The ‘structure-function’ relationship in glaucoma – past thinking and current concepts

Abstract

An understanding of the relationship between functional and structural measures in primary open angle glaucoma (POAG) is necessary for both grading the severity of disease and for understanding the natural history of the condition. This article outlines the current evidence for the nature of this relationship, and highlights the current mathematical models linking structure and function. Large clinical trials demonstrate that both structural and functional change are apparent in advanced stages of disease, while, at an individual level, detectable structural abnormality may precede functional abnormality in some patients whilst the converse in true in other patients. Although the exact nature of the ‘structure-function’ relationship in POAG is still the topic of scientific debate and the subject of continuing research, this article aims to provide the clinician with an understanding of the past concepts and contemporary thinking in relation to the structure-function relationship in POAG.

What is the ‘structure-function relationship’ in glaucoma?

Glaucoma is a family of chronic, progressive and potentially blinding optic neuropathies characterised by distinctive morphological (or ‘structural’) changes of the optic nerve head (ONH) and retinal nerve fibre layer (RNFL) associated with visual field changes. ¹ Primary open angle glaucoma (POAG) is the commonest subtype. Both structural and functional changes result from loss of retinal ganglion cells (RGCs) and their axons. The degree of structural (neuroretinal rim, RNFL) and visual field loss is used to grade the likelihood and severity of POAG both in the clinical setting ² and in large scale clinical trials ^3–5. Broadly speaking, “functional change” in POAG can indicate a disturbance of any test of visual function, although often used synonymously with visual field change. Clinical measurements of structure and function, at any stage of glaucoma, exhibit a wide variability between individuals and on repeated measurements, so the true extent of damage is often difficult to ascertain. Consequently, clinicians use measurements in one domain (structure or function) to support the interpretation of measurements in the other domain. The relationship between structure and function measurements is, therefore, of considerable importance.

Given that both structural and functional parameters decline with progressive glaucoma ^{4, 6} and that both arise from a common pathophysiological process, namely death of RGCs with loss of related axons ^{7, 8}, it would be expected that both structural and functional measurements in glaucoma should be related over the course of the disease. However, the exact nature of the ‘structure-function’ relationship in POAG is still the topic of scientific debate and the subject of continuing research.

Importance of the structure function relationship

An understanding of the structure-function relationship in POAG is necessary for both grading the severity of disease and for understanding the natural history of the condition. In the clinical setting, patients with apparently the same degree of neuroretinal rim loss can have different amounts of visual field loss. Further, some patients have evidence of glaucomatous optic neuropathy without a detectable visual field abnormality whilst others have a glaucomatous visual field without detectable structural abnormality. For the clinician, this poses a diagnostic dilemma regarding the likelihood of disease and as to whether the severity of POAG should be primarily gauged on the basis of structure or function or a combination of both.

The natural history of POAG is one of progressive neuroretinal rim loss, visual field loss ⁶ and in a subset of patients, blindness. ⁹ The relationship between ganglion cell loss and visual field loss for a given stage of disease is still inadequately understood. It is likely that a better understanding of the rates of structural and functional changes in relation to the underlying neuronal counts will develop as improvements in vivo imaging techniques in human eyes lead to a better understanding of the disease processes.

Measuring structure and function

Clinical measurements of structure and function are attempts to quantify the integrity of the anatomical pathway subserving vision, in particular the neural elements damaged in glaucoma, namely the RGCs and their axons. Many factors may confound the measurement of these neural elements and these are discussed below.

Visual function measures can drop to zero (no perception of light), while anatomical measures have a residual non-neural component that can be substantial even in blind eyes. Estimates of the non-neural component for a given individual, from a group mean, may be erroneous. Aside from error in estimating the neural contribution to measurements of structure and function, one needs to consider other factors that may affect the apparent relationship between the number of RGCs and visual function (as measured by perimetry). The nature of the structure-function relationship in glaucoma is influenced by the scale for measurements. ^{10, 11} Imaging devices in common clinical use for measuring the structure of the ONH and RNFL include confocal scanning laser ophthalmoscopy (SLO), scanning laser polarimetry (SLP) and ocular coherence tomography (OCT). These devices provide a quantification of neuroretinal rim area (in mm²) or RNFL thickness (in μm) and, more recently, of macular and “ganglion cell complex” thickness (in μm), usually in reference to normative values. Both mm² and μm are linear metrics of measurement, and should be linearly related to local ganglion cell density.

