**Purpose**:
To investigate the structure–function mapping in the central 10° by relating Humphrey field analyzer (HFA) 10-2 visual field (VF) and circumpapillary retinal nerve fiber layer (cpRNFL) thickness from spectral-domain optical coherence tomography (SD-OCT). We also compared the obtained results with a previously reported mapping between 10-2 VF and the optic disc.

**Methods**:
In 151 eyes of 151 POAG patients and 35 eyes from 35 healthy participants, cpRNFL thickness measurements were obtained using SD-OCT and the 10-2 VF was measured with the HFA. The relationship between visual sensitivity and cpRNL thickness values in the temporal 180° was analyzed using least absolute shrinkage and selection operator (LASSO) regression. The optic disc angle corresponding to each VF test point was then derived using the coefficients from the optimal LASSO regression.

**Results**:
The structure–function map obtained was largely consistent with the mapping reported previously; superior central VF test points correspond to a more vulnerable area of the optic disc, more distant toward the inferior pole from the center of the temporal quadrant (9:00 o'clock for the right eye) while inferior VF test points correspond closer to the center of the temporal quadrant. The prediction error tended to be large in the ‘more vulnerable area' in the map reported previously.

**Conclusions**:
The structure–function map obtained largely confirms the previously reported map; however, some important differences were observed.

^{1}proposed a structure–function mapping based on annotated fundus photographs. Recent developments in spectral-domain optical coherence tomography (SD-OCT) have enabled a very accurate assessment of circumpapillary retinal nerve fiber layer (cpRNFL) thickness, and the structure–function relationship has been derived between OCT images and the 24-2 VF.

^{2–5}

^{6–10}In Hood et al.,

^{11,12}it was suggested that VF tests based on a 6° grid (like the 24-2 test) should be replaced because early glaucomatous damage of the macula can be missed or underestimated. The purpose of the current study was to investigate the structure–function mapping in the central by 10° by relating HFA 10-2 VF sensitivity and cpRNFL thickness measurements using the strength of the relationship between SD-OCT measured cpRNFL thickness and 10-2 HFA VF sensitivity. Due to the large number of variables investigated, least absolute shrinkage and selection operator (LASSO) regression was used to investigate the strength of the structure–function relationship. LASSO regression is similar to standard linear regression, but reduces the likelihood of over fitting the data by assigning spurious variables a coefficient value of zero (i.e., excluding them from the final model) with the L1 regularization (adds penalty equivalent to absolute value of the magnitude of coefficients); other variables, regarded as significantly related to the dependent variable, are included in the model. Ridge regression analysis is a similar approach, but uses L2 regularization (adds penalty equivalent to square of the magnitude of coefficients), and LASSO regression usually outperforms ridge regression, unless coefficients for all variables are roughly of equal size.

^{13}

^{11}in which it was suggested that the macular retinal region can be divided into two regions: a vulnerable area (where the inferior macular region of the retina enters the inferior quadrant of the optic disc) and a less vulnerable area (where the superior macular region and the macular papillary region of the retina enters the temporal quadrant of the optic disc).

^{14}and (4) axial length shorter than 22.0 or longer than 26.0 mm. Thus, the diagnosis of POAG was made irrespective of the presence of glaucomatous VF change so that patients with a large range of glaucomatous damage were enrolled in the study, including those without measurable VF damage. Subjects with other systemic or ocular disorders that could affect VF results were carefully excluded. If both eyes of a patient satisfied these criteria, one eye was randomly chosen.

^{15}following the manufacturer's recommendation.

^{2}area (512 × 128 pixels). Data with a signal strength index < 7 were excluded as recommended by the manufacturer. Images affected by eye movements, involuntary blinking, or saccades were also carefully excluded.

^{16}Then, the relationship between each total deviation value (dB) and the 513 cpRNFL thickness values in the temporal 180° (from −90° to 90° via 360 = 0°) was also analyzed using LASSO regression, so that a optic disc angle corresponds to each VF test point was identified. In this study, cpRNFL thickness was measured every 0.35° and 513-cpRNFL thickness values, corresponding to the temporal 180°, were used in the analysis. With such a large number of variables, it is not appropriate to apply standard ordinary least squares linear regression (OLSLR); hence, LASSO regression was used. LASSO regression is similar to OLSLR, but different in that the sum of the absolute values of the regression coefficients is constrained (penalized); the optimal penalty value is decided by minimizing the prediction error in cross validation. Thus, LASSO regression reduces the likelihood of over fitting the data by assigning redundant variables a coefficient value of zero (i.e., excluding them from the final model); other variables, regarded as significantly related to the dependent variable, are included in the model. LASSO regression is especially useful when the number of independent variables is large because it is likely that some predictors are spuriously associated with the outcome value. Specifically, if

*x*∈

*R*denotes the independent variables and

^{p}*y*∈

*R*denotes the response (please note

*x*are normalized, but the coefficients in the final model were returned on the original scale, and

_{ij}*y*has mean zero), the Lasso algorithm applies a penalty as follows:

_{1}normalization) is replaced by a penalty term of

_{2}normalization). In the current study, we chose LASSO regression, not ridge regression, because LASSO regression usually yields more accurate predictions than ridge regression, unless coefficients for all variables are roughly of equal size.

^{13}LASSO regression also has an advantage over ridge regression in that the final model may involve only a subset of the predictors, which, in turn, improves model interpretability.

