July 2006
Volume 47, Issue 7
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Glaucoma  |   July 2006
Structure–Function Relationships Using Confocal Scanning Laser Ophthalmoscopy, Optical Coherence Tomography, and Scanning Laser Polarimetry
Author Affiliations
  • Christopher Bowd
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
  • Linda M. Zangwill
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
  • Felipe A. Medeiros
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
  • Ivan M. Tavares
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
  • Esther M. Hoffmann
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
  • Rupert R. Bourne
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
  • Pamela A. Sample
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
  • Robert N. Weinreb
    From the Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, California.
Investigative Ophthalmology & Visual Science July 2006, Vol.47, 2889-2895. doi:10.1167/iovs.05-1489
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      Christopher Bowd, Linda M. Zangwill, Felipe A. Medeiros, Ivan M. Tavares, Esther M. Hoffmann, Rupert R. Bourne, Pamela A. Sample, Robert N. Weinreb; Structure–Function Relationships Using Confocal Scanning Laser Ophthalmoscopy, Optical Coherence Tomography, and Scanning Laser Polarimetry. Invest. Ophthalmol. Vis. Sci. 2006;47(7):2889-2895. doi: 10.1167/iovs.05-1489.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

purpose. To assess the strength of the association between retinal nerve fiber layer (RNFL) thickness and optic disc topography measured with confocal retinal tomography (HRT II; Heidelberg Engineering, Dossenheim, Germany), optical coherence tomography (StratusOCT; Carl Zeiss Meditec, Inc., Dublin, CA), and scanning laser polarimetry (GDx with variable corneal compensator, VCC; Carl Zeiss Meditec, Inc.), and visual field (VF) sensitivity and to determine whether this association is better expressed as a linear or nonlinear function.

methods. One hundred twenty-seven patients with glaucoma or suspected glaucoma and 127 healthy eyes from enrollees in the Diagnostic Innovations in Glaucoma Study (DIGS) were tested on HRT II, StratusOCT, GDx VCC, and standard automated perimetry (SAP, with the Swedish Interactive Thresholding Algorithm [SITA]) within 3 months of each other. Linear and logarithmic associations between RNFL thickness (HRT II, StratusOCT, and GDx VCC) and neuroretinal rim area (HRT II) and SAP sensitivity expressed in decibels were determined globally and for six RNFL/optic disc regions (inferonasal, inferotemporal, temporal, superotemporal, superonasal, and nasal) and six corresponding VF regions (superior, superonasal, nasal, inferonasal, inferior, and temporal).

results. The associations (R 2) between global and regional RNFL/optic disc measurements and VF sensitivity ranged from <0.01 (temporal RNFL, nasal VF, and nasal RNFL, temporal VF; linear and logarithmic associations) to 0.26 (inferotemporal RNFL, superonasal VF; logarithmic association) for HRT II; from 0.02 (temporal RNFL, nasal VF; linear association) to 0.38 (inferotemporal RNFL, superonasal VF; logarithmic association) for OCT; and from 0.03 (temporal RNFL, nasal VF; linear association) to 0.21 (inferotemporal RNFL, superonasal VF; logarithmic association) for GDx. Structure–function relationships generally were strongest between the inferotemporal RNFL–optic disc sector and the superonasal visual field and were significantly stronger for StratusOCT RNFL thickness than for other instruments in this region. Global associations (linear and logarithmic) were significantly stronger using OCT compared with HRT. In most cases, logarithmic fits were not significantly better than linear fits when visual sensitivity was expressed in log units (i.e., decibels).

conclusions. These results suggest that structure–function associations are strongest with StratusOCT measurements and are similar between HRT II and GDx VCC and these associations are generally no better expressed logarithmically than linearly when healthy, suspect, and glaucomatous eyes are considered.

