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A Fokker-Planck equation for growing cell populations

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Abstract

Closed form solutions are obtained for a Fokker-Planck model for cell growth as a function of maturation velocity and degree of maturation. For reproduction rules where daughter cells inherit their parent's maturation velocity the complete solution is derived in terms of Airy functions. For more complicated reproduction rules partial results are obtained. Emphasis is given to the relationship of these problems to time dependent linear transport theory.

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Authors and Affiliations

  1. Department of Mathematics, Texas Tech University, 79409, Lubbock, TX, USA

    C. V. M. van der Mee

  2. Center for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute and State University, 24061, Blacksburg, VA, USA

    P. F. Zweifel

Authors
  1. C. V. M. van der Mee
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  2. P. F. Zweifel
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van der Mee, C.V.M., Zweifel, P.F. A Fokker-Planck equation for growing cell populations. J. Math. Biology 25, 61–72 (1987). https://doi.org/10.1007/BF00275888

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  • DOI: https://doi.org/10.1007/BF00275888

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