A logistic function or logistic curve is a common “S” shape (sigmoid curve), with equation: INSERT SHAPE AU257: Pict Element 13 AU258: Anchored Object 147 AU259: Image 15 where e = the natural logarithm base (also known as Euler's number), x 0 = the x-value of the sigmoid's midpoint, L = the curve's maximum value, and k = the steepness of the curve. For values of x in the range of real numbers from -8 to +8, the S-curve shown on the right is obtained (with the graph of f approaching L as x approaches +8 and approaching zero as x approaches -8). The function was named in 1844–1845 by Pierre François Verhulst , who studied it in relation to population growth. The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
Published in Chapter:
Proliferation and Nonlinear Dynamics of Childhood Acute Lymphoblastic Leukemia Revisited
George I. Lambrou (University of Athens, Greece)
Copyright: © 2016
|Pages: 34
DOI: 10.4018/978-1-4666-8828-5.ch015
Abstract
Acute Lymphoblastic Leukaemia (ALL) is the most common neoplasm in children but the mechanisms underlying leukemogenesis along with the dynamics of leukemic cell proliferation are poorly understood. The importance in understanding the proliferation dynamics of leukaemia lies in the fact that our knowledge from the point of first appearance to the moment of clinical presentation, we know almost nothing. Further on, describing cell proliferation dynamics in a more mature, probably mathematical, way it could lead us to the understanding of disease ontogenesis and thus its aetion. This chapter reviews the current knowledge on proliferation dynamics and proliferation non-linear dynamics of the leukemic cell. Furthermore, we present some “in-house” experimental data that support the view that it is possible to model leukemic cell proliferation and explain how this has been performed in in vitro experiments.