Quantification of the Changes in the Openness of the Major Temporal Arcade in Retinal Fundus Images of Preterm Infants With Plus Disease

Abstract

Purpose.: We tested the hypothesis that the openness of the major temporal arcade (MTA) changes in the presence of plus disease, by quantification via parabolic modeling of the MTA, as well as measurement of an arcade angle for comparative analysis. Such analysis could assist in the detection and treatment of progressive retinopathy of prematurity.

Methods.: Digital image processing techniques were applied for the detection and modeling of the MTA via a graphical user interface (GUI) to quantify the openness of the MTA. An arcade angle measure, based on a previously proposed method, also was obtained via the GUI for comparative analysis. The statistical significance of the differences between the plus and no-plus cases for each parameter was analyzed using the P value. The area (A_z) under the receiver operating characteristic curve was used to assess the diagnostic performance of each feature.

Results.: The temporal arcade angle measure and the openness parameter of the parabolic model were used to perform discrimination of plus versus no-plus cases. Using a set of 19 cases with plus and 91 with no plus disease, A_z = 0.70 was obtained using the results of dual-parabolic modeling in screening for plus disease. The arcade angle measure provided comparable results with A_z = 0.73.

Conclusions.: Using our proposed image analysis techniques and software, this study demonstrates, for the first time to our knowledge, that the openness of the MTA decreases in the presence of plus disease.

Introduction

Retinopathy of prematurity (ROP) is a complex disease that affects the process of development of the vascular architecture in the retina of preterm infants and is the leading cause of preventable childhood blindness worldwide.¹ It is estimated that at least 50,000 children worldwide are suffering from blindness caused by ROP.² Based on a study conducted in 1993 in the United States, it was reported that approximately 30,000 preterm babies are born each year with a birth weight of 500 to 1249 g, of whom 1000 are estimated to progress to a level of ROP that requires treatment (threshold disease).³ An analysis of a New York State patient database from 1996 to 2000 indicated that the incidence of ROP among newborn infants was 1 in 511.⁴ Of the 6998 premature infants screened during a 2-year period for the Early Treatment for ROP study in the United States, 68% had ROP.⁵ Gunn et al.⁶ reported an incidence of 81% for ROP in premature infants, based on a screening study conducted over an 18-year period in Australia. The governmental cost of visual impairment from ROP in the United States was estimated at approximately $38 to $65 million per year in 1993,³ which is approximately $60 to $105 million per year after adjusting for inflation in 2013. 

Because ROP can advance rapidly in the first 8 to 12 weeks of life, timely diagnosis and identification of signs of ROP are important for clinical management of the affected infants. In the past decade, it has been established that early detection and treatment of ROP are highly correlated with the presence of plus disease.^7–12 

Plus disease is an indicator of a severely progressing phase of ROP.¹³ An active shunt at the junction of the vascularized and nonvascularized parts of the retina is associated with increased vessel thickness and tortuosity in the posterior part of the retina.¹⁴ Currently, plus disease is diagnosed clinically based on the presence of a certain level of increase in venular dilation and arteriolar tortuosity in at least two quadrants of the eye.¹ The presence of sufficient dilation and tortuosity of the posterior vessels for the diagnosis of plus disease is determined by visual qualitative comparison to a gold-standard retinal fundus photograph.^1,11,15 However, the gold-standard image is believed to be atypical, since it shows more vascular dilation and less tortuosity compared to most cases with plus disease.⁸ 

The Early Treatment for ROP Cooperative Group suggested that the presence of Type 1 ROP should warrant treatment.⁷ One of the conditions that defines Type 1 ROP is the presence of any stage of ROP in zone I (the area within a circle centered on the optic nerve head [ONH] with a radius of two times the distance from the ONH center to the fovea) accompanied by plus disease. The presence of plus disease now is considered to be the main indicator for the need for early treatment. Even though the staging and zone of ROP still are important markers of severity of diagnosis, plus diagnosis almost always is present in acute ROP requiring treatment.^8–11 

The current clinical method for diagnosis of plus disease is subjective. As shown by Chiang et al.,⁹ among 22 recognized ROP experts who performed diagnosis of plus disease on 34 images of preterm infants based on a three-level classification scheme (plus, preplus, and neither), the experts agreed on the diagnosis of only 12% of the images (four of 34). Using a two-level classification scheme (plus and no-plus), the experts agreed on the diagnosis of 21% of the images (seven of 34). It is likely that no optimal visual reference standard exists for the diagnosis of plus disease, as shown by disagreement even among recognized experts.^9,11,16 Such studies show the need for computer-aided methods to quantify the changes in retinal blood vessels in the presence of plus disease. 

