Defining The Problem Of Multidimensional Data Analysis

Single-parameter flow cytometry data can be represented as a histogram plotting frequency of events versus signal intensity. Two-

parameter data can be displayed as a dot plot or as a two-dimensional histogram. With three or more parameters, the data cannot be directly visualized without mathematical reduction or manipulation.

A significant difference exists between multiparameter and multidimensional data analysis (Terstappen and Loken, 1992). In multiparameter analysis, various cellular characteristics are analyzed independently. A cell population is assessed using multiple parameters; however, the parameters are not correlated with each other. In a multidimensional analysis, several characteristics are measured simultaneously for each cell. The correlation between characteristics is maintained and becomes a powerful tool to understand the cellular composition of a complex population. For example, a cell population may be stained using three different antibodies in three different tubes. These tubes, when analyzed in sequence, provide a multiparameter analysis of that cell population: X% of the cells are reactive with antibody 1, Y% of the cells are reactive with antibody 2, and Z% of the cells are reactive with antibody 3. In contrast, by labeling each antibody with a different color, it is possible to stain a cell population with all three antibodies in a single tube, so that the relationships between the staining of a cell with each different reagent is preserved. This permits multidimensional analysis, as each event (cell) generates multiple signals simultaneously.

For multidimensional data analysis, data must be collected in listmode format, thereby maintaining the correlation of the signals for each event. In a standard three-color im-munofluorescence protocol, two light-scatter parameters (forward and right-angle light scatter) are collected along with green (fluorescein isothiocyanate, or FITC), orange (phyco-erythrin, or PE), and red (Caltag's Tandem Conjugates, Pharmingen's Cychrome Conjugates, or Becton Dickinson's peridinim chlorophyll complex, PerCP) signals to generate listmode data with five characteristics per event (see unit 6.2). These five characteristics represent the coordinates for that event in a five-dimensional space. In multidimensional analysis, these coordinates are used to visualize cells with similar characteristics and to distinguish cell populations from one another.

unit 10.4

Data Processing and Analysis

Multidimensional Data Analysis in Immuno-phenotyping

Visualization of a multidimensional space is difficult because most means of human communication are limited to two-dimensional space. The most frequently used approach is to display the combinations of five parameters, taken two at a time as either dot plots or contour plots. With five separate characteristics, there are ten possible combinations of two-parameter displays:

1. Forward light scatter/right angle light scatter

2. Forward light scatter/green fluorescence

3. Forward light scatter/orange fluorescence

4. Forward light scatter/red fluorescence

5. Right-angle light scatter/green fluorescence

6. Right-angle light scatter/orange fluorescence

7. Right-angle light scatter/red fluorescence

8. Green fluorescence/orange fluorescence

9. Green fluorescence/red fluorescence

10. Orange fluorescence/red fluorescence

These two-parameter dot plots can be visualized as the faces of a hypercube. Instead of a cube with three unique faces, five-dimensional space has ten faces, six of which are displayed in Figure 10.4.1. Populations or clusters of cells are identified by different colors. It is important to understand that these two-dimensional displays are simply projections of five-dimensional data. Populations that appear close or overlapping in one projection may be clearly separate in other projections. The multiple projections of the data permitted by multidimensional analysis facilitate maximum separation of event clusters. The basis of multidimensional analysis is the use of color eventing to follow groups of cells in a display and to correlate those groups when viewed from a different perspective (Terstappen et al., 1989).

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