Relationships between anatomic structure of the retinal nerve fiber layer (RNFL) and optic disc (representing ganglion cell distribution) and visual sensitivity (representing ganglion cell function) in glaucoma are investigated to determine the degree to which anatomic measurements reflect visual sensitivity and vice versa. Significant relationships between structure and function are important from a clinical standpoint, because it is assumed that both structural and functional assessments provide related information on the extent of glaucomatous damage at a given time. In addition, these structure–function relationships can provide insight into the amount of neural substrate lost and its effect on visual function, thus providing insight into the nature of glaucoma. 
Currently available imaging techniques used for examining the RNFL and optic disc in glaucoma include confocal scanning laser ophthalmoscopy (CSLO), optical coherence tomography (OCT), and scanning laser polarimetry (SLP). Each of these techniques uses different technologies and light sources to characterize the distribution of RNFL and/or optic disc topography. CSLO uses confocal technology to construct a three-dimensional representation of the retinal surface height from multiple image sections, OCT uses interferometry and a reflection-based edge-detection algorithm to define the thickness of the circumpapillary RNFL, and SLP uses light to penetrate the birefringent RNFL and provide RNFL thickness estimates based on the linear relationship between RNFL birefringence and the retardation of reflected light. 1 Because these techniques use different methods to measure different aspects of the retina applicable to glaucoma, it is possible that their measurements have different associations with visual sensitivity. 
The purpose of the present study was to investigate the structure–function relationship between CSLO, OCT, and SLP and visual function measured using standard automated perimetry (SAP) in a single population. In addition, we investigated whether linear or nonlinear functions better describe structure–function associations when RNFL thickness is expressed linearly and visual sensitivity is expressed in nonlinear form. 
Methods
One eye was randomly selected from all individuals more than 40 years of age enrolled in the University of California, San Diego, Diagnostic Innovations in Glaucoma Study (DIGS) who had good-quality CSLO (HRT II; Heidelberg Engineering, Dossenheim, Germany), OCT (StratusOCT; Carl Zeiss Meditec, Inc., Dublin, CA), and SLP (GDx VCC, Carl Zeiss Meditec, Inc.) imaging, in addition to reliable (false positives and fixation losses ≤25%, false negatives ≤33%), SAP testing (program 24-2 using Swedish Interactive Thresholding Algorithm [SITA], Humphrey Field Analyzer II; Carl Zeiss Meditec, Inc.) and stereophotography of the optic disc (TRC-SS; Topcon Instruments Corp. of America, Paramus, NJ), within 3 months of each other. We chose to include all eyes meeting these criteria to represent the greatest possible range of RNFL topography and visual field (VF) sensitivity. A 3-month testing window was selected to bar the possibility of glaucomatous change between structural and functional testing. 
A total of 127 eyes were included. Of these eyes, 41 were glaucomatous, defined as those with consecutive, repeatable abnormal SAP results with either pattern SD greater than 5% of normal or Glaucoma Hemifield Test outside normal limits (both defined based on the instrument’s normative database); 46 had suspected glaucoma, defined as those with abnormal-appearing optic discs (presence of neuroretinal rim thinning or localized or diffuse RNFL defects indicative of glaucoma, i.e., glaucomatous optic neuropathy) by masked stereophotograph assessment without repeatable abnormal SAP results or those with intraocular pressure (IOP) > 22 mm Hg, with healthy-appearing optic discs without repeatable abnormal SAP results; and 40 were healthy, defined as those with IOP < 23 mm Hg with no history of elevated IOP, healthy-appearing optic discs and no repeatable abnormal SAP results. 
Mean age of study participants was 63.1 ± 10.3 years (SD), 78 (61%) were female and 109 (92%) were white. Average SAP mean deviations (MD) were −3.0 ± 2.1 dB (SD; range, = −8.9–0.1), −0.7 ± 1.2 dB (range, −4.1–1.8), and −0.4 ± 1.1 dB (range, −3.1–1.6 dB) for glaucoma, suspect, and healthy eyes, respectively. 
Beside the testing, each study participant underwent a comprehensive ophthalmic evaluation, including review of medical history, best corrected visual acuity testing, slit lamp biomicroscopy, IOP measurement with Goldmann applanation tonometry, gonioscopy, and dilated fundus examination with a 78-D lens. To be included in the study, participants had to have best corrected visual acuity better than or equal to 20/40, spherical refraction within ± 5.0 D and cylinder correction within ± 3.0 D, and open angles on gonioscopy. Eyes with coexisting retinal disease, uveitis, or nonglaucomatous optic neuropathy were excluded. 
The study methodology was approved by the University of California, San Diego Human Research Protection Program and adhered to the tenets of the Declaration of Helsinki and the Health Insurance Portability and Accountability Act (HIPAA). 
Instrumentation
Confocal Scanning Laser Ophthalmoscopy ( HRT II).
The HRT II (Heidelberg Engineering) employs confocal scanning diode technology to provide topographical measures of the optic disc and parapapillary retina. It has been described in detail elsewhere. 1 Three 15° field-of-view scans, centered on the optic disc and judged to be of acceptable quality by a trained technician were obtained for each tested eye. A mean topography image of these three scans was automatically created by the instrument software (ver. 1.4.1.5). A trained technician outlined the optic disc margin on the mean image using information obtained by viewing simultaneous stereoscopic photographs of the optic disc. Only well-focused, evenly illuminated and centered scans with an SD ≤ 50 μm and sensitivity ≤ 90 were used. 
