Computers in Oncology

The Use of Computers in the Investigation of the Cell
  • E. J. Davison


The purpose of this chapter is to show that the use of mathematical system techniques may be used to obtain insight into the mechanism of cell behavior. In particular, it will be shown that the mathematical model of a cell can be used to find the possible mechanism which explains why a normal cell suddenly becomes tumorous. This will be done by obtaining a mathematical model of a growing cell living in a culture medium, and then systematically examining the behavior of the cell when various disturbances are applied to different parts of the mathematical model of the cell. The motivation for applying such an approach is that mathematical system techniques have been highly successful in explaining and predicting the behavior of technical—industrial processes (see, e.g., Himmelblau and Bischoff, 1968) and recently have given insight into the mechanism of various biological processes (see, e.g., Mesarovic, 1968; Diamant et al., 1970; Palmby et al., 1974). There has been to the author’s knowledge no previous work done on this problem. The idea, however, of describing a cell using a mathematical model is not new. Pollard (1960) and Yeisley and Pollard (1964) described a cell using 5 and 7 differential equations, respectively. Heinmets (1964a, b, 1966) has modeled a cell using 19 differential equations to study various transient responses of the cell assuming no cell division takes place, and his qualitative model shall form the basis of the model to be described in this paper.


Recovery Curve Cell Investigation Split Dose Radiation Factor Internal Pool 
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  1. Davison E. J. (1973). An algorithm for the computer simulation of very large dynamic systems. Automatica 9: 665–675.CrossRefGoogle Scholar
  2. Davison E. J. (1975). The simulation of cell behaviour: normal and abnormal growth. Bull. Math. Biology, 37 (5): 427–458.CrossRefGoogle Scholar
  3. Diamant N. E., Rose P. K., Davison E. J. (1970). Computer simulation of intestinal slow-wave frequency gradient. Am. J. Physiol. 219, (6): 1681–1690.Google Scholar
  4. Elkind M. M., Alescic T., Swain R. W., Moses W. B., Sutton H. (1964). Recovery of hypoxic mammalian cells from sub-lethal X-ray damage. Nature (London) 202: 1190–1193.CrossRefGoogle Scholar
  5. Glueck A. R. (1969) Simulation of cell behavior. Private communication, Princeton Computation Center, Electronic Associates Inc., P. O. Box 582, Princeton, N.J., Oct. 1969 (presented at Washington’ University, Nov. 1969).Google Scholar
  6. Heinmets F. (1964a) Analog computer analysis of a model-system for the induced enzyme synthesis. J. Theoret. Biol. 6: 60–75.CrossRefGoogle Scholar
  7. Heinmets F. (1964b) Elucidation of induction and repression mechanisms in enzyme synthesis by analysis of model system with the analog computer. In Electronic Aspects of Biochemistry, pp. 415–479. Academic Press, New York.Google Scholar
  8. Heinmets F. (1966) Analysis of Normal and Abnormal Cell Growth. Plenum Publishing Corp., New York.Google Scholar
  9. Himmelblau D. M., and Bischoff K. B. (1968) Process Analysis and Simulation Wiley, New York.Google Scholar
  10. Jansson B. (1968). Mathematical description of the growth of tumor cell populations with different ploidi-compositions. 6th Annual Symposium in Math & Computer Science in the Life Sciences, March, Houston.Google Scholar
  11. Little J. B. (1968). Cellular effects of ionizing radiation. N. Engl. J. Med. 278(7):369–376. McCarthy B. J. (1962). The effect of magnesium starvation in the ribosome content of Escherichia coli. Biochim. Biophys. Acta 55: 880–888.Google Scholar
  12. Mesarovic M. D., ed. (1968) Systems Theory and Biology,Springer-Verlag, New York. Palmby F. V., Davison E. J., and Duffin J. (1974). The simulation of multi-neurone networks: modelling of the lateral inhibition of the eye and the generation of respiratory rhythm.Bull. Math. Biol.,36:77–89.Google Scholar
  13. Pollard E. (1960) Theoretical aspects of the effect of ionizing radiation on the bacterial cell. Am. Nat. XCIV: No. 874, 71–84.CrossRefGoogle Scholar
  14. Sinclair W. K., Morton B. A. (1964). Survival and recovery in X-irradiated synchronised Chinese hamster cells. Cellular Radiation Biology Proc., 18th Ann. Symp. Fund. Cancer Res.. Univ. Houston, Texas.Google Scholar
  15. Weinberg R., and Zeigler B. P. (1969) Computer simulation of a living cell: Multilevel control systems. University of Michigan Tech. Report 08228–17-T, Dec. 1969, Ann Arbor, Michigan.Google Scholar
  16. Yeisley W. G., and Pollard E. C. (1964) An analog computer study of differential equations concerned with baterial cell synthesis. J. Theoret. Biol. 7: 485–503.CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • E. J. Davison
    • 1
  1. 1.Department of Electrical EngineeringUniversity of TorontoTorontoCanada

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