Fraction Sense: Foundational Understandings.

The intent of this commentary is to identify elements of fraction sense and note how the research studies provided in this special issue, in related but somewhat different ways, validate the importance of such understandings. Proficiency with fractions serves as a prerequisite for student success in higher level mathematics, as well as serving as a gateway to many occupations and varied contexts beyond the mathematics classroom. Fraction sense is developed through instructional opportunities involving fraction equivalence and magnitude, comparing and ordering fractions, using fraction benchmarks, and computational estimation. Such foundations are then extended to operations involving fractions and decimals and applications involving proportional reasoning. These components of fraction sense are all addressed in the studies provided in this issue, with particular consideration devoted to the significant importance of the use of the number line as a central representational tool for conceptually understanding fraction magnitude.

Training retinal imagers for retinopathy of prematurity (ROP) screening.

PURPOSE: To report the training/certification process of nonphysician imagers, image quality, and factors that affected image quality in the National Eye Institute sponsored multicentered e-ROP study. METHODS: Nonphysician imagers underwent rigorous training and certification in obtaining retinal images, with attention to clarity, focus, and optic disk placement. Image readers measured pupil size in pupil image and graded posterior pole, temporal, nasal, superior, and inferior retinal images and classified them as good, adequate, poor, or missing. Good and adequate images were deemed acceptable. RESULTS: In 4,003 image sessions of 1,257 infants, 3,453 (86.8%) were complete. Of 39,550 retinal images, 91.7% had acceptable quality, 5.6% poor, and 2.7% were missing. Inadequate pupil dilation negatively affected acceptable image quality: 54% acceptable images for pupil <5 mm versus 93% for >6 mm (P < 0.0001). When ventilatory equipment obstructed access to imaged infant, the percent of acceptable image quality decreased: 94% for no support versus 66.6% for oscillatory ventilation (P < 0.0001). Acceptable image quality rates improved from 87% to 90% (P = 0.03) from first 6 months to last 6 months at low patient volume centers, while high patient volume centers remained stable at 95%. CONCLUSIONS: Nonphysicians successfully obtained acceptable quality images for ROP evaluation. Skills improved with experience. Image quality was negatively affected by inadequate pupil dilation and the presence of obstructive ventilatory equipment.

Safety of Retinopathy of Prematurity Examination and Imaging in Premature Infants.

OBJECTIVES: To describe adverse events (AEs) and noteworthy clinical or ocular findings associated with retinopathy of prematurity (ROP) evaluation procedures. STUDY DESIGN: Descriptive analysis of predefined AEs and noteworthy findings reported in a prospective observational cohort study of infants <1251 g birth weight who had ROP study visits consisting of both binocular indirect ophthalmoscopy (BIO) and digital retinal imaging. We compared infant characteristics during ROP visits with and without AEs. We compared respiratory support, nutrition, and number of apnea, bradycardia, or hypoxia events 12 hours before and after ROP visits. RESULTS: A total of 1257 infants, mean birth weight 802 g, had 4263 BIO and 4048 imaging sessions (total 8311 procedures). No serious AEs were related to ROP visits. Sixty-five AEs were reported among 61 infants for an AE rate of 4.9% infants (61/1257) or 0.8% total procedures (65/8311 BIO + imaging). Most AEs were due to apnea, bradycardia, and/or hypoxia (68%), tachycardia (16%), or emesis (8%). At ROP visit, infants with AEs, compared with those without, were more likely to be on mechanical ventilation (26% vs 12%, P = .04) even after adjustment for weight and postmenstrual age. Noteworthy clinical findings were reported during 8% BIO and 15% imaging examinations. Respiratory and nutrition support were not significantly different before and after ROP evaluations. CONCLUSIONS: Retinal imaging by nonphysicians combined with BIO was safe. Noteworthy clinical findings occurred during both procedures. Ventilator support was a risk factor for AEs. Monitoring rates of AEs and noteworthy findings are important to the safe implementation of ROP imaging protocols. TRIAL REGISTRATION: Clinicaltrials.gov: NCT01264276.

