October 2012
Volume 53, Issue 11
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Glaucoma  |   October 2012
In Vivo Analysis of Vectors Involved in Pupil Constriction in Chinese Subjects with Angle Closure
Author Affiliations & Notes
  • Ce Zheng
    From the Singapore Eye Research Institute at the Singapore National Eye Centre, Singapore, Republic of Singapore; the
  • Carol Y. Cheung
    From the Singapore Eye Research Institute at the Singapore National Eye Centre, Singapore, Republic of Singapore; the
  • Tin Aung
    From the Singapore Eye Research Institute at the Singapore National Eye Centre, Singapore, Republic of Singapore; the
    Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore, Republic of Singapore; the
  • Arun Narayanaswamy
    From the Singapore Eye Research Institute at the Singapore National Eye Centre, Singapore, Republic of Singapore; the
  • Sim-Heng Ong
    Department of Electrical & Computer Engineering, National University of Singapore, Singapore, Republic of Singapore; the
  • David S. Friedman
    Wilmer Eye Institute, Dana Center for Preventive Ophthalmology and Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland; and the
  • John C. Allen
    Duke-NUS Graduate Medical School, Singapore, Republic of Singapore.
  • Mani Baskaran
    From the Singapore Eye Research Institute at the Singapore National Eye Centre, Singapore, Republic of Singapore; the
  • Paul T. Chew
    Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore, Republic of Singapore; the
  • Shamira A. Perera
    From the Singapore Eye Research Institute at the Singapore National Eye Centre, Singapore, Republic of Singapore; the
  • Corresponding author: Tin Aung, Singapore National Eye Centre, 11 Third Hospital Avenue, Singapore 168751; tin11@pacific.net.sg
Investigative Ophthalmology & Visual Science October 2012, Vol.53, 6756-6762. doi:10.1167/iovs.12-10415
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      Ce Zheng, Carol Y. Cheung, Tin Aung, Arun Narayanaswamy, Sim-Heng Ong, David S. Friedman, John C. Allen, Mani Baskaran, Paul T. Chew, Shamira A. Perera; In Vivo Analysis of Vectors Involved in Pupil Constriction in Chinese Subjects with Angle Closure. Invest. Ophthalmol. Vis. Sci. 2012;53(11):6756-6762. doi: 10.1167/iovs.12-10415.

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Abstract

Purpose.: To evaluate the acceleration of pupil constriction (APC) in response to illumination using video anterior segment optical coherence tomography (AS-OCT) in angle closure and normal eyes.

Methods.: This was an observational study of 342 Chinese subjects. Iris and angle changes in response to illumination were captured with real-time video recordings of AS-OCT and analyzed frame by frame. APC was calculated using a quadratic function, fitting pupil diameter to a time series. APC was divided into two vector components: acceleration of pupil block (APB) acting perpendicular to the lens surface and acceleration of iris stretch (AIS) acting toward the iris root.

Results.: Of 342 eligible patients, 306 (89.5%) were available for analysis; of whom 136 (41.7%) had angle closure. After adjusting for age, sex, baseline pupil diameter, and iris thickness, APC was significantly lower in angle closure eyes (0.61 mm/s2) than in open-angle eyes (0.90 mm/s2) (P < 0.0001) as was AIS (0.58 mm/s2 vs. 0.89 mm/s2) (P < 0.001). APB was significantly higher in angle closure eyes compared to open-angle eyes (0.14 mm/s2 vs. 0.09 mm/s2) (P < 0.001). After adjusting for age and sex in logistic regression, the magnitude and direction of all vector parameters were significantly associated with presence of angle closure.

Conclusions.: Angle closure eyes have smaller AIS and larger APB in response to illumination as measured using AS-OCT videography. This shows that, comparatively, the iris of angle closure eyes stretches less and develops a more convex configuration in response to illumination.

