A cellular automaton model of brain tumor treatment and resistance

Journal of Theoretical Medicine

Volumn 4, Issue 4, 2002, Pages 223-239

  Schmitz, Jonathan E ^a   Kansal, Anuraag R ^b   Torquato, Salvatore ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b Princeton University   (United States)

Author keywords

Biosystem; Chemotherapy; Computational modeling; Drug resistance; Glioblastoma multiforme; Heterogeneous tumors

Indexed keywords

CISPLATIN; PLATINUM DERIVATIVE;

ARTICLE; BRAIN TUMOR; CANCER CHEMOTHERAPY; COMPUTER SIMULATION; CONTROLLED STUDY; DRUG SENSITIVITY; GENE MUTATION; GEOMETRY; GLIOBLASTOMA; HUMAN; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; NEUROSURGERY; PROGNOSIS; SURVIVAL; TREATMENT OUTCOME; TUMOR GROWTH; TUMOR LOCALIZATION;

EID: 0041976124     PISSN: 10273662     EISSN: None     Source Type: Journal    
DOI: 10.1080/1027366031000086674     Document Type: Article

References (40)

1. Anderson, A.R.A., Chaplain, M.A.J., Newman, E.L., Steele, R.J.C. and Thompson, A.M. (2000) "Mathematical modeling of tumor invasion and metastasis", Journal of Theoretical Medicine 2, 129-154.
2. Berkman, R.A., Clark, W.C., Saxena, A., Robertson, J.T., Oldfield, E.H. and Ali, I.U. (1992) "Clonal composition of glioblastoma multiforme", Journal of Neurosurgery 77, 432-437.
3. Birkhead, B.G., Rankin, E.M., Gallivan, S., Dones, L. and Rubens, R.D. (1987) "A mathematical model of the development of drug resistance to cancer chemotherapy", European Journal of Cancer and Clinical Oncology 23, 1421-1427.
4. Boldrini, J.L. (2000) "Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy", IMA Journal of Mathematics Applied in Medicine and Biology 17, 33-51.
5. Bredel, M. (2001) "Anticancer drug resistance in primary human brain tumors", Brain Research Reviews 35, 161-204.
6. Chadhary, P.M. and Roninson, I.B. (1993) "Induction of multidrug resistance in human cells by transient exposure to different chemotherapeutic drugs", Journal of the National Cancer Institute 85, 632-639.
7. Coldman, A.J. and Goldie, J.H. (1979) "A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate", Cancer Treatment Reports 63, 1727-1731.
8. Coldman, A.J. and Goldie, J.H. (1985) "Role of mathematical modeling in protocol formulation in cancer chemotherapy", Cancer Treatment Reports 69, 1041-1045.
9. Coldman, A.J. and Goldie, J.H. (1986) "A stochastic model for the origin and treatment of tumors containing drug-resistant cell", Bulletin of Mathematical Biology 48, 279-292.
10. Coons, S.W. and Johnson, P.C. (1993) "Regional heterogeneity in the DNA content of human gliomas", Cancer 72, 3052-3060.
11. Costa, M.I.S., Boldrini, J.L. and Bassanezi, R.C. (1995) "Drug kinetics and drug resistance in optimal chemotherapy", Mathematical Biosciences 125, 191-209.
12. Deisboeck, T.S., Berens, M.E., Kansal, A.R., Torquato, S., Stemmer-Rachamimov, A.O. and Chiocca, E.A. (2001) "Pattern of self-organization in tumor systems: complex growth dynamics in a novel brain tumor spheroid model", Cell Proliferation 34, 115-134.
13. Düchting, W. and Vogelsaenger, T. (1985) "Recent progress in modeling and simulation of three-dimensional tumor growth and treatment", BioSystems 18, 79-91.
14. Endicott, L.C. and Ling, V. (1989) "The biochemistry of the P-glycoprotein-mediated multidrug resistance", Annual Reviews in Biochemistry 58, 137-171.
15. Gekeler, V., Beck, J., Noller, A., Wilisch, A., Frese, G., Neumann, M., Handgretinger, R., Ehninger, G., Probst, H. and Niethammer, D. (1994) "Drug-induced changes in the expression of mdr-associated genes - investigations on cultured cell lines and chemotherapeutically treated leukemias", Annals of Hematology 69, S19-S24.
16. German, U.A. (1996) "P-glycoprotein - a mediator of multidrug resistance in tumour cells", European Journal of Cancer 32A, 927-944.