Late recurrence of retinopathy of prematurity after treatment with both intravitreal bevacizumab and laser.

An infant of 36 weeks' postmenstrual age (PMA) and 25 weeks' gestation received bilateral intravitreal bevacizumab injections for type 1 retinopathy of prematurity. He underwent laser photocoagulation in both eyes 5 days later, confluent except for 1 clock hour obscured by hemorrhage in the left eye. Despite initial regression, neovascularization in both vascularized and lasered retina with plus disease recurred, requiring repeat laser bilaterally at 51 weeks' PMA and vitrectomy in the left eye at 54 weeks' PMA. Whereas late recurrence is thought to occur rarely after laser treatment, infants who have received both bevacizumab injections and laser may still require long-term surveillance for recurrence. In this case, fundus photography proved valuable for appreciating recurrent plus disease because the initial treatments had resulted in marked retinal vessel attenuation.

Interactive retinal vessel extraction by integrating vessel tracing and graph search.

Despite recent advances, automatic blood vessel extraction from low quality retina images remains difficult. We propose an interactive approach that enables a user to efficiently obtain near perfect vessel segmentation with a few mouse clicks. Given two seed points, the approach seeks an optimal path between them by minimizing a cost function. In contrast to the Live-Vessel approach, the graph in our approach is based on the curve fragments generated with vessel tracing instead of individual pixels. This enables our approach to overcome the shortcut problem in extracting tortuous vessels and the problem of vessel interference in extracting neighboring vessels in minimal-cost path techniques, resulting in less user interaction for extracting thin and tortuous vessels from low contrast images. It also makes the approach much faster.

The rate of change in retinal vessel width and tortuosity in eyes at risk for retinopathy of prematurity.

PURPOSE: To describe the rate of change in retinal vessel width and tortuosity in eyes that develop treatment-requiring, or type 1, retinopathy of prematurity (ROP) versus eyes that do not develop type 1 ROP. METHODS: Posterior poles of eyes of 41 infants at risk for ROP were imaged longitudinally with a 30° fundus camera. Retinal vessel width and tortuosity were measured with computer-assisted image analysis. The rate of change per day in width and tortuosity up to the development of most severe ROP was calculated from linear regression and eyes with (n = 10) and without type 1 ROP (n = 31) were compared. RESULTS: Eyes that developed type 1 ROP had a greater rate of change in width for venules and 3 widest vessels (P < 0.0001), and a greater rate of change in tortuosity for arterioles and 3 most tortuous vessels (P < 0.0001) than eyes that did not develop type 1 ROP. These vessel parameters discriminate the 2 groups well (area under the ROC curve, 0.79-0.90). A combination of venular width and arteriolar tortuosity had the best discriminative ability (area under the ROC curve, 0.96). CONCLUSIONS: In this pilot study, eyes that eventually developed type 1 ROP demonstrated a faster increase in width and tortuosity of retinal vessels compared with those that did not. Further study of the kinetics of retinal vascular change in a larger sample may allow for the earlier identification of vision-threatening ROP.

Retinal vessel changes after laser treatment for retinopathy of prematurity.

BACKGROUND: The clinical response to retinopathy of prematurity (ROP) treatment is currently assessed subjectively. This study aims to quantify treatment response objectively by assessing changes in digital images of posterior pole retinal vessel width and tortuosity. METHODS: Images of 30 right eyes with type 1 ROP obtained at up to three time points were analyzed: before treatment (T = 0) and 1 (T = 1) and/or 2 weeks (T = 2) after treatment. Width and tortuosity of retinal vessels were analyzed from digital images using computer-assisted image analysis software. RESULTS: Vessel width decreased by 20% (P < 0.004) within the first week and remained stable by the second week after laser treatment. Vessel tortuosity did not significantly change by the first week but decreased 27% (P < 0.01) by second week. CONCLUSIONS: Vessel width appears to decrease dramatic within the first week, whereas the regression of tortuosity follows a slower course.

