PMID: 22351656Feb 22, 2012Paper

Order-of-magnitude estimates of latency (time to appearance) and refill time of a cancer from a single cancer 'stem' cell compared by an exponential and a logistic equation

In Vivo
Ken M AndersonMinu Patel

Abstract

The time required before a mass of cancer cells considered to have originated from a single malignantly transformed cancer 'stem' cell reaches a certain number has not been studied. Applications might include determination of the time the cell mass reaches a size that can be detected by X-rays or physical examination or modeling growth rates in vitro in order to compare with other models or established data. We employed a simple logarithmic equation and a common logistic equation incorporating 'feedback' for unknown variables of cell birth, growth, division, and death that can be used to model cell proliferation. It can be used in association with free or commercial statistical software. Results with these two equations, varying the proliferation rate, nominally reduced by generational cell loss, are presented in two tables. The resulting equation, instructions, examples, and necessary mathematical software are available in the online appendix, where several parameters of interest can be modified by the reader www.uic.edu/nursing/publicationsupplements/tobillion_Anderson_Rubenstein_Guinan_Patel1.pdf. Reducing the proliferation rate by whatever alterations employed, markedly increases the time to reach 10(9) cells originating fr...Continue Reading

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