Introduction
The major mechanism implicated in primary angle closure glaucoma (PACG) is pupil block, which is characterized by increased resistance to aqueous flow from the posterior to the anterior chamber at the level of the lens–iris interface. 1 The etiology of pupil block is poorly understood. Lowe first suggested that pupil block is the consequence of excessive contact between the iris and the anterior lens surface. 2 In 1968, using vector force analysis, Mapstone theorized that pupillary block results from the iris sphincter pulling the iris toward the lens, overcoming resistance of the dilator, and creating a “pupil blocking force.” 1 Huang and Barocas concurred, having used steady-state computer simulations to model the mechanical interaction between the aqueous humor and the iris. 3 However, in vivo measurement of iris muscle vector magnitude and direction is difficult, if not impossible, to obtain with traditional methods. 
Anterior segment optical coherence tomography (AS-OCT) enables quantitative evaluation of dark–light dynamic changes of the anterior chamber configuration. 4 Our recent study, based on the modification of AS-OCT videography, identified a novel association of slower speed of pupil constriction (SPC) with angle closure. Analogous to force, the rate of change in velocity (acceleration) is also a vector. The acceleration of a body is parallel and directly proportional to the net force and inversely proportional to the mass. Hence, vectorial analysis would help us understand the pathophysiological contributors to pupillary block. 
Recently, Aptel and Denis found a loss of iris volume on static AS-OCT images in response to pharmacological dilation in eyes with open angles, whilst the fellow eyes of acute primary angle closure (APAC) patients showed a volume increase. 5 This suggests the importance of iris volume change as a risk factor for PACG (albeit in a supra physiologically induced state), with APAC eyes possibly at one end of a spectrum of iris sponginess. Extracellular fluid transfer, vascular tonus change, or both, may underlie these observations. This theory can also be investigated with vectorial analysis. 
In this study, we describe a method to measure average vector acceleration of pupil contraction (APC) in response to dark–light changes using AS-OCT and to evaluate their association with angle closure. The method described herein is the first to allow an in vivo measurement of dynamic iris vectors. 
Methods
Study Subjects
Chinese subjects above the age of 40 years were prospectively recruited from outpatient clinics of the Singapore National Eye Centre (SNEC). The study conduct adhered to the tenets of Declaration of Helsinki, and the hospital's institutional review board approved the study. Written informed consent was obtained from all subjects. Enrolled subjects belonged to one of three groups: 
  1.  
    Group 1: Primary angle closure (PAC) and PACG. PAC was defined as eyes in which the posterior trabecular meshwork was not visible for at least 180° on nonindentation gonioscopy (narrow angles) with peripheral anterior synechiae (PAS) and/or raised intraocular pressure (IOP) (defined as an IOP greater than 21 mm Hg) but without glaucomatous optic neuropathy (GON). PAS were defined as abnormal adhesions of the iris to the angle that were at least half a clock hour in width and were present to the level of the anterior trabecular meshwork or higher. PACG eyes had narrow angles with GON (defined as vertical cup-to-disc ratio [CDR] ≥0.7, CDR asymmetry >0.2 and/or focal notching) with compatible visual field loss on static automated perimetry using the Swedish Interactive Test Algorithm (SITA) standard algorithm with a 24-2 test pattern on a visual field analyzer (Humphrey Field Analyzer II; Carl Zeiss Meditec, Dublin, CA) with Glaucoma Hemifield Test outside normal limits and an abnormal pattern standard deviation with P < 5% occurring in the normal population and fulfilling the test reliability criteria (fixation losses <20%, false positives <33%, and/or false negatives <33%).
  2.  
    Group 2: Fellow eyes of previous APAC. The following criteria were used to define cases of APAC: ocular or periocular pain, nausea or vomiting or both, and an antecedent history of intermittent blurring of vision; a presenting IOP of >28 mm Hg on Goldmann applanation tonometry; and the presence of at least three of the following signs: conjunctival injection, corneal epithelial edema, middilated nonreactive pupil, and shallow anterior chamber. 6
  3.  
    Group 3: Control subjects (defined by having intraocular pressure ≤21 mm Hg with open angles, healthy optic nerves, normal visual fields, no previous surgery, and no family history of glaucoma) were recruited from an ongoing population-based study of Chinese persons aged 40 years and older (the Singapore Chinese Eye Study).
All angle closure subjects had previously undergone laser peripheral iridotomy (LPI) at least 2 to 3 months before the study visit and were not on any topical pilocarpine or systemic miotics. Subjects with a prior history of intraocular surgery, iridoplasty, laser trabeculoplasty, or evidence of secondary glaucoma were excluded. Eyes with posterior synechiae, extensive peripheral anterior synechiae (>180 degrees), and gross iris atrophy were also excluded. One eye of each eligible subject was considered for the study. If both eyes were eligible (Groups 1 and 3), one randomly selected eye was included for analysis. 
For a different analysis, we also prospectively recruited 29 newly diagnosed subjects above the age of 40 years diagnosed to have PAC or PACG before LPI. The pupil dynamics before and after LPI were compared. 
All subjects were questioned about their medical and ophthalmic history and underwent a standardized ophthalmic examination including fundus examination, gonioscopy with a hand held gonioscope (Ocular Sussman Four Mirror; Ocular Instruments, Bellevue, WA) and optical biometer assessment (IOLMaster; Carl Zeiss Meditec). 
Anterior Segment Optical Coherence Tomography Videography
AS-OCT imaging was performed with an interior segment imaging system (Visante OCT, Model 1000, software version 2.1; Carl Zeiss Meditec). The details of video recording with AS-OCT imaging have been described previously. 4 In brief, OCT imaging was performed with the protocol anterior segment single 0° to 180°. The scan line was manually adjusted to bisect the pupil. The scan acquisition time was 0.125 seconds per line for the Anterior Segment Single scan (limbal to limbal), that is, eight frames were imaged per second. Video-recording software (Camtasia 6.0; TechSmith Corporation, Okemos, MI) was installed on the Visante computer to capture the response to illumination. A single masked observer (CZ) performed all AS-OCT testing. 
The recording of AS-OCT video was started one minute after dark adaption using a standard protocol; the light intensity was approximately 20 lux measured by an exposure meter (Studio Deluxe II L-398; Sekonic, Tokyo, Japan). A torch light illuminated the fellow eye from the temporal side 15° off axis (approximately 1700 lux). The iris and anterior chamber changes from dark to light were recorded. If saccadic eye movements were observed during video capture, the process was repeated but not more than three times to prevent iris muscle fatigue. Each video file was exported as a frame sequence using video editing software (VirtualDub 1.8.5; GNU General Public License). As the proprietary Visante software cannot correct refractive image distortion from screen captures, we wrote a program using mathematical computing software (MATLAB Version 7.0; MathWorks, Natick, MA) to dewarp the image frames from video files and correct image misalignment. 7,8 The accuracy for this program was performed on a performance verification tool (Verification Test Tool; Carl Zeiss Meditec) with anterior segment single protocol. Eighteen cross-sectional images from 360° anterior segment scan were taken at 18 meridians with 10° interval. The accuracy of program correction (dewarp) was excellent for both horizontal and vertical measurement (pupil diameter [PD] and anterior chamber depth [ACD], respectively) with the interclass correlation coefficient (0.99 and 0.98, respectively). 
Measurements AS-OCT Biometric Parameters
Customized software (Anterior Segment Analysis Program [ASAP]) was used in this study to measure AS-OCT biometric parameters. ASAP is a plug-in for image processing software (ImageJ version 1.38x; public domain software, http://imagej.nih.gov/ij/). 9 After a single observer marked the scleral spurs as reference points, ASAP automatically calculated the baseline pupil diameter (measured in the dark), iris thickness (measured at the midpoint between the scleral spur and the pupillary margin), ACD, anterior chamber width (ACW) (scleral spur-to-scleral spur distance), angle opening distance (AOD) at 500 μm, and trabecular-iris space area (TISA) at 500 μm anterior to the scleral spur (Fig. 1). The average of both temporal and nasal measurements for iris thickness was used for the analysis. The reproducibility of this program was reported previously. 10 In brief, AS-OCT measurements were performed in two sessions separated by an interval of one week using the ASAP software in 30 normal subjects. The reproducibility of the AS-OCT measurements was excellent with the intraclass correlation coefficient ranging from 0.89 to 0.97. 
Figure 1. 
 