Standard automated perimetry (SAP) typically utilises a constant size stimulus, the Goldmann size III (0.43 degrees in diameter), at all test locations. Visual field sensitivity or differential light sensitivity is recorded in logarithmic units or decibels (dB) which are related to the luminance of the stimulus relative to the background. The dB is relative to a reference level. Specifically, dBs are used to express a ratio (in reference to the maximum luminance of the perimeter) rather than an absolute quantity. As the maximum luminance differs on different perimeters, a given dB value is not interchangeable on different perimeters with different background and maximum stimulus brightness. Decibels are a non-linear measure: a change by 3 dB represents a doubling or halving of light intensity. When dB increments are plotted against a linear scale, it becomes apparent that identical dB increments at different levels of sensitivity are very different sized increments on a linear scale. Figure 1 shows the relationship between visual field sensitivity, in linear units plotted against visual field sensitivity in dB. A 2 dB decrement from 38 dB to 36 dB is ten-fold greater change in linear units than the same dB change at a sensitivity of 28 dB. The units of measurement for structural and functional parameters are confounding factors in the study of the structure-function relationship.

Figure 1. The non-linear relationship between dB units and linear (L⁻¹) metrics of differential light sensitivity for standard automated perimetry.

A decline of 2 dB from a sensitivity of 32 dB is ten-fold greater, on a linear scale, than a decline of 2 dB from 22 dB.

There is strong evidence that perimetric sensitivity, when expressed in linear units, is linearly related to ganglion cell density in the local retinal region being tested. ^10–13 That is, when ganglion cell density is halved, perimetric sensitivity in linear units is also halved. Physiological evidence comes from massed evoked potentials dominated by ganglion cell responses: the multifocal Visual Evoked Potential (mVEP) which reflects summed ganglion cell input to visual cortex, and the Pattern Electroretinogram (PERG) which reflects the summed activity of retinal ganglion cells. Hood and colleagues found that linear visual perimetric sensitivity was linearly related to the signal portion of the amplitude of the mVEP. ¹⁴ Garway-Heath and colleagues found that linear visual field measures were linearly related to the amplitude of the PERG amplitude, ^{10, 15} and this was confirmed independently by Yang & Swanson.¹⁵ Garway-Heath and colleagues also found that linear visual field measures were linearly related to the area of neuroretinal rim; this was confirmed independently by Shafi et al.¹⁶ Hood and colleagues found that linear visual field measures were linearly related to the neural component of RNFL thickness ¹⁷; this was confirmed independently by Leite and colleagues. ¹⁸

Psychophysical factors influencing the structure-function relationship

Spatial summation describes the relationship between stimulus area (and the number of underlying RGCs) and visual field sensitivity. Studies support the conclusion that linear perimetric sensitivity is linearly related to ganglion cell number. Consider spatial summation for circular luminance (‘brightness’) increments like the SAP stimuli: the long-established ‘Ricco’s law’ states that, when small areas of retina are stimulated, the area of retina stimulated and the visual sensitivity are linearly related (a slope of 1 on log-log axes). In healthy eyes under photopic conditions, this small area (‘Ricco’s area’) increases with distance from fixation and within 15° from fixation it is smaller than the Goldmann size III stimulus used in SAP. This has traditionally been attributed to summation within the receptive field of a retinal ganglion cell ¹⁹, but subsequent studies have indicated that Ricco’s area is determined by optical factors at fixation ²⁰ and by cortical factors across the central visual field ²¹. The assumption that detection is determined by responsiveness of an individual ganglion cell would lead one to expect that perimetric sensitivity for this stimulus would be relatively unaffected by modest amounts of ganglion cell loss ²². By comparison, assessment of cortical pooling effects on spatial summation concluded that sensitivity to the size III stimulus declines with even modest amount of ganglion cell loss ^{21, 23, 24}, and that this is seen even for the much larger stimuli used in frequency-doubling perimetry ²⁵.

