Theoretical basis for sampling statistics useful for detecting and isolating rare cells using flow cytometry and cell sorting.

This paper describes new approaches to calculating the number of cells that need to be processed using flow cytometry (FCM) techniques and the subsequent time required in order to isolate a specific number of cells having selected characteristics. The methods proposed use probabilistic assumptions about the contents of the sample to be sorted, logarithmic/exponential transformations to avert the computer "underflow" and "overflow" limitations of brute force calculations for the parameters of the binomial distribution imposed by existing computer hardware, and an established mathematical procedure for calculating error bounds for the normal approximation to the binomial distribution. Estimates are derived for the total number of cells in the FCM sample volume that must be available for processing and, for given FCM cell sorting decision speeds, the total elapsed times necessary to conduct particular experiments. The proposed approach obviates the need to resort to calculation expediencies such as the theoretically limited Poisson approximation for what can be considered a Bernoulli process mathematically characterized by the binomial distribution. Tables and graphs illustrate the projected times required to complete FCM experiments as a function of "effective" cell sorting decision speeds. Results from this paper also demonstrate that, as the "effective" cell sorting decision speed increases, there may not be a corresponding linear decrease in the time required to sort a given number of cells with selected statistical properties. The focus of this paper is on the use of innovative mathematical techniques for the design of experiments involving rare cell sorting. However, these same computational approaches may also prove useful for the high-speed enrichment sorting of non-rare cell subpopulations.