AS-OCT image showing the automatic measurement of ACD, ACW, PD, and iris thickness.
Figure 1. 
 
AS-OCT image showing the automatic measurement of ACD, ACW, PD, and iris thickness.
Measurements of Magnitude and Direction of Vector Acceleration of Iris Constriction
AS-OCT videography analysis has been described previously by our group. 10 In brief, the frame by frame series in each eye was reviewed by a single examiner (CZ), and images showing changes in pupil diameter compared with the preceding images were selected for iris and angle measurements. A customized algorithm was used to delete the frames with small hippus before and after pupil constriction. 11 The start frame was defined as the fully dilated pupil in the dark, and the end frame was defined as the fully constricted pupil in the light. 
We then measured the vector APC based on pupil diameter to a time series from the onset to the end of pupil contraction (Fig. 2). As changes in the pupil diameter time series are nonlinear, standard second-order polynomials (or quadratic functions) can be fitted to the data (see equation [1]) where YPD is the pupil diameter, x represents time, and A, B, and C are constants. The average acceleration or deceleration in the nonlinear function is equivalent to 2 A (mm/s2). The square of the correlation coefficient (R2) provides an indication of how a trend line accounts for the variation in a data field. Since acceleration is a vector quantity, we further deconstructed the APC following Mapstone's vector force analysis (equation 1). The fraction of acceleration of iris stretch (AIS) reduces the speed of pupil contraction by acting toward iris root. The fraction of acceleration of pupil block (APB) acts perpendicular to the lens surface and forms corresponding angle α and β (equations 1 and 3) with APB and AIS, respectively (Fig. 3). The mean angle α and β (calculated as [angle at dark + angle at light]/2) was used to calculate APB and AIS based on the following trigonometric equations (see equations 2 and 3).    
Figure 2. 
 
PD to a time series. The fitted trend line is a second-order polynomial function that is denoted on the chart along with the square of the correlation coefficient (R 2).
Figure 2. 
 
PD to a time series. The fitted trend line is a second-order polynomial function that is denoted on the chart along with the square of the correlation coefficient (R 2).
Figure 3. 
 
Vector acceleration analysis. APC acts opposite to the pupil constriction, and AIS acts toward the iris root. APB acts perpendicular to the lens surface, forming angles α and β with AIS and direction of pupil constriction.
Figure 3. 
 
