nayha patel thesis (ug optometry)
DESCRIPTION
Undergraduate thesis by Nayha Patel. Runner up for Naylor price 2007. Supervised by Paul H ArtesTRANSCRIPT
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Properties of the Manchester
radial deformation acuity charts
By Nayha Patel
Supervised by Dr Paul H Artes
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Contents
Title Page
1. Abstract
2. Introduction
2.1 Aims and Objectives
3. Visual Acuity & Hyperacuities
4. Radial deformation acuity
4.1 Radial deformation acuity
4.2 RDA Stimuli
4.3 The Manchester RDA charts
4.3.1 The Manchester RDA charts
4.3.2 Manchester RDA chart layout
4.3.3 Recording results
4.3.4 Scoring
5. Psychometric Functions
6. Perceptual Learning
7. Methods
7.1 Subjects
7.1.1 Inclusion Criteria
7.2 Procedure
7.2.1 Sessions
7.2.2 Monocular versus binocular testing
7.2.3 Randomised presentation
7.2.4 Environment
7.2.5 Lighting
7.2.6 Guessing answers
7.3 Data analysis
7.3.1 RDA Distribution
7.3.1.1 Psychometric functions
7.3.1.2 Binocular versus monocular observation
7.3.2 Comparing scoring techniques
7.3.3 RDA associations
7.3.4 Learning
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8. Results
8.1 Distribution
8.1.1 Psychometric Functions
8.1.2 Binocular versus monocular viewing
8.1.3 Fitted threshold versus simple scoring technique
8.2 Scoring Errors
8.2.1 Variability of results
8.2.2 Manchester RDA chart scoring errors
8.2.3 Predicted error on a Manchester RDA chart
8.3 RDA and Contrast Sensitivity
8.4 RDA and logMAR VA
8.5 Learning
9. Discussions
9.1 Limitations and potential improvements to the Manchester
9.1.1 RDA Distribution
9.1.2 Scoring techniques
9.1.3 Scoring Errors
9.1.4 RDA associations
9.1.5 Learning with the Manchester RDA charts
9.2 Future Experiments
9.2.1 Larger testing groups
9.2.2 Binocular versus monocular investigations
9.2.3 Manchester Royal Infirmary studies
10. Conclusions
11. Acknowledgements
12. References
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1. Abstract
PURPOSE. To investigate the properties of the Manchester radial deformation acuity
(RDA) charts in young healthy observers.
METHODS. Ten visually-normal young volunteers (mean age: 19.6 years, age range: 18
to 22 years) were examined on six Manchester RDA charts in four sessions over four
weeks. Five volunteers observed the chart binocularly and five monocularly.
RESULTS. Results were obtained from a simple scoring algorithm as well as by fitting
psychometric functions to the data. In this group of observers radial deformation acuity
(RDA) ranged from 2.73 log RDA to 3.32 log RDA (mean: 2.948 log RDA, SD: 0.21).
The width of the psychometric function (difference between radial deformation at 10%
and 90% performance) ranged from 0.54 to 1.10 (mean: 0.75, SD: 0.23). The simple
scoring technique appeared to be more precise in estimating threshold RDA compared to
the RDA obtained from fitting the psychometric function. Compared to the simple
scoring algorithm, the psychometric function scoring technique overestimated RDA at
higher RDA levels. No associations of RDA with Pelli-Robson CS or logMAR VA
measurements were seen (Pearson correlation co-efficient: r=0.105, p=0.77 for CS,
r=-0.398, p=0.25 for logMAR VA). Of the ten observers, seven showed evidence for a
learning effect. The magnitude of this effect, however, was small compared to the
overall variation.
CONCLUSIONS. The results indicate that the current version (V2) of the Manchester
RDA charts do not provide a sufficiently low radial deformation level (ceiling effect).
The simple scoring technique compared well to psychometric function fitting.
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2. Introduction
The Manchester radial deformation acuity (RDA) charts are a novel shape-discrimination
test. They are designed to screen for diseases which cause retinal distortion, such as age-
related macular degeneration (AMD).
This study will look at the properties of the Manchester RDA charts in ten young,
healthy observers. Five volunteers will be asked to observe the charts monocularly and
five volunteers will asked to observe the charts binocularly to investigate any possible
differences.
Firstly, this study will evaluate two different scoring techniques that can be used to
measure RDA. These are a simple scoring technique and fitting a psychometric function
to the data to score threshold RDA. The variability and error of the two scoring systems
will be quantified according to the number of charts presented. Secondly, RDA scores
will be compared with logMAR visual acuity (VA) and contrast sensitivity to investigate
any associations. Finally, this study will look at the learning effects associated with the
Manchester RDA charts by looking for a correlation between the threshold RDA
measured and the number of charts presented.
Studying the properties of the Manchester RDA chart properties will allow us to
investigate differences between two scoring techniques and determine the most precise
scoring technique for the charts, highlight any limitations of the chart and observe
learning effects. The importance of these properties is outlined below.
The chart is designed to screen for retinal distortion caused by diseases such as AMD.
For clinical use, a threshold RDA criterion will have to be produced. For example, what
RDA threshold measured merits referral in an optometric practice or, merits surgery in a
hospital? There are two ways in which the Manchester RDA chart can be scored. It is
important that the most precise scoring technique is used to determine the threshold
RDA and when exploring remaining properties of the chart. The scoring errors can also
be quantified so that they can be accounted for when the Manchester RDA charts are
used clinical practice. This will estimate a more precise threshold RDA.
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The Manchester RDA chart is a novel vision test so it is important to investigate if
logMAR VA and contrast sensitivity have any correlation with RDA. If a correlation is
found, this would suggest RDA is influenced by these measurements and limits its
usefulness. Ideally we would want no correlation so that the Manchester RDA chart can
be used as a universal screening test suitable for all patients, unaffected by logMAR VA
and contrast sensitivity.
It is seen in practice that patients will learn to perform visual tasks. Examples include
reading a Snellen chart and performing the TNO stereopsis test. Attention and fatigue
have also been associated with visual tasks and the validity of their results (Fahle 1996).
Learning has been investigated and quantified with many visual tasks including visual
field testing (Wild et al., 2006) and stereopsis (Westheimer 1994). However, no one has
yet quantified the amount of learning achieved with the Manchester RDA charts. If
learning can be quantified for the number of charts presented it can be taken into
consideration by the practitioner to give a more accurate RDA threshold for the patient.
Ten, young, visually-healthy volunteers will be recruited to take part in the study. Each
volunteer will have their logMAR VA and contrast sensitivity measured. To participate
in this study these measurements must be within the pre-defined inclusion criteria set.
Following this, the volunteer will be tested on each of the six Manchester RDA charts in
four separate sessions. At each session the scores generated on each chart will be
recorded on a specialised computer programme (Datalogger). Possible conclusions that
may be indicated from the results are discussed below.
There are two different scoring techniques that can be used to measure RDA. Therefore,
each volunteer will have two RDA scores from each chart observed. These will be a
simple threshold RDA and a fitted threshold RDA (interpolated from a psychometric
function). On analysis of these RDA scores it may be found that one scoring technique
is more precise in measuring threshold RDA. The pattern of distribution of the RDA
thresholds may highlight limitations of the Manchester RDA charts. For example, all
volunteers may score the highest RDA presented on the charts. This would be a
limitation of the charts not presenting a low enough radial deformation level to measure
threshold RDA.
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Learning effects will also be highlighted from RDA thresholds measured. For example,
all the volunteers’ RDA thresholds may improve within and over a number of sessions.
This will be evidence to suggest that the volunteer has learnt how to perform the visual
task (learning effect). This is because it is unlikely that a true change in the underlying
sensory process has taken place. If this learning effect can be quantified according to the
number of charts presented, it can be taken into consideration when the final threshold
RDA is measured. This will give a more accurate estimate of threshold RDA.
Finally, associations between logMAR VA and contrast sensitivity with threshold RDA
measurements will highlight limitations of measuring RDA on the Manchester RDA
charts. For example, we may find a positive relationship between logMAR VA and RDA.
This would limit the use of the Manchester RDA chart since threshold RDA could
potentially be predicted from logMAR VA.
RDA may be a useful quantitative vision measurement for early degenerative eye diseases.
