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Perimetry is classically considered the “gold standard” for glaucoma diagnosis, but a significant loss of retinal ganglion cells (25–30%) occurs before any of the typical glaucomatous visual field (VF) defects are detected [

In 1998, Zeimer et al. [

The research protocol followed the tenets of the Declaration of Helsinki and was approved by the ethical committee of University Hospital Ramón y Cajal, Madrid, Spain. Informed consent was obtained from each participant before enrollment after explanation of the nature and possible consequences of the study. A cohort of patients was prospectively selected according to the following inclusion criteria: between 18 and 80 years of age, best corrected visual acuity > 20/40 (Snellen) in the study eye, refractive error within ±5.00 dioptres equivalent sphere and ±2.00 dioptres astigmatism, and transparent ocular structures: crystalline lens opacity < 1 in LOCS III (Lens Opacities Classification System) [

The cohort of patients was divided into 2 groups: patients with glaucoma or “cases” and healthy patients or “controls.” The glaucoma subjects had to meet two diagnosis criteria: (1) glaucomatous appearance of the optic disc evaluated by a glaucoma specialist, defined as focal or diffuse neuroretinal rim narrowing with concentric enlargement of the optic cup, localized notching or both [

All the patients in the study underwent the following series of tests: general anamnesis, basic eye examination, optical coherence tomography with Spectralis OCT® (Heidelberg Engineering, Heidelberg, Germany), and at least two reliable automated conventional perimetry tests of both eyes with Humphrey visual field analyzer (Carl Zeiss Meditec, Dublin, California, USA). The perimetric test was performed with SITA (Swedish interactive threshold algorithm) standard 24-2 strategy. The following reliability criteria were adopted: fixation losses, false-positive rate, and false-negative rate less than 20% [

Descriptive and correlation statistical analyses were carried out using SPSS statistical software for Windows (version 20.0, IBM-SPSS, Chicago, Illinois, USA). Nonparametric regression analyses were coded in GAUSS (9.0 version, light). In order to facilitate analysis, all data were converted to left eye data. A statistical significance of

In order to study differences between the two groups, the following variables were compared: age, sex, laterality, test time, as well as mean and standard deviation of visual field index (VFI), mean deviation (MD), and average thickness total, superior, and inferior (ATT, ATS, ATI). The Kolmogorov-Smirnov test was used to assess the normality of distribution.

A factor analysis, principal component type, was carried out as a first approach to the study of the structure-function relationship. This was based on a previous analysis described by Ferreras et al. in 2008 [

The second approach was nonparametric regression analysis. Nonparametric regression analysis allows the study of the relationship between two variables,

(a) Spatial correspondence between the measuring points of threshold sensitivity in the automatized perimetry (Humphrey, 24-2 program) and the macular thickness map (Spectralis OCT). (b) Graphic scheme of the first nonparametric spatial regression model. The measurements of threshold sensitivity in each of the 16 central points of the visual field are regressed on the macular thickness of the four surrounding areas. (c) Graphic scheme of the second nonparametric spatial regression model. The measurements of threshold sensitivity in each of the 34 central points of the visual field are regressed on the macular thickness of either the four surrounding areas for the 16 central points or the closest one or two areas (depending on the position) for the 18 most eccentric points. (d) Graphic scheme of the third nonparametric spatial regression model. Two separate regressions were performed: the measurements of threshold sensitivity in each of the 4 central points of the visual field on the macular thickness of the four surrounding areas (red) and the measurements in each of the other 30 points (green) on the 4, 2, or 1 (depending on the position) closest areas.

A total of 85 eyes of 58 Caucasian patients selected according to the inclusion criteria were included in this study (44 glaucoma; 41 control). Table

Demographic characteristics and global indices obtained in both groups.

