Ocular Biometry in Preterm Infants: Implications for Estimation of Retinal Illuminance

Abstract

purpose. Retinal illuminance varies with stimulus luminance, pupil size, eye size, and transmissivity of the ocular media. There are few published data to inform estimates of retinal illuminance in early infancy, and no concurrent studies of pupil size and ocular length have been described. The goals were to document simultaneously the measured ocular parameters in growing preterm infants and to estimate the potential errors associated with using either stimulus luminance or troland value as a proxy for retinal illuminance in this population.

methods. Ocular biometry including diameters of the eye, vitreous chamber depth (VCD) and dilated pupil diameter was performed on 111 occasions in 33 preterm infants aged between 30 and 55 weeks’ postmenstrual age.

results. Eye size increased rapidly between 30 and 55 postmenstrual weeks and was comparable to that of term-born infants. The ratio of dilated pupil area to VCD² was highly variable. Retinal illuminance of the infant eye compared with adult eyes was underestimated by both stimulus luminance and troland values.

conclusions. Stimulus luminance and troland values cannot be used to infer retinal illuminance when comparing eyes of markedly differing sizes or transmissivities. Error in estimating retinal illuminance in prematurely born infants is inevitable because of uncertainty regarding media transmissivity, but this discrepancy can be minimized by using directly measured pupil diameter and data presented herein for eye size in this population.

Retinal illuminance is defined as the incident luminous flux per unit of retinal surface area (luminance per square meter). ¹ Knowledge of retinal illuminance is an essential requirement for electrophysiological and psychophysical studies of infant vision. It varies with stimulus luminance, pupil size, eye size, and transmissivity of the ocular media. For brief flash stimuli, retinal illuminance is given by  

\[E_{\mathrm{r}}{=}\left(\ \frac{A_{\mathrm{p}}}{d^{2}}\right)\ {\tau}_{{\lambda}}L,\]

where E _r is retinal illuminance (lumen seconds per square meter), A _p is pupil area (in square millimeters), d is posterior nodal distance (PND) of the eye (in millimeters), ^{2 3} τ_λ is media transmissivity at wavelength λ (dimensionless), and L is stimulus luminance (in candela-seconds per square meter). ^{4 5} In our laboratory, to study rod function in the newborn, short-wavelength flashes (λ ≈ 430 nm) are most commonly used. 

It has been assumed that the infant and adult ratios of dark-adapted pupil area (A _p) to PND squared (d ²) are approximately equal, ⁶ implying that a given stimulus luminance will deliver similar levels of retinal illuminance to the dark-adapted infant and adult eye ^{6 7} (also assuming intraocular light losses to be the same for the infant and adult eye). If these are reasonable assumptions, it would mean that stimulus luminance at the cornea could be used as a proxy for retinal illuminance, removing the need to account for either eye or pupil size. However, the constancy of the ratio A _p:d ² across individual subjects of differing ages and for pharmacologically dilated (rather than dark-adapted) pupils has not been confirmed. 

Many infant rod electroretinographic studies (Fulton AB, et al. IOVS 2004;45:ARVO E-Abstract 1353) ^{6 7 8} have used the troland as a proxy measure of retinal illuminance:  

\[T{=}A_{\mathrm{p}}L,\]

where T is troland value (candela-seconds per square meter per square millimeter), A _p is pupil area (in square millimeters), and L is stimulus luminance (candela-seconds per square meter). ⁹ Intraocular losses are not accounted for. The troland does not account for eye size and therefore may be an inaccurate proxy for retinal illuminance if eye size varies within the population studied—particularly relevant in a population in which the eye is growing rapidly, as in preterm infants. 

We report the results of ocular biometry performed on preterm infants between 30 and 55 weeks’ postmenstrual age. Measurements included diameters of the eye, VCD, and dilated pupil diameter. VCD was taken to represent PND, since the nodal point used to define PND does not equate to any physical landmarks that could be imaged with ultrasound. It is likely that VCD and PND coincide within a fraction of a millimeter: according to eye models, although adult PND is 0.15 mm longer than the VCD, ¹⁰ the infant PND is 0.5 mm shorter than the VCD. ¹¹ Because the resolution of an ultrasound scanner is ∼0.2 mm (Siemens Medical Solutions USA, personal communication, December 1998) and repeatability of ultrasonic ocular measures is ∼0.5 mm, ¹² VCD is likely to be a very reasonable approximation of PND. 

