A framework for comparing structural and functional measures of glaucomatous damage

Abstract

While it is often said that structural damage due to glaucoma precedes functional damage, it is not always clear what this statement means. This review has two purposes: first, to show that a simple linear relationship describes the data relating a particular functional test (standard automated perimetry (SAP)) to a particular structural test (optical coherence tomography (OCT)); and, second, to propose a general framework for relating structural and functional damage, and for evaluating if one precedes the other. The specific functional and structural tests employed are described in Section 2. To compare SAP sensitivity loss to loss of the retinal nerve fiber layer (RNFL) requires a map that relates local field regions to local regions of the optic disc as described in Section 3. When RNFL thickness in the superior and inferior arcuate sectors of the disc are plotted against SAP sensitivity loss (dB units) in the corresponding arcuate regions of the visual field, RNFL thickness becomes asymptotic for sensitivity losses greater than about 10dB. These data are well described by a simple linear model presented in Section 4. The model assumes that the RNFL thickness measured with OCT has two components. One component is the axons of the retinal ganglion cells and the other, the residual, is everything else (e.g. glial cells, blood vessels). The axon portion is assumed to decrease in a linear fashion with losses in SAP sensitivity (in linear units); the residual portion is assumed to remain constant. Based upon severe SAP losses in anterior ischemic optic neuropathy (AION), the residual RNFL thickness in the arcuate regions is, on average, about one-third of the premorbid (normal) thickness of that region. The model also predicts that, to a first approximation, SAP sensitivity in control subjects does not depend upon RNFL thickness. The data (Section 6) are, in general, consistent with this prediction showing a very weak correlation between RNFL thickness and SAP sensitivity. In Section 7, the model is used to estimate the proportion of patients showing statistical abnormalities (worse than the 5th percentile) on the OCT RNFL test before they show abnormalities on the 24-2 SAP field test. Ignoring measurement error, the patients with a relatively thick RNFL, when healthy, will be more likely to show significant SAP sensitivity loss before statistically significant OCT RNFL loss, while the reverse will be true for those who start with an average or a relatively thin RNFL when healthy. Thus, it is important to understand the implications of the wide variation in RNFL thickness among control subjects. Section 8 describes two of the factors contributing to this variation, variations in the position of blood vessels and variations in the mapping of field regions to disc sectors. Finally, in Sections 7 and 9, the findings are related to the general debate in the literature about the relationship between structural and functional glaucomatous damage and a framework is proposed for understanding what is meant by the question, 'Does structural damage precede functional damage in glaucoma?' An emphasis is placed upon the need to distinguish between "statistical" and "relational" meanings of this question.

Fig. 1

(A) A fundus photo of a right eye with the test points for the 24-2 SAP field superimposed. (B) An artist’s sketch of the course of the RGC axons in the retina with the test points for the 24-2 SAP field superimposed.

Fig. 2

The sensitivity (A) and the total deviation (C) plots of a 24-2 SAP test report (B) from an eye with glaucomatous damage in the superior arcuate region.

Fig. 3

(A) A portion of an OCT RNFL thickness report from a commercial machine shown with the pseudo-color scan (B), the scanning circle depicted in green, (C), and the RNFL profile, seen as black line in (D). (E) The approximate locations of the upper (blue) and lower arcuate (red) band of RGC axons. (F) The approximate locations on the RNFL profile are shown related to the corresponding locations around the disc.

Fig. 4

(A) Garway-Heath et al. (2000) map relating regions of the visual field to sectors around the disc. (B) The regions of the RNFL profile that correspond to the superior (blue) and inferior (red) temporal arcuate sectors of the disc. (C) The average RNFL profile for 50 normal controls.

Fig. 5

(A) Sample total deviations and associated probability plots for a 24-2 SAP field test of a patient with glaucoma. The areas enclosed by the red or blue boundaries signify those visual field test locations associated with the inferior and superior arcuate RNFL bundles, respectively. (B) OCT RNFL profiles for the same patient. The vertical dashed pairs of blue and red lines depict the locations of the RNFL scan that map to the arcuate region of the field shown in (A). Note the loss of RNFL thickness in the inferior arcuate sector of the right eye, corresponding to the superior arcuate field loss, as shown in (A), in the same eye.

Fig. 6

An illustration showing why the 24-2 SAP total deviation values are anti-logged before averaging. In the extreme case of a normal region or location (white square) and an adjacent region of complete sensitivity loss (black square), the average calculated field loss for the two areas combined is inaccurate if the values of sensitivity are not first anti-logged before averaging.

Fig. 7

(A) A schematic illustrating the location of the corresponding disc sectors and field regions for the superior arcuate field (left panel) and inferior arcuate field (right panel). (B) RNFL thickness as a function of field loss for the upper field/inferior disc (left panel) and the lower field/superior disc (right panel). Data are shown for patients with AION (n=24; filled gray), asymmetric glaucoma (n=15; filled black), and severe glaucoma (n=16; open symbols), and for the mean of a group of 60 age-similar controls (open square). The theoretical curves are eq. 2 fitted by setting (s_o + b) equal to the control value and b equal to one-third this value [i.e. b=0.33(s_o + b)]. For the three theoretical curves (50^th percentile, 95^th percentile, and 5^th percentile) in the left panel, (s_o + b) was equal to 173.1, 142.0, and 111.0 μm, and for the three theoretical curves in the right panel, (s_o + b) was equal to 165.0, 130.5, and 95.9 μm.