Shape discrimination ability has already been shown to be decreased in patients with age-
related macular degeneration, AMD (Wang 2002). Because the Manchester RDA chart
is a new vision test, many important properties of the test are still unknown. It is
valuable to investigate the properties of the chart itself (e.g. learning effects) and any
factors that may affect RDA measurements (e.g. logMAR VA). The results may advocate
improving the design of the chart or how the chart is used, for example monocular or
binocular viewing.
This study will look at RDA scoring techniques, RDA distribution in monocular and
binocular viewers, RDA associations with logMAR VA and contrast sensitivity and
learning effects as factors which may affect threshold RDA.
2.1 Aims and Objectives
The aim of this study is to investigate the properties of the Manchester RDA charts in
young, healthy observers. Scoring techniques, observation methods (monocular versus
binocular), logMAR VA and contrast sensitivity associations with threshold RDA
measured and learning effects will be investigated. Where applicable the factors will be
quantified.
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The objectives of this study will be to examine RDA in ten visually-healthy, young
volunteers. Five will be tested binocularly and five monocularly. Each volunteer will be
tested weekly for four weeks on the six charts.
This data will be analysed by fitting a psychometric function to it. Psychometric
functions are thought to be the most accurate way of extracting information on stimulus-
response relationships. These will generate what we will call the fitted threshold RDA.
An alternative way of scoring RDA is by using a simple scoring technique. Volunteers
will be asked to stop reading the Manchester RDA chart according to the termination
rule (three consecutive incorrect responses). The threshold RDA is calculated by taking
the smallest RDA level reached (before the termination rule applies) and subtracting 0.10
for each error made (for a more detailed explanation see section scoring 4.3.4. figure 7).
The variation between these two scoring techniques will be calculated and analysed to
generate a predicted error for a specific number of charts presented. The distribution of
RDA in binocular and monocular observers will be plotted to investigate binocular
summation effects on RDA. Threshold RDA scores will be compared to logMAR VA
and contrast sensitivity to highlight any associations. To investigate any possible learning
effects associated with the Manchester RDA charts, threshold RDA from each session
will be plotted for each volunteer. An improvement in threshold RDA can be called a
learning effect since it is unlikely that a true change in the underlying sensory process has
taken place.
The purpose of the investigation is to identify and quantify, where possible, the non-
visual factors that will affect threshold RDA measured and perhaps significantly change
its clinical value as a measure of hyperacuity over time.
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3. Visual Acuity & Hyperacuities
Clinically, ordinary visual acuity (VA) tends to be the most commonly performed test of
vision. VA is a threshold measurement (i.e. smallest level of visual stimulation that a
person can detect) taken by varying the spatial dimension of a target. Within this
definition there are three main sub-divisions described by Westheimer (2003).
Firstly, there is the ‘minimum visible’ measurement. This is performed by varying the
object size, which is a single feature of the target. An example would be to detect if a
target was present or not. Secondly, there is the ordinary VA or ‘minimum resolvable
acuity’ (MAR). This is the ability to discriminate and recognise one target from another.
This involves the subject making a subjective decision based on spatial judgement, for
example, is that an O or a C? Ordinary VA or MAR can be expressed in seconds of arc
or as the log of the MAR (logMAR). Typical values range from 30 seconds of arc to 1
minute of arc for ordinary VA (Westheimer 2003) or -0.14 logMAR to -0.02 logMAR
(Elliott, Yang et al., 1995, figure 1). The targets for visual acuities have to be high contrast.
The British Standards Institute (BSI) states the contrast sensitivity of VA targets should
not be less than 90% (BSI 2003). The final subdivision of VA, and more relevant to this
study, is ‘spatial minimum discriminable’ or ‘hyperacuity.’ This is the ability to determine
the relative location of the same two targets with respect to one another.
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Figure 1: An illustrated Snellen Letter explaining the principle behind measuring VA. You vary
the size of the critical detail and express the angle where it is distinguished approximately 50% of the
time (Extracted from Kolb. H. Fernandez. E. & Nelson website)
Hyperacuities are fascinating to study since they are a visual task whose threshold value
exceeds any expectations based upon retinal receptor spacing (Levi, 1982; Shapley, 1986;
Whitaker, 1992). In visual tasks the human visual system uses hyperacuities to evaluate
spatial resolutions with the precision of a fraction of a photoreceptor’s diameter (Poggio,
1992). This suggests that higher order functions are responsible for this acuity. Typically,
hyperacuities thresholds range from 2 to 8 seconds of arc.
There are several different types of hyperacuities. Vernier acuity is the ability to detect
the smallest perceptible misalignment between two lines (Levi, 1982). Hyperacuities and
vernier acuities are often used synonymously but vernier acuity is simply one type of
hyperacuity (figure 2). Stereoscopic acuity testing is another type of hyperacuity. In
clinical practice, it is used to assess depth perception and binocularity. The visual
processing for stereopsis is thought to be different to that used to detect radial
deformation (Westheimer, 2003). The Manchester RDA charts are based upon a global
shape discrimination hyperacuity task. This involves detection by retinal photoreceptors,
followed by processing of polar arranged, orientation selective cells in V1 in the
extrastriate cortex (Hess, 1999).
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Figure 2: Hyperacuity target examples. (a) and (b) are examples of radial deformation acuity visual
stimuli and (c) and (d) are examples of vernier acuity visual stimuli. (Extracted from Wang 2001)
Hyperacuities can be used to assess the health and function of the retinal photoreceptors.
Reductions in hyperacuities can be indicative of pathological diseases not only affecting
the retinal photoreceptors, but lateral geniculate nuclei (LGN) cells (Moss, 1986) and
striate cortex cells (Parker, 1985; Swindale, 1986).
The hyperacuity stimulus used in the Manchester RDA charts was initially designed to
determine whether a deficit for global shape detection was seen in strabismic amblyopes
(Hess, 1999). The stimulus was then later used in normals to determine whether the
judgement of circularity was done in a localised space of similar size to the stimulus or
whether they were computed as a global shape (Hess, 1999; Wang et al., 1999). More
recently, the RDA stimulus has been used to show how it is not affected by normal
ageing (Wang, 2001) and how AMD affects shape-discrimination (Wang, 2002).
While different areas of the visual pathway have been found to contribute to vernier
hyperacuity abilities, the neural basis of hyperacuities is still not well understood (Spear,
1993). Hyperacuities measured for this study are a global task. This means that the
visual system must integrate visual information over several areas, including a vast array
of retinal photoreceptors and several different visual pathways. This ability to integrate
information over several areas was researched in primates. Primates were found to have
receptor field diameters of 2.0” arc and in comparison 25 x larger threshold value for
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vernier acuity (DeMonasterio, 1975). With this evidence and Westheimer’s hyperacuity
definition, it was most likely that higher order processes must be involved in the
summation of these responses (Westheimer, 2003; DeMonasterio, 1975). Later work
done by Shapley and Victor (1986) in cat ganglion cells found hyperacuities were a result
of high gain (lots of visual information) and low noise (low interference, for example
from eye movements, selective attention) of the receptive field centre mechanism.
All of the above findings suggest that in order to detect radial deformations the
photoreceptors have to compare the signals received from retinal cells with both small
and large receptive fields. A higher order of visual processing must be involved to
perform this hyperacuity task (Hess, 1999). Although research of the mechanism of
hyperacuities is still being explored it is fair to say that the neural processing involved is
likely to be complex. However, since hyperacuities are relatively unaffected by
degenerative changes that affect the optical media, they are useful for assessing retinal
diseases. These include blur, reduced contrast and image diffusion due to light scatter
(Spear, 1993).
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4. Radial deformation acuity
4.1 Radial deformation acuity
Radial deformation acuity (RDA) is the ability to detect different levels of radial
deformations in a circular D4 (4th derivative of Gaussian contour) pattern. It is a
hyperacuity task that is largely unaffected by contrast (Wilkinson, 1998; Hess, 1999;
Wang et al., 1999). Radial deformations in a circular target are processed with the same
precision as deformations in straight lines. RDA is a relatively new type of hyperacuity
(Watt, 1982).
RDA is currently not used in clinical practice for vision assessment but recent studies
have outlined its usefulness. RDA can be applied to detect spatial vision abnormalities in
infants (Birch, 2000). Wang (2001) suggested that RDA may be sensitive enough to
quantify early visual loss in age-related eye diseases, for example age-related macular
degeneration (AMD). In 2002, Wang et al., concluded that shape discrimination may be
useful in assessing the integrity of photoreceptors and therefore as a clinical test for
monitoring AMD. Currently, the clinical value of RDA in retinal diseases is still being
investigated. Some of the advantages of RDA over the more traditional letter acuity
tasks are discussed below.