Thrombocytopenia and retinopathy of prematurity.

BACKGROUND: Platelets may act as vascular endothelial growth factor (VEGF) scavengers, possibly limiting neovascularization in retinopathy of prematurity (ROP). The purpose of this study was to investigate the association between thrombocytopenia (platelets <150,000/µL) and the development of type 1 ROP. METHODS: This was a retrospective 1:1 matched case-control study. Cases required laser; controls developed no or stage 1 ROP and were matched for birth weight within 100 g and gestational age within 1 week. Most recent platelet count prior to laser (case) and matched postmenstrual age (control) were abstracted. Conditional logistic regression was used. RESULTS: A total of 91 cases and 91 controls were reviewed. Of the cases, 25% had thrombocytopenia; of controls, 13% (P = 0.034; OR = 2.38; 95% CI, 1.04-5.43). Birth weight, gestational age, postmenstrual age, and culture-proven sepsis were not confounders in multivariate analysis. The association was significant for zone 1 (n = 16; OR = 9.00; 95% CI, 1.14-71.0) but not for zone 2 (OR = 1.43; 95% CI, 0.54-3.75) cases and controls. CONCLUSIONS: Thrombocytopenia was associated with type 1 ROP, primarily among infants with zone 1 ROP. This effect may result from disease location or disease timing, as posterior disease occurs at an earlier postmenstrual age. Longitudinal studies are required to further examine the roles of cumulative platelet deficits, thresholds, or critical time windows in the observed association.

A clinical prediction model to stratify retinopathy of prematurity risk using postnatal weight gain.

OBJECTIVE: To develop an efficient clinical prediction model that includes postnatal weight gain to identify infants at risk of developing severe retinopathy of prematurity (ROP). Under current birth weight (BW) and gestational age (GA) screening criteria, <5% of infants examined in countries with advanced neonatal care require treatment. PATIENTS AND METHODS: This study was a secondary analysis of prospective data from the Premature Infants in Need of Transfusion Study, which enrolled 451 infants with a BW < 1000 g at 10 centers. There were 367 infants who remained after excluding deaths (82) and missing weights (2). Multivariate logistic regression was used to predict severe ROP (stage 3 or treatment). RESULTS: Median BW was 800 g (445-995). There were 67 (18.3%) infants who had severe ROP. The model included GA, BW, and daily weight gain rate. Run weekly, an alarm that indicated need for eye examinations occurred when the predicted probability of severe ROP was >0.085. This identified 66 of 67 severe ROP infants (sensitivity of 99% [95% confidence interval: 94%-100%]), and all 33 infants requiring treatment. Median alarm-to-outcome time was 10.8 weeks (range: 1.9-17.6). There were 110 (30%) infants who had no alarm. Nomograms were developed to determine risk of severe ROP by BW, GA, and postnatal weight gain. CONCLUSION: In a high-risk cohort, a BW-GA-weight-gain model could have reduced the need for examinations by 30%, while still identifying all infants requiring laser surgery. Additional studies are required to determine whether including larger-BW, lower-risk infants would reduce examinations further and to validate the prediction model and nomograms before clinical use.

Comparison of expert graders to computer-assisted image analysis of the retina in retinopathy of prematurity.

AIMS: To determine correlation of width and tortuosity between expert graders and computer-assisted image analysis of the retina in narrow-field images of eyes with retinopathy of prematurity. METHODS: 11 digital images were selected based on severity of retinopathy of prematurity (ROP). Narrow field images were analysed for width and tortuosity of vessels using computer-aided image analysis of the retina (CAIAR), an image analysis software, and by four ROP experts. Spearman correlation coefficients (ρ) assessed the correlation of CAIAR grading with expert grading. Intra-class correlations assessed agreement among graders. Width and tortuosity were compared among severity of ROP and treatment status using analysis of variance and generalised estimating equations. RESULTS: Expert measurements correlated well with measures from CAIAR for venule width (ρ=0.57-0.66) and arteriole tortuosity (ρ=0.71-0.81). Measurements from four graders agreed moderately well (intra-class correlations were 0.49 and 0.69 for venule width and arteriole tortuosity, respectively). Increased severity of ROP (no pre-plus/plus, pre-plus, plus) was associated with larger width (linear trend p=0.02 in two graders) and tortuosity (linear trend p<0.03 in all graders). Tortuosity measurements by CAIAR and graders were statistically different between treated and untreated eyes (p<0.002). CONCLUSIONS: We found moderate correlation between expert graders' assessment of vessel tortuosity and width and CAIAR using narrow-field images.

