Periodic Hematopoiesis

This page allows you to iterate a difference equation model, given explicitly below, for N steps using selected values of the parameters. The xt variable represents the number of red blood cells (in billions) on day t. τ is a parameter giving the time for cell development in days and γ gives the fraction of cells that die each day. F(x), also given below, is a hill function that gives the cell production as a function of the current number of cells. For the the function F(x), Fo is the maximum production of cells, θ represents the cell level where the cell production is halved, and n is a shape parameter for the function. Finally, xo is the initial red blood cell count. typical parameter values for healthy individuals are listed when the page is first loaded.

τ =
γ =
Fo =
θ =
n =
N =
xo =
xt+1 = a F(xt) + b xt
a = τ / (1 + γ τ)
b = 1 / (1 + γ τ)
F(x) = Fo θn / (θn + xn)

References:

Adler, F. R. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists. Brooks/Cole, Pacific Grove, CA, 1998.

Glass, L. and M. C. Mackey From Clocks to Chaos: The Rhythms of Life. Princeton University Press, Princeton, N.J., 1988.

Othmer, H. G., F. R. Adler, M. A. Lewis, and J. C. Dallon Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology, Prentice Hall, Upper Saddle River, N.J., 1997.