A New "Logicle" Display Method Avoids Deceptive Effects of Logarithmic Scaling for Low Signals and Compensated Data

Background: In immunofluorescence measurements and most other flow cytometry applications, fluorescence signals of interest can range down to essentially zero. After fluorescence compensation, some cell populations will have low means and include events with negative data values. Logarithmic presentation has been very useful in providing informative displays of wide-ranging flow cytometry data, but it fails to adequately display cell populations with low means and high variances and, in particular, offers no way to include negative data values. This has led to a great deal of difficulty in interpreting and understanding flow cytometry data, has often resulted in incorrect delineation of cell populations, and has led many people to question the correctness of compensation computations that were, in fact, correct.

Results: We identified a set of criteria for creating data visualization methods that accommodate the scaling difficulties presented by flow cytometry data. On the basis of these, we developed a new data visualization method that provides important advantages over linear or logarithmic scaling for display of flow cytometry data, a scaling we refer to as "Logicle" scaling. Logicle functions represent a particular generalization of the hyperbolic sine function with one more adjustable parameter than linear or logarithmic functions. Finally, we developed methods for objectively and automatically selecting an appropriate value for this parameter.

Conclusions: The Logicle display method provides more complete, appropriate, and readily interpretable representations of data that includes populations with low-to-zero means, including distributions resulting from fluorescence compensation procedures, than can be produced using either logarithmic or linear displays. The method includes a specific algorithm for evaluating actual data distributions and deriving parameters of the Logicle scaling function appropriate for optimal display of that data. It is critical to note that Logicle visualization does not change the data values or the descriptive statistics computed from them.