SEARCH

SEARCH BY CITATION

Keywords:

  • contrast sensitivity;
  • keratoconus;
  • modulation transfer function;
  • retinopathy

Abstract.

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Purpose:  To test the feasibility of calculating neural contrast sensitivity function (neural CSF) from conventionally measured total contrast sensitivity function (total CSF) and measured modulation transfer function (MTF). Neural CSF considers the retina and the brain, whereas total CSF considers the optical eye media, the retina and the brain together.

Methods:  We studied three groups comprising nine eyes each: one group with normal ocular optics but retinal alterations (mild diabetic retinopathy), one with altered ocular optics and normal retina (keratoconus), and a normal control group.

Results:  Total CSF in the keratoconus and retinopathy groups was significantly lower compared to the control group. Modulation transfer function for keratoconus was lower, and in the retinopathy group was similar to that of the control group. Calculated neural CSF in the diabetes mellitus group was lower than in the control group whereas in the keratoconus group it was similar to that of the control group, with overestimations for some keratoconus cases.

Conclusion:  It is possible to calculate a meaningful neural CSF from measured total CSF and MTF data. The neural CSF represents a CSF adjusted for optical aberrations. This would allow comparison of the neural component of visual function in eyes with different optical aberrations.


Introduction

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Two main factors limit our perception of small detail: the quality of the eye optics forming the image on the retina and the ability of the retina, together with the brain, to resolve that image.

The optical quality of the eye is best described by the modulation transfer function (MTF). The MTF shows the reduction of contrast as a function of spatial frequency. Contrast reduction is defined here as the quotient of image contrast to object contrast. The first studies on the MTF of the human eye were performed by Arnulf & Dupuy (1960), Campbell & Green (1965), van Meeteren (1974) and Artal & Navarro (1994). With the development of aberrometers, based on the Hartmann–Shack principle (Liang et al. 1994; Liang & Williams 1997), the laser ray tracing principle (Navarro & Losada 1997) or the double-pass method (Santamaría et al. 1987; Artal & Navarro 1992; Iglesias et al. 1998), the MTF can be calculated from wavefront data.

Usually, the contrast sensitivity of the entire eye is estimated psychophysically with sinusoidal patterns or letters of different size and contrast. Standard procedures measure spatial frequencies between 1.5 and 18 cycles/degree (cpd). We will call this the total contrast sensitivity function (total CSF) because it considers the optical eye media, the retina and the brain together. Changes of the total CSF in various eye diseases have been investigated. For open-angle glaucoma, for instance, a significant reduction at 12 cpd was found (Sample et al. 1991). For cataract, a reduction at all frequencies (1.5–18 cpd) (Chylack et al. 1993b; Pfoff & Werner 1994) or only at 12–18 cpd was found (Chylack et al. 1993a). Contrast sensitivity at 6 and 12 cpd was significantly lower in a group of patients with diabetes compared to controls (Arend et al. 1997). In insulin-dependent diabetes patients, total CSF was significantly lower for spatial frequencies from 3 cpd and above (Banford et al. 1994).

The ability of the retina together with the brain to resolve an image can be characterized by the neural contrast sensitivity function (neural CSF). The neural CSF can be measured subjectively by an interference fringe technique (Le Grand 1937; Campbell & Green 1965), which theoretically allows a sinusoidal pattern of very high contrast to be projected directly on the retina. In this way the results are not affected by aberration or diffraction from the eye optics. However, this technique is less common in ophthalmological practice today.

To find the relative contributions of optical and neural limitations to human contrast sensitivity, Losada et al. (1993) calculated a neural transfer function by removing the effects of the optical and receptoral degradation from the total CSF. Whitaker & Elliott (1992) separated the optical and neural factors by simulating the optics of the elderly eye and examining its effect on the visual performance of younger observers. Pardhan et al. (1996) compared sampling efficiency and internal noise to find a relative contribution of the optical and neural systems to visual function loss with ageing. Another approach was to estimate the MTF from simulated model functions to analyse the neural and optical origin of alterations in the total CSF (Apkarian et al. 1987; Bour & Apkarian 1994, 1996).

