It is commonly held that structural damage precedes functional damage in glaucoma. However, this statement can mean different things to different people. Here we consider our model in light of three possible meanings of this statement, a fourth possible meaning will be discussed in section 9.1.
7.1 Which test will detect early glaucomatous damage first?
According to the linear model, functional damage (loss in SAP field sensitivity) is related linearly to structural damage (loss of RNFL thickness due to axons). Thus, if the linear model is correct, then structure does not precede function, nor does function precede structure. The strict answer according to the model is that they occur together. In other words, RNFL thickness is linearly related to SAP loss. However, if the question is which test will show statistically significant glaucomatous damage first, then the answer depends upon the relative variation in the test measurements of structure and function among normal eyes. A test with a larger standard deviation among normal eyes, all else being equal, would require a larger deficit to reach statistical significance than would a test with a smaller standard deviation.
illustrates this point using our theoretical curves for the superior arcuate field/inferior temporal disc from (left panel). In , OCT thickness for the inferior disc sector is compared to the loss in sensitivity in the upper arcuate region of the SAP field. The dashed, horizontal, dark gray line indicates the lower 2.5% limit for the RNFL thickness of a control group, while the vertical, light gray vertical dashed line is the lower 2.5% limit for the SAP field test of a control group. That is, 97.5% of the normal RNFL thickness values fall above the horizontal dark gray line and 97.5% of the normal SAP values fall to the right of the vertical light gray line. It is important to note that points falling in the upper right quadrant defined by the intersection of the vertical and horizontal lines represent test results for which both tests were normal, while those falling in the lower left represent test results for which both test results are abnormal. The interesting quadrants are those in which one test is normal and the other is abnormal. In particular, test results in the upper left quadrant signify a normal RNFL thickness, but an abnormal SAP result. On the other hand, a test result in the lower right quadrant signifies a normal SAP test, but an abnormal RNFL thickness.
Fig. 12 Estimating the relative sensitivity of two tests. The theoretical function (dashed and solid curves) relating two tests (RNFL thickness and SAP visual fields) plus an estimation of the variation among normal controls (95% CI), allows the estimation of (more ...)
According to the model, if we ignore measurement error, 95% of the points should fall between the black dashed curves in . The shaded regions indicate the location of points for which the RNFL and SAP tests disagree. In particular, a point that falls in the smaller light gray region has a statistically abnormal SAP test, but a normal RNFL thickness. On the other hand, a point that falls in the larger dark gray region has a statistically abnormal RNFL thickness, but a normal SAP test. Thus, for the upper arcuate field, the model predicts that for the patients for whom the two tests disagree, more will show significant RNFL loss and normal SAP results than will show significant SAP loss and a normal RNFL thickness. Notice that changing the confidence limits of either test will change the relative sizes of the regions in gray and hence the proportion of patients with statistically significant structural loss preceding functional loss. For example, anything that increases the variability of the SAP field results (e.g. inexperienced field takers) would result in a larger dark gray area and a smaller light gray area.
7.2 Does a loss of RGC axons really precede visual field loss?
By ‘structural damage precedes functional damage’ some people mean that substantial RGC loss precedes a loss in SAP sensitivity
. Further, this statement has at least two meanings. On the one hand, a “statistical RGC interpretation” of this statement could mean that a statistically significant RGC loss occurs before a statistically significant SAP loss can be detected (as discussed in the prior section). This interpretation is not in conflict with our model. In fact, for the conditions of , a linear model predicts that the lower boundary of the SAP confidence limit (i.e. −2.4 dB or a 42% loss in sensitivity) is associated with approximately a 42% RGC loss (see eq. 3A
On the other hand, a “relational RGC interpretation” of ‘RGC loss precedes a loss in SAP sensitivity’ could mean that the mathematical relationship between SAP loss and RGC loss is not monotonic. In particular, some people believe that no sensitivity loss of SAP loss occurs until 25 percent or more of the RGCs are lost. This interpretation would be in conflict with our model. However, the published data do not provide strong support for either the statistical or relational interpretation of “RGC loss precedes loss in SAP sensitivity”. A complete review of this issue is beyond the scope of this article, but a consideration of a few of the most commonly referenced papers is warranted.