Some hyperacuities are less affected by exposure duration and contrast compared to VA
(Westheimer, 1982). VA can decrease due to media opacities (e.g. cataract) as they
reduce the contrast of the visual stimulus. It has been shown that RDA stimuli are
unaffected by contrast and largely unaffected by degenerative changes of ageing (Wang,
2001). With RDA we want to screen for diseases which result in retinal distortion, for
example AMD. Having a test that is robust to media changes such as low level cataracts
will mean that our measurement is less influenced by the optical condition of the eye
(cornea, lens). This will make the Manchester RDA charts suitable for patients who have
early cataract or other media opacities. Since no letters have to be read, the chart can
also be used on illiterate patients.
4.2 RDA Stimuli
The RDA stimuli are sinusoidal perturbations of contours constructed from 4th
derivatives of a Gaussian contour. Firstly, they are a low spatial frequency visual target.
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To decrease variables, one spatial frequency in the RDA stimulus would be ideal. Since
this is not possible to produce, the stimulus is a narrow-band of low spatial frequencies.
Low spatial frequencies were used because of what the RDA stimulus was initially
designed for. The circular (D4) contour was the visual target of choice in a study done
by Hess et al., in 1999 to investigate vision in amblyopes. The RDA stimulus targeted
cells in V1 with specific spatial, temporal, orientation and contrast filtering properties.
They found amblyopes had poor sensitivity to sinusoidal deformations due to the
downstream processing from V1 rather than a sampling deficiency (Hess, 1999). A low
spatial frequency stimulus is an advantageous since it makes the target relatively immune
to moderate dioptre blur (Elliott, 1997).
Secondly, the RDA stimuli are suprathreshold high contrast. This makes the stimulus
less sensitive to small changes in contrast which would occur with, for example, low level
cataracts.
Thirdly the amplitude of circular distortion is well controlled in circular D4 contours and
is calculated as below, allowing a large variety of stimuli to be presented (figure 3). The
initial circle is created using the equations below:
CD4 = Lm [1 + c (1 - 4r2 + 4/3r4-e-r2)]
r = √(x2 + y2) – R
σ
σ = √2
πωp
Where σ is the space constant of D4, ωp is the D4 peak spatial frequency, R is the radius of the circular D4 contour and the formula below calculates the deformation of the circle:
R = Rm [1 + Asin [fr arctan (y/x) + θ]]
Where Rm is the mean radius, fr is the radial frequency, A is the amplitude of the radial
deformation and θ is the phase modulation where 0< θ <2π.
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Figure 3: (a) An unmodulated circular D4 contour (b) A modulated circular D4 contour with radial
frequency of 8 cyc/360° and radius modulation of 4% (Hess 1999)
On the Manchester RDA charts the levels of distortion are stated as log RDA. This is
calculated by taking the radial deformation (as calculated above) as a percentage
distortion threshold value. RDA is then stated on the charts as a log of the reciprocal of
this threshold value.
4.3 The Manchester RDA charts
4.3.1 The Manchester RDA charts
The Manchester RDA chart uses a simple, uncomplicated ‘odd-one out’ paradigm. At
each RDA level there are five circles. One circle is deformed and the volunteer must
guess which out of the five circles is deformed. There are six charts, with twenty
increasing RDA levels where the amplitude of deformation decreases. Six charts allow
more variation in presentation which may reduce learning effects that could be seen on
performing the visual task.
The Manchester RDA chart is a hand-held vision test. This has advantages over distance
tasks since is more convenient. For example the charts are portable and both chart
illumination and working distances can be controlled.
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4.3.2 Manchester RDA chart layout
Three Manchester RDA charts are illustrated in Figure 4. On each row there are five D4
circles, one of which is distorted. The choice of five circles increases the repeatability of
the charts since it decreases the chances of correctly guessing the distorted circle.
The amount by which each circle is distorted on each row will decrease by an arbitrary
amount making it increasingly difficult for the observer to guess the distorted circle.
The stimuli will be presented on a board printed in high resolution (600 dpi) as opposed
to computer generated which has previously been used (Hess, 1999; Hess, 1999; Wang et
al., 1999; Wang 2001; Wang 2002). Unlike computer generated RDA stimuli, printed
RDA stimuli are not limited to a particular number of pixels. Printed stimuli therefore
present a crisper, sharper image of the stimulus. The D4 circles are printed on a 0.5%
reflectance background and therefore reflect 50% of the light incident on it.
Figure 4: The Manchester RDA charts. Three out of six charts are shown here. The charts measure
radial deformation acuity. This is the smallest level of radial deformation detected by an observer.
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4.3.3 Recording results
As the charts are being read the responses will be inputted into Datalogger. This is a
programme specifically designed to record RDA responses from each of the Manchester
RDA charts. The screenshot below illustrates the layout of this programme (figure 5).
Before each session, the name, chart and whether the volunteer is carrying out the test
monocularly or binocularly are entered on the right hand side. As the volunteer responds
the responses are entered into the programme. Figure 5 illustrates what Datalogger
programme records after a chart is completed.
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Figure 5: Screenshot of the Datalogger programme. The top screenshot illustrates what the Datalogger
looks like when the programme is opened up. The bottom screenshot illustrates a completed chart, with
details on the right-hand side of the screen of the chart number, volunteer’s name and the eye that was
tested. The green indicates a correct response and the red indicated an incorrect response. This data is
automatically written to a spreadsheet file.
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4.3.4 Scoring
Volunteers are asked to stop guessing according to the termination rule. This is when
three consecutive incorrect responses are given. Volunteers will be offered a second
guess at those RDA levels they incorrectly guessed. If an improvement has been made
on the three consecutive incorrect responses, the volunteer will be allowed to continue
further on the chart until the termination rule applies again.
The spreadsheet generated from Datalogger (figure 6) can be used to mark volunteer’s
responses on a scoring sheet. A simple scoring system is used to calculate the threshold
RDA score, illustrated in figure 7. An alternative way to score threshold RDA is to plot a
psychometric function.
Figure 6: Screenshot of the spreadsheet generated automatically from the Datalogger programme. From
right to left the columns represent: Name, eye tested, date of chart presentation, time, Manchester RDA
chart number, response number, RDA level line number, RDA level, volunteer’s guessed answer, actual
answer and, time taken to make next guess according to previous guess in milliseconds.
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Figure 7: Illustration of the scoring sheet used to calculate the final, simple RDA score, for chart 1. In
this example the observer reached the end of the scoring sheet with scores for 3.10, 3.20 and 3.30 being
the three consecutive incorrect responses given as criteria to stop testing. The observer’s score after the first
round of testing was 2.80 since the lowest correct score was 3.00 but two incorrect responses reduces this
score to 2.80 (3.00 - 0.20).
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5. Psychometric Functions
Psychometric functions will relate an observer’s performance to the intensity of a
psychophysical stimulus (Wichmann and Hill, 2001). One of the ways the sensory
response can be recorded is as a response probability. Another way to record the
sensory response is in terms of effect size. For responses recorded as a probability, a
continuous function is usually seen with a sigmoid profile (figure 8).
Figure 8: A psychometric function relating response probability to stimulus intensity. The stimulus
intensity increases from left to right on an arbitrary scale. The upper and lower asymptotes are the limits
of sensory performance. The threshold response criterion is a specified response probability corresponding
to a particular threshold stimulus value. The slope of the function is the gradient of the function at the
threshold point. (Reproduced with permission from Gilchrist, Gilchrist et al 2005)
There are four operating parameters described by Gilchrist et al., (2005) that can be used
to describe a psychometric function. These are the horizontal asymptotes (upper and
lower asymptotes), the location of the function on the abscissa and the local gradient or
slope at some specific location. Each parameter will now be discussed.
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The horizontal asymptotes are the limits of sensory performance and are further divided
into the upper and lower asymptotes (Gilchrist et al., 2005). The upper asymptote is the
limit of accuracy of perceptual processes. The lower asymptote is where the observer
begins to guess, for example guesses a stimulus is presented even if it is absent
(Wichmann and Hill, 2001).
The location parameter, which is parameter of the function on the abscissa, will have the
same units as the stimulus (Gilchrist et al., 2005). For example, in this study the location
parameter will be measured in log RDA. It is more generally interpreted as the sensory
threshold. Therefore, this parameter is also known as the threshold parameter (Gilchrist
et al., 2005). The location of this parameter is a specified response probability which will
correspond to a particular stimulus value. For this study, to measure threshold RDA, the
location of this parameter will be at the level midway between chance performance and
the upper asymptote of the response probability.