The purposes of the study were to compare ocular length with dilated pupil measurements in individual infants and to estimate the errors associated with using either stimulus luminance or trolands as a proxy for retinal illuminance in this population. Since study of rod function in the newborn in our laboratory is mostly achieved with short-wavelength flashes, media transmissivity has been specified at 430 nm throughout. 

Materials and Methods

Patients

Eligible infants were those who fulfilled locally agreed to criteria for ROP screening (i.e., <31 completed weeks’ gestation and/or <1251 g birth weight). The infants ranged in maturity from 30 to 55 postmenstrual weeks and ranged in weight from 1080 to 6800 g. Postnatal ages ranged from 9 to 194 days. 

Procedure

Biometry was performed to coincide with ROP screening examinations. For the purposes of the study, screening examinations began as soon as the infant was self-ventilating and clinically stable and were repeated at the discretion of the attending ophthalmologist (usually at 2-week intervals), until the retinas were fully vascularized. Further measurements were made at ∼50 postmenstrual weeks. For each examination, the infant’s pupils were dilated with 1 drop each of 0.5% cyclopentolate and 2.5% phenylephrine, repeated after 30 minutes. The study was approved by the local research ethics committee and informed, written consent was obtained from the parents. The study conformed to the tenets of the Declaration of Helsinki. 

Ultrasonic Measurement of Eye Size

Ultrasound recordings were made (Acuson 128 XP; Siemens Medical Solutions USA., Inc., Malvern, PA; or an ATL 5000 HDI system, Philips Medical Systems, Bothell, WA) with a 7-MHz linear probe held over the eyelid. Measurements were made of the diameters of the eyeball in both longitudinal and transverse planes with VCD defined as the distance between the posterior surface of the lens capsule and the posterior pole (Fig. 1) . The average of the two VCD measurements made in each of the longitudinal and transverse planes was used. Most of the measurements were made by one radiologist (SM), who also reviewed the few measurements made in his absence. 

An estimate of retinal surface area (RSA) was derived using the formula  

\[A{=}2{\pi}Rd,\]

where A is RSA (in square millimeters), R is the mean of the superior–inferior and axial globe radii, and d is the mean VCD from longitudinal and transverse planes (in millimeters). ¹³  

Direct Measurement of Pupil Diameter

Pupil diameters were measured approximately 60 minutes after completion of the dilation protocol by using a half-moon ruler divided into in 0.5-mm increments. The measurements were made under bright light and were repeated until two researchers independently agreed on their value. 

Estimation of Error Propagation

Relative contributions of eye size and pupil size variability to uncertainty in retinal illuminance estimates were derived by calculating standard deviations and means of A _p and VCD² from 26 measurements from 26 infants aged around 50 postmenstrual weeks. This age was chosen, as media transmissivity data for similarly aged term-born infants are available to provide an estimate of the relative contribution of media transmissivity to the uncertainty in retinal illuminance. ¹⁴  

Results

Because of the potentially confounding effects of laser photocoagulation on retinal and/or ocular growth, ^{15 16} only data from infants who did not require treatment for ROP are considered in this article. We included 111 ultrasound measurements made from 33 infants. Linear regression analysis showed that no individual subject significantly influenced results and therefore repeated measures could remain within the data set. 

Superior–inferior and transverse diameters increased with maturity, with transverse diameters being slightly larger than superior–inferior diameters. Mean transverse diameter increased from 13 mm at 30 postmenstrual weeks to 18 mm at 50 postmenstrual weeks, and superior–inferior diameter increased from 12.5 mm at 30 postmenstrual weeks to 17.5 mm at 50 postmenstrual weeks (Fig. 2) . 

Mean VCD increased from 8.5 to 11 mm between 30 and 55 postmenstrual weeks. During this time, VCD (d) can be estimated from the sigmoidal regression equation as follows:  

\[d{=}\ \frac{16.7}{1{+}\left[\left(\ \frac{\mathrm{age}}{28.3}\right)\ ^{{-}1.31}\right]}\]

where d is VCD (in millimeters) and age is in postmenstrual weeks. The accuracy of this estimate is ±1.2 mm. 

As a result of increasing eye size, calculated RSA (equation 3)almost doubled between 30 and 55 postmenstrual weeks: from ∼350 to 650 mm² (Fig. 3) . 

Dilated pupil diameter showed wide variability. The mean diameter increased with increasing maturity from 5 to 8 mm between 30 and 55 postmenstrual weeks (Fig. 4) . Average dilated pupil diameter was within adult limits at ∼50 postmenstrual weeks. Infants who developed threshold ROP showed no difference in dilated pupil diameter compared with unaffected or prethreshold infants. 