Cortical pooling of ganglion cell responses can be characterized in terms of multiple spatial mechanisms or multiple cortical detectors with peak responses at different spatial frequency ²⁶, where Ricco’s area is determined by the spatial mechanism with the greatest sensitivity to small luminance increments ²¹. Perimetric sensitivity across the central visual field is relatively constant when the stimulus is scaled to Ricco’s area, consistent with spatial mechanisms varying in spatial scale with eccentricity ²⁷. Cortical pooling provides a new understanding of the well-established result that effects of spatial summation for perimetric stimuli can be altered in patients with glaucoma ^28–30. A recent study of spatial summation in early glaucoma suggested that decline in ganglion cell density reduces the sensitivity of higher-frequency cortical spatial mechanisms mediating detection in normal eyes, so that the mechanism mediating detection in a glaucomatous defect pools the same number of ganglion cells as the corresponding higher-frequency mechanism that mediates detection at that visual field location in normal eyes. ³¹ Cortical pooling analysis demonstrates that such a reduction in sensitivity of higher-frequency mechanisms would result in a linear decline in sensitivity with decline in ganglion cell density, a slope of 1 on log-log axes ²¹. For the central 15°, the slope of the relationship is no longer 1, so that a unit increase in area gives rise to less than a unit increase in sensitivity (figure 2).

Figure 2. The ‘Hockey-Stick’ model relating sensitivity and ganglion cell (GC) receptive field number (both in log units).

The datapoints from Garway-Heath et al. (2000) 12 and empirical plot of Swanson et al. (2004)³⁸ is indicated by the black symbols and solid black line respectively. Anderson & Knighton’s (1988) function ⁶⁶, with RGC receptive field number derived from acuity perimetry, is approximated by the grey solid line. The size of the stimulus in relation to the critical area may explain the change in slope at 15 degrees eccentricity. The spatial summation curve predicted by a model of cortical pooling is shown for comparison ²¹. See text for details.

The ‘Structure-function timeline’ and the linear structure-function model

Raed and Spaeth studied the relationship between optic disc cupping and visual field change ⁶. They found that many eyes had visual field damage when masked ‘expert’ evaluation of the optic disc did not expect field damage; they hypothesized from these cross-sectional data that minimal visual field change occurred when the cup-disc ratio (CDR) enlarged from 0.3 to 0.6 and that more marked visual field loss occurred when the CDR enlarged from 0.6 to 1.0. The notion of ‘preperimetric glaucoma’ was subsequently popularised in the early 1980’s by reports which demonstrated clinically detectable ONH changes in eyes without detectable visual field damage ^{32, 33}. This clinical observation received support from the interpretation of comparisons of histological ganglion cell data with prior perimetric data from post-mortem eyes, concluding that visual field sensitivity declines after ganglion cell loss ^{7, 34}. The concept of a ‘functional reserve’ followed, which described a functional latency period in the natural history of glaucoma where structural change occurred without functional change ²². A number of successive investigators showed that the relationship between visual field measurements (in dB) and structural measures of glaucomatous optic neuropathy (in linear units) is curvilinear ^{10, 35–37}. That is, in early POAG, structural loss appears greater than functional loss, whilst in more advanced disease, it appears as if function changes at a greater rate than structure. Garway-Heath demonstrated that this curvilinear relationship may be a consequence of measuring visual function in logarithmic units, whilst ganglion cell measures are measured in linear units ^{10, 12}. In addition, the structure-function relationship became more linear when sensitivity was plotted in linear units and spatial summation affects were accounted for ¹⁰. This ‘linear’ model of the ‘structure-function relationship (i.e. a linear relationship when both structure and function are recorded in linear units) has been supported by studies of the relationship between visual field sensitivity and PERG amplitude ^{10, 15}, and the signal portion of the amplitude of the multifocal VEP ¹⁴. Swanson and colleagues developed an empirical model to simulate the neural response of ganglion and cortical cells to perimetric stimuli and found this could explain a linear relationship between depth of visual field defect relative to normal (in %) and percentage of ganglion cells damaged ³⁸.