The final parameter of the psychometric function is the slope parameter. This is the
gradient of the tangent at the threshold location parameter. It determines the rate at
which the response probability changes per unit change in the stimulus level (Gilchrist et
al., 2005). Treutwein (1995) reported that threshold estimation dominated experimental
psychophysics and the other parameters described above were ignored. However, it has
more recently been found that the slope parameter is an important measure of perceptual
performance. The clinical significance is now appreciated for the slope parameter
(Chauhan et al., 1993; Patterson et al., 1980; Strasburger, 2001). Subsequent to these
findings, the mathematical models on which psychometric functions estimated slope and
threshold parameters have been developed (Kaernbach, 2001; King-Smith et al., 1997;
Kontsevich et al., 1999; Snoeren et al., 1997).
All of the parameters discussed above will vary according to the mathematical model
used to plot the psychometric function. Such models include cumulative Gaussian,
logistic, Weibull, or Gumbel functions (Wichmann and Hill, 2001). The estimated range
of variation in parameter values is likely to be very small for the threshold parameter and
upper and lower asymptote parameters. It is possible to define threshold in terms of
some associated response probability, and the upper and lower asymptotes are response
probabilities. Therefore the variation in the values for these parameters is not a
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significant problem (Gilchrist et al., 2005). The slope parameter variability in comparison
is larger. This is because the slope does not have any fixed unit or range of values for its
interpretation.
Variation in parameter values is seen as more of a problem when it comes to comparing
psychometric function slope parameter data with other data fitted to the same
experimental data. For example, in this study, further investigations using psychometric
functions would have to use the same mathematical model to compare their results to
ones found in this study.
Psychometric functions are useful since they consider the observer’s performance when
generating a fitted threshold RDA (Wichmann and Hill, 2001). This may measure a
more accurate RDA threshold compared to the simple scoring technique (described in
section 4.25). This is because all of the subjects’ responses are being used to derive
threshold, rather than just a small part as in the simple scoring method. However, Hazel
and Elliott (2002) found no advantage of fitting a psychometric function to the data
generated for observers reading a logMAR chart (logMAR VA versus percentage of
letters called correctly). They found psychometric functions to over-estimate visual
acuity measurements by approximately two letters (0.02 logMAR).
For this study psychometric functions will be used to estimate a fitted threshold RDA for
each volunteer. Furthermore, we have expressed the slope according to the
parameterisation originally suggested by Alcalá-Quintana et al., in 2004. We expressed
the slope as the width of the psychometric function is the distance between the RDA
levels associated with performance levels of 0.28 and 0.92 (corrected for the 0.20
probability that the observer will guess correctly). The width of the psychometric
function will illustrate how quickly each volunteer went from being able to detect the
radial deformation to guessing which circle was deformed. The widths of the
psychometric functions will be compared. This will illustrate whether the step sizes at
which radial deformation decreases is precise enough to measure RDA on the
Manchester RDA charts. For example, a steeper slope will suggest the observer quickly
regresses from being able to detect radial deformation to not being able to detect radial
deformation on the Manchester RDA charts. Finally, this project will look at the learning
effects associated with the Manchester RDA charts.
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6. Perceptual Learning
Perceptual learning can be described as the ability to extract information from the
environment as a result of learning in that environment (Sireteanu, 1995). For the
purpose of this study perceptual learning is the change in RDA score over time. There
are four main mechanisms of perceptual learning that have been reviewed by Goldstone
in 1998. These are attention weighting, stimulus imprinting, differentiation and
unitization. The attention weighting mechanism shows increasing attention allows for
perceptual adaptation i.e. learning (Goldstone, 1998). Depending on the stimuli the
information is processed within different pathways, and different visual tasks show
different visual adaptation and therefore learning patterns. Secondly, stimulus imprinting
can allow perception to adapt. This involves the retinal receptors and higher visual
pathways which are known to respond to certain visual stimuli specifically. Thirdly, the
differentiation mechanism separates stimuli psychophysically and into categories
including complex and simple and differential dimensions. Finally, the fourth
mechanism is unitization, which works in the opposite direction to differentiation. It
constructs what differentiation separated from the stimuli (Goldstone, 1998).
Perceptual learning is important to consider as it is sensitive to training, and is seen to
occur for visual detection and discrimination threshold testing. Perceptual learning can
be disrupted if the patient is asked to perform a different hyperacuity task with different
stimuli (Seitz, 2005). In this study however, the volunteer will only be exposed to one
type of hyperacuity task and therefore perceptual learning can be assumed to be
continuous.
Perceptual learning can be influenced by cognitive aspects such as global pattern
structure, attention and motivation which must be considered in every learning task
(Fahle, 1996). Obviously, the more driven a person is to learn the more attention they
will pay and therefore, this will not only affect how well they perform at the visual task
but the score they achieve at the end. Perceptual learning is an early stage visual
processing task (Poggio, 1992; Fahle, 1996)
Perceptual learning will occur without feedback so patients do not need to know whether
they have correctly completed the visual task (Fahle 1995). This discovery by Fahle et al.,
25
led to the hypothesis that current models for perceptual learning are not biologically
plausible. Although it was found that learning was slower without feedback this was
highly dependent on the target stimulus that was used in the experiment. Fahle et al.,
concluded that the HyperBF-like model for learning would take place in two distinct
ways. Firstly the unsupervised learning which create or ‘tune’ centres do not require
feedback. Secondly, supervised learning which determines ‘synaptic’ weights for the
coefficients does require feedback.
Perceptual learning and hyperacuities are linked and it has been suggested that the ability
of humans to perform hyperacuities to some extent depends on a fast learning process –
fast perceptual learning (Poggio, 1992). The proposed model is that the cortex sets up
task-specific modules that receive input from retinal photoreceptor cells and after a short
training period the cells are able to solve the task. In agreement with Hess et al., (1999)
the learning stage is provided by the circular centre-surround and orientation cells in V1.
Perceptual learning is important to consider in all visual tasks since it occurs all the time
and could be a good indicator of how repeatable and accurate a visual test can be at
diagnosing ocular diseases.
26
7. Methods
7.1 Subjects
Ten young, visually healthy volunteers were informed about the study and their level of
involvement. Written consent was then obtained from each volunteer. Volunteers could
participate in the study if they fell into the inclusion criteria set for this study.
7.1.1 Inclusion Criteria
All volunteers had to be over the age of eighteen years old for legal reasons. There was
no upper age boundary set as there is no significant evidence at present to suggest that
RDA is affected by age in healthy volunteers. Volunteers were included in the study if
they had a VA of equal to or better than 0.20 logMAR on the ETDRS chart. Stereopsis
had to measure at least 120” seconds of arc on the TNO test i.e. each volunteer must
have good binocular vision. Finally, volunteers needed to score at least 1.50 log units
monocularly on the Pelli-Robson contrast sensitivity chart.
7.2 Procedure
There were six Manchester radial deformation acuity (RDA) charts to be completed at
each session. Sessions were scheduled at times that were convenient for the volunteer.
7.2.1 Sessions
All the volunteers were tested on all six charts weekly for a period of four weeks. The
session duration varied between 20 to 30 minutes. Due to time constraints, having to
input responses into Datalogger and inter-subject response and intra-subject response
variability, no breaks were given between each of the six charts used at each session.
7.2.2 Monocular versus binocular testing
Half the volunteers completed the RDA chart binocularly and half monocularly. For
monocular testing, the volunteer and eye tested were chosen at random. The eye was
occluded with an elasticated, leather eye patch.
7.2.3 Randomised presentation
At each session a specific chart order was used and kept standard inter-participants. This
was chosen at random and changed at each test session.