Vector acceleration analysis. APC acts opposite to the pupil constriction, and AIS acts toward the iris root. APB acts perpendicular to the lens surface, forming angles α and β with AIS and direction of pupil constriction.
Statistical Analysis
Standard second-order polynomial fitting was performed using spreadsheet software (Excel 2003; Microsoft, Redmond, WA). Statistical analysis was performed using statistical analysis software (SPSS Statistics Version 17.0; IBM, Armonk, NY). Differences in mean values of parametric data among eyes of different subjects were examined using the independent samples Student's t-test. For ordinal data, the Mann-Whitney U test was used to compare medians of independent samples. Because anterior segment biometric parameters are well known to be associated with age and sex, the association of the vector parameters (both magnitude and direction) with the presence of angle closure was evaluated using logistic regression models to determine the odds ratio (OR) and 95% confidence interval (CI) after adjusting for age and sex. The multivariate adjusted OR and 95% CI were obtained after adjustment for age, sex, ACD, ACW, and baseline pupil diameter. 
Results
Out of 342 recruited subjects, we excluded 36 subjects due to the following reasons: posterior synechiae (n = 3), poor quality of the AS-OCT video images (n = 19), and excessive eye movements during video capture (n = 14), leaving 306 participants (89.5%) for the final analysis. This comprised 136 subjects with angle closure (96 PAC/PACG and 40 fellow eyes of APAC) and 170 normal control subjects (Table 1). All subjects were Chinese, and the mean age (± SD) was 60.9 ± 7.8 years. Compared to angle closure subjects (Group 1 and Group 2), open-angle subjects (Group 3) were younger, had longer AL and ACW, and had deeper ACD (all with P < 0.01). As expected, open-angle eyes also had larger anterior chamber angle (AOD500 and TISA500, all with P < 0.01, data not shown) than closed-angle eyes. The mean gonioscopic grading (Shaffer) for each group (1, 2, and 3) was 1.60 (1.05), 1.91 (1.00), and 3.48 (0.71), respectively, and no difference was found between two closed-angles groups. 
Table 1. 
 
Comparison of Demographic and Clinical Data and AS-OCT Measurements between Open- and Closed-Angle Groups
Table 1. 
 
Comparison of Demographic and Clinical Data and AS-OCT Measurements between Open- and Closed-Angle Groups
Open-Angle, n = 170 Closed-Angle, n = 136 P Value*
Mean 95% CI (Lower) 95% CI (Upper) Mean 95% CI (Lower) 95% CI (Upper)
Age, y 58.67 57.43 59.75 63.41 62.05 64.80 < 0.001
Sex, male/female 68/102 50/86 0.563†
Axial length, mm 24.37 24.14 24.62 22.94 22.78 23.10 < 0.001
Anterior chamber depth, mm 2.65 2.60 2.71 2.08 2.03 2.12 < 0.001
Dark-room gonioscopy, Shaffer 3.48 3.36 3.59 1.69 1.50 1.86 < 0.001‡
Vertical cup-to-disc ratio 0.41 0.39 0.43 0.52 0.49 0.56 < 0.001
Visual field MD, dB −1.21 −1.51 −0.91 −3.56 −4.23 −2.96 < 0.001
Visual field PSD, dB 2.15 1.98 2.36 3.00 2.53 3.51 0.001
AS-OCT measurement
 Iris speed, mm/s 1.56 1.44 1.69 1.22 1.13 1.31 < 0.001§
 Anterior chamber width, mm 11.52 11.47 11.57 11.30 11.24 11.37 < 0.001
 Len's vault, dark, mm 0.39 0.35 0.44 0.89 0.84 0.93 < 0.001
 Pupil diameter, dark, mm 4.14 4.02 4.24 3.89 3.76 4.01 0.005
 Iris thickness, dark, mm 0.45 0.44 0.46 0.45 0.44 0.46 0.904‖
 Iris concavity, dark, mm 0.15 0.14 0.16 0.20 0.19 0.22 < 0.001‖
Anterior chamber angle
 AOD500, dark, mm 0.23 0.20 0.25 0.13 0.11 0.15 < 0.001‖
 TISA500, dark, mm2 0.063 0.055 0.072 0.034 0.028 0.041 < 0.001‖
The 95% CI of SPC for for each group (1, 2, and 3) was 1.13 to 1.30 mm/s, 1.03 to 1.29 mm/s, and 1.49 to 1.60 mm/s, respectively. There was no significant difference in SPC between Group 1 and Group 2 (P = 0.502 adjusted for age and ACW, Table 1). We then combined Group 1 and Group 2 as “closed-angle” category and compared those with open angles. 
The R 2 for second-order polynomials was between 0.81 and 0.99 (mean R 2 = 0.93). After adjusting for age, sex, baseline pupil diameter, and iris thickness, the SPC and APC (1.22 mm/s vs. 1.53 mm/s with P < 0.001 and 0.61 mm/s2 vs. 0.90 mm/s2 with P < 0.001, respectively) were significantly slower in the angle closure eyes than in the open-angle eyes (Table 2). The AIS (0.58 mm/s2 vs. 0.89 mm/s2 with P < 0.001) was larger in the open-angle group, while APB (0.14 mm/s2 vs. 0.09 mm/s2 with P < 0.001) was larger in the angle closure eyes. During the dark-light change, both α and β values were lower for angle closure eyes than for the open-angle eyes (all with P < 0.001), a reflection of the different directions of vector acceleration of iris constriction in these eyes. 
Table 2. 
 
Comparison of Vectors Involved in Pupil Constriction between Open- and Closed-Angle Groups
Table 2. 
 