Risk stratification of preplus retinopathy of prematurity by semiautomated analysis of digital images.

OBJECTIVE: To determine whether quantitative analysis of retinal vessel width and tortuosity from digital images discriminates which eyes with preplus retinopathy of prematurity (ROP) progress to treatment severity. METHODS: Posterior pole images of eyes at first clinical diagnosis of preplus ROP were obtained using a 30 degrees-field, noncontact fundus camera. Width and tortuosity of retinal vessels were analyzed from digital images using computer-assisted image analysis software. Mean width and tortuosity of venules and arterioles were compared in 19 preplus eyes that regressed spontaneously and 11 preplus eyes that progressed to treatment severity. Receiver operating characteristic curve analysis was performed to assess whether width and tortuosity discriminated between groups. RESULTS: Mean widths of venules alone, arterioles alone, and the 3 widest vessels were higher in preplus progressed eyes (P < .04). Mean tortuosity of the 3 most tortuous vessels was higher in preplus progressed than in preplus regressed eyes (P = .01). Most vessel width and tortuosity variables predicted which eyes with preplus progressed to treatment moderately well, with an area under the receiver operating characteristic curve of 0.72 to 0.82. CONCLUSIONS: Digital image analysis of retinal vessel width and tortuosity may be useful in predicting which preplus ROP eyes will require treatment. Because vascular abnormalities are a continuum and clinical diagnosis is subjective, quantitative analysis may improve risk stratification for ROP.

Semiautomated digital image analysis of posterior pole vessels in retinopathy of prematurity.

Plus disease is a major indicator for treatment in retinopathy of prematurity (ROP), and computer-assisted image analysis of vessel caliber and tortuosity in the posterior pole may indicate disease progression and severity. We sought to determine whether semiautomated digital analysis of posterior pole vessels using narrow field images with varying severity of ROP correlated with vessel width and tortuosity.

Image analysis of posterior pole vessels identifies type 1 retinopathy of prematurity.

Identification of type 1 retinopathy of prematurity (ROP) relies heavily on the presence of characteristics of plus disease, especially tortuosity. However, a relatively infrequent subset of eyes with type 1 ROP, eyes with zone 1, stage 3 ROP without plus disease, is included in treatment indications. We examined if posterior pole vessel width is associated with type 1 ROP in a subset of eyes with zone 1, stage 3 ROP without plus disease and whether vessel width differentiates type 1 from non-type 1 ROP.

The rate of retinal vessel dilation in severe retinopathy of prematurity requiring treatment.

PURPOSE: To assess whether the rate of change of retinal vessel diameter can help identify infants at the highest risk for severe retinopathy of prematurity (ROP). DESIGN: Thirty-five infants at risk for ROP were included in this prospective, longitudinal study. METHODS: Images were obtained using the NIDEK NM200D noncontact camera (NIDEK Inc, Aichi, Japan) at the time of ROP examinations in the intensive care unit. Vessel diameters were measured from digital fundus photographs of right eyes in a masked fashion using VesselMap image analysis software (IM-EDOS GmbH, Weimar, Germany). The rate of change of vessel diameter was calculated based on the linear regression slope and was compared between eyes in which type 1 ROP requiring treatment developed and in controls without ROP or with ROP less severe than type 1. RESULTS: Multivariate analysis showed that the group of eyes in which type 1 ROP developed had a greater increase in diameter over time in the inferior temporal veins (P = .01), superior temporal veins (P < .0001), mean temporal veins (P < .0001), superior temporal arteries (P = .02), and mean temporal arteries (P = .004). The area under receiver operator characteristic curve for venous diameter change was 0.96 for the superior temporal vein, 0.86 for the inferior temporal vein, and 0.96 for the mean temporal vein. CONCLUSIONS: On average, the rate of retinal vessel change was greater in eyes with type 1 ROP requiring treatment than in control eyes. The rate of venous diameter change had the best discriminative ability to differentiate between the 2 groups.

