PROBABILITY STATE MODELING: A NEW PARADIGM FOR CYTOMETRIC ANALYSIS - Flow Cytometry in Drug Discovery and Development - page 272

14.2 PARAMETRIC EQUATIONS

In mathematics, you can easily write equations that define a line in n dimensions. The
trick is to define a set of equations that all depend on the common variable, t.

p 1 ¼ p 1 0 þ p 1 1 t

p 2 ¼ p 2 0 þ p 2 1 t

...
pn ¼ pn 0 þ pn 1 t

These equations are called parametric equations [1]. They allow us to easily
describe objects such as lines, surfaces, and volumes in any number of dimensions. A
general characteristic of these equations is that rather simple parametric equations can
describe highly complex objects (see Figure 14.1).

1 ¼ sinð7 Þ

p t

p 2 ¼ sinð8 t Þ

What do parametric equations have to do with the field of cytometry? In this
chapter, I hope to convince you that future of cytometric analysis is about to
change in a radical way and these parametric equations are at the very heart of this
change.

1.0

0.5

0.0

-0.5

-1.0

-1.0 -0.5 0.0 0.5 1.0

sin(7 t )

FIGURE 14.1 Complex graphical object constructed from simple parametric equations. The
relatively simple parametric equations, sin(7t) and sin(8t), can create a complex graphical
object when one is plotted against the other.