The Hood-Kardon model (described below) extrapolates the linear structure-function model to define the relationship between visual field sensitivity (in dB) and RNFL thickness (in μm) and accounts for a ‘non-neural’ structural component ¹⁷. In other words, in eyes blind with glaucoma, visual field sensitivity can drop to zero, whilst RNFL thickness reaches a basement effect around 44–60 μm. ³⁹ This residual has been attributed to the presence of presence of glial supportive tissue and blood vessels within the RNFL. The Hood-Kardon model has been extended to rim area, where the non-neural residual appears to be smaller. ¹⁶

Which goes first- Structure or function?

It is often asserted that structural abnormalities precede visual field changes in the development of glaucoma. In fact, there is substantial evidence to suggest that abnormalities of the visual field can precede detectable abnormalities of the ONH or RNFL. The contemporary opinion is that detectable structural and function changes can occur concurrently in some patients, whilst either structural or functional change is apparent first in others.⁴⁰ Many clinicians will be familiar with the statement ‘at least 25% to 35% RGC loss is associated with abnormalities in visual field testing’, a conclusion arising largely from interpretation of the work of Quigley and colleagues ^{7, 41}. In fact, Quigley’s articles on this topic are amongst the most frequently cited articles in the literature in Ophthalmology ⁴². However, their data do not fully support the aforementioned conclusion. In their 1989 study, Quigley et al established normal ranges for RGC density at each visual field test location from only 5 eyes ⁷. When normal confidence limits for healthy eyes are considered, all but four datapoints had RGC density below normal confidence limits for healthy eyes and also had perimetric defects. Consider figure 3, which has been adapted from a later publication by the same group ⁴¹. This shows the relationship between mean deviation, MD (dB) and percentage retinal ganglion cell count. Using the regression line on this plot, a patient with an RGC count equal to an ‘average healthy eye’ (RGC count of 100%) would be expected to have an MD of −6 dB (solid grey lines, figure 3). On inspecting the data, it is apparent that many eyes with normal RGC counts had abnormal MD on automated perimetry. Three eyes had RGC counts greater than 100% with MD worse than −5 dB (dark grey shaded box), as if some healthy eyes had perimetric abnormalities. Indeed, when they grouped test locations by probability score for perimetric defect, the locations with p < 5% on perimetry had ganglion cell counts averaging 97% of mean normal. In other words, many of the locations with perimetric sensitivity below the normal range must have had ganglion cell counts above the mean normal value. Even for locations with more severe perimetric damage (p < 0.5%), the average value for ganglion cell number was 71% of mean normal, well within normal limits based on the means and SDs given in their Figure 1. Overall, most locations had ganglion cell numbers in the normal range yet still had statistically significant perimetric defects.

Figure 3. Adapted from Kerrigan-Baumrind et al. (2000) ⁴¹.

A percentage retinal ganglion cell (RGC) count of 100% (i.e. mean normal) corresponds to a Mean Deviation, MD, value of nearly −6 dB (solid grey lines). The grey shaded box shows points which correspond to a percentage RGC of 100% or greater (Three of these eyes have a MD of less than −5 dB). The lighter grey shaded box shows additional points which lie have a RGC count of greater than 67% and correspond to points which are statistically within confidence limits for normality (at p=5%, one tailed). The black dotted line corresponds to the MD value corresponding to a (one-tailed) p=5% for their data.

Similarly, Harwerth’s histological data from monkey eyes show that perimetric defects can be present in early glaucoma and a sensitivity loss of greater than 5 dB can be present for minimal amounts of ganglion cell loss ⁸. Histological studies, albeit in monkey eyes, allow a more precise quantification of ganglion cell number than use of an imaging surrogate, and permit quantification of ‘ganglion cell loss’ from fellow non-glaucomatous eyes of the same animal. Consequently, correlations between sensitivity and ganglion cell density are typically higher than correlations reported between sensitivity and structural surrogates of ganglion cell density made in clinical studies. Harwerth’s study has often been incorrectly cited as supporting the idea that structure precedes function.^43–48.