27
Name DOB
Eye
Tested RE Refraction LE Refraction
RE
LogMAR
LE
LogMAR
RE Contrast
Sensitivity (log)
LE Contrast
Sensitivity (log)
Stereoacuity
(seconds of arc)
CEs 06.03.86 Binocular -1.00/-1.00x5 -0.75/-1.25x170 -0.22 -0.16 2.00 1.80 60"
DM 04.09.87 Binocular -1.50/-0.25x10 -1.25/-1.00x160 -0.06 -0.06 1.90 1.95 30"
JR 10.10.88 Binocular -3.25DS -3.25DS -0.06 -0.04 1.75 1.80 60"
MP 05.01.87 Binocular +0.25/-0.50x105 +1.00/-0.75x48 -0.10 -0.02 1.65 1.70 120"
MM 06.06.84 Binocular 0.00/+0.25x40 -.25/+0.25x160 -0.16 -0.20 1.75 1.60 60"
MH 28.03.86 RE +0.50/-1.25x15 +0.50/-0.25x175 -0.02 -0.04 1.60 1.60 60"
TC 06.05.88 LE +3.00/-0.50x125 +2.25/-0.25x115 -0.06 -0.08 1.75 1.80 60"
AK 25.07.85 RE +1.50DS +1.50DS -0.26 -0.26 1.90 1.80 30"
CaE 20.06.88 RE -6.50/-0.75x25 -7.50/-0.25x155 -0.22 -0.20 1.85 1.80 30"
FT 09.10.85 RE -0.25DS -0.50DS -0.12 0.02 1.55 1.60 30"
Table 1: Clinical data of the ten volunteers who participated in this study
28
7.2.4 Environment
A 40cm (±10cm) working distance was employed each time the chart was read.
Volunteers were given time to adopt a comfortable position as discomfort can affect
attention. A measuring tape was used to set the chart reading distance each time a chart
was being read.
7.2.5 Lighting
Lighting was kept constant during each chart that was read. The chart was directly
illuminated with a 100 watt light bulb fixed to the ceiling of the room and fluorescent
light stand. The fluorescent lighting stand position was adjusted until lumination incident
on the chart measured between 500-600 lux. A digital lightmeter was used (Center 337
Mini-lightmeter by Onsite Tools) to measure this and lighting was checked at every
session.
7.2.6 Guessing answers
Volunteers were verbally forced to guess the answers on each RDA level (forced choice).
They were stopped after three consecutive incorrect responses were given on each chart
(termination rule). Volunteers were given another final opportunity at levels where they
guessed incorrectly.
7.3 Data analysis
7.3.1 RDA Distribution
7.3.1.1 Psychometric functions
Psychometric functions according to the Gumbel-model were fitted using Bayesian
estimation in the open-source statistical software R by my project supervisor (Kuss et al.,
2005a; Kuss et al., 2005b). This function will allow us to estimate a fitted threshold RDA
for each chart. This threshold RDA will be compared to the threshold RDA derived
from the simple score technique.
The simple scoring technique will be the hypothesised model from which the
psychometric function is generated. Therefore a simple comparison of the two results
will show the goodness of the fit of the psychometric function.
The slope parameter of the psychometric function will illustrate the transition from when
volunteers can detect the radial deformation to when this becomes too difficult. A steep
29
slope would suggest the transition is very fast in contrast to a flatter slope indicating a
very slow transition.
7.3.1.2 Binocular versus monocular observation
The fitted RDA thresholds plotted against the slope of the psychometric function will
illustrate differences in the distributions of RDA in volunteers tested binocularly and
monocularly.
7.3.2 Comparing scoring techniques
A simple RDA scoring technique and a fitted threshold RDA interpolated from a
psychometric function technique were used to measure each volunteer’s threshold RDA
on each chart. Each volunteer completed six charts at every one of the four sessions.
An average RDA from each session and from all sessions was calculated for each scoring
system for each volunteer. These results were plotted on a scatterplot to illustrate the
distribution. 5% and 95% confidence intervals will show the precision of each scoring
system. A narrow confidence interval will indicate high precision of the scoring
techniques and a broad confidence interval will indicate a poor precision of the scoring
techniques.
To assess the variability between the two scoring techniques, standard deviations of the
average RDA scores were calculated and plotted.
To quantify the error generated, the RDA generated from most accurate scoring
technique was used. For each volunteer the standard deviation of their RDA scores was
divided by the square root of the number of charts that had been presented. This was
done for each chart and for each session. The spread of these two bar charts (individual
chart and sessional error) allowed construction of a predicted scoring error according to
the number of Manchester RDA charts presented.
7.3.3 RDA associations
By comparing the scoring techniques as described above, the most precise threshold
RDA was plotted against each volunteer’s logMAR VA and contrast sensitivity to
highlight any associations.
30
7.3.4 Learning
To assess whether there is a learning effect associated with the Manchester RDA charts,
the volunteers’ most precise threshold RDA was plotted for each of the four sessions
and the rank correlation coefficient was calculated.
31
8. Results
8.1 Distribution
8.1.1 Psychometric Functions
The psychometric functions in this group of ten volunteers are shown in figure 9. The
psychometric functions shown on the left hand side are from volunteers who observed
the chart monocularly (AK, TC, CaE, FT, MH). Those shown on the right hand side are
from binocular observers (CEs, DM, JR, MP, MM). The numbers shown beneath each
function are the threshold and slope parameters (slope is expressed as the width of the
psychometric function). The threshold parameter will be called the fitted threshold RDA
(log radial deformation).
The highest fitted threshold RDA is seen in CEs (3.32 log RDA). The highest RDA level
presented at the bottom of the Manchester RDA chart is 3.30 log RDA. Therefore,
CEs’s psychometric function illustrates a ceiling effect where her fitted threshold RDA is
greater than the radial deformation presented on the chart. This is also seen for MM’s
psychometric function (3.31 log RDA). Both CEs and MM were tested binocularly.
The lowest fitted threshold RDA were seen in TC (2.73 log RDA) and FT (2.73 log
RDA) both of whom were tested monocularly.
The slope parameter (expressed as the width of the psychometric function) illustrates the
transition from when volunteers see the radial deformation and when they don’t see. For
some volunteers the transition is very steep and for others it is very shallow. There
seems to be no specific pattern as to how the slope parameter varies between each
volunteer. The steepest slopes were seen with AK (0.54) and FT (0.54), both
monocularly tested. The flattest slope is seen in MM (1.2) who was tested binocularly.
However, CEs’ and MM’s psychometric function illustrates a ceiling effect. This will
affect the slope and threshold parameters interpolated so this result may not be true.
32
Response Probability
Figure 9:
Psychometric functions for each
volunteer for all four testing
sessions. Those volunteers in
the first column were tested
monocularly and those in the
second column were tested
binocularly. The legend
numbers are the fitted RDA
threshold for the 24 charts (left)
and the slope parameter
expressed as the width of the
psychometric function (right).
Stimulus Intensity (log radial deformation)
33
8.1.2 Binocular versus monocular viewing
Five volunteers were chosen at random to complete the chart monocularly and five
completed the charts binocularly. AK, TC, CaE, FT and MH were monocular observers.
CEs, DM, JR, MP and MM were binocular observers. The distribution of fitted
threshold RDAs estimated within these two groups is illustrated in figure 10.
The slope parameter value and fitted threshold RDA scores were interpolated from the
psychometric functions illustrated in figure 9. In this group of volunteers no significant
relationship is seen between the slope and fitted threshold RDA (R-square=0.16, p=0.25).
No significant difference is seen in fitted threshold RDA values between volunteers
tested monocularly and volunteers tested binocularly (p=0.31, Mann-Whitney U test).
Figure 10: Relationship between the slope and fitted threshold parameters of the psychometric functions
(R-square 0.16, p=0.25). Interestingly, CEs and MM scored highest fitted threshold and were tested
binocularly. Red initials are those volunteers tested binocularly, black initials are those tested
monocularly.
34
8.1.3 Fitted threshold versus simple scoring technique
Volunteers were tested on six charts at four sessions. Two scoring techniques were used
to score each chart. The average RDA (24 charts) for each scoring technique was
calculated for each volunteer. Figure 11 illustrates this distribution.
The simple scoring technique underestimates RDA at higher RDA levels. A greater
difference is seen between the two scoring techniques at higher RDA levels compared to
lower RDA levels.
In this group of subjects the RDA scores are seen to range from 2.75-3.25 log RDA
using the fitted threshold scoring technique and from 2.80-3.20 log RDA using the
simple scoring technique.
There is a linear positive association between the simple scoring technique (RDA score)
and fitting a psychometric function to the data (fitted threshold) (R-square=0.98). The
slope of this graph (0.67) indicates that in this group of volunteers, the scoring error is
dependent on the RDA measured. It is seen that the simple scoring RDA technique may
be a slightly more precise scoring technique. The narrow confidence intervals show both
scoring techniques have high precision.