Kerrigan-Baumrind et al. (2000)
compared SAP field loss to post-mortem RGC counts in humans. They concluded that a statistically significant SAP field defect did not occur until 25% to 35% of the RGC’s were lost. To calculate the RGC loss, they compared the RGC counts postmortem in glaucoma patients to those in a group of normal controls. However, a 25–35% loss in RGC count relative to the mean RGC count in normal eyes is not
statistically significant as it fell within the 95% confidence limits of their normal RGC counts. Thus, the ‘statistical interpretation’ of the statement that ‘RGC loss precedes loss in SAP sensitivity’ is not supported. Further, when they plotted local SAP sensitivity loss against local RGC loss for 429 pairs of local field points, the correlation (r2
) was only 0.03. That is, there was no support for an association between the functional test result and RGC loss under their measurement conditions and in their group of glaucoma patients. In other words, there was also no support for the ‘relational RGC interpretation’ of the statement that ‘RGC loss precedes loss in SAP sensitivity’. In fact, according to the regression line fitted to their scatter plot of MD (mean deviation) versus percent of normal RGC, 100% of normal RGC count was associated with a MD worse than −6 dB, i.e. a significant field loss (see their ). In other words, a normal RGC count was associated with a −6 dB loss, i.e. SAP sensitivity loss preceded
a loss of RGCs (Garway-Heath, 2004
). While RGC loss may precede the detection of SAP field loss in humans, the data from Kerrigan-Baumrind et al. (2000)
do not provide strong support for this contention.
In an elegant series of papers, Harwerth and colleagues (e.g. Harwerth et al., 1999
; Harwerth et al., 2002
) compared post-mortem RGC counts to behavioral SAP sensitivity loss in monkeys with experimental glaucoma. Unlike the human work, they could measure RGC loss more accurately relative to the normal state because the non-glaucomatous opposite eye served as the control and the RGC counts from the two eyes of a normal monkey are similar. While their work is often taken as support for the Kerrigan-Baumrind et al. conclusion, their monkeys showed, on average, a functional loss greater than −6 dB even when the average RGC loss was minimal, less than 10% (see Fig. 2B in Harwerth et al., 2002
). That is, a significant SAP field loss, on average, was associated with minimal RGC loss. Thus, while there may be significant RGC loss before SAP tests are abnormal, the current primate data on post-mortem counts provide weak support for this idea.
7.3 Relationship to other models
Recently, Harwerth et al., 2007
proposed a model that relates OCT RNFL thickness to SAP sensitivity loss in monkeys. While their model is framed in a very different form, it can be reformulated in a form similar to our model (Section 4.2). In particular, they found that log RGC count is linear with log SAP sensitivity (linear on log axes) (Harwerth et al., 2004
). We assume the relationship is linear on linear axes. [If the slope of their function were 1.0, then we would be in agreement. However, their slope ranges from 1.25 to 2.32 depending upon eccentricity in the retina (Harwerth et al., 2004
).] Second, they assume that all the RNFL thickness measured with the OCT is attributable to RGC axons. Thus, there is no residual thickness in their model. As shown above, there is a residual RNFL thickness, b, which remains after all sensitivity to light has been lost (). Third, they found that in the normal eye, the SAP sensitivity varies with RGC count and, thus, RNFL thickness. In contrast, we have shown that, to a first approximation, the sensitivity of normal eyes does not depend upon RNFL thickness ().
The black curves in show the fit of a model, based upon their assumptions, to our data from with our model’s predictions shown as the gray curves. To be fair, we did not fit the model in the same way that they did. To fit the model, we made the assumptions directly above plus we assumed that the slope of the function relating RGC axons to SAP loss was 1.5, the value they give for an eccentricity of 10°. If we allow for the same residual as in our model, then a model based upon their assumptions yields the dashed black curve. (In fact, the current, unpublished version of their model has a residual portion assumed to consist of glial cells (R. Harwerth, personal communication.) This dashed curve is close to the mean prediction of our model (gray curve), although it does not fit our data quite as well. Further work is needed to see if the data from controls and patients can distinguish between our model and theirs.