Data from large clinical trials illustrate that perimetric damage can precede ONH changes in 35% to 86% of patients, figure 4. In the Ocular Hypertension Treatment Study (OHTS), a visual field endpoint was reached first in 35% of patients (structural change in 55%) ^{3, 49} whilst this figure was 60% and 86% for the European Glaucoma Prevention Study (EPGS) and Early Manifest Glaucoma Trial (EMGT) respectively ^{5, 50}.

Figure 4. Percentage of patients who had the first detectable glaucomatous change on structural or functional testing or both tests in 3 major Clinical Trials;

OHTS = Ocular Hypertension Treatment Study; EMGT = Early Manifest Glaucoma Trial; EGPS = European Glaucoma Prevention Study

Identification of the relative frequency of structural and functional change within a study cohort depends on the reference standard used to assess this change and the relative specificity and sensitivity (true negative and true positive rates) of the criteria to define that change has taken place. A good illustration of the importance of an appropriate reference standard and of identifying criterion specificity is given by two papers published back-to-back in a journal in 2006 ^{51, 52}. The first study aimed to establish the sensitivity of imaging devices to identify glaucoma and, appropriately, used visual function as the reference standard for classification of eyes as glaucomatous or healthy ⁵³. The second study aimed to establish the sensitivity of various vision function tests to identify glaucoma and, appropriately, used a structural definition of glaucoma as the reference standard. Both studies presented the sensitivity of the tests under consideration for a specificity of 80% (false flagging of glaucoma in 20% of healthy subjects). The studies found that the imaging devices had a sensitivity to identify early glaucoma of about 70 to 75% and the vision function tests had a sensitivity of about 50 to 65%. Thus, in the first study, 25 to 30% of subjects with glaucomatous visual field loss had no detectable structural defect with the criterion applied and, in the second study, 35 to 50% of subjects with glaucomatous optic neuropathy had no detectable vision function loss. Thus, the evidence points to either structural or functional loss being the first detectable sign of glaucoma in different subjects.

Similarly, Strouthidis et al evaluated data from 198 patients with ocular hypertension followed prospectively over seven years with serial SLO (HRT, Heidelberg Retina Tomograph, Heidelberg Engineering) and SAP. With test specificity fixed at 90%, approximately 20% of patients were identified progressing on HRT alone and a similar proportion progressing on visual field alone, whilst 12% deteriorated with both tests. When test specificity was increased to 97%, the corresponding percentages fell to 9, 15 and 4% ⁵⁴. This indicates that when criteria for change are matched for similar levels of specificity, the proportions of patients with early disease progressing by structure and function are similar. A corresponding result was obtained in a study of progression in patients with manifest glaucoma⁵⁵.

The concept of ‘ganglion cell dysfunction’ (rather than death) may explain why, in some patients, perimetric defects precede identifiable structural changes. In early stages of ganglion cell insult, cells may become dysfunctional leading to a reduction in visual field sensitivity, so that ‘measured structure’ may not be representative of functioning ganglion cell or axonal number. Measured functional deficit can exceed functional impairment predicted from structural measurement alone ⁵⁶. Harwerth’s lab translated clinical visual field and RNFL thickness data to a common neuronal count and found that although the two were in general agreement, neuronal deficits predicted from function were often greater than those predicted from structure.

Further evidence for ganglion cell dysfunction arises from studies of electrophysiology. Investigations of the PERG show that the reduction in RGC signal is greater than predicted from RNFL thickness measurements alone ⁵⁷ and that a reversible reduction of PERG amplitude can be induced by elevating intraocular pressure ⁵⁸. Psychophysical evidence of RGC dysfunction is consistent with shrinkage of dendritic fields ⁵⁹.

