Multidimensional Gating To Separate Overlapping Populations

Multidimensional data analysis can be used to separate populations seemingly inseparable in any two-dimensional plot. Figure 10.4.3 shows four-parameter data that were computergenerated using WinList 2.0 (Verity Software) to mimic immunofluorescence data. Two populations were created with centers at channels 16 and 28 (128 channels full scale) in each of the four parameters. The two populations had the same dispersion around the central points with respect to each of the four parameters. Six combinations of two parameters were constructed from the four-parameter data (Fig. 10.4.3A-F). Identical triangular regions (R1 to R6) were drawn in each of the six plots to include the dimmer, channel 16-centered population. A Boolean combination of these

101 102 103 CD4 PE

Figure 10.4.1 Six of the ten two-parameter faces of a five-dimensional hypercube. Color identifies populations recognized in other projections. Normal peripheral blood cells were stained with CD8-FITC, CD4-PE, and CD45-PerCP. Forward and right-angle scatter along with the three antigens define the five-dimensional space. CD4+ lymphocytes are red, CD8+ lymphocytes are blue, monocytes are dark green, and neutrophils and eosinophils are green. See color figure.

Figure 10.4.2 (A) Schematic diagram depicting the relationship between two regions R1 and R2 in a single plane defined by parameters 1 and 2. Table 10.4.1 shows various logical combinations of R1 and R2 that can be used to identify specific regions herein. (B) Schematic diagram depicting similar relationships between R1 and R2 in a three-dimensional display. See color figure.

Figure 10.4.2 (A) Schematic diagram depicting the relationship between two regions R1 and R2 in a single plane defined by parameters 1 and 2. Table 10.4.1 shows various logical combinations of R1 and R2 that can be used to identify specific regions herein. (B) Schematic diagram depicting similar relationships between R1 and R2 in a three-dimensional display. See color figure.

Data Processing and Analysis

Multidimensional Data Analysis in Immuno-phenotyping regions was made: Gate 1 = [R1 & R2 & R3 & R4 & R5 & R6]. Using this logic, an event must lie within all of the triangular regions to be included in the gate. If an event is outside of any of the regions, it is not included within this gate. Events that satisfied Gate 1 are colored red (Fig. 10.4.3B and C). A second gate was constructed to identify all events that lie outside any of the regions: Gate 2 = [not R1 or not R2 or not R3 or not R4 or not R5 or not R6]. These events are colored green (Fig. 10.4.3B and D). Figure 10.4.3B displays all the events, but colored either red or green depending on whether they are included in Gate 1 or Gate 2. For compari son, only the red population is depicted in Figure 10.4.3C, whereas the green population is shown in Figure 10.4.3D. Note that many of the green dots lie within the triangle of R4 (Fig. 10.4.3D), indicating that they must lie outside the triangle in one of the other projections.

The effectiveness of multiparameter separation of these two populations using combinations of the six triangular regions is demonstrated by the analysis of each population separately, shown in Figure 10.4.4. A histogram of the combined populations (Fig. 10.4.4A) can be compared with the overlapping histograms of the red and green populations after multi-

Table 10.4.1 Identification of Regions in Figure 10.4.2 by Boolean Logic Combinations of R1 and R2

Combination

Regions identified

[R1]

Red, yellow

[R1 and not R2]

Red

[R1 and R2]

Yellow

[R1 or R2]

Red, yellow, blue

[Not R1 and not R2]

Gray

[Not R1 or not R2]

Red, blue, gray

[R1 or not R2]

Red, yellow, gray

Figure 10.4.3 Six two-dimensional projections of four-parameter data. WinList 2.0 was used to generate two populations with identical dispersions in all four parameters, one centered at 16, the other at 28. Triangular regions (R1 to R6) were defined in each projection and gates were defined as described in the text. Gate 1 events are colored red, while Gate 2 events are colored green. Both populations are displayed in B. Only the red population is displayed in C and only the green in D. See color figure.

Figure 10.4.3 Six two-dimensional projections of four-parameter data. WinList 2.0 was used to generate two populations with identical dispersions in all four parameters, one centered at 16, the other at 28. Triangular regions (R1 to R6) were defined in each projection and gates were defined as described in the text. Gate 1 events are colored red, while Gate 2 events are colored green. Both populations are displayed in B. Only the red population is displayed in C and only the green in D. See color figure.

parameter separation using the six identical regions (Fig. 10.4.4B). These can be compared with overlapping histograms generated from two separate listmode files in which the two populations were never mixed (Fig. 10.4.4C). The positions and shapes of the two histograms are identical whether the populations were obtained from two separate listmode files (Fig. 10.4.4C) or mixed and then separated using the multidimensional approach (Fig. 10.4.4B). To quantify the separation, 4% of the dimmer population was excluded from the red population (recovery = 96%) when this population was analyzed alone. Less than 2% of the brighter population was included in the gate (purity = 98%) when assessed separately.

This example illustrates that even when populations overlap, it is possible to achieve almost complete separation using multidimensional analysis. The ability to separate populations depends on several factors: the variability within a population, separation between populations, and availability of multiple independent parameters by which to separate the populations. It is crucial to use independent parameters that have no correlation with each other. In this example, complete separation was obtained using four separate parameters.

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