Comparison of Vectors Involved in Pupil Constriction between Open- and Closed-Angle Groups
Closed-Angle, n = 136 Open-Angle, n = 170 Mean Difference P Value*
(Mean, 95% CI) (Mean, 95% CI) (95% CI)
Magnitude
 APC mm/s2 0.61 (0.51–0.70) 0.90 (0.83–0.97) −0.28 (−0.39 to −0.18) < 0.001
 APB mm/s2 0.14 (0.12–0.16) 0.09 (0.07–0.19) 0.05 (0.03–0.08) < 0.001
 AIS mm/s2 0.58 (0.49–0.66) 0.89 (0.82–0.96) −0.31 (−0.42 to −0.20) < 0.001
Direction
α degree 74.37 (73.75–74.94) 77.33 (76.64–77.81) −3.35 (−4.04 to −2.66) < 0.001
β degree 92.49 (91.72–93.28) 97.04 (96.33–97.78) −3.20 (−4.12 to −2.28) < 0.001
Iris speed, mm/s 1.22 (1.15–1.29) 1.53 (1.47–1.59) −0.31 (−0.40 to −0.22) < 0.001
The results of univariate and multivariate analysis are shown in Table 3. After adjusting for age and sex in logistic regression, all of the vector parameters (both magnitude and direction) were associated significantly with angle closure. In addition, ORs were obtained for vector parameters (adjusting for age, sex, ACD, baseline pupil diameter, and ACW [Model B, Table 4]); APC (OR, 2.58; 95% CI, 1.19–5.59; P = 0.017), AIS (OR, 2.58; 95% CI, 1.19–5.59; P = 0.017), angle α (OR, 1.13; 95% CI, 1.01–1.26; P = 0.029), and angle β (OR, 1.14; 95% CI, 1.04–1.26; P = 0.005) were independently associated with angle closure. Although APB was associated with angle closure on univariate analysis, this association disappeared after adjusting for other biometric risk factors (OR, 1.14; 95% CI, 1.04–1.26; P = 0.005), suggesting that, although APB was associated with angle closure, it is likely to be due to the biometric changes occurring in the eye. As both angle α and β showed significant association with angle closure, we further adjusted each other based on Model B. Significance still existed after such adjustment (OR = 1.52 for angle α and OR = 1.38 for angle β, respectively, all with P < 0.001). 
Table 3. 
 
Relationship of Vector Parameters and Angle Closure
Table 3. 
 
Relationship of Vector Parameters and Angle Closure
Variable Model A* Model B
OR (95% CI) P Value OR (95% CI) P Value
Magnitude
 APC mm/s2 4.29 (2.33–7.89) < 0.001 2.58 (1.19–5.59) 0.017
 APB mm/s2 0.013 (0.00–0.167) 0.001 0.35 (0.02–7.17) 0.494
 AIS mm/s2 4.76 (2.53–8.96) < 0.001 2.73 (1.26–5.93) 0.011
Direction
α degree 1.33 (1.21–1.45) < 0.001 1.13 (1.01–1.26) 0.029
β degree 1.25 (1.17–1.34) < 0.001 1.14 (1.04–1.26) 0.005
Table 4. 
 
Comparison of Vector Parameters between Subgroups of Angle Closure versus Normal Controls
Table 4. 
 
Comparison of Vector Parameters between Subgroups of Angle Closure versus Normal Controls
Variable PAC, n = 49 PACG, n = 47 Fellow Eye of APAC, n = 40 Normal, n = 170
Mean (95% CI) P * Mean (95% CI) P * Mean (95% CI) P * Mean (95% CI)
Magnitude
 APC mm/s2 0.65 (0.52–0.79) 0.002 0.65 (0.52–0.78) 0.002 0.54 (0.39–0.68) < 0.000 0.90 (0.83–0.97)
 APB mm/s2 0.13 (0.10–0.16) 0.019 0.12 (0.09–0.15) 0.105 0.15 (0.12–0.19) 0.001 0.09 (0.07–0.11)
 AIS mm/s2 0.63 (0.49–0.77) 0.002 0.59 (0.45–0.73) < 0.000 0.51 (0.36–0.66) < 0.000 0.89 (0.81–0.97)
Direction
α degree 74.01 (73.06–74.97) < 0.000 74.53 (73.56–75.50) < 0.000 73.85 (72.81–74.89) < 0.000 77.51 (77.00–78.02)
β degree 94.22 (93.05–95.39)† 0.001 94.17 (92.99–95.36)† 0.001 90.33 (89.05–91.60) < 0.000 96.58 (95.95–97.21)
Finally, no differences were observed in vector parameters between the three clinical subgroups of angle closure except for angle β, which was significantly smaller in those fellow eyes of APAC, compared with those with PAC (P < 0.001) and PACG (P < 0.001) (Table 4). There was no significant change for all of the vectors parameters before and after LPI (Table 5). 
Table 5. 
 
Comparison of Vector Acceleration of Pupil Constriction before and after LPI
Table 5. 
 