The Structure-Function Relationship – Current concepts

At present, there are four quantitative models relating structure (or ganglion cell number) and function in glaucoma:

1. The Hood-Kardon Model

The Hood-Kardon model adopts the linear structure-function relationship, but predicts RNFL thickness (μm) from dB visual field measurements ¹⁷. There are several underlying assumptions of this model, made explicit by the authors. Firstly, that RNFL thickness is related to linear visual field sensitivity in a linear manner with a slope of 1 (i.e., curvilinear relationship between visual field sensitivity in dB). This would seem to be a valid assumption for the peripheral visual field, based on the evidence outlined previously, but may not be accurate for the central visual field. Secondly, RNFL thickness is independent of sensitivity at normal levels of visual field sensitivity; in other words, there is no structure-function relationship in healthy eyes. There is limited evidence in the literature concerning this assumption at present. Thirdly, the ‘non-neural’ component of RNFL thickness can be approximated as a third of mean normal RNFL thickness in all eyes. This may be an oversimplification and, although there is a paucity of data regarding RNFL thickness in eyes severely damaged by glaucoma, Sihota et al. showed that RNFL thickness in 17 eyes blind with glaucoma varied from about 35 μm to 55 μm ³⁹. Despite the potential limitations of the model, clinical data fit the model well ^17,60.

2. The Harwerth Model

Harwerth’s observations were based on comparisons of perimetric data with histological data in monkey eyes, and found a linear relationship with visual field sensitivity and ganglion cell number when both are plotted in decibels, with the slope of the relationship increasing with eccentricity ^{61, 62}. Harwerth’s model has been validated against human histological data ⁶³, with fair agreement between measured SAP sensitivity and sensitivity predicted from RGC counts, and extended for clinical application to describe the relationship between visual field sensitivity and RNFL thickness from OCT ^{56, 62}.

3. The Drasdo model

Drasdo et al ⁶⁴ developed an improved map of normal ganglion cell density within the central visual field, using histological data on lateral displacement of RGC bodies from foveal cones. Subsequently, Drasdo et al⁶⁵ used this map to develop a model relating ganglion cell receptive field densities to perimetric sensitivities. This model has linear contrast sensitivity linearly related to ganglion cell densities for perimetric values of 0 to 29 dB, then becoming nonlinear at higher sensitivities. In the macula, this nonlinearity means that substantial declines in ganglion cell density will cause only moderate perimetric losses for this model.

4. The ‘Hockey-Stick’ model

Anderson and Knighton found that the relationship between sensitivity and ganglion cell receptive field density (measured from grating acuity) was linear with a slope of 1 at greater eccentricities and with a slope of 0.16 in the macula.⁶⁶ Similarly, Swanson and colleagues replotted empirical data from Garway-Heath et al. on visual field sensitivity against log ganglion cell number ¹², using normal estimates of sensitivity ⁶⁷ and histological ganglion cell counts ⁶⁸, and showed that a two-line or ‘hockey stick’ fit gives a reasonable fit to the the data; Pan & Swanson produced a model which approximated the hockey-stick but avoids a sharp break in slope, see figure 2. This plot bears a striking resemblance to spatial summation curves which predict a shallower slope for test locations nearer fixation and a steeper slope peripherally ^{28, 31, 69}. The change in slope can be explained by the size of the (Goldmann size III) test stimulus in relation to the critical area (Ricco’s area). The critical area is the largest stimulus size for which a one to one relationship holds for this relationship. For stimulus areas larger than critical area, sensitivity changes less with stimulus size and the 1:1 relationship no longer holds. Although probability summation of neural detectors ⁷⁰ is the most widely accepted explanation for the shallower slope between sensitivity stimulus size in the macula, an alternative explanation, in terms of detection of the stimulus by multiple cortical spatial filters has also been provided ²¹.

The Hockey-Stick model, Drasdo’s model and Harwerth’s model all predict a shallower structure-function slope (with both structure and function in log units) within the macula and an increase in slope with retinal eccentricity. Harwerth’s data show a wide variation in sensitivity (typically spanning more than 10 dB) for a given ganglion cell density (dB), standard errors around the mean slopes are not given ⁶¹.

