On the regional variability of averaged cell area estimates for the human corneal endothelium in relation to the extent of polymegethism
- 302 Downloads
To assess variability in the coefficient of variation (COV) in cell area estimates when using different numbers of cells for endothelial morphometry.
Using non-contact specular microscopy images of the corneal endothelium, 4 sets of 20 cases were selected that included 200 cells and had overall (global) COV values of less than 30 (group 1), 31–40 (group 2), 41–50 (group 3) and over 50% (group 4). Subjects could be normal, or had ophthalmic disease (such as diabetes), a history of rigid or soft contact lens wear or were assessed after cataract surgery. A step-wise analysis was undertaken, 20 cells at a time, of the variability in cell area estimates when using different numbers of cells for the calculations.
Variability in the average cell area values was higher if only 20–60 cells were used in the calculations and then tended to decrease. The standard deviation values on these average cell area values and the calculated COV showed the same overall trends and were more than twice as large for endothelia with marked polymegethism. Using more than 100 cells/image in markedly polymegethous endothelia only increased the variability in the calculations.
These analyses indicate that substantial region variability in cell area values can be expected in polymegethous endothelia. The analysis further confirm that using only small numbers of cells (e.g. less than 50/image) in such cases is likely to yield far less reliable estimates of COV.
KeywordsCorneal endothelium Morphometry Cell areas Human Polymegethism Non-contact specular microscopy
As viewed in vivo by specular microscopy, the corneal endothelium of young healthy adults appears as a mosaic of cells having uniform size and shape [1, 2]. The cell size, as reported in the most endothelial assessments, is assessed as the endothelial cell density (ECD), in cells/mm2, and provides a very useful indicator of the status of the endothelial cell layer . However, when even some of this uniformity is reduced, then actual considerations of the variation in cell size (area) has been considered important. A specific term was introduced to describe the non-uniformity (i.e. heterogeneity) to the endothelial mosaic, namely polymegethism. This estimates the increased variation in cell areas, reported as the coefficient of variation or COV .
In early studies , it was noted that substantial differences in cell area variation could exist and that any estimates of ECD could be very much dependent on the overall (global) COV assigned to an endothelial cell layer (assessed by wide-field specular microscopy). For the COV estimates themselves, a later retrospective analysis of published endothelial images indicated that the reliability of any COV calculations would be predictably less if cell area heterogeneity appeared to be present, i.e. whether images were subjectively considered to be normal (homogeneous) or showing some evidence of heterogeneity (polymegethism) . The analysis was, however, limited by the fact that relatively few images were available for analysis and some included somewhat fewer cells than others, often less than 100/image. As a result it was not possible to systematically assess how much the reliability in COV calculations might be reduced according to the extent (or severity) of the perceived polymegethism.
The essential basis of determining the extent of polymegethism is to measure the areas of the cells and then to calculate the average value of the cell area and the standard deviation (SD) of this average area value. It is this SD value that is then used to estimate the area variability as a standardised variance, generally known as the coefficient of variation (abbreviated as CV or COV) based on SD/average cell area calculation. This relative variance can be presented as a fraction (e.g. 0.5 for a moderately polymegethous endothelium) or (more usually) as a percentage (e.g. 50%). In general terms, an increased COV could result from the presence of even a few rather larger cells or small cells, or a combination of both . Stated another way, from a theoretical perspective it could be that parts of an endothelial image could be largely normal with only small regions (or portions) of the mosaic showing larger or smaller cells. The overall estimates of COV have been reported to be dependent on the number of cells measured and therefore included in the calculations [5, 7].
Small field endothelial images taken from normal corneas of young adults with modern day instruments can be expected to include over 100 cells [8, 9, 10, 11], while in evaluation of corneas after surgical interventions it has been noted that a good quality image should contain at least 75 cells . Assessments of published images indicated that measuring this number of cells (i.e. 75/image) should give reasonably reliable data in terms of predicted variability in cell areas . Notwithstanding, a systematic analysis of the regional variability in endothelial cell areas within a single image and the impact this on the reliability of the COV data does not appear to have been undertaken in relation to the overall cell area variability. This is important since some contemporary investigators have stated that they have opted to measure relatively few cells (≤ 30/image) in undertaking endothelial analyses whether these be of normal corneas, comparing image analysis systems, assessments of diseases such as diabetes or following interventions such as cataract surgery [12, 13, 14, 15, 16, 17, 18]. With the use of just a few cells, the estimates of COV (for example) could be influenced by regional variability in cell areas, i.e. the COV data generated (and reported on) could have rather smaller or much larger values. If no indication is provided of the number of cells actually measured, then such uncertainty in COV estimates also exists.