Comparison of Vector Acceleration of Pupil Constriction before and after LPI
Pre-PI Post-PI P *
Magnitude
 APC mm/s2 0.71 ± 0.39 0.63 ± 0.42 0.425
 APB mm/s2 0.69 ± 0.38 0.61 ± 0.41 0.416
 AIS mm/s2 0.14 ± 0.09 0.12 ± 0.08 0.238
Direction
α degree 74.76 ± 4.24 73.66 ± 3.90 0.134
β degree 94.04 ± 4.76 95.60 ± 4.48 0.058
Discussion
To our knowledge, this is the first in vivo study in which the vectors generated by the iris during pupil constriction from illumination have been characterized. As pupil constriction is influenced by several different forces, the quadratic trend line in our study accurately summates the entire dynamics of the system during the change from dark to light. 
The magnitude of the APB, acting perpendicularly to the lens, was significantly larger in angle closure eyes (0.14 mm/s2 vs. 0.009 mm/s2, P < 0.001). This finding supports Mapstone's theory that the net effect of the iris sphincter and dilator is to produce iris tip posterior pressure against the lens to cause relative pupil block. 1 The magnitude of AIS was larger in the open-angle eyes than the angle closure eyes and was shown to be associated with angle closure. Moreover, by removing lens vault (LV) as the major factor that contributes to lens–iris interactions, AIS still showed a significant association with angle closure. This implies that the irides of angle closure eyes may have inherently abnormal biomechanical properties. Quigley et al. 16 hypothesized that it “may be only in irides with the poorest fluid conductivity, i.e., the worst ability to lose fluid with dilation, which acute, symptomatic pressure elevation occurs with iris apposition.” Histological studies suggesting that the iris muscles and stroma of angle closure eyes may be different from open-angle eyes support this finding. 12,13 The evidence that the iris' “sponge-like” characteristics could be a contributing feature in angle closure is mounting. Our data also support the work by Quigley et al. 14 on iris thickness preillumination and postillumination. 
Mapstone's vector force analysis was the first theoretical consideration of pupillary block that incorporated iris muscle and material stretch forces. 1 Using novel image techniques, like ultrasound biomicroscopy (UBM) or AS-OCT, we have been able to show that the iris configuration hypothesized by Mapstone does occur. 1921 As the vector force theory of pupil block cannot be directly tested with biometric measurements made in normal eyes, investigators previously used computer simulations to elucidate the mechanics. Tiedeman's oversimplified model treated the iris as an infinitely thin membrane whose properties do not change. 15 Huang and Barocas proposed computer simulations of interactions between the aqueous and an active iris. 3 In our study, which is a natural progression from theirs, APC and AIS were statistically significantly associated with angle closure even after adjustment for ACW, baseline pupil diameter, LV, and other risk factors. The result was comparable to our previous study for SPC indicating that decreased iris sponge-like behavior is likely to play a role in the development of angle closure and ultimately PACG. Quigley et al. recently reported that changes in iris area and volume in response to illumination differ between open- and closed-angle eyes. 16 This differential dynamic response of the iris may implicate the iris stroma. 
In our study, after adjustment for age and sex, APB exhibited association with angle closure, which supports a pupil block mechanism; however, this association disappeared after adjusting for other factors and, in particular, ACD. In Huang's computer simulations, both α and β values were lower for PACG (α = 73.7, β = 85.7) than for normal eyes (α = 77.7, β = 99.3) in the pupil constricted state. The real-time measurements of angles α and β in our study are similar to those of previous computer simulation models. There seems to be no doubt that the higher fractions of APB from AIS in closed-angle eyes were due to the lower angles of α and β, which is reflective of differences in the other biometric parameters like shallower ACD, smaller ACW, and larger LV. 
LPI may facilitate iris mobility by relieving pupillary block and flattening the iris contour and would, therefore, be expected to increase SPC. Yet, although this occurred, neither magnitude nor direction of vectors was shown to be significantly different before or after LPI in this sample of subjects studied. On the other hand, LPI is not likely to alter the iris “sponginess” factor. 
Standard second-order polynomials were used to fit the pupil diameter to a time series. Excellent R 2 for second-order polynomials was achieved in this study; however a less fitting function could potentially be used. Other functions, like double exponential functions, have been reported to describe the viscoelastic characteristics of living tissue. 18 Further studies are needed to explore viscoelastic characteristics of iris in closed-angle eyes. 