Campbell & Green (1965) measured the total CSF in the classical way and the neural CSF using an interference fringe technique. They calculated the MTF as the ratio of total CSF to neural CSF (Fig. 1). In the 1960s this was the only way to obtain the MTF. This technique of estimating the MTF was improved by Morrison & McGrath (1985), Webb et al. (1997) and Felipe et al. (1997). Today, it is possible to estimate the MTF using wavefront data. Therefore, we wanted to test the feasibility of calculating neural CSF from conventionally measured total CSF and aberrometrically measured MTF.

image

Figure 1.  The calculation of the modulation transfer function (MTF) (‘contrast ratio’, closed circles) by Campbell & Green (1965) from measured total contrast sensitivity function (contrast CSF) (open circles) and measured neural contrast sensitivity function (neural CSF) (continuous smooth curve) using an interference fringe technique.

Download figure to PowerPoint

Materials and Methods

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

We studied three groups comprising nine eyes each: one group with normal ocular optics but with retinal alterations [diabetes mellitus with mild diabetic retinopathy (mean age and standard deviation 54 ± 10 years)], one with altered ocular optics and normal retina [mild to moderate keratoconus (mean age 30 ± 7 years)] and a normal control group (mean age 32 ± 3 years). Our research adhered to the tenets of the Declaration of Helsinki and informed consent was obtained from all participants. Total aberrations and corneal topography were measured using iTrace (Tracey Technologies, Houston, Texas, USA). The iTrace system projects a thin laser beam (wavelength 785 nm) through the entrance pupil. The location at which this beam strikes the retina is measured by capturing the exiting scattered light and focusing it onto X and Y position-sensitive linear arrays. This procedure is repeated for 256 separate points and takes 400 ms. Automated refraction from iTrace aberrometry, maximum corneal curvature and corneal astigmatism from iTrace topography for all eyes are given in Table 1, along with age, natural pupil size and best-corrected visual acuity. Maximum corneal curvature (Kmax) is given in dioptres as the steepest simulated keratotopography reading. Corneal topography maps for the keratoconus group are given in Fig. 2.

Table 1.   Demographic and basic visual, refractive and topographic data of the eyes investigated in the control (C1–C9), retinopathy (R1–R9) and keratoconus (K1–K9) groups.
GroupAge (years) Pupil (mm)*BCVA (decimal scale) Sph (D) Cyl (D) Axis (degrees)Kmax (D)Astig (D) Strehl ratio Comments**
  1. BCVA, best-corrected visual acuity; Sph, sphere; Cyl, cylinder; Axis, axis of the cylinder; Kmax, maximum corneal curvature; Astig, corneal astigmatism derived from topography.

  2. * Natural pupil size as measured by the aberrometer.

  3.  Refraction data from aberromatric readings calculated for a 3 mm pupil.

  4.  Strehl ratio for higher-order aberrations and a 3 mm pupil.

  5. ** MC, mild cataract; C, Cataract; OH, Ocular hypertension; MO, macular oedema.

C1355.81.00−1.03−0.3116439.90.80.93 
C2304.41.000.02−0.92  546.82.00.85 
C3344.11.00−0.01−0.37 3343.20.70.87 
C4326.21.000.57−0.28 1144.21.50.80 
C5355.11.00−2.34−2.33  343.82.10.89 
C6346.11.00−2.66−0.63  145.81.50.89 
C7254.61.00−1.25−0.7 3545.90.90.77 
C8315.71.00−1.72−0.13 2444.00.70.88 
C9335.51.000.26−0.42 2041.20.80.73 
Mean325.3    43.91.20.84 
R1633.50.703.74−0.8010246.70.30.77 
R2564.80.650.57−0.87 6045.91.30.70MC, OH
R3434.20.802.12−0.4313943.80.70.76 
R4565.00.850.54−0.3516846.11.30.62 
R5673.00.603.38−2.17 8242.70.90.44C
R6633.20.803.35−0.88 7847.00.50.78 
R7624.80.60−0.67−0.6010842.40.20.42C, MO
R8434.00.703.20−1.07 9443.60.30.75 
R9374.40.95−2.19−0.61 9143.20.60.72 
Mean544.1    44.60.70.66 
K1265.51.00−3.76−3.52 4748.83.90.31 
K2396.10.75−1.81−5.54 6449.35.90.18 
K3225.90.85−2.53−6.16 9752.32.10.15 
K4306.60.800.38−3.99 9845.04.30.21 
K5315.80.652.84−3.05 9247.93.40.28 
K6205.30.95−1.07−0.47 6144.91.30.37 
K7306.00.75−7.34−1.22 9851.91.00.13 
K8435.30.901.29−4.74 7346.14.20.26 
K9306.40.750.29−4.23 7446.04.80.23 
Mean305.9    48.03.40.24 
image