RNFL thickness measurements and neuroretinal rim area measurements were obtained for 64, 5.625° sectors around the optic disc. Rim area was included in the analyses in addition to RNFL thickness because the HRT II is specifically designed to measure optic disc topography and not RNFL thickness, whereas other techniques are specifically designed to measure RNFL thickness. The 5.625° sector size was determined by the available sector size dictated by data exportable from the GDx VCC, to match sector size among instruments. 
We selected RNFL thickness and neuroretinal rim area as candidates for association with visual sensitivity, because they are more likely to be related to retinal ganglion cell count than the composite parameters available using these imaging instruments. 2  
Optical Coherence Tomography (StratusOCT).
The StratusOCT (Carl Zeiss Meditec, Inc.) measures RNFL thickness with a low-coherence light source projected onto the retina. This measurement beam’s reflected light source is compared with the reflectance of a reference beam reflected from a reference mirror at a known position to determine the thickness of the retina. An edge-detection algorithm is used to define the posterior border of the RNFL (the anterior border is defined by the large difference in reflectance along the vitreoretinal interface). Details of this technique have been described. 1 Only well-focused and centered scans with a signal strength ≥7 were included. In addition, all scans were subjectively evaluated to confirm that the RNFL detection algorithm followed closely the anterior and posterior RNFL borders. 
RNFL thickness measurements were obtained for 256, 1.406° circumpapillary points using a 3.4-mm scan diameter (software ver. 4.0). Sector number and size were dictated by the available data export and were then converted into 64, 5.625° sectors to match the sector size used for the HRT II and GDx VCC. 
Scanning Laser Polarimetry (GDx VCC).
The GDx VCC (Carl Zeiss Meditec, Inc.) measures the retardation of light reflected from the birefringent RNFL fibers and provides an estimated RNFL thickness based on the linear relationship between observed retardation, measured with a prototype instrument, and RNFL thickness determined histologically. Details of this technique have been described previously. 1 Because corneal polarization axis and magnitude affect SLP measurements and are not similar in all eyes, the GDx VCC employs a variable corneal polarization compensator that allows eye-specific compensation. After determining the axis and magnitude of corneal polarization in each eye by macular scanning, three appropriately compensated retinal polarization images per eye were automatically obtained and combined to form each mean image used for analysis. Only well-focused, evenly illuminated, and centered scans with residual anterior segment retardation ≤15.0 nm and typical scan scores ≥80, 3 determined by GDx VCC (ver. 5.5.0) software, were included. Lower values of the typical scan score indicate the presence of atypical patterns of retardation that can generate spurious RNFL thickness measurements. 
RNFL thickness measurements were obtained for 64, 5.625° sectors under the instrument’s circumpapillary measurement ellipse. Sector number and size are dictated by the available data export provided by the software used. 
For each instrument, the 64, 5.625° sectors were combined to create inferonasal (227–271°), inferotemporal (272–309°), temporal (310–39°), superotemporal (40–79°), superonasal (80–118°), and nasal (119–226°) sectors that closely approximated those suggested previously (Fig. 1) . 4 Global measurements (360°) also were obtained. 
Standard Automated Perimetry.
SAP-measured visual sensitivities were calculated by averaging measured thresholds from each test point within six VF regions corresponding to the six retinal sectors described above (in Fig. 1 ). A mean SAP threshold also was obtained by averaging thresholds at each test point to investigate the global structure–function association between mean SAP sensitivity and mean RNFL and rim area measurements. 
Statistical Analyses
We compared mean global measurements among healthy, suspect, and glaucomatous eyes, using all investigated parameters from HRT II, StratusOCT, and GDx VCC, by ANOVA with post hoc Tukey honestly significant difference (HSD) pair-wise comparisons. 
Structure–function associations were investigated by using linear (y = ax + b) and logarithmic (y = a + b lnx) regression between RNFL thickness measurements (HRT II, StratusOCT, and GDx VCC) and rim area (HRT II) and visual sensitivity (raw thresholds), measured with SAP and expressed in decibels. The results are reported as R 2. Both linear and logarithmic regressions were used because structural measurements using HRT, OCT, and GDx are expressed in linear units (millimeters, square millimeters, and micrometers) and functional measurements are expressed in logarithmic units (decibels). 
To compare the strength of association with visual sensitivity across instruments, the absolute value of the studentized residuals from each model (i.e., association between anatomic measure and visual sensitivity for each instrument) were log transformed (because absolute value of the residuals were not normally distributed) and compared by repeated-measures ANOVA with pair-wise Tukey post hoc comparisons. Studentized residuals were used because they are scale free (they represent the residuals in standard deviation form) and the measurement scales are different across imaging parameters investigated in the present study (e.g., micrometers of RNFL thickness and square millimeters of neuroretinal rim area). 