Various semiautomated computer-aided programs have been designed to diagnose plus disease by quantification of the changes in the thickness and tortuosity of the blood vessels.^{10,11,15,17,18} Even though a direct relationship appears to exist between increasing venule thickness and increasing severity of ROP, the detection of small changes in venule thickness requires high-resolution imaging, as these changes are at or below the spatial resolution of typical retinal imaging systems.¹⁵ Arteriolar tortuosity has shown higher correlation with the presence of plus disease in some studies, but such a correlation has not been consistent across all trials.^8,18,19 Moreover, the detection of arterioles presents an image processing challenge; arterioles have lower contrast compared to venules and their thickness can be below the resolution limit of even high-resolution retinal fundus images of premature infants.²⁰ It also has been observed that the distinction between arterioles and venules becomes difficult in the presence of zone I disease.²¹ Approximately 20% of the time, even experts cannot distinguish between arterioles and venules in retinal images of preterm infants.²² Such factors and limitations indicate a need for quantification of other diagnostic factors, such as changes in the architecture of the major temporal arcade (MTA), including changes in its angle of insertion.^{1,2,15,23–25} 

A change in the openness of the MTA has been observed as a sequela of ROP, as well as an indicator of compromised structural integrity of the macular region.^1,2,23 The angle of insertion of the MTA has been loosely defined as the angle between the superior and inferior temporal arcades (STA and ITA) as they diverge from the ONH and extend toward the periphery of the retina.^23,24 Despite the clinical importance of abnormal changes in the architecture of the MTA, the angle of insertion or the openness of the MTA has been quantified in only three studies dealing with ROP^24–26 and one study dealing with plus disease.²⁷ 

As shown in our previous studies,^26–28 parabolic modeling of the MTA can be useful in analyzing changes to the openness of the MTA for the diagnosis of proliferative diabetic retinopathy (PDR),²⁸ plus disease,²⁷ and ROP.²⁶ The aim of the present study is to test further the hypothesis that plus disease affects the architecture of the MTA and reduces the angle of insertion or the openness of the MTA, via parabolic modeling of the MTA as well as by measuring the temporal arcade angle (TAA), using the method of Wong et al.²⁵ for comparative analysis. 

Materials and Methods

Database of Fundus Images of the Retina

The proposed methods were tested with retinal fundus images from the Telemedicine for ROP In Calgary (TROPIC) database (Hildebrand PL, et al. IOVS 2009;50:ARVO Abstract 3151). Written consent was obtained from the parents of the subjects to capture and use the images in the TROPIC database. The tenets of the Declaration of Helsinki were followed during the conduction of the proposed study. The images of the TROPIC database were captured using the RetCam 130 camera (wide-field [130°]; Clarity Medical Systems, Pleasanton, CA, USA) and have a size of 640 × 480 pixels. The spatial resolution of the RetCam 130 images is estimated to be 30 μm per pixel.²⁹ In total, 110 images from 41 patients (16 females, 25 males) were selected from the database for the present study. Sample size calculation was not performed for the TROPIC database, because it is a collection of information and generally any information drawn from the database indicates descriptive statistics. In the present study, the total number of cases selected for each stage of ROP (30) was kept close to the total number of available plus cases (19). In most cases, five different images were available for each eye of each patient from each visit, representing different retinal fields to provide collectively a full photographic documentation of the retina. In each case, the image with the highest quality and highest visibility of the MTA was chosen. Patients corresponding to 90 of the 110 images were diagnosed with no ROP or with stages 1 or 2 ROP (30 images per category), and patients corresponding to 20 images were diagnosed with stage 3 ROP. Of the 110 selected images 19 were from patients diagnosed with plus disease (stages 2 and 3 of ROP) and 91 showed no signs of plus disease. At most, two images from the same patient were included for the same stage of ROP (one image from each eye). Images of the same eye from the same patient were included only if the ROP stages were different at the time of imaging, as diagnosed by an expert retinal specialist (ALE). Table 1 provides the mean and SD of the birth weight (BW), gestational age (GA), and chronological age (CA) of the patients. 

