Flow cytometry histograms: transformations, resolution, and display

Abstract

Flow cytometry data analysis routinely includes the use of one- or two-parameter histograms to visualize the data. These histograms have traditionally been plotted with either a linear or logarithmic scale. However, the recent trend of performing the logarithmic conversion in software has made apparent some limitations of the traditional visual presentation of logarithmic data. This review discusses the mathematics of presenting data on a histogram and emphasizes the difference between scaling and binning. The review introduces the concept of an effective resolution to describe how the bin width changes in a variable bin-width histogram. The change in effective resolution is used to explain the commonly observed valley and picket fencing artifacts. These result from the effective resolution of the display histogram being too high for the data being presented. Recently, several different binning transformations have been described that are becoming more popular because they allow one to view a large dynamic range of data on a single plot, while allowing the display of negative data values. While each of the transforms is based upon different equations, they all exhibit very similar properties. All of the transforms bin the data logarithmically at high channel values and linearly at low channel values. The linear scaling of the lower channels serves to limit the effective resolution of the histogram, thus minimizing the valley and picket fencing artifacts. The newer transformations are not without their own limitations and recommendations for the appropriate manner of presenting flow cytometry data using these newer transformations are discussed.