To determine whether linear or nonlinear fits best described each structure–function association, two-tailed paired t-tests were performed on the log absolute values of the residuals for each regression model. 
Results
Comparisons of mean global HRT II, StratusOCT, and GDx VCC measurements among healthy, suspect, and glaucomatous eyes are shown in Table 1 . For HRT RNFL thickness and GDx VCC RNFL thickness a significant difference was found between glaucomatous eyes and both healthy and suspect eyes (ANOVA P < 0.001, Tukey HSD with α = 0.05). For HRT rim area a significant difference was found between glaucomatous and healthy eyes (ANOVA P = 0.003, Tukey HSD with α = 0.05). For StratusOCT RNFL thickness values in glaucomatous, healthy, and suspect eyes all were significantly different from one another (ANOVA P < 0.001, Tukey HSD with α = 0.05). 
Results investigating structure (expressed in linear scale) to function (expressed in dB scale) associations using linear and logarithmic regression are shown in Table 2 . Linear and logarithmic associations were strongest between the inferotemporal RNFL and the superonasal VF for StratusOCT and GDx. These associations were similar between inferotemporal and superotemporal RNFL and corresponding VF locations for HRT II. For inferotemporal RNFL, linear associations ranged from R 2 = 0.16 for HRT II rim area to R 2 = 0.33 for OCT, and logarithmic associations ranged from R 2 = 0.21 for GDx VCC to R 2 = 0.38 for OCT (all P < 0.0001). For superotemporal RNFL, linear associations ranged from R 2 = 0.13 for GDx VCC to R 2 = 0.19 for both OCT and HRT RNFL, and logarithmic associations ranged from R 2 = 0.15 for GDx VCC to R 2 = 0.25 for OCT and HRT RNFL (all P < 0.0001). Global structure–function associations (i.e., between the average of all RNFL sectors and average of all VF areas) ranged from R 2 = 0.08 for HRT II rim area (P = 0.001) to R 2 = 0.23 for OCT (P < 0.0001) using linear regression, and from R 2 = 0.08 (P = 0.001) for HRT II rim area to R 2 = 0.25 (P < 0.0001) for OCT using logarithmic regression. 
Repeated measures ANOVAs on the log absolute values of the model residuals showed a difference in linear and/or logarithmic associations among imaging instruments in the inferotemporal, superotemporal, and nasal RNFL sectors as well as globally. Pair-wise comparisons indicated that both the linear and logarithmic structure–function associations in the inferotemporal RNFL sector were stronger for OCT-measured RNFL thickness than for all other instruments (P < 0.05). In the superotemporal sector, the logarithmic associations for OCT and HRT II RNFL thickness were stronger than the GDx VCC measured logarithmic association (P < 0.05). In the nasal sector, OCT- and GDx VCC–measured logarithmic associations were stronger than the logarithmic HRT II RNFL association. Finally, differences in both linear and logarithmic associations were observed globally, with the OCT-based associations stronger than both HRT II-based associations (P < 0.05; Table 2 ). 
Although visual sensitivity was expressed with a nonlinear scale and RNFL thickness and HRT II rim area were expressed using a linear scale, associations with visual sensitivity were improved significantly using logarithmic compared to linear fits only for HRT measurements (inferotemporal and superotemporal parapapillary regions; two-tailed paired t-tests, P < 0.05). Figure 2shows linear and logarithmic structure–function relationships when structure was measured in the inferotemporal region for each instrument. 
Discussion
Measurements from HRT II, StratusOCT and GDx VCC were significantly associated with VF sensitivity in the present study. These results support those previously shown histopathologically, photographically, and with various optical imaging devices. 5 6 7 8 9 Associations were strongest, in general, between the inferotemporal RNFL and neuroretinal rim and the superonasal VF. The strength of the cross-sectional structure–function association varied among the imaging instruments investigated, with OCT demonstrating stronger associations than other instruments, primarily inferotemporally, but also superotemporally and globally. Despite the fact that RNFL measurements were expressed in linear scale, and VF sensitivity was expressed in logarithmic scale, in most cases, logarithmic regression did not provide a significantly better fit to the data. Finally, structure–function associations were weak to modest overall, with structural measurements explaining no more than 40% of the variance in functional measurements. 
Other studies investigating structure–function relationships have reported significant relationships similar to those reported in the present study, with the same imaging instruments. With the previous generation HRT II-compatible HRT, significant linear associations between global and regional optic disc topography and VF sensitivity have been shown. For instance, Iester et al. 10 reported a correlation between neuroretinal rim area and VF MD of 0.44 (Pearson’s r) in 294 healthy, ocular hypertensive, and glaucomatous eyes. The correlation was strongest in glaucomatous eyes compared with ocular hypertensive and healthy eyes. Other HRT studies have demonstrated that the most defective neuroretinal rim sectors (inferior sectors) are associated with the most defective VF areas (nasal sectors). 11 12  
Recently, Garway-Heath et al. 13 demonstrated significant linear and quadratic relationships between HRT temporal neuroretinal rim area (in square millimeters) and SAP-measured visual sensitivity (dB) in 74 healthy and glaucomatous eyes. R 2 for the linear fit was 0.30 and R 2 for the quadratic fit was 0.38. The larger R 2 associated with a curvilinear fit in their study and others suggested that, to be most representative of structural damage for all stages of glaucoma, visual sensitivity may be best expressed in a nonlog format (e.g., 1/Lambert). However results from the present study do not support this theory, in that we found that a logarithmic fit was rarely better than a linear fit, despite the fact that SAP sensitivities were expressed in logarithmic form (i.e., as decibels). Structure–function studies using HRT II have been infrequent, probably because the association has been well established using the previous-generation instrument. 