Figure 11: Relationship between log RDA score and log fitted threshold RDA interpolated from
psychometric function plots (R-square=0.98, slope=0.67). RDA scores are seen to range from 2.75-
3.25 using the fitted threshold scoring technique and from 2.80-3.20 using the simple scoring technique.
Red lines are 5% and 95% confidence intervals for linear regression.
35
8.2 Scoring Errors
8.2.1 Variability of results
The variability for each type of scoring technique was calculated for each volunteer. This
was done by computing the standard deviation (SD) of all 24 measurements. The SD of
both the RDAs measured by the two different scoring techniques was determined. Figure
12 shows a comparison of the variability.
There appears to be a greater variation with the fitted threshold RDA scores compared
to the simple scoring technique RDA scores.
There is more variation in the two scoring techniques seen in volunteers who scored
lower on the Manchester RDA charts. For instance, TC and FT both scored 2.73 log
RDA on the fitted threshold scoring technique and 2.80 log RDA by the simple scoring
technique respectively. There is a ≈0.10 log RDA difference in the two different scoring
techniques seen for TC and FT.
CEs and MM both scored the highest RDA with both scoring techniques. However,
they both seem to have very different amounts of variation between both the scoring
techniques compared to each other. CEs has less variation with both scoring techniques
compared to MM.
Figure 12: Variability
of two different scoring
techniques used to score
RDA (simple and fitted
threshold RDA) across
the 6 charts and 4
sessions.
36
Some individual charts fitted threshold RDA scores were estimated from a psychometric
function which was step-like. This gave the slope of the psychometric function an
inaccurate value of zero. Figure 13 illustrates the distribution of variability omitting these
step-like psychometric function fitted RDA thresholds with zero slopes.
The distribution of variability is very similar to figure 12. This means omitting the step-
like psychometric function data does not make much difference to the distribution of
variability.
Figure 13:
Variability of two different
scoring techniques used to score
RDA (simple and fitted
threshold RDA) across the 6
charts and 4 sessions, omitting
individual chart psychometric
functions with step-like slopes.
37
8.2.2 Manchester RDA chart scoring errors
The simple scoring technique is a more precise way of scoring RDA on the Manchester
RDA charts (figure 11). Figure 14 shows the error generated by the simple scoring
technique against the number of charts presented. The error was calculated by taking the
SD (variation) of the simple RDA threshold of n number of charts and dividing the SD
by the square root of n.
An error in the range of +/- 0.4 log RDA for each individual chart (figure 14). This
seems to be skewed towards +0.4 log RDA illustrating an overestimation of RDA with
the simple scoring technique.
Figure 14: The error for each individual Manchester RDA chart and the number of charts which were
seen with this error. Error=(SD simple RDA threshold of n number of charts) / √n number of charts.
38
Figure 15 illustrates the sessional chart error. This was calculated from the threshold
RDA averaged from four sessions. This shows less error of -0.2 to +0.1 compared to
figure 14. Therefore, RDA is slightly underestimated when an average is taken.
Figure 15: The RDA averaged error over four sessions and how many charts were seen with this error.
Error=(SD averaged RDA over four sessions) / √n number of charts.
39
8.2.3 Predicted error on a Manchester RDA chart
From calculating the errors produced on each individual chart and within each session a
predicted error according to the number of charts tested can be calculated (figure 16).
This was done by using the standard error of mean (SEM) equation (SEM=SD of single
measurement - √number of measurements).
The predicted score error decreases by almost 0.70 log RDA by the time 5 charts are
used to measure RDA. When ten charts are used to measure RDA the predicted scoring
error is close to 0.05 log RDA error. The spread of the error generated from single
measurements and over the four sessions (figures 14 and 15) are in good agreement with
this predicted theory.
Figure 16: Manchester RDA chart spread of predicted error.
Calculated curves of predicted measurement error with 1 to 20 averaged measurements. The black line
shows the relationship between the predicted error (standard error of the mean) if single measurement had
an SD of 0.15. If ten such measurements were combined, the error of the combined measurements would
be close to 0.05. Red lines show predicted curves for SDs of 0.20 (top curve) and 0.10 (bottom curve).
The empirical data (red dots) of single measurements and 4 combined measurements show good agreement
with theory.
40
8.3 RDA and Contrast Sensitivity
In this group of subjects there is no significant association between RDA and contrast
sensitivity (Pearson correlation coefficient r=0.10478, p=0.77, figure 17). These results
show that RDA can not replace or predict contrast sensitivity, or vice versa. It can be
said that in this group of subjects, RDA is not influenced by contrast sensitivity.
Interestingly, CEs scored the highest threshold RDA (3.30 log RDA) and has the highest
contrast sensitivity in this group (CEs=1.90 log CS). However, DM had a similar
contrast sensitivity score to CEs (DM=1.925 log CS) but showed a lower threshold RDA
(2.80 log RDA). FT scored the lowest RDA (2.70 log RDA) and had the lowest contrast
sensitivity (FT=1.55 log CS).
Figure 17: Relationship between contrast sensitivity and log RDA score. Those initials in red are
volunteers who were tested binocularly and those in black were tested monocularly. (Pearson correlation
coefficient r =0.10478).
41
8.4 RDA and logMAR VA
This group of volunteers show no significant association between RDA and logMAR VA.
(Pearson correlation coefficient r=-0.3982, p=0.25, figure 18). In this group of volunteers
RDA is unaffected by logMAR VA. From this observation it can be said that RDA
cannot replace or predict logMAR VA, or vice versa.
Worthy of note is perhaps the fact that both MM and CEs who both scored the highest
RDA scores (CEs=3.20 log RDA, MM=3.20 log RDA) have almost the same logMAR
acuity (CEs=-0.19 logMAR VA, MM=-0.18 logMAR VA).
Figure 18: Relationship between log RDA score and logMAR VA. Those initials in red are
volunteers tested binocularly and those in black were tested monocularly. (Pearson correlation coefficient
r=-0.3982).
42
8.5 Learning
Figure 19 shows the variation in RDA over the four sessions. The rank correlation
coefficient is listed under each volunteer’s name. A value of greater than 0 shows
positive correlation between the number of sessions and log RDA. A value of less than 1
is negative correlation. A rank correlation of 0 shows no association.
Seven volunteers scored positive rank correlations and improved their RDA score over
the four sessions (FT, MM, TC, AK, DM, MD, JR). MH was the only volunteer to show
no improvement in RDA over the four sessions. Two volunteers showed a decrease in
threshold RDA over the four sessions (CaE, CEs). However, CEs showed a ceiling
effect on the charts (figure 9). Therefore, threshold RDAs for CEs and MM used for this
graph may not be precise.
Figure 19: Threshold RDA for each session for each volunteer (simple scoring technique). The charts are ordered from the volunteer
who has the highest Spearman-rank correlation coefficient (the most consistent with learning effect with each RDA result being higher
than the result previously). Negative values indicate that the order of the results was opposite that expected from a learning effect.
43
9. Discussions
9.1 Potential improvements to the Manchester RDA charts
9.1.1 RDA Distribution
The distribution of fitted threshold RDA in this group of volunteers showed a ceiling
effect (figure 9). The lowest threshold RDA stimulus presented at the bottom of the
Manchester RDA chart is -3.30 log radial deformation. This study has shown two
volunteers (CEs and MM) could still correctly identify 19 out of 20 RDA stimuli
presented on the charts. To avoid this ceiling effect the Manchester RDA charts need to
present a lower threshold RDA stimulus.
Ideally, the Manchester RDA chart’s lowest threshold RDA level should be 3.50 log
RDA so that a clear cut off point is seen without a ceiling effect. This would be when no
observer would be able to detect the radial deformation. It is important not to include
too many difficult levels because it can upset patients when they cannot see more than
half the chart. To more precisely decide on the lowest threshold RDA stimulus
presented, the experimental protocol described for this study should be repeated with the
improved charts on visually healthy volunteers before it is tested on non- visually healthy
volunteers.
The slope parameter of the psychometric functions (expressed as the width of the
psychometric function) illustrated the transition of seeing to not seeing a radial
deformation. Specifically this implied what the step sizes for radial deformation should
be used on the Manchester RDA charts. For some psychometric functions fitted
(particularly those fitted to single chart data) a step-like function (slope=0) was seen as
opposed to a sigmoid function. This revealed that for some volunteers, the steps
between each RDA level increased too quickly. That is to say the amount by which
radial deformation decreased was too quick, and an observer went from seeing a radial
deformation to not seeing one in the space of one line. Ideally, a smooth transition
should be seen.