Table 1

 

The Mean and SD of BW, GA, and CA, in Grams (g), Weeks, and Days, Respectively, for Normal Patients and Patients Diagnosed With Plus Disease

Parameter	Normal, Mean ± SD, = 91	Plus, Mean ± SD, = 19
BW, g	818.00 ± 210.78	815.89 ± 203.71
GA, wk	26.73 ± 1.88	24.95 ± 1.77
CA, d	71.05 ± 23.67	69.84 ± 13.00

Procedure for Measurement of the Arcade Angle

The present work uses the principal concepts of the method of Wong et al.²⁵ for the measurement of the TAA via a graphical user interface (GUI)²⁸ for comparative analysis. The semiautomated procedure for the measurement of the TAA starts by prompting the user to mark the center of the ONH, after which a circle with a radius that is specified by the user is drawn on the image.²⁸ The procedure then prompts the user to mark the point of intersection of the circle with the superior venule; the same is repeated for the inferior venule. The TAA is measured as the angle between the three manually marked points, where the center of the ONH is the vertex of the angle.²⁸ In the present work, circles of radii r = 60 and 120 pixels were used to measure the TAA. The values for the radii were selected based on values provided in the study of Wong et al.²⁵ 

Detection and Modeling of the MTA

In the present work, image processing filters that are sensitive to oriented patterns (Gabor filters) were used for the detection of the MTA.³⁰ An image processing algorithm for the detection of parabolic forms (the generalized Hough transform [GHT]) was used with the result of the filtering step to perform single- and dual-parabolic modeling of the MTA, STA, and ITA.³¹ The proposed methods were implemented via the GUI, which facilitated user input for selection of the required parameters for the detection and modeling of the MTA.²⁸ 

The grayscale magnitude response output image of the Gabor filters was binarized using a sliding threshold via the GUI and then the binarized image was skeletonized to obtain the center lines of the vessels. For each image, a suitable threshold was selected to obtain a binary image containing only the MTA. The user can specify the maximum number of connected pixels to be removed to eliminate small vessel segments that may remain after the thresholding step. 

The user was required to indicate if the current image was an image of the left or right eye for the GHT modeling procedure. The user then was prompted to mark the approximate location of the ONH in a separate window. Given the average width of the ONH (ONHW) of approximately 1.05 mm in preterm infants²⁹ and the spatial resolution of the RetCam images, the vessel skeleton map used to derive the GHT modeling procedure was horizontally restricted from 0.25 × ONHW nasal to 2 × ONHW temporal to the ONH center to enable the modeling procedure to fit a parabola to the MTA close to the posterior pole. 

Evaluation of the Diagnostic Performance

The P value, indicating the statistical significance of the differences between the values of the openness parameters of the parabolic models (a_MTA, a_STA, and a_ITA), as well as the TAA for cases with no plus disease compared to the values of the same for the cases with plus disease were obtained via the t-test function in Matlab software (MathWorks, Natick, MA, USA).^32,33 To assess the diagnostic performance of the parameters derived, receiver operating characteristic (ROC) analysis was performed using the ROCKIT software.³⁴ The values of the area under the ROC curve (A_z), their SE and asymmetric 95% confidence intervals (CI_a) were obtained from ROCKIT. Considering the imbalance between the number of cases in the two categories, 19 no-plus cases were selected randomly for classification against the 19 cases of plus disease and the corresponding A_z value was recorded; this procedure was repeated 50 times to obtain an average A_z value, and the symmetric 95% confidence interval (CI_s) was calculated by assuming a t-distribution for the obtained A_z values and degrees of freedom = 49. 