The present analyses were undertaken to assess this possible regional variability in COV values for endothelial images with different extents of polymegethism. This was done by considering the overall average area and COV values for endothelial images and then systematically investigating the effect of using different numbers of cells to actually calculate the COV values.
The study was approved by the university-based ethics committee and formed part of ongoing studies on the corneal endothelium of students, staff and patients presenting for routine eye examinations at the eye clinic. Protocols conformed to the Declaration of Helsinki and all subjects provided informed consent, and could be any age over 18 years and be considered as healthy and having normal corneas, or had abnormal corneas because of known ophthalmic disease (such as diabetes), a history of rigid or soft contact lens wear or were assessed after cataract surgery.
Single images of the central corneal endothelium were taken using non-contact specular microscopy (Topcon SP-3000P model, although a few were taken with the older model SP-2000P) and the images downloaded to a thermal printer (Sony Videographic Printer, model UP-897). A numerical code ID number was affixed to the print which was then scanned at 400 d.p.i. to generate a JPEG image file. From such files collected over a 10 year period (2007–2016), examples were selected that contained large numbers of clearly defined contiguous cells but with a different extent of polymegethism from mild to marked (see results). These images were reprinted onto A3-sized white paper, the cell outlines of 200 cells manually marked (see results) and numbered in sequence from the top to the bottom of the image. The marking of the cell–cell borders was undertaken on the very highly magnified (A3) prints and so minimising the chance of any errors, with the author having many years of experience in undertaking this cell marking process. The areas of the outlined cells were then measured by manual planimetry as previously detailed, with this process, especially on the enlarged prints, being expected to be to repeatable (and accurate, as based on the image scale marker) to within ± 2% or better [19, 20].
Using spread sheets in Systat v.11 (Systat, Evanston, IL), the average area values from sequential sets of 20 cells (i.e. numbers 1–20, 21–40 from the top of the images) were calculated. These sets of regional estimates of the average cell areas (from groups of 20 cells) were then used to calculate a progressive estimate of the overall average cell area based on calculating the numerical mean of the average values obtained from 3 regions (60 cells in total), 4 regions (80 cells), etc. up to 10 regions (200 total cells/image). The SD on these estimates was also calculated as well as the COV values (for 3, 4, 5 regions, etc.). Box plots were generated to illustrate the overall variability. All data sets were checked for normality using the default Shapiro–Wilk option in Systat. Where appropriate, 2 sample t tests (for normally distributed data sets) and rank-ordered Friedman tests (nonparametric) were used for comparisons with statistical significance set at p < 0.05.
The main interest in the present study was now to systematically evaluate how such regional differences in average cell area values (for sets of 20 cells) might differ according to the overall extent of the polymegethism considered to be present. For all analyses, the same step-wise progressive averaging was used, i.e. 3 regions averaged (for the first 20 + 20 + 20 cells in each image), regions 1 to 4 averaged (i.e. a total of 4 for the number of endothelial regions used in the calculations), all the way up to 10 regions analysed (200 cells/endothelium). The selected data included four sets of 20 different images which either showed no polymegethism (overall global COV calculation of < 30%) or had different extents of polymegethism from mild (overall global COV of 31–40%), to moderate (overall global COV of 41–50%) to marked (> 50% COV).
This study represents the most detailed analysis so far reported of the potential variability in the outcome of corneal endothelial morphometry. It is accepted that these analyses might be considered as a statistical ‘overkill’ in that, essentially, averages of averages from repeated calculations are being generated. The analysis is also presented to illustrate how misleading some global statistics for cell area and COV values can also be. Notwithstanding, the approach used serves the purpose of highlighting cell area variability not revealed in simple global calculations. As illustrated, such group mean values ± SD for cell area values have only limited utility to illustrate any differences. Similarly, the outcome in Fig. 4c again illustrates that the presence of a few outliers can be revealed using box plots (and/or calculations of the IQRs and proportion of outliers) even if other analyses such as those shown in Fig. 4a do not reveal their presence. In reporting comparisons between sets of endothelia, the utility of box plots in revealing important heterogeneity should be noted (and indeed recommended).