Figure 2.  Corneal topographies for the nine keratoconus patients, represented as axial maps colour-coded with fixed 1.5-dioptre steps between 37 and 58 dioptres and fixed central value for the colour coding. The scale of the raster is 1 mm.

Download figure to PowerPoint

Total CSF was measured using the CST 1800 and a fact Chart (Vision Science Research Corporation, San Ramon, California, USA). The fact Chart consists of high-quality, digitally produced printed sine wave gratings for five spatial frequencies (1.5, 3, 6, 12 and 18 cpd) and nine steps of contrast (0.15 log units apart) (Ginsburg 2006). The range of contrasts in log units are as follows: 1.5 cpd, 0.85–2.00; 3 cpd, 1.00–2.20; 6 cpd, 1.08–2.26; 12 cpd, 0.90–2.08; 18 cpd, 0.60–1.81. The fact Chart sits inside a view-in test box and is seen by the patient at infinity. It is illuminated with white light from an incandescent lamp to give a luminance of 80 cd/m2 (photopic conditions). Each contrast sensitivity test field has a size of 1.8 degree on the central part of the fovea, which corresponds to a diameter of about 500 μm. The test was performed with best spectacle correction for distance and with natural pupil size.

MTF for a 3 mm pupil was calculated from Zernike coefficients obtained from the optical aberration measurements. In order to allow comparison to the total CSF (obtained with best spectacle correction), the MTF had to be calculated for higher-order aberrations only, eliminating the Zernike coefficients for defocus and astigmatism. Numerical MTF data were calculated using software custom-made by Gerard de Wit PhD, consulting services at Optical Diagnostics (http://www.opticaldiagnostics.com). This software calculates the two-dimensional MTF by radial averaging the three-dimensional MTF with an angular resolution of one data point per degree. The three-dimensional MTF is obtained from the optical transfer function as the Fourier transform of the Point Spread Function (PSF). The PSF is calculated from the amplitude spread function using the inverse Fourier transform of the pupil function. The Fourier transform sampling diameter in the pupil plane was set to 14 mm and the resolution was set to 256. The Strehl ratio was calculated as the quotient of the surface under the measured two-dimensional MTF to the surface under the diffraction-limited MTF.

Neural CSF was calculated as the quotient of total CSF and MTF for each measured spatial frequency:

  • image(1)

Confidence intervals for the mean at different spatial frequencies were calculated with confidence coefficient set to 0.95.

Results

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Control eyes showed the normal pattern of the total CSF and the MTF (Fig. 3A,D). Neural CSF was higher than total CSF. The individual curves were close together (Fig. 3G). In the retinopathy group, total CSF curves were more disperse and lower than in the control group (Fig. 3B). MTF curves were close below the curves from the controls, except two eyes with early cataract (Fig. 3E). Neural CSF curves were all below the values from the control group (Fig. 3H).

image

Figure 3.  Total contrast sensitivity function (total CSF), modulation transfer function (MTF) and neural contrast sensitivity function (neural CSF) for the control group (A, D, G), the diabetic retinopathy group (B, E, H) and the keratoconus group (C, F, I). Mean and confidence intervals (CI) in dark grey. CSF is given in log units and diffraction-limited MTF (DL in D, E, F) as a dotted black line.

Download figure to PowerPoint

In the keratoconus group, total CSF curves were also more disperse and lower than in the control group (Fig. 3C). MTF curves were much lower than in the control group (Fig. 3F). These low MTF curves, considering higher-order aberrations, did not seem to correlate with high maximum corneal curvature nor with high corneal astigmatism (Table 1). However, corneal topographies with strong irregularities near the pupil centre (K7, K3 and K2 in Fig. 2) corresponded to low MTF curves (Fig. 3F) and low Strehl ratio (Table 1). Neural CSF of the keratoconus group were close to the values of the control group with some underestimations for low spatial frequencies (K3 and K5) and some overestimations for higher spatial frequencies (K1, K2, K4 and K8) (Fig. 3I).