_{−90}) + (0.025 × cpRNFL

_{−89.6}) + (0.078 × cpRNFL

_{−70.0}) + (0.0051 × cpRNFL

_{−67.5}) + (0.017 × cpRNFL

_{−39.7}) + (0.030 × cpRNFL

_{−38.7}) + (0.028 × cpRNFL

_{−38.3}), and the optic disc angle corresponding to the VF test point was calculated as: (0.088 × −90 + 0.025 × −89.6 + 0.078 × −70.0 + 0.0051 × −67.5 + 0.017 × −39.7 + 0.030 × −38.7 + 0.028 × −38.3) / (0.088 + 0.025 + 0.078 + 0.0051 + 0.017 + 0.030 + 0.028) = −69.6°.

^{17}in Figures 2A and 2B, for the purpose of interpretation in the figures. In addition, the results are superimposed on the RNFL tracings in the papers by Jansonius et al.

^{18}as shown by Hood et al.

^{11}in Figure 2C to help interpret the results considering the relation between retinal ganglion cell locations and VF test points. In general, the results presented here are consistent with the mapping reported by Hood et al.

^{11}; in particular, superior central VF test points correspond to a more vulnerable area of the optic disc more distant toward the inferior pole from the center of the temporal quadrant (9:00 o'clock for the right eye) while inferior VF test points correspond closer to the center of the temporal quadrant. More specifically, less vulnerable areas correspond to sectors 1, 2, 3, 4, and 15 and more vulnerable areas correspond to sectors 12, 13, and 14.

^{16}In general, the results were consistent with the results shown in Figures 2 and 3; the angles shown in Figure 2 had strong correlation in Figure 4, and also the correlation in Figure 4 was weak in the least vulnerable area, whereas opposite tendency was observed in the more vulnerable area (both in Figs. 3, 4).

*P*< 0.01).

^{11}the RNFL stream was traced and the corresponding angle on the optic disc was identified. In general, the current mapping was consistent with that reported by Hood et al.

^{19}In particular, a more vulnerable region of the optic nerve head (between 40° and 67.5° inferior to the papillomacular bundle on the retina) corresponds to an area of the superior 10-2 HFA hemifield where there are very few test points with 24-2 HFA. In a recent report, VF test points in both the 24-2 and 10-2 HFA VFs were clustered into 11 clusters, four sectors were allocated to the 10-2 HFA VF region, and the cpRNFL sector most closely related was identified.

^{20}Similar to the current results, many more VF test points in the inferior hemifield (

*n*= 12) were found to correspond to temporal cpRNFL sectors (the papillomacular area) compared with the superior VF hemifield (

*n*= 5 test points). Weber et al.

^{21}reported that there is a preserved “central isle” of the VF in advanced glaucoma patients (with largest extend to the temporal lower quadrant and smallest extend to the upper nasal quadrant), and recommended the use of a 2° spacing test like the 10-2 HFA VF in these cases. In the current study, the wider area of the 10-2 HFA VF—outside the ‘central isle' region

^{21}—was divided into just two clusters (1 in the superior hemifield and 1 in the inferior hemifield) so it is not possible to observe the detailed structure–function mapping in this region. Indeed in our previous report, VF information was best summarized by dividing test points in the 30-2 and 10-2 HFA VFs into much smaller clusters (total of 65 clusters) with 29 clusters in the 10-2 VF area.

^{22}In general, these tendencies were also shown in the map obtained using a univariate analysis between each cpRNFL thickness and TD value (Fig. 4).

^{11}First, the mapping by Hood et al.

^{11}suggested that most temporal VF test points just above or beneath the horizontal line correspond to the most inferior or superior angles on the optic disc. In contrast, we observe that the farthest nasal test points in the superior hemifield correspond to a less inferior angle (sector 3 in Fig. 1) compared with more central test points correspond to sector 4 in Figure 1. A similar tendency was observed for the two farthest nasal test points in the inferior hemifield (sector 14 in Fig. 1). The reason for these contradicting results is not clear but it may be due to large interindividual variability of the temporal raphe,

^{23}which has an impact on the structure–function relationship.

^{12}Thus, these nasal VF test points can relate to the superior or inferior retina, and hence may correspond more closely to a temporal 0° angle in the optic disc, compared with more central VF test points.

^{11}(the temporal area on the optic disc). In the current study, the relationship between the magnitude of lambda and predicted sensitivity was significant: lambda values tended to be large where predicted visual sensitivity was low (Fig. 5). More specifically, as shown in Figure 6, the absolute prediction error tended to be large in the more vulnerable area where the lambda value was large. This may be because the region of RNFL that corresponds to these field locations is variable, for example, due to differences in optic nerve head position, causing a wider region of the RNFL to be ‘predictable'. In addition, it could be that these field locations are inherently more variable, so a wider region of RNFL is used in the predictions to 'smooth out' this variability. This raises a question about the usefulness of the proposed LASSO prediction model in areas where lambda is large. However, the correlation coefficients between the predicted TD values and actual TD values were high in this area. Further, as shown in Figure 6, the SD values of the TD values in this area were high compared with those in the least vulnerable area; thus, the predicted TD value was more variable in the more vulnerable area, compared with in the least vulnerable area. However, as discussed, the larger absolute prediction error in the more vulnerable area may simply be inherited from the inherently larger variability of TD values in this region.

^{5,24}; hence, a further study in myopic eyes is needed to shed light on this issue.

^{11}

**Y. Fujino**, None;

**H. Murata**, None;

**M. Matsuura**, None;

**M. Yanagisawa**, None;

**N. Shoji**, None;

**K. Inoue**, None;

**J. Yamagami**, None;

**R. Asaoka**, None

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