Using the previous-generation OCT and SAP, Schuman et al. 14 first showed a significant association between mean RNFL thickness and the presence of VF defects. Subsequent studies by Hoh et al. 15 and Zangwill et al. 16 showed linear associations between OCT-measured RNFL thickness and SAP mean and pattern deviation indices. Similar to the present study, El Beltagi et al. 17 showed significant linear structure–function relationships that were strongest between the inferotemporal RNFL and the superonasal VF (e.g., R 2 as high as 0.57). However, their methodology differed considerably from that used in our study. First, they expressed visual sensitivity in average MD in each VF zone and assessed its association with deviation from normal RNFL thickness. Second, they used a VF map from Weber and Ulrich consisting of 21 sectors and assessed the linear association with RNFL thickness measured in clock hours, compared with the current scheme using six sectors for both VF and RNFL measurement. Finally, eyes in their study were selected based on the presence of VF defects, probably increasing the strength of association. 
Using the currently available GDx VCC, Bowd et al. 18 demonstrated improved structure–function associations compared with those obtained with fixed corneal compensation (see also Bagga et al. 19 and Schlottmann et al. 20 ). More recently, Reus and Lemij 21 demonstrated local structure–function relationships using GDx VCC in glaucomatous eyes with a methodology similar to that used in the present study (e.g., similar RNFL and VF sectors). In their study, associations using linear regression on visual function expressed in dB ranged in strength from R 2 = 0.29 for nasal RNFL to R 2 = 0.48 for superotemporal RNFL. Structure–function associations in healthy eyes alone were weak (i.e., statistically nonsignificant) except for the superotemporal RNFL-inferonasal VF association. GDx VCC structure–function associations in our study were weaker than those reported by Reus and Lemij in glaucomatous eyes, possibly because of their inclusion of more advanced glaucoma (mean MD in glaucomatous eyes = −9.39 dB compared with −3.0 dB) and our inclusion of healthy eyes, most likely having a very large range in the number of retinal ganglion cells, and glaucoma suspect eyes with little VF damage (mean MD in glaucoma suspect eyes was −0.7 dB). A more recent study by Reus and Lemij 22 showed structure–function associations with SAP were similar in strength (i.e., explained a similar amount of variability) using GDx VCC and HRT II rim area. Statistically, our results allow the same conclusion; however, R 2 values in our studies are consistently lower than those reported by these authors. 
In the present study we did not find any improvement in the strength of the GDx VCC or OCT structure–function associations when fitting data in which visual sensitivity was expressed in decibels with curves, instead of lines. These results differ from those of Schlottmann et al. 20 who found that logarithmic regression showed small but significant improvement over linear regression in the inferonasal RNFL and inferotemporal RNFL. Similarly, Reus and Lemij 21 found an improvement in linear fit when visual sensitivity was expressed in linear scale (i.e., nonlog) compared with when it was expressed in decibel (i.e., log) scale. In the present study, several differences between R 2 values comparing structure–function relationships expressed linearly with those expressed logarithmically were greater than those reported by Schlottmann et al. 20 ; however the variability of the mean differences in model residuals in our study was large. 
In an attempt to identify the best mathematical description of the structure–function association using imaging and SAP, Leung et al. 23 used linear and four nonlinear models to assess the association between global visual sensitivity and mean RNFL thickness in healthy, suspect, and glaucomatous eyes measured using StratusOCT and GDx VCC and found second- and third-order polynomial curves, respectively, to be better fits than lines when visual sensitivity was expressed in decibels. When sensitivity was expressed in 1/Lambert (i.e., nonlog), a linear fit was best for both instruments. When healthy eyes were removed from the analyses, logarithmic (for GDx VCC) and second-order polynomial (for OCT) curves were better fits than lines when visual sensitivity was expressed in decibels. When sensitivity was expressed as 1/Lambert, second-order polynomial (for GDx VCC) and linear fits (for OCT) were best. In their study, although significant differences according to Akaike information criteria were found between best fits, the differences in R 2 for each fit were quite small. Finally, when all participants were included in their study, global linear and logarithmic structure–function associations for OCT and GDx VCC were much larger than in the present study (range, R 2 = 0.59–0.68 compared with R 2 = 0.14–0.25). This difference may be attributable to the large difference in glaucoma severity between studies (SAP MD range, −30.0 to −2.4 dB; mean, −11.1 dB for Leung et al., compared with range, −8.9–0.1 dB, mean, −3.0 dB for our study). Leung et al. did not directly compare the strength of associations with visual sensitivity for OCT and GDx VCC. 
