or with clustering (squares). Lines represent the fixed effects of L/FS as derived from model 3 for the uniform (dashed) and nonuniform (solid) levels of the NUF factor.
Figure 5
 
Scatter plot of reading speed as a function of L/FS (natural log transformed and centered). Each data point corresponds to a correctly read sentence. Symbols represent the two levels of the nonuniformity factor: uniform (crosses) or with clustering (squares). Lines represent the fixed effects of L/FS as derived from model 3 for the uniform (dashed) and nonuniform (solid) levels of the NUF factor.
Table
 
Results of the Mixed-Effects Models When Regressing Reading Speed on Nonuniformity of Fixations (Model 1), on Letters per Forward Saccade (Model 2), and on Both Factors With an Interaction Term (Model 3)
Table
 
Results of the Mixed-Effects Models When Regressing Reading Speed on Nonuniformity of Fixations (Model 1), on Letters per Forward Saccade (Model 2), and on Both Factors With an Interaction Term (Model 3)
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