The ‘structure-function dissociation’

Data from large clinical trials shows that in some patients structural changes may precede functional changes whilst in others the converse is true. In fact, both change together only in a small percentage of patients ^{5, 49, 50}. At first glance, this would seem surprising given that structure and function are related by the models described. However, this is in fact what would be predicted for equal loss with expected sources of variability: normal between-subject variability, measurement imprecision, different measurement (dynamic) ranges and different statistical boundaries for defining ‘abnormality’ all contribute to this dissociation. ⁶⁰

Sources of imprecision in the study of the structure-function relationship

Imaging measurements of neuroretinal rim in the ONH and of thickness of the RNFL include non-neural elements such as glial tissue and blood vessels. Nevertheless, structural parameters, such as neuroretinal rim area measured by the HRT, correlate with ganglion cell counts in animal eyes, and, therefore, provide a surrogate measure of ganglion cell loss in the glaucomatous eye. A caveat is that studies of the relationship between disc topography and optic nerve fibres have included fewer than 15 eyes ^{71, 72} and correlations between rim area parameters and optic nerve fibres are, at best, of the order of (Pearson’s) r=0.85, indicating that rim area itself is an imperfect marker for ganglion cell number. The morphology of the ONH varies considerably between individuals, confounding attempts to quantify RGC/axon integrity from measurements of the neuroretinal rim, and measurements may be influenced also by changes to non-neural support tissue, such as the lamina cribrosa, in the glaucomatous process.

Regarding RNFL measurements, there are uncertainties concerning the extent of the non-neural components of the RNFL and how these may change with ageing and in disease. Furthermore, axon diameter and density vary around the ONH, so that relationship between axon number and RNFL thickness likely changes around the ONH circumference. An approach which may overcome some of these difficulties is to image a structure more directly related to RGC numbers – the RGC layer in the macula. This is now possible with spectral-domain OCT and initial work associating RGC thickness parameters with visual function is showing promise ^{73, 74}. Measurements of visual function by SAP are related to the number of RGCs underlying the stimulus ⁸ but RGC dysfunction and varying amounts of media opacity and intraocular stray light alter the measured visual function ⁷⁵ and, therefore, the relationship between RGC numbers and retinal sensitivity measurements. Not surprisingly, data are not available relating imaging measures of structure and SAP measurements of function to ganglion cell number in human eyes.

Spatial structure/function relationship

Relating structure and function rim in patients with glaucoma requires knowledge about the anatomical correspondences of rim, or peripapillary RNFL, sector with visual field test locations. The most widely utilised structure-function map was derived by Garway-Heath, ⁷⁶ although a number of other correspondence maps exist ^{62, 77–81}. Garway-Heath et al. utilised 69 greyscale photographs of the retinal nerve fibre layer in patients with discrete and traceable RNFL bundles and/or defects ⁷⁶. The spatial arrangement of RNFL defects was related to visual field test locations by overlaying the 24-2 visual field test grid on individual photographs. The topographic destination of nerve fibre layer defects from of each of the 52 locations (excluding blind spot locations) was documented in terms of degree location (Temporal disc = 0 degrees). It is important to note that this map, which has been employed by a number of subsequent studies ^{10, 13, 16, 82}, represents an ‘average’ structure-function correspondence and it was identified in the original study that the position of the ONH relative to the fovea had an influence on the trajectory of RNFL bundles. More recently, Jansonius and colleagues developed a novel mathematical model to describe the course of retinal nerve fibre layer trajectories from nerve fibre layer tracings of 27 fundus images ⁸⁰, which is in overall agreement with the map of Garway-Heath. There appears to be considerable variability around the optic nerve head entry point for a given visual field location, typically spanning 20–30 degrees. This is likely to be a major source of imprecision in the evaluation of the quantitative structure-function relationship and a likely cause of poor structure-function correlation in some eyes. It is likely that the development of more ‘individualised’ structure-function maps in the future will further improve structure function correlations.

Both visual field and structural measurements are subject to significant between-subject and test-retest variability, which are major sources of imprecision in structure-function comparisons. Ganglion cell number in normal human eyes varies by a factor of two across individuals, and both structural and perimetric indices have normal ranges that cover a substantial portion of linear scales. For instance, histological data on normal human eyes yield standard deviations at individual locations about one-third of the mean ⁴¹, so a patient starting with mean normal ganglion cell density would require more than 50% loss of ganglion cells before falling below the one-tailed 95% confidence limit for normal.