This sharp transition was seen more frequently at levels 2.60, 2.70, 2.80, 2.90 and 3.00 log
RDA. As a solution the Manchester RDA charts could present RDA levels where the
amount of radial deformation decreases in 0.05 steps rather than 0.10 steps. This may
44
also improve the precision by which RDA is measured. An alternative would be to have
a coarse and fine Manchester RDA chart.
In this group of volunteers, no association was seen between the slope (expressed as the
width of the psychometric function) and fitted threshold interpolated from the
psychometric functions (p=0.25, figure 10). It was seen that the volunteers who had
lower RDA thresholds had a slower transition (smaller slope) between seeing and not
seeing the radial deformation. Those volunteers who had higher thresholds had slightly
higher slope values. This result also implies the step sizes by which radial deformation
decreases are too coarse. From this distribution it is suggested the optimum step size
should be between 0.25-0.33 (p=0.25, R-Square, p=0.31, Mann-Whitney U test, figure 10).
However, the step sizes already decrease radial deformation by 0.10, so this distribution
of fitted threshold RDA and slope values may change when lower threshold radial
deformation levels are presented on the chart.
There was no significant difference seen in the distribution of fitted threshold RDA
scores in the two groups of binocular and monocular observers (figure 10). However, this
may be because only ten volunteers participated in this study. To ascertain with more
confidence if a binocular summation effect is seen with viewing the Manchester RDA
charts, fifty-five binocular and fifty-five monocular volunteers would need to be tested
(DSS researcher's toolkit online).
9.1.2 Scoring techniques
From the data collected from this volunteer group, the more accurate scoring technique
cannot be determined but it can be seen that the simple scoring technique is more precise
(figure 11). However, the results clearly demonstrate that the error generated with each
scoring technique is dependent on the threshold RDA measured (R-square=0.98,
slope=0.67). The psychometric functions over-estimates threshold RDA when higher
RDA levels were measured compared to the simple scoring technique (figure 11). Ideally,
we would want a scoring technique where error is independent of RDA measured
(slope=1.0).
It is evident that the lowest threshold RDA level presented on the Manchester RDA
chart is not low enough (3.30 log RDA). This may explain the RDA distribution
described above since the upper scoring boundary is different for each scoring technique.
For a fitted threshold RDA interpolated from a psychometric function, there is no upper
45
limit for the RDA interpolated. For the simple scoring system the highest RDA that can
be scored is limited to 3.30 log RDA.
The result described above correlates with those Hazel and Elliott (2002) found when
they fitted psychometric functions to data generated from observers reading a logMAR
chart (logMAR VA versus percentage of letters called correctly). They also found
psychometric functions to over-estimate VA measurements by approximately two letters
(0.02 logMAR).
We can say the fitted RDA thresholds were more variable over time than the RDA
thresholds measured by the simple scoring technique (figures 12 and 13). Since omission
of step-like functions made little difference to this variability it is unlikely that the fit of
the psychometric function is the reason for the greater variation. This result was
surprising since psychometric functions are thought to be the most accurate way of
extracting information on stimulus-response relationships (Wichmann and Hill, 2001).
9.1.3 Scoring Errors
The range of error generated from the simple scoring technique decreases as the number
of charts tested increases (figures 14 and 15). For a <0.05 error in the threshold RDA
score measured our results predict a range of fifteen to twenty charts should be tested
(figure 16). For this study each volunteer completed six Manchester RDA charts. For six
Manchester RDA charts our results predict a 0.09 log RDA scoring error. Ideally, we
would want to testing times to be short and scoring errors to be small for the Manchester
RDA chart. This error generated may be less if the steps by which radial deformation
decreases is changed. This may reduce the number of step-like psychometric functions
fitted and perhaps change the distribution of scoring error. This would in turn affect the
predicted error and the number of charts presented to have an error of <0.05 (currently
our data suggest 15-20 charts for a <0.05 error).
9.1.4 RDA associations
Contrast sensitivity and logMAR VA showed no association with RDA in this group of
subjects. However, it was an interesting result that both CEs and MM had the highest
contrast sensitivity and RDA. In order to see a stronger association between contrast
sensitivity and threshold RDA a bigger testing group will be required. This would be
similar to that needed to see a binocular summation effect (one hundred and ten
volunteers). In addition to a larger testing group, our study methodology would also
46
have to change so each observer has their RDA measured monocularly and binocularly,
to account for the effect of inter-subject variability on the threshold RDAs measured.
9.1.5 Learning with the Manchester RDA charts
Seven of the volunteers who completed the Manchester RDA charts showed some
evidence of a learning effect (figure 19). These were FT, MM, TC, AK, DM, MP and JR.
FT’s threshold RDA improved at each testing session and she showed a definite learning
effect (Rank correlation coefficient r=1). This can be called a learning effect since it is
unlikely that a true change in the underlying sensory process has taken place. Evidence
seen against a learning effect (Rank correlation coefficient r ≤ 0) may be the result of
fatigue (MH, CaE, CEs). This study did not look at the fatigue effects. Fatigue effects
may have explained the step-like slopes seen from individual chart data fitted to a
psychometric function. To quantify fatigue effects more charts would have to be
observed in one session. From this small group of volunteers we cannot say whether
there is a significant learning effect associated with the Manchester RDA charts.
9.2 Future Experiments
9.2.1 Larger testing groups
Larger testing groups would be beneficial for the study of associations. Associations
were difficult to find in such a small testing group. There may be an association between
contrast sensitivity and RDA. Having more than ten data points will allow a visual
association to be seen more clearly. One hundred and ten data points will allow us to
determine whether binocular summation affects RDA with more certainty (number of
volunteers required to investigate binocular summation).
It was difficult to conclude whether binocular summation affected RDA in such a small
testing group so larger testing groups could confirm whether performing the Manchester
RDA charts is difference monocularly versus binocularly.
These associations may reveal the need for further investigations, for example
quantifying the effect of the association.
9.2.2 Binocular versus monocular investigations
Once the association has been identified from a larger testing group it will be important
to investigate and quantity these effects so that they can be considered when scoring
RDA.
47
If threshold RDA measurements are found to be positively associated with logMAR VA
or contrast sensitivity, one may expect binocular RDA to be better than monocular RDA.
Quantifying how much RDA should improve by binocularly will also be of clinical
importance should this value vary in visually normal and non-visually normal observers.
9.2.3 Manchester Royal Infirmary studies
After all the properties of the Manchester RDA chart have been identified on visual
normals the chart should be tested on patients who may have retinal eye diseases, for
example macular degeneration, diabetic maculopathy and central serous retinopathy. It
will be interesting to look at how the associations researched in this study change in these
patients and whether the Manchester RDA chart would be a useful diagnostic tool in
clinical practice.
48
10. Conclusions
Firstly, this study has highlighted limitations of the Manchester RDA charts themselves.
The lowest threshold RDA stimulus presented on the Manchester RDA chart is not low
enough to measure RDA in young, healthy observers. The lowest threshold RDA
stimulus should be at least 3.50 log RDA.
Secondly, this study has shown psychometric function fitted RDA thresholds yield higher
RDA thresholds at higher RDA testing levels. This relationship is reversed for lower
RDA testing levels. Scoring errors for RDA decreased as the number of Manchester
RDA charts presented increased. Presenting between fifteen to twenty Manchester RDA
charts will generate a less than 0.05 log RDA error compared to presenting 6 Manchester
RDA charts which generates a 0.09 log RDA error (almost one step of RDA level on the
chart). Thirdly, in this group of visually normal, healthy, young volunteers no statistical
association is seen between RDA and logMAR VA measurements or RDA and contrast
sensitivity measurements.
Furthermore, in seven out of ten volunteers some evidence of a learning effect is seen
but it was not very large compared to the variation between subjects. To ascertain if
binocular summation affects threshold RDA a total of one hundred and ten volunteers
would need to be tested, fifty-five monocularly and fifty-five binocularly.
This study has indicated future research on the Manchester RDA charts. Initially, it will
be necessary to measure RDA on a larger group of visually-normal, healthy, young
volunteers. This may determine the most accurate technique to score RDA. Once
associations and factors affecting RDA have been quantified, RDA should be measured
on volunteers who have retinal eye diseases, for example age-related macular
degeneration, diabetic maculopathy and central serous retinopathy. The analysis of these
results should conclude the clinical advantages for testing RDA.
