A Simple Alternative to the Logarithmic Transform for Flow Cytometric Fluorescence Data Displays
Francis L. Battye
The Walter & Eliza Hall Institute
A logarithmic transform is often used in graphic displays of flow cytometric fluorescence data in order to cope with the wide dynamic range of values obtained. Its disadvantage is its inability to handle zero or negative values such as may arise after application of fluorescence compensation or in data acquired using high-resolution digital electronics. The pile up of low, zero and negative values along the display edges can confuse visual interpretation of the data and distort estimation of fluorescence compensation values.
Two alternative transforms, Biexponential and Hyperlog, have been suggested for bringing negative values back onto the display by tending towards linear functions at the low end of the scale. Both display alternatives are difficult to interpret visually because they are not quite linear at the low end and not quite logarithmic at mid-scale. Additionally, in current implementations of Biexponential, the form of the scale depends upon the data displayed, thus hampering side-by-side comparisons of data files.
This paper describes an alternative that is mathematically simple, fixed independently of the data displayed and allows straightforward interpretation by the average observer. It consists of a logarithmic scale at high values and a linear scale at low values with a fixed transition point chosen so that the slope (first derivative) of the transform is continuous at that point, thus assuring a smooth transition of histogram bin widths. The scale extends to the negative of the transition value that is reached at the bottom of the display. Display interpretation is simple and intuitive because of the familiar linear and logarithmic sections. In the present implementation the linear section extends over the first quarter of the display while the remainder is logarithmic; reminiscent of the traditional logarithmic scale on which experienced observers are accustomed to seeing “negative” events in the first of four decades.