The mean total CSFs in the keratoconus and retinopathy groups were significantly lower for 6, 12 and 18 cpd compared to the control group (Fig. 4A). The difference was 0.4 log units at 6 cpd, 0.5 log units at 12 cpd and 0.7 log units at 18 cpd. The confidence intervals for the mean of the MTF for all spatial frequencies were overlapping for the control and the retinopathy groups. The MTF values for the keratoconus group were significantly lower (Fig. 4B). Calculated neural CSF in the retinopathy group was significantly lower for 6, 12 and 18 cpd compared to the control group (Fig. 4C). The difference was 0.4 log units at 6 and 12 cpd, and 0.6 log units at 18 cpd. Neural CSF was similar in the keratoconus and control groups. Overlapping confidence intervals for the mean indicate that there was no significant difference.

image

Figure 4.  Mean and confidence interval of total contrast sensitivity function (total CSF), modulation transfer function (MTF) and neural contrast sensitivity function (neural CSF) for all investigated groups: controls (C), diabetic retinopathy (R) and keratoconus (K). CSF is given in log units.

Download figure to PowerPoint

Discussion

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Diabetes mellitus patients with mild diabetic retinopathy were chosen as a group with normal ocular optics and retinal alterations because these patients are younger than those with other retinal diseases and have only mild alterations of the retina, which still permits the reading of standard contrast sensitivity charts. However, there was a difference in the mean age between the retinopathy group (54 years) and the two other groups (30 and 32 years, respectively). This probably explains the somewhat lower MTF in the retinopathy group (Fig. 4B). For the total CSF and neural CSF, possible aging effects are superimposed on the effects because of retinopathy (Fig. 4A,D). Patients with mild to moderate keratoconus usually have a normal retina and the only altered condition is ocular optics, making them suitable for the group with altered ocular optics and normal retina.

Total CSF was measured for five spatial frequencies between 1.5 and 18 cpd to include the peak of the total CSF (between 3 and 6 cpd), which relates to functional vision. The highest spatial frequency of the FACT Chart is 18 cpd because that spatial frequency is in the range of spatial frequencies needed to identify a 20/20-size letter (from 12 to 30 cpd depending on the letter) (Ginsburg 1978, 2006). Although a normal observer can see 100% contrast sine wave gratings up to spatial frequencies of 50 cpd, it was not practical to use higher spatial frequencies for the two groups with ocular pathologies, who are not able to resolve such fine detail. The contrast measurement resolution was limited to 0.15 log units because of the predefined contrast steps of the FACT Chart. With computerized forced-choice tracking programming of finer contrast steps, this would have been possible.

Total CSF and MTF had to be measured under different conditions. Total CSF was obtained with best spectacle correction whereas aberrometry is usually performed without spectacle correction. Therefore, MTF had to be calculated for higher-order aberrations only, eliminating the Zernike coefficients for defocus and astigmatism. This elimination of the Zernike coefficient removes the defocus and astigmatism components completely for the MTF measurements, whereas the optical correction with trial lenses always leaves a residual error for the total CSF measurement. Furthermore, total CSF was measured under photopic conditions with a pupil size of around 5 mm, whereas MTF could only be calculated for a 3 mm pupil because of small natural pupil sizes in the retinopathy group (Table 1). Because it has been demonstrated that pupil size has a considerable effect on the MTF (Campbell & Gubisch 1966; Artal & Navarro 1994), we calculated the MTF for constant pupil size for all patients.

