Although a qualitative description of the corneal specular image suffices for many applications, more quantitative information is desirable for others. The aim of quantitative analysis is to assign a number (or set of numbers) to the specular photomicrograph that can provide a measure of the endothelial status.

Various of morphological parameters that can be quantified. These include cell size (cell area or cell density), polymegathism (variation of cell size such as coefficient of variation of mean cell area), pleomorphism (variation of cell shape such as percent of hexagonal cells or coefficient of variation of cell shape), cell perimeter, average cell side length, cell shape, and so forth. Histograms or frequency distributions of these quantities can also be determined. To date only cell size, pleomorphism, and polymegathism and several variables related to these parameters have proven useful in determining endothelial status.

Two equivalent parameters have been used to quantify endothelial cell size. They are mean cell area and cell density (or cell count). Cell area has most often been expressed in units of µm² per cell and cell density in units of cells per mm². The two quantities are related by the following equations:

Mean cell area (µm²/cell) = 10E6/cell density (cells/mm²)

or

Cell density (cells/mm² = 10E6/mean cell area (µm²/cell)

Two different methods, fixed frame analysis and variable frame analysis, can be used to measure either of these two parameters of cell size.

Fixed Frame Analysis of Cell Size

In fixed frame analysis one counts the number of cells within a frame or window of constant area. All cells lying completely within the frame are counted as whole cells. However, along the boundary of the frame there are many cells that lie only partly in the frame, and for these cells it is usually impossible to determine the fraction of the cellular area that lies within the borders of the frame. Each cell that is only partially within the frame is counted as one half cell regardless of the fractional area of that cell located within the frame. The total number of cells (the cell count) is then taken as the sum of the number of whole and half cells within the frame. To speed up the counting process one commonly invokes a symmetry principle and counts all cells cut by two sides of the frame as whole cells and does not count those cells cut by the other two sides of the frame. As long as the number of boundary cells is small compared to the total number of whole cells within the frame, and cellular pleomorphism is not too great, this method can give reasonably accurate values for mean cell size. The size is obtained by dividing the cell count by the area of the frame and expressed as cell density in cells per mm². The area of the frame must be referred to the endothelium. This is accomplished by dividing the actual area of the frame by the square of the linear magnification of the specular microscope, and if the cells were counted from an enlargement of the negative, by the square of the linear magnification of the enlargement. One can also divide the area by the cell count and report mean cell area as well. In practice, except for very rough estimates of cell count, a minimum of 35 contiguous cells should lie within the counting frame, although for most studies it is preferable to have 50 to 100 cells within the counting frame. Otherwise the errors associated with the counting method itself will generally be too large to provide meaningful numbers.

Variable Frame Analysis of Cell Size

Variable frame analysis, originally proposed by Laing,7 is most conveniently done using a computer based analysis system such as the Bambi system (Bio-Optics, Inc. Arlington, MA). This method eliminates the problem of counting fractional cells along the boundary, thus providing a more accurate determination of mean cell size than fixed frame analysis, again assuming that cellular pleomorphism is not too great and that the cell sample is representative of the area under study.

In variable frame analysis, one first measures the variable area occupied by an integral number of cells by tracing around a contiguous group of cells with a mouse. The user then marks each cell by clicking it with the mouse. The computer then calculates the cell density by dividing the number of marked cells by the area of the frame. An equivalent value, the mean cell area, can also be obtained by dividing the frame area by the number of cells that have been circumscribed.

Using variable frame analysis, errors due to the counting method are very small as compared to fixed frame analysis so that many fewer cells must lie within the frame. Furthermore, with variable frame analysis, additional information can be obtained. If one traces around the smallest cell in the image and marks it, the computer calculates the cell density assuming that all cells are this small. If one then traces around the largest cell in the image and marks it, the computer calculates the cell density assuming that all cells are this large. These two numbers give the range of cell densities (or the range of cell areas) that exist in this image providing more information regarding the endothelium than if only the mean cell density is obtained.

Errors associated with counting and sampling

All quantitative cell analysis methods inherently include some errors associated with the counting method used. Fortunately, the variable frame method greatly reduces counting method errors as compared to the fixed frame method, and there is seldom a problem obtaining sufficient cells using the variable framd method to obtain a cell count having an acceptably small counting error.

In addition to errors associated with the counting method, there are sampling errors associated with the possibly irregular distribution of cells throughout the endothelium. One must ask whether or not the sample being analyzed is representative of the area of the endothelium that one is concerned with (e.g. the central area) or whether the sample is one showing atypical cells within the endothelium. In the event that extensive cellular pleomorphism is present, the number of cells within a frame, either fixed or variable, may not be representative of the entire population of endothelial cells, and the cell density or the mean cell area calculated may not be representative of the endothelium.

Individual Cell Analysis

In fixed frame analysis only average cell size can be determined. The same holds true for variable frame analysis if only a group of cells is circumscribed. However, using the variable frame technique, single cells can be traced with the stylus of the planimeter or digitizer, and this then permits individual cell analysis. Such an analysis provides much more information about the endothelial cell pattern than can be obtained with methods that determine only cell density or average cell area.

Individual cell analysis can be performed either manually, semi-automatically, or fully automatically. The first computerized manual analysis system was developed by Laing and associates.9,29 In this system (the Bio-Optics Mandig system) the cell boundaries are traced with a special pen or a cross-hair cursor of a digitizer. As this is being done, the x and y coordinates of the boundary points are automatically entered into a computer. The computer determines when the cell has been completely circumscribed and calculates the area (or other programmed morphologic parameters) of that cell. It then instructs the operator to trace another cell. The cell density or mean cell area can be obtained by averaging the data on a group of cells. In addition, a frequency distribution (or histogram) of cell size can be obtained. Although such frequency distributions provide considerable information about the endothelium, few studies were done before the use of the personal computer7,8,30,31 since the procedure was extremely tedious.

Laing et al10 developed semi-automated methods utilizing video images that eliminated much of the tedium associated with endothelial analysis. These methods also enabled additional morphometric parameters to be easily determined. The system developed (the Bio-Optics Bambi system) requires the initial digitization of the cells using a mouse and then calculates all of the morphometric parameters believed to be possibly important. The system enables the addition of new programs to calculate additional parameters should this be desirable. Poor endothelial images can be contrast-enhanced to improve them. Images and data files can be instantly printed, stored, retrieved, and transferred to other computers, as desired. This system is widely used for the evaluation of the endothelium32-35.

43. Corkidi G, Toledo R, Usisima R, Marquez J, Valdez J, Grane E. Parametric images in automated morphometry evaluation of human corneal endothelium. Invest Ophthalmol Vis Sci. 1991;32(Suppl):1176.