Results

Figures 1 and 2 show the results of single- and dual-parabolic modeling, as well as the measurement of the TAA using circles of radii r = 60 and 120 pixels for two images from the TROPIC database; one image contains no signs of plus disease (Fig. 1) and the other shows signs of plus disease (Fig. 2). In both cases, the single- and dual-parabolic models are providing accurate fits to the arcade close to the posterior pole (close to the ONH). The TAA obtained using the circle of radius r = 120 pixels is providing a measure close to the macular region, whereas the TAA obtained using the circle of radius r = 60 pixels is providing a measure close to the posterior pole. 

Figure 1

 

(a) Image 1701 of the TROPIC database, which does not show any signs of plus disease. (b) Single-parabolic model with a_MTA = 65. (c) Dual-parabolic model with a_STA = 66 and a_ITA = 42; the ITA portion of the dual-parabolic model is providing a more accurate fit close to the ONH, whereas the MTA model in (b) is providing an average fit to the ITA. The TAA measures using circles of radii (d) r = 120 pixels with TAA = 128.14° and (e) r = 60 pixels with TAA = 141.99°. It can be observed that the TAA obtained using the radius r = 60 pixels is providing an angle measure closer to the ONH compared to the one obtained using the radius of r = 120 pixels.

Figure 2

 

(a) Image 3602 of the TROPIC database, of a patient diagnosed with plus disease. (b) Single-parabolic model with a_MTA = 14. (c) Dual-parabolic model with a_STA = 15 and a_ITA = 18; both models are providing fits close to the posterior pole. Temporal arcade angle measures using circles of radii (d) r = 120 pixels with TAA = 94.38° and (e) r = 60 pixels with TAA = 100.28°.

Table 2 shows the results of statistical analysis of the single- and dual-parabolic model parameters, as well as the TAA measures. The results obtained using 91 cases with no plus disease compared to 19 cases with plus disease indicated highly statistically significant differences (P value < 0.01) for the TAA measures obtained using circles of radii r = 120 and 60 pixels. Table 3 also indicates the number of trials of 50 for which P values indicated statistically significant differences between the plus and no-plus sets of parameters. The area under the ROC curve, A_z, for the TAA with r = 60 pixels and the |a_STA| parameter are ≥0.70, indicating satisfactory performance in classification or diagnosis. By treating the patient attributes of BW, GA, and CA as separate features, the same statistical analysis was performed to analyze the diagnostic power of the attributes. The results indicated that the difference in mean GA of the patients with plus disease compared to normal cases is statistically significant, and also provides a high value of A_z = 0.82 in discrimination between the two classes. 

Table 2

 

Values of the A_z, Their SE, CI_a, and P Values Obtained in the Discrimination of 19 Cases With Plus Versus 91 With No Plus Disease Using the TAA With Radii of r = 60 and 120 Pixels, the Parameters of the Single- (|a_MTA|) and Dual- (|a_STA| and |a_ITA|) Parabolic Models, as Well as the BW, CA, and GA of the Patients

Parameter	(SE)	CIa, = 0.025	Normal, Mean ± SD, = 91	Plus, Mean ± SD, = 19	Value
TAA, r = 60	0.73 (0.066)	[0.589, 0.844]	132.52 ± 14.82	119.70 ± 17.14	0.000**
TAA, r = 120	0.69 (0.064)	[0.560, 0.805]	115.73 ± 14.73	105.14 ± 13.94	0.005**
|aMTA|	0.67 (0.075)	[0.513, 0.801]	43.09 ± 24.75	35.94 ± 38.62	0.280
|aSTA|	0.70 (0.064)	[0.560, 0.808]	51.53 ± 54.06	28.61 ± 14.97	0.094
|aITA|	0.66 (0.073)	[0.511, 0.790]	58.26 ± 55.26	46.83 ± 58.77	0.413
BW, g	0.51 (0.075)	[0.367, 0.654]	818.00 ± 210.78	815.89 ± 203.71	0.968
GA, wk	0.82 (0.055)	[0.690, 0.904]	26.73 ± 1.88	24.95 ± 1.77	0.000**
CA, d	0.50 (0.055)	[0.390, 0.604]	71.05 ± 23.67	69.84 ± 13.00	0.831

 The mean and SD of each parameter for the no-plus and plus disease cases also are provided.