Garway-Heath and colleagues have argued that structural measures (e.g. neural rim) more closely approximate a linear function if plotted against linear SAP loss, as opposed to log SAP loss (Garway-Heath et al., 1999
; Garway-Heath et al., 2002
; Garway-Heath, 2004
). While their work is consistent with a linear model, it does not specify the precise linear relationship (i.e. the slope and intercept of the linear function) between structural loss and SAP field loss. It would be of interest to see if their structural and electrophysiological data can distinguish between the linear model described here and other plausible alternatives.
Swanson et al. (2004)
, building upon aspects of previous models of spatial vision, proposed a theoretical framework for predicting the loss in SAP sensitivity with local loss in RGC. The details of their psychophysical model are relatively complicated, but the essence of the predictions can be explained fairly simply. For peripheral visual field sensitivity, the SAP threshold (expressed in linear not dB units) will decrease linearly with percent RGC loss. They concluded that, for these conditions, their model supported the Hood et al. (2002)
prediction of a linear relationship between behavioral loss in sensitivity and RGC loss. However, for central visual field sensitivity at the fovea, SAP sensitivity loss is predicted to decrease less rapidly with RGC loss than the loss predicted by our linear model. In the next section, we examine the data for the central portion of the SAP field.
7.4 The papillomacular bundle and the linear model
Our initial tests of the linear model were restricted to the arcuate regions as defined in . We chose to focus on these regions because they were completely within the 24-2 SAP field and they are the sites of early glaucomatous damage. The question naturally arises as to whether the data for the central macular field region and the associated papillomacular bundle (dark gray in ) also can be described by the linear model. Because of the greater density of RGCs in the macula, a different model may describe the results (for example, see Swanson et al., 2004
in Section 7.3).
shows the central field results for the 24 patients with AION (gray circles), the 15 patients with asymmetrical glaucoma (black circles), and the 16 patients with severe glaucoma (open circles). Here the RNFL thickness of the papillomacular sector (dark gray in -left panel) is plotted against the field loss in the central macular region (dark gray in -right panel). As in , the vertical line at 0 dB is the 95% confidence limit for RNFL thickness for the same age-matched control group. The curves are the predictions from the model. These curves have their starting points at 0 dB based upon the mean of the controls (solid curve) and the end points of the confidence interval (dashed curves). The formula for estimating the asymptote, b, of these curves was taken, as in the case of , from the AION data for the asymmetrical patients. In the case of the papillomacular sector, the residual thickness is no longer simply 33% of the normative value (see equation in figure caption). As can be seen in , the relationship between the residual b and the RFNL thickness in the healthy eye for the papillomacular bundle (open squares) was different from that of the arcuate regions (filled symbols). In particular, the residual thickness for the macular region tended to be a relatively larger percentage of the total RNFL thickness than the 33% value found for the arcuate regions, suggesting a larger proportional contributions from non-axonal elements (e.g. glia and blood vessels) to the RNFL thickness of the papillomacular bundle.
Fig. 14 (A) RNFL thickness as a function of field loss for the papillomacular bundle (center gray region in ) for the same patients as in . Data are shown for patients with AION (n=48 eyes; filled gray), asymmetric glaucoma (n=30 eyes; filled black), (more ...)
shows the central data for the 60 controls plotted as in . As in the case of the arcuate regions, there is a weak positive correlation (solid black line: r=0.17; slope=1.9 μm/dB). However, the grouped data (filled symbols) fall far from the predictions (gray curve) of a model that assumes that the same relationship (eq. 3a
) between RNFL thickness and sensitivity holds for both controls and patients. The OCT thickness for the central region is relatively independent of the sensitivity in this region for healthy eye. The model (eq. 3b
) describes the central data in reasonably well. The points in fall, in general, between and around the dashed curves and, the best fitting line (solid) for the control data in is close to the line (middle dashed) predicted by the model (eq. 3b
According to the Swanson et al (2004)
model, more points should fall below the solid theoretical curve in , than fall below the solid curve in , at least for the early part (up to −10 dB or so) of the curve. However, the difference between the Swanson et al predictions and those of our model are subtle compared to the spread in the RNFL thickness values. Other methods are needed to distinguish between these predictions.