Total CSF will also be affected by pupil size (Strang et al. 1999), although this is less documented in the literature. Therefore, some error was introduced in our calculations by comparing our MTF of a fixed pupil size (3 mm) to our total CSF with natural pupil sizes (mean 5.3, 4.1 and 5.9 mm in the control, retinopathy and keratoconus groups, respectively). Our MTF for the 3 mm pupil size was higher than it would have been using larger pupil sizes. This effect has already been described by Campbell & Gubisch (1966), who gave the MTF for different pupil sizes. Especially at 12 and 18 cpd, an MTF for 3 mm pupil size is about 20% higher than an MTF for 5 mm pupil size. This means that our calculated neural CSF using eqn 1 gave lower values, as expected. Another possible source of error is the comparisons of the MTF based on measurements gained with monochromatic laser light in the near infrared to the total CSF measured with polychromatic white light from an incandescent lamp. Therefore, total CSF was measured with the contribution of chromatic aberration, but the MTF was not. This might have introduced some error, especially at higher spatial frequencies (Artal et al. 1996).

The calculated neural CSF of our control group is in good agreement with the neural CSF measured by Dressler & Rassow (1981) (Fig. 5). They measured the neural CSF in 95 normal eyes (age 12–71 years) using an interference fringe technique. The neural CSFs measured using the same technique in single patients by Campbell & Green (1965) and Webb et al. (1997) are about 0.3 log units higher than our calculated neural CSF in the control group (Fig. 5). This is probably because of the use of our MTF for smaller pupil size, as explained earlier.

image

Figure 5.  Mean and confidence interval of neural contrast sensitivity function in log units for the control group (C) and data from the literature: Campbell & Green (1965), Dressler & Rassow (1981) and Webb et al. (1997).

Download figure to PowerPoint

The calculated neural CSF in the retinopathy group was significantly lower than that in the control group for spatial frequencies above 3 cpd. A lower neural CSF was expected because of the involvement of the fovea with diabetic retinopathy. The calculated neural CSF in the keratoconus group was not significantly different compared to the control group for all spatial frequencies between 1.5 and 18 cpd. In four cases, neural CSF was overestimated for higher spatial frequencies (Fig. 3I: K1, K2, K4 and K8).

It has been demonstrated that at certain spatial frequencies ‘notches’ may be present in keratoconus (Apkarian et al. 1987; Woods et al. 1996). Because we measured only a limited number of spatial frequencies, this may introduce some uncertainties about the actual course of the total CSF and therefore could result in an incorrect estimation of the neural CSF. Another possible source of error is that some keratoconus eyes can be better corrected by spectacles than others. However, we could not find a correlation between best-corrected visual acuity and overestimated neural CSF.

Mathematically, overestimation of the neural CSF may be caused by underestimating of MTF or overestimating of total CSF (eqn 1). The values of the MTF at 12 and 18 cpd in the keratoconus group were relatively low. Variation caused by measurement error of very low values in the denominator of an equation can have a strong influence on the output of such an equation. On the other hand, overestimation of total CSF might have occurred in some keratoconus patients because of neural compensation of the optical defect. It has been shown that the brain can adapt to a particular higher-order aberration pattern (Artal et al. 2004; Chen et al. 2007). Such neural adaptation may lead to an overestimated total CSF for a relatively bad MTF and finally to an overestimated neural CSF (eqn 1).

The neural and optical origin of alterations in total CSF has been discussed previously (Apkarian et al. 1987; Bour & Apkarian 1994, 1996). However, MTF had to be estimated from a simulated model function because of the lack of aberrometers in clinical use at the time of these studies. We believe that it is possible to calculate a meaningful neural CSF from measured total CSF and MTF data. This neural CSF represents a CSF adjusted for optical aberrations, allowing a comparison of the neural component of visual function in eyes with different optical aberrations. Possible applications include the study of neural adaptation in patients with multifocal intraocular lenses or of the changes in the neural CSF in early glaucoma patients. The possibility of estimating (neural) CSF independently from optical aberrations could also improve early diagnosis in patients with neural disorders such as multiple sclerosis. Future experiments should better control pupil size for the measurement of total CSF and MTF and consider or test neural compensation for higher-order aberrations.

Acknowledgements

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

The authors thank Rodrigo Arcari de Araujo and Adriana Ríos for their participation in the clinical measurements. This study has been supported in part by two grants from the Spanish Ministry of Health, Instituto Carlos III: Red Temática de Investigación Cooperativa en Salud RD07/0062 and Proyecto de Investigación de Tecnologías Sanitarias PI08/90726.

References

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References