One of the limitations of this study was that it was cross sectional; hence, temporal and causal relationships can be only conjectured. Second, although we excluded eyes on medications such as pilocarpine that can affect pupillary responses, we did not exclude subjects on brimonidine, which is known to induce pupillary miosis and could potentially affect SPC. 17 As there were only four patients in the closed-angle group (2.9%) using brimonidine, this may not have been significant. Third, it is not known whether our results in Chinese subjects could be extrapolated to other racial groups. AS-OCT videography was also limited to its scan acquisition time of 0.125 seconds. A midpupil size or any fixed-pupil size may be a better approach to measure angle α and β values; however, the scan speed of the instrument may thus limit the frames available for identifying precise midpupil size. The objective of this study was to evaluate the vector characteristics of the iris in angle closure and normal eyes. Other static or dynamic factors such as iris configuration, tissue strain rate, and iris convexity, which may contribute to angle closure, were not evaluated. 5,19,22 In addition, it is not known whether our findings would hold if the other meridians were also analyzed by the AS-OCT videography. 
In summary, this study demonstrates, using in vivo AS-OCT videography analysis, that APC and AIS were larger, whereas APB was smaller, in angle closure eyes compared with those with open angles. The results compared favorably with both Mapstone's pupil block vector analysis and Quigley's iris sponginess theory. Our study findings implicate both iris–lens interactions and inherent iris property differences in angle closure. 
References
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Cheung CY Zheng C Ho CL Novel anterior-chamber angle measurements by high-definition optical coherence tomography using the Schwalbe line as the landmark. Br J Ophthalmol . 2011;95 (7):955–959. [CrossRef] [PubMed]
Rasband WS. ImageJ, US. National Institutes of Health, Bethesda, Maryland, USA. http://imagej.nih.gov/ij/ .
Zheng C Cheung CY Narayanaswamy A Pupil dynamics in Chinese subjects with angle closure. [published online ahead of print January 31 2012]. Graefes Arch Clin Exp Ophthalmol . PMID: 22290071.
Bergamin O Kardon RH. Latency of the pupil light reflex: sample rate, stimulus intensity, and variation in normal subjects. Invest Ophthalmol Vis Sci . 2003;44 (4):1546–1554. [CrossRef] [PubMed]
He M Lu Y Liu X Ye T Foster PJ. Histologic changes of the iris in the development of angle closure in Chinese eyes. J Glaucoma . 2008;17 (5):386–392. [CrossRef] [PubMed]
Chua J Seet LF Jiang Y Increased SPARC expression in primary angle closure glaucoma iris. Mol Vis . 2008;14:1886–1892. [PubMed]
Quigley HA. Angle-closure glaucoma-simpler answers to complex mechanisms: LXVI Edward Jackson Memorial Lecture. Am J Ophthalmol . 2009;148 (5):657–669. e651. [CrossRef] [PubMed]
Tiedeman JS. A physical analysis of the factors that determine the contour of the iris. Am J Ophthalmol . 1991;111 (3):338–343. [CrossRef] [PubMed]
Quigley HA Silver DM Friedman DS Iris cross-sectional area decreases with pupil dilation and its dynamic behavior is a risk factor in angle closure. J Glaucoma . 2009;18 (3):173–179. [CrossRef] [PubMed]
McDonald JE 2nd, El-Moatassem Kotb AM, Decker BB. Effect of brimonidine tartrate ophthalmic solution 0.2% on pupil size in normal eyes under different luminance conditions. J Cataract Refract Surg . 2001;27 (4):560–564. [CrossRef] [PubMed]
Fung YC. Biomechanics: Mechanical Properties of Living Tissues . Berlin, Germany: Springer; 1993:242–314.
Shabana N Aquino MC See J Quantitative evaluation of anterior chamber parameters using anterior segment optical coherence tomography in primary angle closure mechanisms [published online ahead of print May 18, 2012]. Clin Experiment Ophthalmol. doi: 10.1111/j.1442-9071.2012.02805.x .
See J Chew P Friedman D Changes in anterior segment morphology in response to illumination and after laser iridotomy in Asian eyes: an anterior segment OCT study. Br J Ophthalmol . 2007;91 (11):1485–1489. [CrossRef] [PubMed]
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Footnotes
 Supported by grants from the National Medical Research Council, Singapore and from the the National Research Foundation, Singapore.
Footnotes
 Disclosure: C. Zheng, None; C.Y. Cheung, None; T. Aung, Carl Zeiss Meditec (F, R); A. Narayanaswamy, None; S.-H. Ong, None; D.S. Friedman, None; J.C. Allen, None; M. Baskaran, None; P.T. Chew, None; S.A. Perera, None
Figure 1. 
 
