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In numerostudies in a cell renewal system periodically adjusted cell renewal process

Journal of Theoretical Biology
Publication Date
DOI: 10.1016/0022-5193(65)90039-1
  • Design
  • Mathematics


Abstract Previous studies have emphasized the simple birth and death stochastic process with constant “rates” λ and μ as an appropriate mathematical model for describing the kinetics of the parenchymal cell renewal system in cirrhosis of the liver in rats. In connection with current experimental studies of artificially induced cirrhosis in rats it has been found necessary to extend the model to cover the experimental situation in which the birth and death parameters, λ and μ respectively, must be allowed to reflect the intermittent administration of cirrhosis-producing toxic substances. For these studies a new model, referred to as the Periodically Adjusted Cell Renewal Process is introduced here. This model bears a close relation to Kendall's Generalized Birth and Death Process with periodic birth and death rate functions and leads to a convenient Monte Carlo procedure of use in in numero studies for the generation of sample curves of such processes. Two such ensembles of curves corresponding to a special example are reported and discussed. Values for the required parameters of the stochastic model and for the associated Monte Carlo procedure carried out on the IBM 7094 of the Harvard Computing Center were obtained by estimation from experimental data consisting of counts of [ 3H]thymidine labeled, DNA-synthesizing hepatocytes, assayed by radioautography. It is pointed out that the stochastic approach adopted here for the mathematical interpretation of the kinetics of cellular proliferation in the experimentally produced cirrhotic process of rats reflects the morphological irregularities produced by this process and extends the customary deterministic approach, allowing as it does random irregularities about the central tendency. Finally, the usefulness of such simulation methods in designing, conducting and interpreting experiments in this and analogous problems in cell kinetics is discussed.

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