Fig. 8

The amplitude (signal-to-noise ratio) of a local multifocal visual evoked potential (mfVEP) versus local relative SAP field sensitivity is shown for the mean results for the better (open symbols) and affected (filled symbols) of 20 patients (10 glaucoma and 10 AION) with asymmetrical damage. The smooth curve is the fit of a linear model. Modified from Hood et al (2002).

Fig. 9

The linear model’s predicted change in RNFL thickness with changes in SAP field loss express on linear-linear (A) and log-linear (B) coordinates.

Fig. 10

Residual RNFL thickness, b, for 9 patients with unilateral AION shown as a function of the RNFL thickness of the corresponding region of the other (unaffected) eye for the upper and lower arcuate field regions (filled symbols) and center (open symbols) of the field. For the filled symbols, the solid line is the best fitting line; the residual thickness is about 1/3 (33%) of the initial/healthy thickness (s_o + b), as indicated by the dashed line. For the open symbols, the dotted line is the line of best fit, b = 25.3 + 0.088(s_o + b).

Fig. 11

RNFL thickness as a function of threshold deviation from age-matched normal eyes for the upper field/inferior disc (A) and lower field/upper disc (B). Open symbols are the results for 60 normal eyes and filled symbols the mean of these data grouped into bins of size 10 after rank ordering them base upon field loss. The dashed lines show the mean and 95% confidence intervals (CI) and the solid the best fitting line to all 60 data points. The gray curve is the same function (eq. 3a) as in Fig. 7B, extended here for values of relative sensitivity greater than 0 dB.

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 the relative sensitivity (ratio of gray areas) of two tests. The 95% CI for the OCT comes from Fig. 11 and the 95% CI for the SAP region is 0±1.96SD, where SD is the standard deviation of the SAP total deviation losses for 60 age-matched controls. See text for details.

Fig. 13

Same data as in Fig. 7B with theoretical curves (solid and dashed black) based upon work by Harwerth et al (2007). See text for details.

Fig. 14

(A) RNFL thickness as a function of field loss for the papillomacular bundle (center gray region in Fig. 4A) for the same patients as in Fig. 7B. Data are shown for patients with AION (n=48 eyes; filled gray), asymmetric glaucoma (n=30 eyes; filled black), and severe glaucoma (n=16 eyes; open symbols). The theoretical curves are eq. 3a,b fitted by setting (s_o + b) equal to the control value and b, based upon Fig. 10, equal to 25.3 + 0.088(s_o + b). For the three theoretical curves, (s_o + b) was equal to 95.1, 70.4, and 45.7 μm. (B) RNFL thickness as a function of threshold deviation from age-matched normal eyes for the papillomacular bundle (center gray region in Fig. 4A) for the same 60 controls as in Fig. 11. The dashed lines show the mean and 95% confidence intervals (CI) and the solid the best fitting line to all 60 data points. The gray curve is the same function (eq. 3a) as in panel A, extended here for values of relative sensitivity greater than 0 dB.

Fig. 15

The right eye of a normal control was misaligned with respect to the circular scan line so that the disc was off center. The black curve is the RNFL profile for the misaligned circular scan, while the gray curve is the RNFL profile when the circular scan was properly centered on the disc. The profiles change in predictable and systematic ways. (A) Disc right of center: the peaks shift in the nasal direction. (B) Disc left of center: the peaks shift in the temporal direction. (C) Disc above center: the superior peaks increase and inferior peaks decrease in amplitude. (D) Disc below center: the inferior peaks increase and superior peaks decrease in amplitude.

Fig. 16

(A) The same graph as in Fig. 7B(left panel) with the 5 measurements (red +) for the outlier indicated by the asterisk in Fig. 7B. Note that all repeat measurements were still outlier points (B) The average RNFL thickness for the better (gray line profile) and affected (black line profile) eye of this patient. The solid red and blue lines show the boundaries of the Garway-Heath et al. arcuate regions (see Fig. 4A) and the dashed red lines indicate the shift needed to bring the outlier onto the theoretical curve (the filled red symbol in Fig. 16A).

Fig. 17

Results from patient with unilateral AION illustrating the effects of blood vessels on the OCT RNFL profile. (A) The disc image of the unaffected right eye showing the location of the peaks in the RNFL profile in the lower panel of (B). (B) A single scan and the associated RNFL profile of the unaffected eye. Note that the location of the major and minor maxima of the RNFL correspond to the location of the major arterial blood vessels, which cause a vertical linear shadow or dark strip in their locations of the B-scan. (C) The total deviation plot for the 24-2 SAP of the affected left eye. (D) A single scan and the associated thinned RNFL profile of the affected eye. The arrows indicate the locations of 4 blood vessels, which appear to contribute to the residual thickness where they are located (red arrows).

Fig. 18

A schematic showing 4 possible meanings of the question ‘Does structure precede function.?’ (A) and how the model presented in Section 4 answers these questions (B).