AS-OCT image showing the automatic measurement of ACD, ACW, PD, and iris thickness.
Figure 1. 
 
AS-OCT image showing the automatic measurement of ACD, ACW, PD, and iris thickness.
Figure 2. 
 
PD to a time series. The fitted trend line is a second-order polynomial function that is denoted on the chart along with the square of the correlation coefficient (R 2).
Figure 2. 
 
PD to a time series. The fitted trend line is a second-order polynomial function that is denoted on the chart along with the square of the correlation coefficient (R 2).
Figure 3. 
 
Vector acceleration analysis. APC acts opposite to the pupil constriction, and AIS acts toward the iris root. APB acts perpendicular to the lens surface, forming angles α and β with AIS and direction of pupil constriction.
Figure 3. 
 
Vector acceleration analysis. APC acts opposite to the pupil constriction, and AIS acts toward the iris root. APB acts perpendicular to the lens surface, forming angles α and β with AIS and direction of pupil constriction.
Table 1. 
 
Comparison of Demographic and Clinical Data and AS-OCT Measurements between Open- and Closed-Angle Groups
Table 1. 
 
Comparison of Demographic and Clinical Data and AS-OCT Measurements between Open- and Closed-Angle Groups
Open-Angle, n = 170 Closed-Angle, n = 136 P Value*
Mean 95% CI (Lower) 95% CI (Upper) Mean 95% CI (Lower) 95% CI (Upper)
Age, y 58.67 57.43 59.75 63.41 62.05 64.80 < 0.001
Sex, male/female 68/102 50/86 0.563†
Axial length, mm 24.37 24.14 24.62 22.94 22.78 23.10 < 0.001
Anterior chamber depth, mm 2.65 2.60 2.71 2.08 2.03 2.12 < 0.001
Dark-room gonioscopy, Shaffer 3.48 3.36 3.59 1.69 1.50 1.86 < 0.001‡
Vertical cup-to-disc ratio 0.41 0.39 0.43 0.52 0.49 0.56 < 0.001
Visual field MD, dB −1.21 −1.51 −0.91 −3.56 −4.23 −2.96 < 0.001
Visual field PSD, dB 2.15 1.98 2.36 3.00 2.53 3.51 0.001
AS-OCT measurement
 Iris speed, mm/s 1.56 1.44 1.69 1.22 1.13 1.31 < 0.001§
 Anterior chamber width, mm 11.52 11.47 11.57 11.30 11.24 11.37 < 0.001
 Len's vault, dark, mm 0.39 0.35 0.44 0.89 0.84 0.93 < 0.001
 Pupil diameter, dark, mm 4.14 4.02 4.24 3.89 3.76 4.01 0.005
 Iris thickness, dark, mm 0.45 0.44 0.46 0.45 0.44 0.46 0.904‖
 Iris concavity, dark, mm 0.15 0.14 0.16 0.20 0.19 0.22 < 0.001‖
Anterior chamber angle
 AOD500, dark, mm 0.23 0.20 0.25 0.13 0.11 0.15 < 0.001‖
 TISA500, dark, mm2 0.063 0.055 0.072 0.034 0.028 0.041 < 0.001‖
Table 2. 
 
Comparison of Vectors Involved in Pupil Constriction between Open- and Closed-Angle Groups
Table 2. 
 
Comparison of Vectors Involved in Pupil Constriction between Open- and Closed-Angle Groups
Closed-Angle, n = 136 Open-Angle, n = 170 Mean Difference P Value*
(Mean, 95% CI) (Mean, 95% CI) (95% CI)
Magnitude
 APC mm/s2 0.61 (0.51–0.70) 0.90 (0.83–0.97) −0.28 (−0.39 to −0.18) < 0.001
 APB mm/s2 0.14 (0.12–0.16) 0.09 (0.07–0.19) 0.05 (0.03–0.08) < 0.001
 AIS mm/s2 0.58 (0.49–0.66) 0.89 (0.82–0.96) −0.31 (−0.42 to −0.20) < 0.001
Direction
α degree 74.37 (73.75–74.94) 77.33 (76.64–77.81) −3.35 (−4.04 to −2.66) < 0.001
β degree 92.49 (91.72–93.28) 97.04 (96.33–97.78) −3.20 (−4.12 to −2.28) < 0.001
Iris speed, mm/s 1.22 (1.15–1.29) 1.53 (1.47–1.59) −0.31 (−0.40 to −0.22) < 0.001
Table 3. 
 
Relationship of Vector Parameters and Angle Closure
Table 3. 
 
Relationship of Vector Parameters and Angle Closure
Variable Model A* Model B
OR (95% CI) P Value OR (95% CI) P Value
Magnitude
 APC mm/s2 4.29 (2.33–7.89) < 0.001 2.58 (1.19–5.59) 0.017
 APB mm/s2 0.013 (0.00–0.167) 0.001 0.35 (0.02–7.17) 0.494
 AIS mm/s2 4.76 (2.53–8.96) < 0.001 2.73 (1.26–5.93) 0.011
Direction
α degree 1.33 (1.21–1.45) < 0.001 1.13 (1.01–1.26) 0.029
β degree 1.25 (1.17–1.34) < 0.001 1.14 (1.04–1.26) 0.005
Table 4. 
 
Comparison of Vector Parameters between Subgroups of Angle Closure versus Normal Controls
Table 4. 
 
Comparison of Vector Parameters between Subgroups of Angle Closure versus Normal Controls
Variable PAC, n = 49 PACG, n = 47 Fellow Eye of APAC, n = 40 Normal, n = 170
Mean (95% CI) P * Mean (95% CI) P * Mean (95% CI) P * Mean (95% CI)
Magnitude
 APC mm/s2 0.65 (0.52–0.79) 0.002 0.65 (0.52–0.78) 0.002 0.54 (0.39–0.68) < 0.000 0.90 (0.83–0.97)
 APB mm/s2 0.13 (0.10–0.16) 0.019 0.12 (0.09–0.15) 0.105 0.15 (0.12–0.19) 0.001 0.09 (0.07–0.11)
 AIS mm/s2 0.63 (0.49–0.77) 0.002 0.59 (0.45–0.73) < 0.000 0.51 (0.36–0.66) < 0.000 0.89 (0.81–0.97)
Direction
α degree 74.01 (73.06–74.97) < 0.000 74.53 (73.56–75.50) < 0.000 73.85 (72.81–74.89) < 0.000 77.51 (77.00–78.02)
β degree 94.22 (93.05–95.39)† 0.001 94.17 (92.99–95.36)† 0.001 90.33 (89.05–91.60) < 0.000 96.58 (95.95–97.21)
Table 5. 
 
Comparison of Vector Acceleration of Pupil Constriction before and after LPI
Table 5. 
 
Comparison of Vector Acceleration of Pupil Constriction before and after LPI
Pre-PI Post-PI P *
Magnitude
 APC mm/s2 0.71 ± 0.39 0.63 ± 0.42 0.425
 APB mm/s2 0.69 ± 0.38 0.61 ± 0.41 0.416
 AIS mm/s2 0.14 ± 0.09 0.12 ± 0.08 0.238
Direction
α degree 74.76 ± 4.24 73.66 ± 3.90 0.134
β degree 94.04 ± 4.76 95.60 ± 4.48 0.058
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