**  P < 0.01.

Table 3

 

Values of the Mean of the A_z, Their SE, and CI_s Obtained in the Discrimination of 19 Cases With Plus Disease Against 19 Randomly Selected No-Plus Cases, Repeated 50 Times

Parameter	Mean (SE)	CIs, α = 0.025	Statistical Significance
TAA, r = 60	0.74 (0.0076)	[0.721, 0.752]	18**, 19*
TAA, r = 120	0.69 (0.0101)	[0.672, 0.712]	12**, 15*
|aMTA|	0.70 (0.0102)	[0.683, 0.724]	0**, 0*
|aSTA|	0.71 (0.0100)	[0.687, 0.727]	4**, 15*
|aITA|	0.67 (0.0086)	[0.651, 0.685]	0**, 0*

 The confidence intervals were obtained by assuming a t-distribution for the A_z values.

**  Of the 50 trials, the results indicated statistically highly significant differences in the number of trials indicated, with P ≤ 0.01.

*  The differences were statistically significant in the number of trials indicated, with 0.01 < P ≤ 0.05.

As mentioned previously, considering the fact that the numbers of available cases for the two categories are not similar, varying sets of 19 cases with no plus disease were selected randomly and the statistical analysis was repeated with equal numbers of cases from the two categories; this was repeated 50 times to obtain the average A_z, SE, and CI_s values. Table 3 presents the results of this analysis. The A_z values indicate satisfactory performance of the TAA (r = 60) and a_STA measures. 

Table 4 shows the Pearson correlation coefficients, indicating the relationship between the five image-based features and the three patient attributes. The levels of statistical significance of the correlation coefficients also are provided. The results indicated that there is little to no correlation³⁵ between the image-based openness measures and the patient attributes of BW, GA, and CA. Only the correlation measure between TAA with r = 60 and GA was statistically significant using the t-test. 

Table 4

 

Pearson Correlation Coefficients of the Image-Based Diagnostic Features and the Patients' Attributes

Parameter		BW	GA	CA
TAA, r = 60	Pearson correlation coefficient	0.130	0.198	−0.055
	Statistical significance	0.176	0.038*	0.568
TAA, r = 120	Pearson correlation coefficient	0.149	0.180	−0.111
	Statistical significance	0.121	0.059	0.248
|aMTA|	Pearson correlation coefficient	−0.090	−0.006	−0.007
	Statistical significance	0.351	0.951	0.942
|aSTA|	Pearson correlation coefficient	−0.009	0.017	0.138
	Statistical significance	0.927	0.856	0.151
|aITA|	Pearson correlation coefficient	−0.045	0.013	0.016
	Statistical significance	0.641	0.891	0.867

*  A significance value < 0.05 indicates a statistically significant correlation. In all cases n = 110.

Bivariate correlation analysis of the image-based features, shown in Table 5, indicated that all feature pairs except one have a fair-to-excellent level of relationship.³⁵ The feature pair of |a_STA|/|a_ITA| showed little to no correlation, whereas the TAA₆₀/TAA₁₂₀ pair showed an excellent correlation.³⁵ All other feature pairs showed either a fair or a moderate level of correlation.³⁵ In all instances, with the exception of the |a_STA|/|a_ITA| pair, correlation coefficients were statistically highly significant. 

Table 5

 

Pearson Cross-Correlation Coefficients of the Image-Based Diagnostic Features

Parameter		TAA, = 60	TAA, = 120	|aMTA|	|aSTA|
TAA, r = 120	Pearson correlation coefficient	0.860
	Statistical significance	0.000**
|aMTA|	Pearson correlation coefficient	0.383	0.558
	Statistical significance	0.000**	0.000**
|aSTA|	Pearson correlation coefficient	0.461	0.545	0.326
	Statistical significance	0.000**	0.000**	0.001**
|aITA|	Pearson correlation coefficient	0.375	0.546	0.536	0.101
	Statistical significance	0.000**	0.000**	0.000**	0.293

 In all cases n = 110.

