Comparison of phase-specific chemotherapy models with and without taking into account drug resistance

Proceedings of the IASTED International Conference on Biomedical Engineering

Volumn , Issue , 2004, Pages 469-473

  Smieja, J ^a   Swierniak, A ^a  

^a SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Biomedical modelling; Drug resistance; Phase specific chemotherapy

Indexed keywords

BIOMEDICAL ENGINEERING; CYTOLOGY; DRUG INTERACTIONS; GENES; MATHEMATICAL MODELS; PROBLEM SOLVING; TUMORS;

BIOMEDICAL MODELING; CELL CYCLE; DRUG RESISTANCE; PHASE SPECIFIC CHEMOTHERAPY;

CHEMOTHERAPY;

EID: 11144274566     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (16)

1. B.F.Dibrov, A.M. Zhabotinsky, I.A. Neyfakh, H.P.Orlova, L.I. Churikova, Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivity of therapy, Math.Biosci., 73, 1-31, 1985.
2. Webb G.F., Resonances in periodic chemotherapy scheduling. Proc. World Congress Nonlin. Analysis, Tampa, Florida, 1993.
3. J.H. Goldie, A.J. Goldman, A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate, Cancer Treat. Rep, 63, 1979, 1727-1733.
4. L.E. Harnevo, Z. Agur, Use of mathematical models for understanding the dynamics of gene amplification, Mutat. Res., 292, 1993, 17-24.
5. Baserga R. The Biology of Cell Reproduction, (Cambridge, MA: Harvard University Press, 1985).
6. G.W. Swan, Role of optimal control theory in cancer chemotherapy, Math. Biosci., 101, 1990, 237-284.
7. A. Swierniak, A. Polanski, Z. Duda, M. Kimmel, Phase-Specific Chemotherapy of Cancer: Optimisation of Scheduling and Rationale for Periodic Protocols, Biocybernetics and Biomedical Engineering, 16, 1997, 13-43.
8. A. Swierniak, M. Kimmel, A. Polanski, Infinite dimensional model of evolution of drug resistance of cancer cells, Journal of Mathematical Systems, Estimation and Control, 8(1), 1998, 1-17.
9. J. Smieja, Z. Duda, A. Swierniak, Optimal Control for the Model of Drug Resistance Resulting from Gene Amplification, Preprints of 14th World Congress of IFAC, L, 1999, 71-75.
10. D.E. Axelrod, K.A. Baggerly, M. Kimmel, Gene amplification by unequal chromatid exchange: Probabilistic modelling and analysis of drug resistance data, J. Theor. Biol., 168, 1994, 151-159.
11. M. Kimmel, D.E. Axelrod, Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity, Genetics, 125, 1990, 633-644.
12. A. Polanski, M. Kimmel, A. Swierniak, Qualitative analysis of the infinite-dimensional model 'of evolution of drug resistance, Advances in Mathematical Population Dynamics - Molecules, Cells and Man, World Scientific, 1997, 595-612.
13. A. Świerniak, A. Polański, M. Kimmel, A. Bobrowski, J. Śmieja, Qualitative analysis of controlled drug resistance model - inverse Laplace and semigroup approach, Control and Cybernetics, 28, 1999, 61-74.
14. J. Śmieja, A.Świerniak, Z.Duda, Gradient Method for Finding Optimal Scheduling in Infinite Dimensional Models of Chemotherapy, Journal of Theoretical Medicine, 3, 2001, 25-36.
15. Z. Duda, A gradient method for application of chemotherapy protocols, Journal of Biological Systems, vol. 3: No.1, 1995, 3-11
16. Śmieja J., A. Świerniak, Different models of chemotherapy taking into account drug resistance stemming from gene amplification, Applied Mathematics and Computer Science, 2003.