Test-retest variability inflates measures of between-subject variability, and in damaged eyes may limit ability to assess progression. For perimetry with size III, test-retest variability of perimetric sensitivity in damaged areas of the visual field can span the entire dynamic range of the perimeter ^83–85. For perimetry with sinusoidal stimuli there is no such increase in test-retest variability for damaged regions of the visual field.^{55, 86} Sources of variability in structural measurements are many and include poor image quality, lens opacity and cylindrical error, poor acuity, low analysis confidence in OCT images, atypical scan pattern in SLP images, and operator and instrument variability ^87–91 A recent study of spectral domain OCT the between-session coefficient of variation for mean RNFL was about 4% and this rose to 10% for the temporal clock hour RNFL thickness ⁹². A recent study identified that between-individual difference accounted for 87% and 71% of the total variance in OCT and SAP measurements, respectively, in healthy eyes ⁶⁰

Other factors influencing the structure-function relationship

When perimetric sensitivities are reported in dB and imaging measures are reported in linear units, the correlation between structural and functional measures varies with severity of damage. Gonzalez-Hernandez and colleagues correlated visual field sensitivity in dB and RNFL thickness in linear units, dividing their study population into those with MD greater than 22.42 dB and those with MD less than 22.42, the value of 22.42 being based on the ‘breakpoint’ of two populations with different linear regression slopes. The correlation coefficients in these 2 groups were 0.18 and 0.35 respectively, and the authors concluded that the range of disease severity influences the inferred relationship. Investigators of another study did not find a significant correlation between sensitivity and RNFL thickness in healthy eyes and eyes classified as having “preperimetric glaucoma”, but a significant curvilinear relationship between the two measures was found in glaucoma patients ⁹³.

Linear regression analysis has been widely used to compare structural and functional measures. Although two discordant measures can be significantly correlated when sample size is high, regression analysis provides little information about the level of agreement between measures ⁹⁴. The strength of the structure-function regression can be affected by sample size, range of glaucoma severity ⁹⁵, units of perimetric measurement ^{10, 82} and measurement variability. An additional consideration is the inappropriate use of linear regression techniques which assume no error in the independent variable, which is clearly not the case; this results in an inaccurate estimation of the slope of association between variables. Analysing agreement between structural and functional parameters is complicated by different units of measurement. Some have computed each measure as a percentage of mean normal, allowing Bland-Altman plots of agreement to be graphed ^{15, 16, 86}.

Future directions in structure-function research

It remains to be seen whether with rapidly developing imaging technology in time may provide methods for counting RGC nuclei in vivo, permitting direct comparison with retinal sensitivity. This may increase our understanding of the relationship of sensitivity with underlying cell loss in glaucoma.

The standard 24-2 grid has visual field test points that are unevenly distributed with respect to their optic disc sector correspondence ⁷⁶ and to the distribution of RGC density;. The conventional Goldmann size III stimulus covers a variable number of RGC receptive fields across the central 30 degrees. A distribution of test locations that better represents the distribution of RGCs and a stimulus which is ‘scaled’ by estimates of RGC receptive field density can be expected to yield stronger structure-function correlations. Adaptation of the spatial correspondence map to include factors that explain individual variation in the correspondence of retinal locations to peripapillary RNFL sectors would further improve structure-function associations. Additional research is also required to elucidate the relationship between stimulus area and retinal sensitivity in glaucomatous regions of the visual field and to establish whether a linear relationship between stimulus area and retinal sensitivity, with a slope of 1, holds.

Combining structural and functional testing improves the diagnostic ability to detect glaucoma ^{96, 97}. It is likely that the next decade will witness integration of structural and functional test results to monitor glaucoma for clinical use. Visual field sensitivity can be predicted from structural measurements ^{73, 98}. As the predicted and measured visual field have different sources of error, integrating them to produce a ‘combined’ visual field may result in a more reproducible measurement that is more sensitive for identifying progression than standard automated perimetry alone. An alternative integrated approach for using structure and function to identify progression is to analyse both together in a Bayesian hierarchical model ⁹⁹. This seems to result in a greater proportion of glaucomatous and suspect eyes identified with progression than analyses of structure or function separately, with maintained estimated specificity.