The lack of consensus among studies regarding significant differences between linear and nonlinear estimates of structure–function associations might be influenced by the statistical techniques used to test the differences. Examining model residuals, we found few significant differences between linear and nonlinear fits, although R 2 values for logarithmic fits were usually larger. Garway-Heath et al. 13 defined stronger nonlinear fits, compared with linear fits, when the coefficient of the nonlinear term reached statistical significance. Leung et al. 23 reported significant but small differences among linear and multiple nonlinear fits using Akaike information criteria and ANOVA. However, choice of statistical techniques alone probably cannot account for different results across all studies, because Schlottmann et al. 20 showed small but significant improvements in structure–function associations with logarithmic regression using analysis of model residuals, similar to the analyses used in the present study. In the present study, it is possible that the increased R 2 observed with nonlinear fitting did not reach significance because of the somewhat limited number of study participants, although more participants were included in this study than in several others, including Schlottmann et al. 20  
Significant cross-sectional structure–function associations suggest that VF sensitivity is a reasonable surrogate measurement for underlying neural health, measured using optical imaging techniques. However, weak or modest structure–function relationships, like those reported herein, do not necessarily suggest that VF sensitivity is not related to neural health. Several studies have provided evidence that the temporal onset of structural and functional defects, detectable using current techniques, is different. For instance, the recent Ocular Hypertension Treatment Study 24 and European Glaucoma Prevention Study 25 both showed that, in many eyes, structural defects develop before functional defects, whereas, in a similar number of other eyes, functional defects develop first (with both kinds of defects developing in some eyes simultaneously). This finding suggests that to characterize the structure–function relationship accurately using current techniques, the consideration of a temporal lag between structural and functional testing might be necessary. This idea is intuitive because it is likely that diseased retinal ganglion cells begin to malfunction before dying, resulting in reduced visual sensitivity without a detectable structural loss (i.e., cell “sickness” precedes cell death). In addition, it also is likely that ganglion cell loss (e.g., measured by counting axons) precedes detectable visual sensitivity loss in areas of the VF where redundancy of ganglion cells is high. Recently, Harwerth et al. 26 have suggested, based on evidence from behaving primates with experimental glaucoma, that the ideal descriptor of the structure–function relationship is different at different levels of neural loss. For instance, the association is better described by percentage loss when the amount of cell loss is small and better described by log–log loss when cell loss is greater than approximately 3 dB. 
Another potential reason for weak structure–function associations found in several studies is the possibility that the local topography-to-function maps used are not optimal or that devising a “correct” structure–function map is not possible. A recent publication by Gardiner et al. 27 demonstrated that although predicted structure–function associations occur, unpredicted structure–function associations also occur. These authors assessed the correlations between 36 HRT measured normalized rim area sectors and each of the 52 standard SAP test points and found that although expected correlations were significant (e.g., inferotemporal RNFL associated with superonasal VF), unexpected correlations also were significant (e.g., superotemporal RNFL associated with superior VF; see also Sanchez-Galeana et al. 28 ). However, for both of these studies, it is possible that the presence of diffuse RNFL thinning and/or VF loss, or the large number of correlations investigated (i.e., multiple comparisons) contributed to the number of significant but unexpected correlations reported. 
Even if the cross-sectional structure–function relationships measured using currently available surrogate techniques are modestly strong at best, structural testing and perimetry still are essential for patient treatment. We know that neural loss will necessarily result in functional loss and if neural loss is detected early, some future functional loss may be spared with treatment. In addition, we know that psychophysical results represent visual function and that worsening visual function demands treatment. Our results suggest that StratusOCT RNFL thickness measurements may provide a better cross-sectional representation of visual function than HRT II and GDx VCC measurements. This study is the first to investigate the relative difference in strength of these associations using the three most commonly used optical imaging instruments in the same population. Using the same sample population controls for the important effects of population demographics and disease severity. Although age was constant across all between-instrument analyses, the strength of the structure–function associations reported for each instrument may be influenced by age because age-corrected measurements (e.g., SAP pattern deviation) were not used. 
Because we report significant structure–function associations using all instruments tested, our results suggest that RNFL thickness (and neuroretinal rim area) measured with optic imaging is an indicator of visual function measured psychophysically, albeit not a perfect one. Results from our study provide additional support to suggest that the “best” mathematical descriptor of the association of the RNFL/disc topography structure to visual sensitivity most likely depends on the instruments used to test the association, the locations at which the associations are tested, and the characteristics of the study population. 
 