Ratio of Pupil Area to VCD²

This ratio was highly variable, ranging from 0.15 to 0.53 during the preterm period and from 0.27 to 0.60 at 50 postmenstrual weeks (Fig. 5) . The mean ratio increased from 0.30 to 0.41 between 30 and 55 postmenstrual weeks. By comparison, reported data from term-born neonates and from adults show a more stable ratio of less than 0.2. ¹⁸  

Implications for Estimates of Retinal Illumination

Typical values for VCD, pupil diameter, and media transmissivity at 430 nm are documented in Table 1 . Based on these values, the likely retinal illuminance ranges achieved at 40 weeks’ postmenstrual age (typical term age), 50 weeks’ postmenstrual age (10 weeks postterm) and adult eyes by an arbitrary 1-cd · s · m⁻² stimulus are presented in Figure 6 , as well as the relative trolands delivered by the same arbitrary stimulus. 

This fixed-luminance stimulus is likely to deliver 0.48 log units more retinal illuminance to a newborn eye and 0.45 log units more retinal illuminance to a 10 weeks postterm eye than it will to an adult eye (dilated pupils), meaning that stimulus luminance is not a good proxy for retinal illuminance when comparing eyes differing greatly in size or in media transmissivity (Fig. 6) . If eyes are more similar in size and transmissivity, the discrepancy is less (e.g., this fixed luminance stimulus is likely to deliver only 0.03 log units more retinal illuminance to the newborn eye than to the 10-week postterm eye). Stimulus luminance is therefore a reasonable proxy for retinal illuminance when comparing eyes of similar size and media transmissivity. 

Conversely, expressing outcomes in trolands implies that the fixed luminance stimulus delivers 0.18 log units less “retinal illuminance” to the newborn eye and 0.05 log units less to the 10-week-old eye than to the adult eye (dilated pupils)—in fact a reversal of the actual retinal illuminance delivered. 

Discussion

In this study, eye growth was documented between 30 and 55 postmenstrual weeks in direct conjunction with measurements of dilated pupil diameter. 

Our eye growth data agree closely with previous studies including data collected in utero, ex utero, and postmortem, with our 95% prediction intervals enclosing all values from other studies. ^{3 13 17 20 21 22} At term-corrected age, our prematurely born infants have eye measurements exactly matching published data from term-born infants ²⁰ suggesting that preterm birth per se does not significantly affect eye growth. 

Dilated pupil diameters in this study tended to be larger than reported elsewhere, and were also larger than pupil diameters reported in dark-adapted conditions. ²³ The combination of anticholinergic (0.5% cyclopentolate) and sympathomimetic (2.5% phenylephrine) drops used in this study is more effective in preterm infants than anticholinergic drops alone. ²⁴ In single-drug dilating protocols, smaller dilated pupil sizes have been reported in newborn term infants than in our term-aged prematurely born infants (5 mm dilation with 0.5% cyclopentolate ¹⁸ and 4.5–5 mm with 2.5% phenylephrine alone ¹⁹ ). This resulted in larger pupil area:VCD² ratios for the present study than in the term infant study. ¹⁸ It should be noted that, at term-corrected age, the preterm infants in this study were at least 10 weeks old: it is possible that chronological age, light exposure, or both exert a positive effect on maximum pupillary dilatation. This would also partly explain the tendency for the ratio of pupil area to VCD² to increase between 30 and 50 postmenstrual weeks in the group of typical preterm infants reported herein. 

The second purpose of the study was to estimate the errors associated with using either stimulus luminance or troland value as a proxy for retinal illuminance in this preterm infant population. The uncertainty of a function (e.g., retinal illuminance as expressed in equation 1 ) is a result of the uncertainties of its variables (e.g., the measured variability of VCD², A _p and τ_λ. Assuming a nominal stimulus, uncertainty in media transmissivity, ¹⁴ pupil area, and VCD² account for 34%, 46%, and 20% of variability in estimated retinal illuminance, respectively, in these infants. 

Our findings have implications for the estimation of retinal illuminance. If the retinal illuminances received by eyes of differing sizes or (particularly) differing media transmissivities are to be compared, only units of retinal illuminance (equation 1)will be accurate. In the more extreme case of comparing a newborn eye with an adult eye, using stimulus luminance or troland value as a proxy for retinal illuminance will underestimate true retinal illuminance by ∼0.48 or 0.65 log units, respectively, in the newborn eye relative to the adult eye. The effect is less when comparing eyes of more similar sizes, such as during the first 10 weeks of life, or when pupils are less aggressively dilated. Stimulus luminance and troland value underestimate retinal illuminance by 0.03 and 0.14 log units, respectively, in newborn eyes relative to 10-week postterm eyes. The effect would also be less for longer wavelengths of light where transmissivity of the infant and adult eye are similar. For example, stimulus luminance and troland value underestimate retinal illuminance by 0.30 and 0.47 log units, respectively, in newborn eyes relative to adult eyes for light of wavelength 550 nm, 0.18 log units less of an underestimate than with 430 nm light. 