**  Significance values of <0.01 indicate highly significant correlations.

Analysis of the openness measures related to images from the same eye of the same patient that progressed to plus disease, and in some instances to a higher stage of ROP, on average over six patients and eight imaging instances, showed decreases of 6.5, 4.3, 8.4, 4.4°, and 5.3° in the |a_MTA|, |a_STA|, |a_ITA|, TAA₆₀, and TAA₁₂₀ parameters, respectively. 

Discussion and Conclusions

To our knowledge, this is the first study to quantify the effects of plus disease on the openness of the MTA, STA, and ITA, using semiautomated methods to perform single- and dual-parabolic modeling, as well as measurement of the TAA for comparative analysis. In the present study, the diagnostic performance (in terms of A_z as shown in Tables 2, 3) of the parameters of the single- and dual-parabolic models is comparable to that provided by the TAA measures obtained based on the method of Wong et al.²⁵ via the GUI. However, the TAA measures provide better statistical performance compared to the parameters of the parabolic models. All of the studied measures showed a similar trend: There was a decrease in the openness of the MTA in the presence of plus disease. The decreasing trend in the openness of the MTA also was observed over time in patients who progressed to plus disease and/or higher stages of ROP. Although the A_z values obtained for the TAA measures and the parameters of the parabolic models were not high, the results are encouraging. 

Several theories explain the underlying mechanisms that cause morphologic vascular changes in the presence of plus disease. It was first theorized that such changes occur as a result of a reduction in capillary resistance,³⁶ the fact the venules are more distensible than arterioles,³⁷ and an increase in the blood flow in the presence of plus disease.³⁸ The increase in the blood flow is thought to be caused by an increase in the angiogenic stimulus, that leads to a larger arteriovenous shunt.³⁸ However, it has been shown that not only does the blood flow not increase in the presence of plus disease,³⁹ it actually could decrease in the central retinal artery of infants with plus disease.⁴⁰ Another theory relates the changes in the blood vessels to an increase in VEGF in the presence of plus disease.^41–43 Prematurity and supplemental oxygen are factors in the suppression of vessel growth in premature infants.⁴³ Lack of a complete retinal vasculature causes an increase in VEGF, which, in turn, causes neovascular proliferation of blood vessels that ultimately leads to tractional retinal detachment and blindness.⁴³ It has been postulated that an increase in VEGF could be associated with changes in pericytes and smooth muscle cells, which lead to a decreased ability to regulate blood flow, and as a result, to susceptibility to fluctuations in oxygen levels in the vascular bed.⁴⁴ An increase in VEGF also is cited as a probable cause for neovascularization and proliferation of vessels in PDR, which consequently could lead to tractional retinal detachment.^45,46 As shown in our previous study,²⁸ the openness of the MTA also decreases in the presence of PDR. It is possible that the same pathological mechanisms, such as an increase in VEGF and neovascular proliferation of blood vessels, in PDR and plus disease, cause the straightening or narrowing of the MTA. Regardless of the cause, the present study showed that plus disease, similar to PDR, has an effect on the architecture of the MTA; to our knowledge, such an effect has not been quantified or analyzed previously. 

Ells and MacKeen⁴⁷ illustrated that the changes that occur in the MTA may be dynamic as they alter the posterior architecture of the MTA over time. Based on this observation, we believe that the TAA measures proposed by Wilson et al.²⁴ and Wong et al.²⁵ may not accurately reflect such changes that occur over the entire posterior architecture of the MTA, as the TAA measures define the openness of the MTA based on only three points on the arcades. Furthermore, the TAA is sensitive to the exact position of the center of the ONH. The parabolic modeling procedure is dependent only on an approximate location of the ONH instead of the specific location of the center of the ONH.³¹ 

Based on the results provided in Table 2, the patient attributes of BW and CA do not show any statistically significant differences in the mean of the normal cases compared to the plus cases, whereas the difference in the mean GA of the two classes is statistically highly significant. The GA showed a high power of discrimination between normal and plus cases with A_z = 0.82. These two results could indicate that plus disease may not be a developmental process and may be more probable in less developed retinas, that is, the lower the GA, the higher the probability of occurrence of plus disease. There appears to be no correlation between the values of the image-based openness measures and patient attributes. 

