Evaluation of a Method for Estimating Retinal Ganglion Cell Counts Using Visual Fields and Optical Coherence Tomography.

The structure–function relationship between retinal ganglion cell (RGC) density (structure) and light sensitivity (function; i.e., behavioral thresholds) is not fully understood, nor is the change in this relationship when RGCs undergo atrophy as the result of neurodegenerative diseases such as glaucoma. Early attempts to assess this relationship in human subjects1–,3 analyzed postmortem histology to measure structure, whereas more recent work has used optical coherence tomography (OCT), an in vivo imaging technique4 that allows for direct measurements of the anatomy of the human eye. These imaging data also can be used to identify early structural changes in the human retina that are consistent with glaucomatous neurodegeneration.5,6 In particular, this technique allows for visualization of the individual layers of retinal anatomy in a manner similar to histology,7,8 allowing the opportunity to test structure–function models by using OCT data from the eyes of a large number of human individuals rather than a smaller number of postmortem human donor eyes. To date, there are three predictive structure–function models pertaining to glaucoma that have been applied to OCT data: the models of Harwerth et al.,9,10 Hood and Kardon,11 and Wollstein et al.12 (Malik et al.13 provides an overview of several important structure–function models, including those using structural measures other than OCT.) The relatively new Wollstein et al.12 model focuses primarily on the clinical relevance of the relationship between visual sensitivity and OCT; this model is geared toward determining the association between statistically significant visual field (VF) loss and statistically significant structural loss. On the other hand, the Harwerth et al.9,10 model and the Hood and Kardon11 model both attempt to describe the nature of the structure–function relationship in glaucoma. Harwerth et al.14 originally developed a model based on a mechanically-induced experimental model of glaucoma in rhesus macaques. These monkeys were trained to perform VFs, and these behavioral data were compared with RGC density obtained from analysis of postmortem histology. Along with previous histological studies in human subjects,1–,3 the work of Harwerth et al.10 was a fundamental step in advancing the discourse regarding glaucomatous structure–function relationships. In particular, Harwerth et al.10 proposed a quantitative model, stating that when both measures were plotted on a logarithmic scale, visual sensitivity was linearly related to ganglion cell density with a nonzero intercept that varied with retinal eccentricity, or rather that the relationship was nonlinear when both structure and function were expressed in linear units. (Hereafter, the term “linear” is used only to describe a relationship that is linear when both measures are expressed in linear units.) The Harwerth et al.10 nonlinear model (H-NLM) was later modified to describe OCT data from human subjects by using the thickness of the retinal nerve fiber layer (RNFL) around the optic disc as a proxy for the number of RGC axons. Later iterations of the model included a correction for age15,16 and stage of disease.17 One attractive aspect of the H-NLM is that it converts both visual sensitivity and OCT-derived RNFL thickness to estimates of numbers of RGC bodies and axons, particularly appealing as glaucoma is a disease of the RGCs. Another approach was that of Hood, Kardon, and colleagues,11,18–,22 who directly compared visual sensitivity to OCT-derived RNFL thickness and proposed a linear relationship with a nonzero intercept (residual nonneuronal RNFL thickness) when both measures are expressed in linear units. Thus, a 50% loss in visual sensitivity compared with age-matched normative data should be associated with a 50% loss in the neuronal component of the RNFL. However, unlike the H-NLM, the Hood and Kardon linear model (HK-LM) does not predict that RNFL thickness will have a strong association with greater-than-normal (>100%) visual sensitivity and does not correct structural measurements for age or stage of disease. Thus, the HK-LM has considerably fewer parameters than the H-NLM, although it is also less ambitious in its scope, as it does not attempt to relate either functional or structural measures to estimates of RGCs. Newer frequency-domain OCT (fdOCT)23 has a faster acquisition rate, as well as higher axial resolution. Thus, fdOCT data should theoretically provide a more accurate measurement of RNFL thickness than older time-domain OCT (tdOCT). Additionally, although circle scans around the optic disc acquired from tdOCT are usually not perfectly centered, potentially affecting the accuracy and precision of RNFL thickness measurements,11,24,25 the volume scans produced by the fdOCT allow for postacquisition adjustment of the location of a derived circle scan. Several independent groups have compared the predictions of the HK-LM to the RNFL thickness measurements derived from fdOCT data, and these studies26–,29 suggest that the HK-LM generalizes fairly well to fdOCT data. Although the H-NLM has been applied to fdOCT data, these studies30–,34 used the RGC estimates derived from the H-NLM for further modeling, rather than formally assessing the validity or accuracy of the model itself. Because parameters have been added to the H-NLM over time, it is particularly important to assess the generalizability of the model. Harwerth et al.10 previously applied the H-NLM to two different independent datasets and concluded that the H-NLM could “be generalized to other patient populations with equal results.” Moreover, Harwerth et al.10 directly compared the performance of the H-NLM to the HK-LM and concluded that although the performance of the models was “very similar, both in terms of the accuracy and the precision,” the HK-LM was “less precise.” However, given the importance of the H-NLM, there are several aspects of this validation that warrant further investigation. First, the generalizability of a model can be determined only if the parameters are fixed before application to an independent dataset. Whereas the Harwerth et al.10 validation of the H-NLM did not involve the addition of any new explicit parameters, there is at least one important implicit parameter that was changed before the H-NLM was applied to new datasets: a new topographic “map” relating measurement of axons near the optic disc to RGC bodies throughout the retina. Additionally, the previous validation study of the H-NLM compared the H-NLM to the HK-LM using different topographic maps for the two models. Finally, the validation study used older tdOCT data instead of the fdOCT data used in subsequent studies30–,34 by other groups. The impact of the work by Harwerth et al.10 cannot be underestimated. In the past few years, many publications30,32–,37 from outside groups have used the H-NLM as a basis for further modeling. In fact, regarding a new model that uses the H-NLM to estimate RGC counts, a recent review38 has said that “[i]ts use in clinical trials may potentially overcome the limitations of currently available conventional parameters.” Given this rise in prominence of the H-NLM, the purpose here was 3-fold: to apply the H-NLM to an independent fdOCT dataset and assess its generalizability, particularly with regard to the impact of different topographic maps; to compare the performance of the H-NLM and HK-LM using appropriate statistics, while controlling for differences in the topographic maps; and to use simulations to explore the underlying assumptions of the H-NLM with a view toward assessing their validity and accuracy.