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 how cytometry (FCM) techniques and th e subsequent time required in order to isolate a specific number of ce lls having selected characteristics. The methods proposed use probabil istic assumptions about the contents of the sample to be sorted, logar ithmic/exponential transformations to avert the computer ''underflow'' and ''overflow'' limitations of brute force calculations for the para meters of the binomial distribution imposed by existing computer hardw are, and an established mathematical procedure for calculating error b ounds for the normal approximation to the binomial distribution, Estim ates are derived for the total number of cells in the FCM sample volum e that must be available for processing and, for given FCM cell sortin g decision speeds, the total elapsed times necessary to conduct partic ular experiments. The proposed approach obviates the need to resort to calculation expediencies such as the theoretically limited Poisson ap proximation for what can be considered a Bernoulli process mathematica lly characterized by the binomial distribution, Tables and graphs illu strate the projected times required to complete FCM experiments as a f unction of ''effective'' cell sorting decision speeds, Results from th is paper also demonstrate that, as the ''effective'' cell sorting deci sion speed increases, there may not be a corresponding linear decrease in the time required to sort a given number of cells with selected st atistical properties, The focus of this paper is on the use of innovat ive mathematical techniques for the design of experiments involving ra re cell sorting, However, these same computational approaches may also prove useful for the highspeed enrichment sorting of non-rare cell su bpopulations. (C) Wiley-Liss, Inc.