It has been assumed here that PND is approximately equal to VCD. If, as in adults, ¹⁰ PND is shorter than VCD, then the underestimate of retinal illuminance resulting from using luminance or troland units will be slightly less than just stated. 

No data currently exist regarding optical media density in the preterm period. Hence, studies in this population must make assumptions about retinal illuminance. The error in calculating retinal illuminance can be minimized by using directly measured pupil diameter and eye-size data from the present study. Further studies of optical media density in infants, particularly during the preterm weeks, would also be of great use. 

 Supported by Grant 2501.2651.42 from the Royal National Institute for the Blind.

 Submitted for publication May 3, 2007; revised July 18 and August 23, 2007; accepted December 4, 2007.

 Disclosure: H. Mactier, None; S. Maroo, None; M. Bradnam, None; R. Hamilton, None

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

Ultrasound images illustrating VCD (A–B). Left: longitudinal image with superior–inferior diameter (C–D). Right: transverse image with axial diameter (E–F).

Figure 2.

 

Changes in VCD (circles; dashed black lines), transverse diameter (triangles; dotted gray lines) and superior-inferior diameters (squares; dashed gray lines) with maturation. Regression lines enclose 95% of data points. Filled symbols: data from full-term infants and adults. ¹⁷

Figure 3.

 

Changes in retinal surface area with maturity. Regression lines enclose 95% of data points. Filled symbols: data from full-term infants and adults. ¹⁷

Figure 4.

 

Changes in dilated pupil diameter with maturation. Regression lines enclose 95% of data points. Square: mean (errors: 95% reference values) adult values.

Figure 5.

 

Changes in ratio of pupil area to VCD² with maturation. Dashed regression line: indicates trend toward higher ratios with age. Open square data points and shaded gray area: normal range (95% reference values) for term-born neonates and adult values. ¹⁸ Filled squares: data from adult and infants based on estimated infant eye size. ⁶

Table 1.

 

Summary of Typical Dilated Pupil Diameters, VCD, and Media Transmissivity in Infants at 40 and 50 Postmenstrual Weeks and in Adults

	Term-Aged Infant	10-Weeks after Term	Adult	Notes/Sources
Dilated pupil diameter (mm)	7 (5.5 to 8.5)	8 (6.5 to 9.5)	8.5 (7 to 10)	Other dilating protocols achieve less dilation, ie around 5 mm in term-aged infants. 18 ;19
VCD (mm)	10.2 (9 to 11.4)	11.3 (10.1 to 12.5)	16.7* (14.7 to 18.7)*	*From Bron AJ et al. 17
Ocular media transmissivity at 430 nm	0.71† (0.86 to 0.59)†	0.63‡ (0.54 to 0.71)‡	0.43‡ (0.47 to 0.39)‡	†Extrapolated from Hansen and Fulton, 7 Figure 8–3.
				‡Interpolated from Hansen and Fulton, 7 Figure 8–3.
Log RI achieved by a 1-cd-s · m−2 stimulus	−0.59 (−0.22 to −0.96)	−0.62 (−0.30 to −0.94)	−1.07 (−0.76 to −1.37)	Range derived from range limits of pupil diameter, VCD, and transmissivity to give lowest and highest values (see Fig. 6 )
Log troland value achieved by a 1-cd-s · m−2 stimulus	1.56 (1.38 to 1.75)	1.69 (1.52 to 1.85)	1.74 (1.59 to 1.90)	Range derived from range limits of pupil diameter to give lowest and highest values (Fig. 6)

 Data are from the current study unless stated and are expressed as mean values (95% reference range).

Figure 6.

 

Left: retinal illuminance achieved by a 1 cd-s · m⁻² stimulus in three typical eyes; Right: troland values achieved by the same stimulus in the same three eyes. Dashed horizontal lines: matched mean adult values. Error bars, likely 95% reference intervals (Table 1) . PM, postmenstrual.

The authors thank the infants and their parents who participated in this study, and John Dudgeon, Consultant Ophthalmologist, and the nursing and medical staff in the pediatric department of The Queen Mother’s Hospital, Glasgow, for their patience and cooperation.