These analyses are presented in detail to illustrate that, overall, predictably less reliable results can be expected from corneal endothelial morphometry when less than 100 cells/image are analysed. The results can be applied to most studies undertaken where the overall endothelial cell density is greater than 2000/mm2. It is accepted that in some scenarios, it is simply not possible to measure more than 25 cells/small field endothelial image when the endothelial cell density is extremely low (i.e. less 1000/mm2) as a result of substantial cell loss in some corneal grafts for example . However, based on published studies over many years, the extent of cell loss following routine cataract surgery (or similar) can now be expected to be very substantially less, and corneas considered suitable for use in graft operations can also be expected to have cell density values above 2000/mm2. Therefore, reasonable quality images from post-surgical endothelia should contain 75–100 cells for analyses [7, 21]. Further studies are, however, needed on post-graft endothelia where the cell density values may be considerably lower.
Overall, these analyses are presented to illustrate how any estimates of the variability in cell areas in corneal endothelial images will be expected to be notably different according to the extent of the polymegethism considered to be evident. For this study, a balanced set of examples showing mild, moderate or marked polymegethism were selected for analyses. Overall, a predictable effect is present, illustrated in part C of Figs. 6, 7, 8, 9; as the grade (or extent) of polymegethism increases so also the uncertainty in the estimates of the cell area variability gets greater and greater. It should be noted that these results (part C of Figs. 6, 7, 8, 9) are all normalised to their individual absolute values to avoid any substantial influence of absolute values of the cell areas. The COV estimates given in these figures are not the same as those obtained in overall (global) calculations using all area values from cells from each image. These latter values were essentially up to 30% for uniform endothelia, up to 40% for mild polymegethism, up to 50% for moderate polymegethism and to 60% for marked polymegethism. Based on observations made over many years, these global estimates of COV estimates are considered to be representative of what might be encountered for the types of cases included. Stated another way, a global COV value of less than 20% for human corneal endothelia should be considered as remarkable, and if less than 10% should be carefully scrutinised as possibly an error. The same applies for global COV values in excess of 60% (again for human corneas) as being unusual and possibly an error. Similarly, if the global COV estimates for endothelia considered to be from healthy corneas are 40% or more, then the fidelity of the image analysis should be considered.
The present analyses using these relative values for COV (variability) are presented to try to further illustrate that measuring only a few cells (≤ 50) in small field endothelial images of corneas exhibiting some degree of polymegethism is unlikely to yield acceptably ‘reliable’ estimates for cell morphometry indices. If moderate-to-marked polymegethism is present and only 50 cells or less are used/image then the outcome of any resultant global calculations of COV are unlikely to be reliable, i.e. they could easily be different by ± 10% (or more) with just a few more or a few less cells measured. Such differences could have a substantial impact in deciding the outcome of any comparative studies, especially as to whether or not any statistical differences were detectable (or not). It is hopefully self-evident that it should be incumbent on investigators to provide some reasonable indication of the number of cells measured/image in presenting endothelial analyses. This number, as far as possible, should be consistent when group-by-group comparisons are being made.
As a closing point, the present analyses show that there does not appear to be any obvious benefit in trying to measure more cells/image when even slight polymegethism is evident. This is because the apparent ‘error’ in the COV estimates does not predictably decrease as the number of measured cells increase. As indicated by McCarey and colleagues , a reasonable quality image should contain at least 75 contiguous cells suitable for analysis and so a target count of 75–100 cells/image should be striven for. If, for whatever reason, this is not achievable, then discussion of the results should take into account the added uncertainty in the data obtained. This will apply especially when comparisons are being made between different disease conditions or surgical interventions.
No funding was received for this research.
Compliance with ethical standards
Conflict of interest
The author certifies that he has no affiliations with or involvement in any organisation or entity with any financial interest (such as honoraria; educational grants; participation in speaker’s bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.
All procedures in studies involving human participants were in accordance with the ethical standards of Glasgow Caledonian University and with the 1964 Declarations of Helsinki and its later amendments.
- 4.Hirst LW, Yamauchi K, Enger C, Vogelpohl W, Whittington V (1989) Quantitative analysis of wide-field specular microscopy. II. Precision of sampling from the central corneal endothelium. Investig Ophthalmol Vis Sci 30:1972–1979Google Scholar
- 15.Urban B, Raczyńska D, Bakunowicz-Łazarczyk A, Raczyńska K, Krętowska M (2013) Evaluation of corneal endothelium in children and adolescents with type 1 diabetes mellitus. Mediat Inflamm. https://dx.doi.org/10.1155/2013/913754
- 17.Singh I, Kumar D, Singh S (2015) Specular microscopic changes in corneal endothelium after cataract surgery in different age group. J Med Sci Clin Res 3:3619–3628Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.