The radius of the circle used for the measurement of the TAA in the work of Wong et al.²⁵ is not clearly defined or justified. This parameter must be formally related to a physiological measure, such as the average ONHW. 

If the angle of the retinal raphe (the line going through the center of the ONH and the fovea) is large with respect to the horizontal axis of the image, it could lead to a much larger openness parameter for one of the dual-parabolic models than the other. The retinal raphe angle may be corrected either manually or by using methods to detect the center of the ONH and the fovea. However, as shown by Chiang et al.,⁴⁸ retinal fundus images of preterm infants typically lack a clear depiction of the fovea. The two parameters of the dual-parabolic models may be combined using pattern classification techniques to incorporate the independent information from the STA and ITA models into classification methods. It also is possible to estimate the retinal raphe as the principal axis⁴⁹ of the skeleton of the MTA and correct for the rotation that might exist in the image. 

The large variations that could exist in the openness parameter of the parabolic models, as explained in the previous paragraph, could be the reason for the large SD values observed, which also could be the reason for obtaining large P values for the results of parabolic modeling as shown in Table 2. 

Upon close inspection, it becomes clear that, first, the STA and ITA are asymmetric, and second, more accurate modeling of each arcade may be possible by applying models based on higher-order curves compared to using second-order parabolic curves. A high-order curve fitting method may provide more accurate results in terms of modeling and parameterization of the MTA. We are designing additional methods for modeling and parameterization of the divergence of the MTA and the angle information provided by the Gabor filters used to detect the retinal blood vessels. 

It has been observed that changes in the tortuosity and thickness of the vessels that occur in the presence of plus disease are dynamic and analysis of such changes from one visit to another could lead to improved diagnosis and analysis of plus disease.¹⁸ Indeed, a decrease in the openness of the MTA was observed in this study in images of the same eyes of the same patients who progressed to plus disease. Further longitudinal analysis of this observation with more cases would be of interest. 

Given that the results of the TAA with r = 60 pixels provided the best discriminatory performance in the present study and that this angle was measured closer to the ONH compared to the parabolic modeling procedure, it could be beneficial to restrict the GHT modeling procedure to fit a parabolic model closer to the ONH; that is, more posteriorly than in the proposed method. 

Many of the previously conducted studies on diagnosis of plus disease have used relatively small databases of images, including even smaller numbers of cases with plus disease^9–11,17,50 than the present study. The number of cases (with and without plus disease) used in the present study, although limited, was larger in comparison to the cited studies. Inclusion of more cases with plus disease will help to strengthen the statistical analysis. 

The methods used in the present study were semiautomated as in other published studies with a similar application.⁸ The parameters of the methods used for the detection and modeling of the MTA will need to be set automatically or derived adaptively based on the characteristics of each individual image. 

Quantification of changes in the MTA in the presence of plus disease could be used along with other quantitative diagnostic features of plus disease, such as thickness and tortuosity measurements of blood vessels, along with pattern classification methods to provide better discrimination for computer-aided diagnosis of plus disease, and ultimately, timely treatment of ROP. 

In this study, we demonstrated, for the first time to our knowledge, that the openness of the MTA decreases in the presence of plus disease. Future research will include combining measures of tortuosity and thickness of the blood vessels with the openness of the MTA, which may yield better results in the diagnosis of plus disease. 

Acknowledgments

The authors thank April Ingram for help with the TROPIC images and Tak Fung, PhD, for help with statistical analysis. 

A preliminary and shorter version of this work was presented at the International Association of Science and Technology for Development (IASTED) conference on Signal and Image Processing, Banff, Alberta, Canada, July 18–19, 2013. 

Supported by the Natural Sciences and Engineering Research Council of Canada. 

Disclosure: F. Oloumi, None; R.M. Rangayyan, None; A.L. Ells, None