JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A Chemotherapy-Diffusion Model for the Cancer Treatment and Initial Dose Control
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 48, Issue 3,  2008, pp.395-410
  • 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;
  PDF(new window)
 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.
 Keywords
Chemotherapy cancer treatment;a diffusion model;initial dose control;an approach to solutions of coupled diffusion equations;
 Language
English
 Cited by
 References
1.
R. T. Dorr, and D. D. Hoff, Cancer chemotherapy Handbook Appeleton and Lange,Connecticut(1994).

2.
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. crossref(new window)

3.
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.

4.
J. A. Sherratt, Cellular growth control and traveling waves of cancer, SIAM J. Appl. Math., 53(6)(1993), 1713-1730. crossref(new window)

5.
J. A. Adam, A simplified mathematical model of tumor,Math. Biosci, 81(1986), 229-244. crossref(new window)

6.
J. A. Adam, A Mathematical model of tumor growth III. Comparison with experiment, Math. Biosci, 86(1987), 213-227. crossref(new window)

7.
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. crossref(new window)

8.
A. T. Look, On congenic transcription factors in the acute human leukimias, Science, 278(1997), 1059-1064. crossref(new window)

9.
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. crossref(new window)

10.
N. F. Briton, Reaction- Diffusion Equations and their Applications to Biology, Academic, New York(1986).

11.
J. D. Murray, Mathematical Biology, Second Edition. Springer Verlag(1993).

12.
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.

13.
H. N. Ismail and E. M. Elbarbary, Restrictive Pade approximation and parabolic partial differential equations, Int. J. Comput. Math., 66(1998), 343. crossref(new window)

14.
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. crossref(new window)

15.
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. crossref(new window)

16.
H. Poorkarimi and J. Wiener, Bounded solutions of nonlinear parabolic equations with time delay, Electronic J. of Differential Equations, Conference 02(1999), 87-91