**Purpose.**:
To evaluate the structure–function relationship between ganglion cell–inner plexiform layer (GCIPL) thickness at the macula and 10-2 standard automated perimetry (SAP) in glaucoma and to evaluate the relationship using a recently proposed linear model.

**Methods.**:
In a cross-sectional analysis, structure–function relationship was determined in 50 glaucomatous eyes (40 patients, mean deviation: −15.4 ± 7.5 dB) and 21 control eyes (13 subjects, mean deviation: −3.4 ± 3.0 dB), which had undergone 10-2 SAP and GCIPL imaging on the same day. Functional loss was derived from total deviation numerical values on 10-2 SAP and calculated on both a linear (reciprocal of Lambert) and a decibel scale after accounting for the retinal ganglion cell displacement at the macula. Strength of relationship was reported as coefficient of determination (*R*^{2}) of the linear regression models fitted to the data separately for different sectors. The relationship was also evaluated using a linear model.

**Results.**:
The *R*^{2} for the associations between GCIPL thickness sectors and the corresponding sector SAP total deviation values ranged from 0.19 (for superonasal GCIPL sector) to 0.60 (for average GCIPL thickness) when functional loss was calculated on the decibel scale and 0.16 (for superonasal sector) to 0.54 (for inferior sector) on the linear scale. All associations were statistically significant (*P* < 0.05). The linear model fitted the data reasonably well.

**Conclusions.**:
Significant structure–function associations were found between GCIPL thickness measurements at the macula and the functional loss measured on 10-2 SAP in glaucoma. Best fit was found for the inferior and average GCIPL sector thickness. The linear model was useful to study the structure–function relationship.

^{1–9}Standard automated perimetry (SAP) has been the preferred method to evaluate the corresponding functional loss in glaucoma.

^{10–18}One of the reasons for this imperfect relationship is the inability to conduct precise local measurements to compare structure with corresponding retinal areas of function because for a given region of the retina, the axons in the RNFL are originating from different regions.

^{19}Studies evaluating the structure–function relationship in glaucoma at the macula are limited. Earlier studies with SDOCT used the RNFL thickness at the papillomacular bundle to correlate with macular function.

^{18,20,21}However, the RNFL of the temporal region has been shown to demonstrate a high degree of variability, even in healthy individuals.

^{22}Multiple studies subsequently evaluated the structure–function relationship at the macula using the inner retinal layer thickness at the macula obtained with SDOCT.

^{20,23–25}Inner retinal layer thickness at the macula generally included the RNFL, ganglion cell layer, and the inner plexiform layer thickness (together called the ganglion cell complex, GCC). Measuring specifically the ganglion cell and inner plexiform layer (GCIPL) thickness at the macula is expected to improve the structure–function relationship in glaucoma, and a few recent studies have evaluated this.

^{19,26–29}The other issue to note is that most of the previous studies used the 24-2 program of SAP to evaluate the functional changes at the macula.

^{20,23–27,29}However, the 24-2 program estimates retinal sensitivity at the macula using only 16 points, each of which is 6° apart. The sampling density of the 24-2 program to estimate visual sensitivity at the macula may therefore be inadequate. Also the locations of the ganglion cells stimulated by the central 24-2 visual field (VF) test points are farther from the fovea because the ganglion cells in the fovea are displaced.

^{30,31}

^{22}

^{9}The other was a cross-sectional study to evaluate the structure–function relationship using microperimetry, SAP, and SDOCT in glaucoma. Written informed consent was obtained from all participants, and the Ethics Committee of L V Prasad Eye Institute approved both the study methodologies. All methods adhered to the tenets of the Declaration of Helsinki for research involving human subjects.

^{26,32}Ganglion cell analysis (GCA) is software that measures the GCIPL thickness within a 14.13-mm

^{2}elliptical annulus centered on the fovea with an inner vertical radius of 0.5 mm and outer vertical radius of 2 mm, stretched horizontally by 20%. The thickness parameters derived from GCA are the average GCIPL thickness across the entire elliptical annulus and the thickness at six 60° sectors of the elliptical annulus.

^{33}This map also considered the displacement of the RGCs at the macula by using equations derived from histological analysis to approximate the location of the RGCs with each SAP test point.

^{30}Standard automated perimetry–measured visual sensitivity loss was calculated by first converting the decibel (dB) scale values at each test location on the total deviation numerical plot to a linear scale (reciprocal of Lambert scale) using the following formula:

*P*value less than 5% and the glaucoma hemifield test result was outside normal limits.