Glaucoma | Healthy | ||||||||
---|---|---|---|---|---|---|---|---|---|

Mean | SD | Max | Min | Mean | SD | Max | Min | ||

Age (years) | 68.43 | 10.93 | 85 | 35 | 47.93 | 19.24 | 78 | 24 | <0.001 |

VFI^{a} |
80.84 | 16.24 | 98.00 | 27.00 | 99.0 | 0.95 | 100 | 96 | <0.001 |

MD^{b} |
−7.73 | 5.58 | −0.74 | −23.28 | −1.083 | 1.32 | 1.72 | −3.39 | <0.001 |

ATT^{c} |
269.75 | 12.77 | 297.00 | 250.00 | 290.00 | 16.77 | 329.00 | 254.00 | <0.001 |

ATS^{d} |
274.34 | 15.02 | 309.00 | 252.00 | 290.68 | 17.46 | 332.00 | 251.00 | <0.001 |

ATI^{e} |
265.39 | 13.81 | 292.00 | 244.00 | 291.10 | 16.30 | 326.00 | 257.00 | <0.001 |

^{a}Visual field index. ^{b}Mean deviation. ^{c}Total average thickness. ^{d}Superior average thickness. ^{e}Inferior average thickness.

The measure of sampling adequacy (MSA), KMO (Kaiser-Meyer-Olkin) measure, was greater than 0.6 in all cases and the total variance explained by the selected components was >80%.

In the glaucoma group, the factor analysis determined 4 regions or factors in both superior and inferior hemifields of the automatized perimetry, and 5 regions in the superior hemigrid and 7 in the inferior hemigrid of the Spectralis OCT macular grid (Figures

(a) Nonparametric regression between the regions of the superior hemifield (1–4 superior visual field, SVF) and inferior hemigrid (1–7 inferior macula, IM) obtained through factor analysis and that showed significant correlation according to Pearson’s correlation coefficient (shown at the bottom right of the graphics) in the glaucoma group. Values of threshold sensitivity (decibels) are represented in the

(a) Nonparametric regression between the regions of the inferior hemifield (1–4 inferior visual field, IVF) and superior hemigrid (1–5 superior macula, SM) obtained through factor analysis and that showed significant correlation according to Pearson’s correlation coefficient (shown at the top right of the graphics) in the glaucoma group. Values of threshold sensitivity (decibels) are represented in the

In contrast, in the control group, the factor analysis determined 3 regions or factors in the superior hemifield and 5 in the inferior hemifield of the automated perimetry, and 3 regions in the superior hemigrid and 5 regions in the inferior hemigrid of the Spectralis OCT macular grid.

Pearson’s correlation coefficients showed statistically significant differences between the associated anatomical-functional regions in the glaucoma group (Figures

Figures

The first model used studied the function-structure relationship between the 16 central points in the visual field and the complete macular grid (Figure

(a) Regression curves obtained with the application of the first model in the glaucoma (left) and control (right) groups. Dashed lines represent 90% confidence intervals. Values of threshold sensitivity (decibels) are represented in the

For the second model, the 18 points in the visual field located around the previous 16 were added to the regression curve, so that the model studied the function-structure relationship between 34 central points in the visual field and the complete macular grid (Figure

The third model divided the data into two subgroups: the peripheral and the central macular areas (Figure

None of these three models revealed any significant correlation between structure and function in the control group (Figures

We successfully drew a map linking functional and structural damage in the glaucoma group using Humphrey perimetry and the posterior pole asymmetry analysis of the Spectralis OCT regions, obtained completely from an objective analysis, and several functions that provide the mean sensitivity that would correspond to each given macular thickness in glaucoma patients.

In contrast, consistently with previously studies, we have not found any relevant correlation between structure and function in healthy patients [

Factor analysis is a data reduction tool for statistical analysis that summarizes data supplied by a group of variables into a smaller set of representative factors. Ferreras et al. [

Some previous studies on the structure-function relationship maintain that the units of measurement in both must be the same (linear or logarithmic) [

Our VF maps, although with some differences, are overall similar to those obtained in previous studies in which factor analysis of the visual field was carried out [

All the global parameters used to measure total macular thickness (ATT, ATS, and ATI) were significantly lower in the glaucoma group than in the control group. This agrees with previous studies [

Although most of previous studies agree that the inferior hemimacula shows the strongest correlation with the VF, they do not agree that the peripheral nasal region has the strongest correlation [

Further studies with protocols to map both regions separately, in different populations and with larger samples, are required in order to confirm whether this region indeed presents better structure-function correlation than the temporal region.