Figure 1.
 
Retinal nerve fiber layer/neuroretinal rim area regions and corresponding visual field regions used to measure structure–function associations among anatomic measurements obtained with HRT II, StratusOCT and GDx VCC and visual sensitivity measurements obtained using standard automated perimetry (SAP). N, nasal region; B, blind spot (points not included in analysis).
Figure 1.
 
Retinal nerve fiber layer/neuroretinal rim area regions and corresponding visual field regions used to measure structure–function associations among anatomic measurements obtained with HRT II, StratusOCT and GDx VCC and visual sensitivity measurements obtained using standard automated perimetry (SAP). N, nasal region; B, blind spot (points not included in analysis).
Table 1.
 
HRT II, StratusOCT, and GDx VCC Global Measurements Compared among Healthy, Suspect and Glaucoma Eyes
Table 1.
 
HRT II, StratusOCT, and GDx VCC Global Measurements Compared among Healthy, Suspect and Glaucoma Eyes
Healthy Eyes (n = 40) Suspect Eyes (n = 46) Glaucoma Eyes (n = 41) P
Global HRT II RNFL thickness (mm) 0.267 (0.084) 0.245 (0.064) 0.208 (0.064) < 0.001*
Global HRT II rim area (mm2) 1.45 (0.29) 1.35 (0.23) 1.24 (0.31) 0.003, †
Global StratusOCT RNFL thickness (μm) 97.0 (10.2) 89.6 (12.5) 78.5 (15.4) < 0.001, ‡
Global GDx VCC RNFL thickness (μm) 51.7 (4.2) 50.2 (5.9) 43.5 (5.7) < 0.001*
Table 2.
 
Structure–Function Associations (R 2)
Table 2.
 
Structure–Function Associations (R 2)
InfNas Disc Sup VF InfTemp Disc* SupNas VF Temp Disc Nas VF SupTemp Disc, † InfNas VF SupNas Disc Inf VF Nas Disc, ‡ Temp VF Global Disc, § Global VF
HRT RNFL (lin) 0.07 (0.003) 0.19 (<0.0001) <0.01 (0.809) 0.19 (<0.0001) 0.07 (0.003) <0.01 (0.912) 0.11 (<0.0001)
HRT RNFL (log) 0.06 (0.007) 0.26 (<0.0001), ∥ <0.01 (0.880) 0.25 (<0.0001), ∥ 0.09 (0.001) <0.01 (0.817) 0.11 (<0.0001)
HRT rim area (lin) 0.04 (0.026) 0.16 (<0.0001) 0.01 (0.188) 0.17 (<0.0001) 0.10 (0.003) 0.02 (0.116) 0.08 (0.001)
HRT rim area (log) 0.04 (0.027) 0.25 (<0.0001), ∥ 0.02 (0.140) 0.20 (<0.0001) 0.10 (0.004) 0.02 (0.084) 0.08 (0.001)
OCT RNFL (lin) 0.06 (0.004) 0.33 (<0.0001) 0.02 (0.148) 0.19 (<0.0001) 0.15 (<0.0001) 0.08 (0.001) 0.23 (<0.0001)
OCT RNFL (log) 0.07 (0.002) 0.38 (<0.0001) 0.03 (0.097) 0.25 (<0.0001) 0.17 (<0.0001) 0.11 (0.0004) 0.25 (<0.0001)
GDx RNFL (lin) 0.06 (0.007) 0.19 (<0.0001) 0.03 (0.056) 0.13 (<0.0001) 0.16 (<0.0001) 0.08 (0.001) 0.14 (<0.0001)
GDx RNFL (log) 0.05 (0.009) 0.21 (<0.0001) 0.04 (0.055) 0.15 (<0.0001) 0.18 (<0.0001) 0.10 (0.001) 0.14 (<0.0001)
Figure 2.
 
Scatterplots showing the associations between inferotemporal measurements from HRT II, GDx VCC, and StratusOCT and superonasal visual field sensitivity expressed in decibels. Black lines: linear fits; gray lines: logarithmic fits. R 2 values are shown for each fit. A logarithmic fit was significantly better than a linear fit for HRT rim area and HRT RNFL thickness (both P < 0.05). Linear and logarithmic associations with visual field sensitivity were stronger for OCT compared with all other instruments (P < 0.05).
Figure 2.
 
Scatterplots showing the associations between inferotemporal measurements from HRT II, GDx VCC, and StratusOCT and superonasal visual field sensitivity expressed in decibels. Black lines: linear fits; gray lines: logarithmic fits. R 2 values are shown for each fit. A logarithmic fit was significantly better than a linear fit for HRT rim area and HRT RNFL thickness (both P < 0.05). Linear and logarithmic associations with visual field sensitivity were stronger for OCT compared with all other instruments (P < 0.05).
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Figure 1.
 