49
11. Acknowledgements
I would first and foremost like to acknowledge and thank all my volunteers (AK, CEs,
CaE, DM, FT, JR, MH, MP, MM and TC) for donating their free time to participate in
this study. Their dedication and commitment is very much appreciated. I would
especially like to thank CEs and AH for also donating their time for the pilot study.
I would like to acknowledge and thank my project supervisor, Paul Artes. His guidance
throughout the project was always available. He was very positive about the results
collected and I am grateful to him for plotting the psychometric functions for this study.
I would like to thank my family and friends for their encouragement and feedback into
this project.
50
12. References
Alcalá-Quintana, R., & Garcia-Pérez, M. A. (2004). The role of parametric assumptions
in adaptive Bayesian estimation. Psychological Methods 9(2), Jun 2004, 250-271.
Birch, E. E., Swanson, W. H., & Wang, Y. (2000). "Infant hyperacuity for radial
deformation." Investigative Ophthalmology and Visual Science 41(11): 3410-3414.
BSI. (2003). "Visual acuity test types — Part 1: Test charts for clinical determination of
distance visual acuity — Specification."
From http://www.bsonline.bsi-
global.com/server/PdfControlServlet/bsol?pdfId=GBM05%2F30021439&format=pdf.
Chauhan, B.C., Tompkins, J.D., LeBlanc, R.P. & McCormick, T.A. (1993)
"Characteristics of frequency-of-seeing curves in normal subjects, patients with suspected
glaucoma, and patients with glaucoma." Investigative Ophthalmology and Visual Science
34 (13), pp. 3534-354
DeMonasterio, F. M. G., P (1975). "Functional properties of ganglion cells of the rhesus
monkey retina." Journal of Physiology 251: 167-195.
DSS. "DSS Researcher's toolkit." from
http://www.dssresearch.com/toolkit/spcalc/power_a2.asp.
Elliott, D. B. (1997). Assessment of Visual Function. Clinical Procedures in Primary Eye
Care. K. Benson, Butterworth-Heinemann: 75-76.
Elliott, D. B., K. C. H. Yang, et al. (1995). "Visual acuity changes throughout adulthood
in normal, healthy eyes: Seeing beyond 6/6." Optometry and Vision Science 72(3): 186-
191.
Fahle, M., & Henke-Fahle, S (1996). "Interobserver variance in perceptual performance
and learning." Investigative Ophthalmology and Visual Science 37(5): 869-877.
51
Fahle, M., Edelman, S., & Poggio, T. (1995). "Fast perceptual learning in hyperacuity."
Vision Research 35(21): 3003-3013.
Gilchrist, J.M., Jerwood, D., Sam Ismaiel, H. “Comparing and unifying slope estimates
across psychometric function models” (2005) Perception and Psychophysics, 67 (7), pp.
1289-1303.
Goldstone, R. L. (1998). "Perceptual Learning." Annual Review of Psychology 49: 585-
612.
Hazel, C. A. and D. B. Elliott (2002). "The dependency of logMAR visual acuity
measurements on chart design and scoring rule." Optometry and Vision Science 79(12):
788-792.
Hess, R. F., Y. Z. Wang, et al. (1999). "Are judgements of circularity local or global?"
Vision Research 39(26): 4354-4360.
Hess, R. F., Wang, Y. -., Demanins, R., Wilkinson, F., & Wilson, H. R. (1999). "A deficit
in strabismic amblyopia for global shape detection." Vision Research 39(5): 901-914.
Kaernbach, C. (2001) "Slope bias of psychometric functions derived from adaptive data."
Perception and Psychophysics 63 (8), pp. 1389-1398
King-Smith, P.E. & Rose, D. (1997) "Principles of an adaptive method for measuring the
slope of the psychometric function." Vision Research 37 (12), pp. 1595-1604
Kolb. H. Fernandez. E. & Nelson, R. from
http://webvision.med.utah.edu/KallSpatial.html.
Kontsevich, L.L. & Tyler, C.W. (1999) "Bayesian adaptive estimation of psychometric
slope and threshold." Vision Research 39 (16), pp. 2729-2737
Kuss, M., Jakel, F. & Wichmann, F.A.. (2005a). "Approximate Bayesian Inference for
Psychometric Functions using MCMC Sampling." Max Planck Institute for Biological
Cybernetics Technical Report No. 135: 1-30.
52
Kuss, M., Jakel, F. & Wichmann, F.A.. (2005b). "Bayesian inference for psychometric
functions." Journal of Vision 5(5): 478-492.
Levi, D. M., & Klein, S. (1982). "Hyperacuity and amblyopia." Nature 298(5871): 268-
270.
Moss, C. F., & Lehmkuhle, S. (1986). "Spatial displacement sensitivity of X- and Y-cells
in the dorsal lateral geniculate nucleus of the cat." Vision Research 26(7): 1027-1040.
Parker, A., & Hawken, M. (1985). "Capabilities of monkey cortical cells in spatial-
resolution tasks." Journal of the Optical Society of America. A, Optics and image science
2(7): 1101-1114.
Patterson, V.H., Foster, D.H. & Heron, J.R. (1980) "Variability of visual threshold in
multiple sclerosis. Effect of background luminance on frequency of seeing." Brain 103
(1), pp. 139-147
Poggio, T., Fahle, M., & Edelman, S. (1992). "Fast perceptual learning in visual
hyperacuity." Science 256(5059): 1018-1021.
Seitz, A. R., Yamagishi, N., Werner, B., Goda, N., Kawato, M., & Watanabe, T. (2005).
"Task-specific disruption of perceptual learning." Proceedings of the National Academy
of Sciences of the United States of America 102(41): 14895-14900.
Shapley, R., & Victor, J. (1986). "Hyperacuity in cat retinal ganglion cells." Science
231(4741): 999-1002.
Sireteanu, R., & Rettenbach, R. (1995). "Perceptual learning in visual search: Fast,
enduring, but non-specific." Vision Research 35(14): 2037-2043.
Snoeren, P.R. & Puts, M.J.H. (1997) "Multiple parameter estimation in an adaptive
psychometric method: MUEST, an extension of the QUEST method." Journal of
Mathematical Psychology 41 (4), pp. 431-439.
Spear, P. D. (1993). "Neural bases of visual deficits during aging." Vision Research
33(18): 2589-2609.
53
Strasburger, H. (2001) "Invariance of the psychometric function for character
recognition across the visual field" Perception and Psychophysics 63 (8), pp. 1356-1376..
Swindale, N. V., & Cynader, M. S. (1986). "Vernier acuity of neurones in cat visual
cortex." Nature 319(6054): 591-593.
Treutwein, B. "Adaptive psychophysical procedures." (1995) Vision Research 35 (17), pp.
2503-2522.
Wang, Y.-., Wilson, E., Locke, K. G., & Edwards, A. O. (2002). "Shape discrimination in
age-related macular degeneration." Investigative Ophthalmology and Visual Science
43(6): 2055-2062.
Wang, Y. (2001). "Effects of aging on shape discrimination." Optometry and Vision
Science 78(6): 447-454.
Watt, R. J., & Andrews, D. P. (1982). "Contour curvature analysis: Hyperacuities in the
discrimination of detailed shape." Vision Research 22(4): 449-460.
Westheimer, G. (1982). "The spatial grain of the perifoveal visual field." Vision Research
22(1): 157-162.
Westheimer, G. (1994). "The Ferrier Lecture, 1992 - Seeing depth with two eyes:
Stereopsis." Proceedings of the Royal Society of London - B. Biological Sciences
257(1349): 205-214.
Westheimer, G. (2003). Visual Acuity. Adler's Physiology of the Eye. P. L. Kaufman, &
Alm, A.A,. United States of America, Mosby: 453-469.
Whitaker, D., Rovamo, J., MacVeigh, D., & Makela, P. (1992). "Spatial scaling of vernier
acuity tasks." Vision Research 32(8): 1481-1491.
Wichmann, F. A. and N. J. Hill (2001). "The psychometric function: I. Fitting, sampling,
and goodness of fit." Perception and Psychophysics 63(8): 1293-1313.
54
Wild, J., Kim, L., Pacey, I. & Cunliffe, I. (2006). "Evidence for a learning effect in short-
wavelength automated perimetry." Ophthalmology 113(2): 206-215.
Wilkinson, F., Wilson, H. R., & Habak, C. (1998). "Detection and recognition of radial
frequency patterns." Vision Research 38(22): 3555-3568.