17. Gerweck, L.E., Kornblinth, P.L., Burlett, P., Wang, J. and Sweigert, S. (1977) "Radiation sensitivity of cultured glioblastoma cells", Radiology 125, 231-241.
18. Holland, E.C. (2000) "Glioblastoma multiforme: the terminator", Proceedings of the National Academy of Science 97, 6242-6244.
19. Jansson, B. and Revesz, I. (1974) "Analysis of the growth of tumor cell populations", Mathematical Biosciences 19, 131-154.
20. Jelsma, R. and Bucy, P.C. (1967) "Treatment of glioblastoma multiforme of brain", Journal of Neurosurgury 27, 388-400.
21. Kansal, A.R., Torquato, S., Chiocca, E.A. and Deisboeck, T.S. (2000a) "Emergence of a subpopulation in a computational model of tumor growth", Journal of Theoretical Biology 207, 431-441.
22. Kansal, A.R., Torquato, S., Harsh, IV, G.R., Chiocca, E.A. and Deisboeck, T.S. (2000b) "Simulated brain tumor growth dynamics using a three-dimensional cellular automaton", Journal of Theoretical Biology 203, 367-382.
23. Kayama, T., Yoshimoto, T., Fujimoto, S. and Sakurai, Y. (1991) "Intratumoral oxygen pressure in malignant brain tumors", Journal of Neurosurgury 74, 55-59.
24. Kim, H.J. and Kim, I.M. (2001) "Formation of river networks in heterogeneous surfaces", Journal of the Korean Physical Society 2, 497-499.
25. Kraus, M. and Wolf, B. (1993) "Emergence of self-organization in tumor cells - relevance for diagnosis and therapy", Tumor Biology 14, 338-353.
26. Markus, M., Bohm, D. and Schmick, M. (1999) "Simulation of vessel morphogenesis using cellular automata", Mathematical Biosciences 156, 191-206.
27. Michelson, S. (1989) "Mathematical models for multidrug resistance and its reversal", Cytotechnology 12, 315-324.
28. Michelson, S., Ito, K., Tran, H.T. and Leith, J.T. (1989) "Stochastic models for sub-population emergence in heterogeneous tumors", Bulletin of Mathematical Biology 51, 731-747.
29. Okabe, A., Boots, B. and Sugihara, K. (1992) Spatial Tesselations (Wiley, New York).
30. Panetta, J.C. (1998) "A mathematical model of drug resistance: Heterogeneous tumors", Mathematical Biosciences 147, 41-61.
31. Patel, A.A., Gawlinski, E.T., Lemieux, S.K. and Gatenby, R.A. (2001) "A cellular automaton model of early tumor growth and invasion: the effects of native tissue vascularity and increased anaerobic metabolism", Journal of Theoretical Biology 213, 315-331.
32. Paulus, W. and Peiffer, J. (1989) "Intratumoral histologic heterogeneity of gliomas. A quantitative study", Cancer 64, 442-447.
33. Poppenborg, H., Munstermann, G., Knopfer, M.M., Hotfilder, M. and Wolff, J.E.A. (1997) "C6 cross-resistant to cisplatin and radiation", Anticancer Research 17, 2073-2077.
34. Salcman, S., Scholtz, H., Kaplan, R. and Kulik, S. (1994) "Long-term survival in patients with malignant astrocytoma", Neurosurgery 34, 213-219.
35. Shah, M.A. and Schwartz, G.K. (2001) "Cell cycle-mediated drug resistance: an emerging concept in cancer chemotherapy", Clinical Cancer Research 7, 2168-2181.
36. Torquato, S. (1984) "Bulk properties of two-phase media. 1. Cluster expansion for the dielectric constant of dispersions of fully penetrable spheres", Journal of Chemical Physics 81, 5079-5088.
37. Torquato, S. (2002) Random Heterogeneous Materials: Microstructure and Macroscopic Properties (Springer-Verlag, New York).
38. Tracqui, P., Cruywagen, G.C., Woodward, D.E., Bartoo, G.T., Murray, J.D. and Alvord, E.C. (1995) "A mathematical model of glioma growth: the effect of chemotherapy on spatio-temporal growth", Cell Proliferation 28, 17-31.
39. Yung, W.A., Shapiro, J.R. and Shapiro, W.R. (1982) "Heterogeneous chemosensitivities of subpopulations of human glioma cells in culture", Cancer Research 42, 992-998.
40. Zhang, W., Hara, A., Sakai, N., Andoh, T., Yamada, H., anf, P.H., Gutin, Y.N. and Kornblinth, P.L. (1993) "Radiosensitization and inhibition of deoxyribonucleic acid repair in rat glioma cells by long term treatment with 12-o-tetradecanoylphorbol 13-acatate", Neurosurgery, 432-437.