^{34}Visual fields were classified as normal otherwise. All glaucomatous eyes had VF defects involving one or more of the central four points of the 24-2 field and had 10-2 VF performed to evaluate the central VF defect in greater detail. The VF examination and the HD-OCT examination were done on the same day in all the subjects.

*y*=

*ax*+

*b*) regression between GCIPL thickness and visual sensitivity loss expressed in both linear and dB scale. The associations are reported as the coefficient of determination (

*R*

^{2}) of the linear regression models. Locally weighted scatterplot smoothing (lowess) curves were also used to fit the relationship graphically. Lowess is a modeling method that combines the linear least square regression with the nonlinear regression.

^{35}It does this by fitting simple models to localized subsets of the data to build up a function that describes the deterministic part of the variation in the data, point by point. Lowess curve has an advantage in describing the structure–function relationship because it does not require the specification of a function (e.g., linear, quadratic) to fit a model to all of the data in a given sample.

^{19,22}This model makes some basic assumptions to evaluate the structure–function relationship. It proposes that the thickness of a structure (GCIPL here),

*R*, measured with OCT is made up of two components, thickness due to retinal ganglion cell bodies and dendrites, called signal or

*s*, and the residual thickness due to glial cells and blood vessels, called base level or

_{o}*b*, so that the measured GCIPL thickness is given by the equation

*s*decreases, but the residual

_{o}*b*does not change. So the above equation is written as where

*D*is the loss of visual sensitivity on the dB scale, represented on the total deviation numeric map. Base level or

*b*is taken as the GCIPL thickness corresponding to a decrease in the visual sensitivity of more than 15 dB (compared to age-matched normal) on the total deviation numeric plot.

^{19}

*P*value of 0.05 was considered statistically significant.

**Table 1**

*R*

^{2}values of the linear regression models evaluating the structure–function relationships between GCIPL thickness measurements (expressed in linear scale) and visual sensitivity loss expressed in dB and linear scales. The strongest

*R*

^{2}values were found with the average inferior and inferotemporal sector GCIPL thickness measurements. The

*R*

^{2}values varied according to the severity of VF loss. The

*R*

^{2}for association between structure and function was not statistically significant (

*P*> 0.05) with any GCIPL parameter in normal subjects and in glaucomatous eyes with MD worse than −15 dB on 10-2 VF. The

*R*

^{2}value was statistically significant (

*P*< 0.05) with most GCIPL parameters in glaucomatous eyes with MD better than −15 dB. In glaucomatous eyes with MD better than −15 dB,

*R*

^{2}values ranged between 0.04 (for inferonasal GCIPL thickness) and 0.46 (for superior GCIPL thickness) when visual sensitivity loss was represented in dB scale. The

*R*

^{2}values ranged between 0.06 (for inferonasal GCIPL thickness) and 0.51 (for inferior GCIPL thickness) when visual sensitivity loss was represented in linear scale.

**Table 2**

^{22}fit to the GCIPL sectors in our data. The base level

*b*was calculated as the GCIPL thickness corresponding to a mean loss of sensitivity of 15 dB or lower in each sector. The mean value of

*b*ranged between 49.0 μm (in the inferotemporal GCIPL sector) and 60.0 μm (in the superonasal GCIPL sector). The dashed lines in the figures were derived by joining the mean GCIPL thickness in a particular sector in normal subjects with base level

*b*in the sector, according to the method proposed by Hood and Kardon.

^{22}Figures 1 and 2 show the model with the visual sensitivity loss in dB and in linear scale, respectively. Solid lines in the figures represent the lowess curves fit to the actual data. The simple linear model fitted our data reasonably well. Compared with the lowess curves, the predicted curves seemed to overestimate structural damage in eyes with moderate VF loss (visual sensitivity loss between −5 and −15 dB).

**Figure 1**

**Figure 1**

**Figure 2**

**Figure 2**

^{19,28}Raza et al.

^{19}evaluated the structure–function relationship using GCIPL thickness in a small sample of 19 control and 14 glaucoma subjects. Spectral-domain OCT used in the study was from a different manufacturer (3D-OCT 1000; Topcon, Inc., Paramus, NJ, USA), and the GCIPL sectors consisted of five concentric ring sectors with radius ranging from 3.4° to 9.7° from the fovea. The authors found that the correlation coefficients were higher (0.71–0.74) within the central 7.2° compared to beyond this region (0.53–0.65).

