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A Chemotherapy-Diffusion Model for the Cancer Treatment and Initial Dose Control

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초록

A one site chemotherapy agent-diffusion model is proposed which accounts for diffusion of chemotherapy agent, normal and cancer cells. It is shown that, by controlling the initial conditions, consequently an initial dose of the chemotherapy agent, the system is guaranteed to evolute towards a target equilibrium state. Or, growth of the normal cells occurs against decay of the cancer cells. Effects of diffusion of chemotherapy-agent and cells are investigated through numerical computations of the concentrations in square and triangular cancer sites.

Abstract

A one site chemotherapy agent-diffusion model is proposed which accounts for diffusion of chemotherapy agent, normal and cancer cells. It is shown that, by controlling the initial conditions, consequently an initial dose of the chemotherapy agent, the system is guaranteed to evolute towards a target equilibrium state. Or, growth of the normal cells occurs against decay of the cancer cells. Effects of diffusion of chemotherapy-agent and cells are investigated through numerical computations of the concentrations in square and triangular cancer sites.

참고문헌 (16)

  1. R. T. Dorr, "Cancer chemotherapy Handbook Appeleton and Lange" (1994), Connecticut
  2. J. M. Murray, "Optimal drug regimens in cancer chemotherapy for single drugs that block progression through the cell cycle", Math. Biosci, 123, pp.183~193 (1994)
  3. A. Y. Yukovler, "Molgavekar Guest Editors, Modeling and data analysis in cancer studies", Special Issue of Math. and Comput. Modeling, 33, pp.12~13 (2001)
  4. J. A. Sherratt, "Cellular growth control and traveling waves of cancer", SIAM J. Appl. Math, 53(6), pp.1713~1730 (1993)
  5. J. A. Adam, "simpli¯ed mathematical model of tumor", Math. Biosci, 81, pp.229~244 (1986)
  6. J. A. Adam, "A Mathematical model of tumor growth III. Comparison with experiment", Math. Biosci, 86, pp.213~227 (1987)
  7. S. T. R. Pinho, "Chemotherapy model for the treatment of cancer with metastasis", Math. and Comput. Modeling, 36, pp.773~803 (2002)
  8. A. T. Look, "On congenic transcription factors in the acute human leukimias", Science, 278, pp.1059~1064 (1997)
  9. J. A. Leach, "An analysis of a two-cell coupled nonlinear chemical oscillator", Dyn. and Stability of Systems, 6(4), pp.341~366 (1991)
  10. N. F. Briton, "Reaction- Di®usion Equations and their Applications to Biology" (1986), Aca-demic, New York
  11. J. D. Murray, "Mathematical Biology" (1993), Springer Verlag
  12. H. I. Abdel-Gawad, "On the behaviour of solutions of a two-cell cubic autocatalator reaction model", Proc. Aust. Math Soc, ANZIAMJ44(E), pp.1~32 (2002)
  13. H. N. Ismail, "Elbarbary, Restrictive Pade approximation and parabolic partial di®erential equations", Int. J. Comput. Math, 66, pp.343~ (1998)
  14. H. N. Ismail, "Approximation for the solution of the schrodinger equation", Int. J. Comput. Math, 79(5), pp.603~ (2002)
  15. H. I. Abdel-Gawad, "An approach to solutions of coupled semilinear partial di®erential equations with applications", Math. Meth. Appl. Sci, 23, pp.845~864 (2000)
  16. H. Poorkarimi, "Bounded solutions of nonlinear parabolic equations with time delay", Electronic J. of Di®erential Equations Conference, 02, pp.87~91 (1999)

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