Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2008.48.3.395
Title & Authors
A Chemotherapy-Diffusion Model for the Cancer Treatment and Initial Dose Control Abdel-Gawad, Hamdy Ibrahim; Saad, Khaled Mmohamed;
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.
Chemotherapy cancer treatment;a diffusion model;initial dose control;an approach to solutions of coupled diffusion equations;
R. T. Dorr, and D. D. Hoff, Cancer chemotherapy Handbook Appeleton and Lange,Connecticut(1994).
J. M. Murray, Optimal drug regimens in cancer chemotherapy for single drugs that block progression through the cell cycle, Math. Biosci, 123(1994), 183-193.
A. Y. Yukovler and S. H. Molgavekar Guest Editors, Modeling and data analysis in cancer studies, Special Issue of Math. and Comput. Modeling, 33(2001), 12-13.
J. A. Sherratt, Cellular growth control and traveling waves of cancer, SIAM J. Appl. Math., 53(6)(1993), 1713-1730.
J. A. Adam, A simplified mathematical model of tumor,Math. Biosci, 81(1986), 229-244.
J. A. Adam, A Mathematical model of tumor growth III. Comparison with experiment, Math. Biosci, 86(1987), 213-227.
S. T. R. Pinho, H. I. Freed man and F. A. Nani, Chemotherapy model for the treatment of cancer with metastasis, Math. and Comput. Modeling, 36(2002), 773-803.
A. T. Look, On congenic transcription factors in the acute human leukimias, Science, 278(1997), 1059-1064.
J. A. Leach, J. H. Merkin and S. K. Scott, An analysis of a two-cell coupled nonlinear chemical oscillator Dyn. and Stability of Systems, 6(4)(1991), 341-366.
N. F. Briton, Reaction- Diffusion Equations and their Applications to Biology, Academic, New York(1986).
J. D. Murray, Mathematical Biology, Second Edition. Springer Verlag(1993).
H. I. Abdel-Gawad and K. M. Saad, On the behaviour of solutions of a two-cell cubic autocatalator reaction model, Proc. Aust. Math Soc., ANZIAMJ44(E)(2002), 1-32.
H. N. Ismail and E. M. Elbarbary, Restrictive Pade approximation and parabolic partial differential equations, Int. J. Comput. Math., 66(1998), 343.
H. N. Ismail, E. M. Elbarbary, and A. A. Elbietar, Approximation for the solution of the schrodinger equation, Int. J. Comput. Math., 79(5)(2002), 603.
H. I. Abdel-Gawad and A. M. Elshrae, An approach to solutions of coupled semilinear partial differential equations with applications, Math. Meth. Appl. Sci., 23(2000), 845-864.
H. Poorkarimi and J. Wiener, Bounded solutions of nonlinear parabolic equations with time delay, Electronic J. of Differential Equations, Conference 02(1999), 87-91