The application of nonparametric regression analysis between each pair of areas that had shown a significant Pearson correlation allowed for the confirmation, quantification, and accurate detection of the characteristics of this relationship. All pairs displayed similar characteristics, especially in the relationships between peripheral and central regions, although some distinctive features were also observed. The shape of the curve resembles the “hockey” or “broken stick” statistical model used by several authors to determine the cut-off point at which peripapillary RNFL thickness begins to show correlation with visual field defects [

Nonparametric spatial regression is the third approach to assess structure-function correlation that is suggested in this study. This approach moves away from the principles of classic statistical analysis towards more recent trends and innovations in the field, and it allows for the adoption of a novel perspective to the study of the structure-function relationship. The three nonparametric spatial regression models applied offer an alternative approach that bypasses the need to factor analysis and estimates on average an unknown relationship that is presupposed to exist in all the patients. The estimated function provides the mean sensitivity that would correspond to each given macular thickness, both in glaucoma patients and in healthy ones.

The earliest studies on the structure-function relationship were carried out using statistical models that in one or another way tried to explain this relationship in a linear manner [

There are several facts that suggest a priori that the structure-function relationship at macular level may adjust better to a curvilinear model than to linear regression.

On the one hand, it has been demonstrated that there is a “floor effect” or residual thickness, which has been studied extensively in perimetry-peripapillary RNFL correlations. This concept can also be applied to the measurement of macular thickness if understood from a wider perspective.

On the other hand, several studies suggest that structural defects precede alterations in the visual field [

Other authors [

In conclusion, none of the statistical models currently available fits or can explain thoroughly the characteristics of the relationship between structure and function in glaucoma.

The nonparametric spatial regression models suggested in this study try to resolve many of the weakness in previous studies. Their greatest advantage is that no preestablished functional form is imposed on the data, therefore allowing for the data to determine and draw both linear and nonlinear relationships. They also allow for the use of the most commonly used units of measurement and enable the use of all the values obtained in the analysis of both tests. The relationships can be spatially mapped in order to explore correspondences in more depth than through the application of global parameters or point averages in specific regions. We obtain a function than provides the mean sensitivity that would correspond to each given macular thickness in glaucoma patients improving our understanding of the structure-function relationship.

Although carrying out the correlation study between structure and function using the posterior pole asymmetry analysis provided with Spectralis OCT has several advantages, it is limited by the fact that it can only measure the total thickness of the macula and not the specific layers that are usually more affected in glaucoma (retinal ganglion cell layer). This can increase data noise and the results can also be affected by other eye conditions. This protocol adjusts better to the 24-2 pattern than other systems and we chose this pattern because it is the most often used in clinic in the diagnosis and monitoring of glaucoma; however, it is possible that some relevant information was lost, especially in the centremost points in the visual field [

Another limitation of this study is that statistically significant differences in age were found between the two groups. Patients were obtained prospectively and included in one or another group according to the inclusion criteria. The fact that glaucoma is a more frequent pathology in elderly people and that for being included in the control group it was required to lack any other ophthalmic pathology explains this difference. Previous studies have shown that RNFL thickness and visual field sensitivity decrease with age [

This study explores the relationship between structure and function in glaucoma, using novel statistical approaches, and some of which had not been employed previously in this field. The VF test point measures show significant correlation with the corresponding macular thickness points, varying across different regions. The map linking structural damage and functional damage and the corresponding point-to-point functions can be used in the future to improve glaucoma diagnosis and be an additional structural assessment tool.

Further work is necessary in order to confirm these results. The development of more powerful image resolution and better analytical algorithms as well as better functional tests will eventually allow for more accuracy in the assessment of these relationships.

The authors declare that there is no conflict of interest regarding the publication of this article.

The authors are grateful to Jordi Jaumandreu for his assistance and contribution to the statistical analysis of this report.