Retinal nerve fiber layer/neuroretinal rim area regions and corresponding visual field regions used to measure structure–function associations among anatomic measurements obtained with HRT II, StratusOCT and GDx VCC and visual sensitivity measurements obtained using standard automated perimetry (SAP). N, nasal region; B, blind spot (points not included in analysis).
Figure 1.
 
Retinal nerve fiber layer/neuroretinal rim area regions and corresponding visual field regions used to measure structure–function associations among anatomic measurements obtained with HRT II, StratusOCT and GDx VCC and visual sensitivity measurements obtained using standard automated perimetry (SAP). N, nasal region; B, blind spot (points not included in analysis).
Figure 2.
 
Scatterplots showing the associations between inferotemporal measurements from HRT II, GDx VCC, and StratusOCT and superonasal visual field sensitivity expressed in decibels. Black lines: linear fits; gray lines: logarithmic fits. R 2 values are shown for each fit. A logarithmic fit was significantly better than a linear fit for HRT rim area and HRT RNFL thickness (both P < 0.05). Linear and logarithmic associations with visual field sensitivity were stronger for OCT compared with all other instruments (P < 0.05).
Figure 2.
 
Scatterplots showing the associations between inferotemporal measurements from HRT II, GDx VCC, and StratusOCT and superonasal visual field sensitivity expressed in decibels. Black lines: linear fits; gray lines: logarithmic fits. R 2 values are shown for each fit. A logarithmic fit was significantly better than a linear fit for HRT rim area and HRT RNFL thickness (both P < 0.05). Linear and logarithmic associations with visual field sensitivity were stronger for OCT compared with all other instruments (P < 0.05).
Table 1.
 
HRT II, StratusOCT, and GDx VCC Global Measurements Compared among Healthy, Suspect and Glaucoma Eyes
Table 1.
 
HRT II, StratusOCT, and GDx VCC Global Measurements Compared among Healthy, Suspect and Glaucoma Eyes
Healthy Eyes (n = 40) Suspect Eyes (n = 46) Glaucoma Eyes (n = 41) P
Global HRT II RNFL thickness (mm) 0.267 (0.084) 0.245 (0.064) 0.208 (0.064) < 0.001*
Global HRT II rim area (mm2) 1.45 (0.29) 1.35 (0.23) 1.24 (0.31) 0.003, †
Global StratusOCT RNFL thickness (μm) 97.0 (10.2) 89.6 (12.5) 78.5 (15.4) < 0.001, ‡
Global GDx VCC RNFL thickness (μm) 51.7 (4.2) 50.2 (5.9) 43.5 (5.7) < 0.001*
Table 2.
 
Structure–Function Associations (R 2)
Table 2.
 
Structure–Function Associations (R 2)
InfNas Disc Sup VF InfTemp Disc* SupNas VF Temp Disc Nas VF SupTemp Disc, † InfNas VF SupNas Disc Inf VF Nas Disc, ‡ Temp VF Global Disc, § Global VF
HRT RNFL (lin) 0.07 (0.003) 0.19 (<0.0001) <0.01 (0.809) 0.19 (<0.0001) 0.07 (0.003) <0.01 (0.912) 0.11 (<0.0001)
HRT RNFL (log) 0.06 (0.007) 0.26 (<0.0001), ∥ <0.01 (0.880) 0.25 (<0.0001), ∥ 0.09 (0.001) <0.01 (0.817) 0.11 (<0.0001)
HRT rim area (lin) 0.04 (0.026) 0.16 (<0.0001) 0.01 (0.188) 0.17 (<0.0001) 0.10 (0.003) 0.02 (0.116) 0.08 (0.001)
HRT rim area (log) 0.04 (0.027) 0.25 (<0.0001), ∥ 0.02 (0.140) 0.20 (<0.0001) 0.10 (0.004) 0.02 (0.084) 0.08 (0.001)
OCT RNFL (lin) 0.06 (0.004) 0.33 (<0.0001) 0.02 (0.148) 0.19 (<0.0001) 0.15 (<0.0001) 0.08 (0.001) 0.23 (<0.0001)
OCT RNFL (log) 0.07 (0.002) 0.38 (<0.0001) 0.03 (0.097) 0.25 (<0.0001) 0.17 (<0.0001) 0.11 (0.0004) 0.25 (<0.0001)
GDx RNFL (lin) 0.06 (0.007) 0.19 (<0.0001) 0.03 (0.056) 0.13 (<0.0001) 0.16 (<0.0001) 0.08 (0.001) 0.14 (<0.0001)
GDx RNFL (log) 0.05 (0.009) 0.21 (<0.0001) 0.04 (0.055) 0.15 (<0.0001) 0.18 (<0.0001) 0.10 (0.001) 0.14 (<0.0001)
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