Progression to severe retinopathy predicted by retinal vessel diameter between 31 and 34 weeks of postconception age.

OBJECTIVE: To assess the predictive value of early retinal vascular diameter measurements for the development of severe retinopathy of prematurity (ROP) in high-risk preterm infants. METHODS: Digital fundus images were taken of 78 eyes at risk for ROP with a noncontact camera during fundoscopic examination when infants were 31 to 34 weeks of postconception age. Vessel diameters were measured for the major superior and inferior temporal arteries and veins with the use of VesselMap software. Mean vessel diameters from eyes that developed severe ROP requiring treatment were compared with those that developed less severe ROP not requiring treatment or no ROP. RESULTS: All 4 major temporal retinal vessels showed significantly larger average diameters in the group of eyes that developed severe ROP requiring treatment. Multivariate analysis adjusted by birth weight, gestational age, and chronologic age showed similar results. Early retinal vessel diameter measurements showed good predictive value for the progression to severe ROP requiring treatment (area under the receiver operating characteristic curve, 0.75-0.94). CONCLUSIONS: At 31 to 34 weeks of postconception age, average retinal vessel diameter measurements were significantly larger in infants who developed severe ROP requiring treatment than in infants who developed less severe ROP or no ROP.

Quantitative analysis of retinal vessel diameter reduction after photocoagulation treatment for retinopathy of prematurity.

PURPOSE: To evaluate the feasibility of using semiautomated analysis of digital fundus images to quantify effects of photocoagulation on retinal vessel diameter in retinopathy of prematurity (ROP). DESIGN: Case series. METHODS: Fourteen eyes of seven patients with threshold ROP and 12 eyes of six controls were included. Fundus images were captured before and after photocoagulation, or one to three weeks apart in controls, using an NM200D camera (Nidek, Inc, Aichi, Japan). VesselMap software (Imedos, Jena, Germany) measured vessel diameter. The t test analysis was used to assess vessel changes. RESULTS: The authors observed a significant reduction in average largest retinal vein diameter of -18% +/- 16% (+/-1 standard deviation). The average largest artery diameter trended down by -12% +/- 16%. Compared with controls, diameter reduction was significant in veins (P = .014) and arteries (P = .016). CONCLUSIONS: The diameter of retinal vessels decreases after photocoagulation. VesselMap analysis of digital images is feasible and may be helpful in quantifying treatment effects.

Semiautomated analysis of retinal vessel diameter in retinopathy of prematurity patients with and without plus disease.

PURPOSE: To determine the feasibility of using semiautomated analysis of digital fundus images to quantify the differences in retinal vascular diameter between retinopathy of prematurity (ROP) patients with and without plus disease. DESIGN: Case-control study. METHODS: Thirty eyes of 15 patients with ROP were included in this study. Fourteen eyes of seven patients had plus disease and 16 eyes of eight patients had no evidence of plus disease. Digital fundus images were captured using an NM200D (Nidek, Inc, Aichi, Japan) camera. Vessel diameters were determined using VesselMap software (Imedos, Jena, Germany). The Student t test analysis was used to compare diameters of vessels with and without plus disease. RESULTS: We found that the average venous diameter is significantly larger by 15% in the group with plus disease. CONCLUSIONS: VesselMap analysis of digital images is feasible. This method is able to distinguish between veins with and without plus disease, and may be useful in telemedicine screening strategies.