Bulletin of Mathematical Biology

, Volume 45, Issue 4, pp 507–519 | Cite as

Stochastic models for cell kinetics

  • Peter Jagers
Article

Abstract

A survey is given of branching process type methods in cell kinetics. Some results are given that allow circadian rhythm and do not require complete independence between cells. Some more classical results on balanced exponential growth are given and some comments are made on flow microfluorometry.

Keywords

Circadian Rhythm Cycle Time Mitotic Index Cell Kinetics Growth Fraction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Hopper, J. L. and P. Brockwell. 1978. “A Stochastic Model for Cell Populations with Circadian Rhythms.”Cell Tissue Kinet. 11, 205–225.Google Scholar
  2. Jagers, P. 1975.Branching Processes with Biological Applications. London: Wiley.Google Scholar
  3. — 1977. “Use Explicit Models in the Inference on Population Growth.”Bull. Int. statist. Inst. 47, 418–422.MathSciNetGoogle Scholar
  4. Jagers, P. and O. Nerman. 1983. “Limit Theorems for Sums Determined by Branching and other Exponentially Growing Processes.”Stoch. Proc. Appl. In press.Google Scholar
  5. — and K. Norrby. 1974. “Estimation of the Mean and Variance of Cycle Times in Cinémicrographically Recorded Cell Populations during Balanced Exponential Growth.”Cell Tissue Kinet. 7, 201–211.Google Scholar
  6. Klein, B. and P. D. M. MacDonald. 1980. “The Multitype Continuous Markov Branching Process in a Periodic Environment.”Adv. appl. Prob. 12, 81–93.MATHMathSciNetCrossRefGoogle Scholar
  7. Mode, C. J. 1971.Multitype Branching Processes. New York: Elsevier.Google Scholar
  8. Nerman, O. 1981. “On the Convergence of Supercritical General (C-M-J) Branching Processes.”Z. Wahrscheinlich keitstheorie verw. Gebiete 57, 365–395.MATHMathSciNetCrossRefGoogle Scholar
  9. Puck, T. T. 1962. “Cell Accumulation as a Result of a Specific Inhibitor to a Random Culture.”Anim. Cell Newsletter 3, 1–4.Google Scholar
  10. Valleron, A.-J. and P. M. D. MacDonald (Eds). 1978.Developments in Cell Biology, 2. Mathematics and Cell Kinetics. Amsterdam: Elsevier/North-Holland.Google Scholar

Copyright information

© Society for Mathematical Biology 1983

Authors and Affiliations

  • Peter Jagers
    • 1
  1. 1.Chalmers University of TechnologyGothenburgSweden

Personalised recommendations