^{19}Another study by Ohkubo et al.

^{28}also used 3D-OCT for GCIPL thickness measurements and correlated the GCIPL thickness with the visual sensitivity of all 68 points of 10-2 VF separately. They found the correlation coefficients in the central 5.8° to range between 0.36 and 0.72.

^{28}These results, however, cannot be directly compared to those of our study as the GCIPL sectors were not comparable between the studies.

^{28}also found the strongest structure–function correlations to be with inferior sectors when they evaluated the GCIPL measurements against the total deviation numeric values. A similar study evaluating the relationship between GCIPL thickness and visual sensitivities on microperimetry also found stronger structure–function correlations with inferior compared to the superior sectors.

^{33}Inferior sectors are also the ones reported to have greater ability to diagnose perimetric glaucoma.

^{3–8}These are also the sectors at the macula that are more vulnerable and that manifest structural changes earlier in glaucoma as demonstrated by Hood et al.

^{31}These may be the reasons for a stronger structure–function relationship in the inferior GCIPL sectors. However, it is also useful to note that the differences in structure–function associations in different sectors may in part be due to the number of data points close to normal values, as opposed to local differences in the strength of an underlying relationship.

^{10}found that the visual sensitivity expressed in linear scale defined the structure–function relationship better than visual sensitivities expressed as a dB scale. Bowd et al.

^{11}showed that a linear fit between structure and function with visual sensitivity expressed as a dB scale was comparable to a logarithmic fit in describing the structure–function relationship. Hood and Kardon

^{22}showed that a simple linear model can describe the structure–function relationship well. Previous studies have used this model to evaluate the structure–function relationship using RNFL,

^{18,20}inner retinal,

^{20}and also GCIPL thickness

^{19,33}measurements at the macula. This model uses visual sensitivity loss as determined on the total deviation numeric plot as the functional measure, and not the visual threshold as has been used in most of the other studies. The total deviation numeric plot adjusts the visual sensitivity loss according to the age of the subject. In this way the age-related variability in the functional measurement is minimized. For the GCIPL measurements, though there are no age-corrected values, the change with age has been reported to be small.

^{36}We also used lowess curves to estimate the structure–function relationship. The advantage of the lowess curve is that it does not need the specification of a function to model the relationship in a given sample. The shape of the lowess curves and the predicted curve from the Hood and Kardon

^{22}model shows the lag between structural and functional components in glaucoma. In early stages of glaucoma, the decline in GCIPL thickness is rapid and there is a lag in the visual sensitivity loss. But as the glaucoma damage becomes severe, GCIPL thickness reaches a base level beyond which only the visual sensitivity declines. The base level noted in our study ranged from 49 μm (63% of the thickness in control subjects) in the inferotemporal GCIPL sector to 58 μm (76% of the thickness in control subjects) in the superotemporal sector. A possible limitation in the estimation of

*b*from our data is that the number of eyes with a mean visual sensitivity loss of >15 dB in different GCIPL sectors ranged from as low as 4 (in superotemporal sector) to as high as 24 (in inferior sector). Raza et al.

^{19}have also reported GCIPL base level values of 50% to 80% of the control values at different eccentricities in their small sample of glaucomatous eyes. The simple linear model fitted our data reasonably well. However, compared with the lowess curves, the predicted curves seemed to overestimate structural damage in eyes with moderate VF loss. Raza et al.

^{19}also noticed a systematic bias with the linear model but unlike what was seen in our study, they found that the model underestimated the structural damage in eyes with early VF sensitivity loss. Our results may be partly due to an overestimation of the visual sensitivity loss in our data. On inspection of the VFs of our study, we found that the total deviation probability plots of most of the VFs were worse than the pattern deviation plots in spite of acceptable reliability indices and media clarity. It is important to note that the simple linear model was initially developed for evaluating the structure–function relationship with the RNFL thickness. Therefore more work may be needed to refine the model for structure–function evaluation at the macula and to evaluate the reasons for discordance between the actual data and the model in certain situations.

**H.L. Rao**, Allergan (C), Cipla (C);

**M. Qasim**, None;

**R.S.M. Hussain**, None;

**M. Januwada**, None;

**L.N. Pillutla**, None;

**V.U. Begum**, None;

**A. Chaitanya**, None;

**S. Senthil**, None;

**C.S. Garudadri**, Allergan (C), Merck (C), Alcon (C)

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