×

Analysis of wave solutions of an adhenovirus-tumor cell system. (English) Zbl 1237.35156

Summary: We discuss the biological background and the mathematical analysis of glioma gene therapy for contributing to cancer treatment. By a reaction-diffusion system, we model interactions between gliom cells and viruses. We establish some sufficient conditions on model parameters which guarantee the permanence of the system and the existence of periodic solutions. Our study has experimental and theoretical implications in the prospective management strategy of therapy.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C50 Medical applications (general)
35K57 Reaction-diffusion equations
35B10 Periodic solutions to PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. Claes, A. J. Idema, and P. Wesseling, “Diffuse glioma growth: a guerilla war,” Acta Neuropathologica, vol. 114, no. 5, pp. 443-458, 2007. · doi:10.1007/s00401-007-0293-7
[2] J. R. Bischoff, D. H. Kirn, A. Williams et al., “An adenovirus mutant that replicates selectively in p53-deficient human tumor cells,” Science, vol. 274, no. 5286, pp. 373-376, 1996. · doi:10.1126/science.274.5286.373
[3] C. Heise, A. Sampson-Johannes, A. Williams, F. McCormick, D. D. Von Hoff, and D. H. Kirn, “ONYX-015, an E1b gene-attenuated adenovirus, causes tumor-specific cytolysis and antitumoral efficacy that can be augmented by standard chemotherapeutic agents,” Nature Medicine, vol. 3, no. 6, pp. 639-645, 1997. · doi:10.1038/nm0697-639
[4] E. A. Chiocca, K. M. Abbed, S. Tatter et al., “A phase I open-label, dose-escalation, multi-institutional trial of injection with an E1B-attenuated adenovirus, ONYX-015, into the peritumoral region of recurrent malignant gliomas, in the adjuvant setting,” Molecular Therapy, vol. 10, no. 5, pp. 958-966, 2004. · doi:10.1016/j.ymthe.2004.07.021
[5] N. L. Komarova, “Mathematical modeling of tumorigenesis: mission possible,” Current Opinion in Oncology, vol. 17, no. 1, pp. 39-43, 2005. · doi:10.1097/01.cco.0000143681.37692.32
[6] A. S. Novozhilov, F. S. Berezovskaya, E. V. Koonin, and G. P. Karev, “Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models,” Biology Direct, vol. 1, article no. 6, 2006. · doi:10.1186/1745-6150-1-6
[7] J. T. Oden, A. Hawkins, and S. Prudhomme, “General diffuse-interface theories and an approach to predictive tumor growth modeling,” Mathematical Models & Methods in Applied Sciences, vol. 20, no. 3, pp. 477-517, 2010. · Zbl 1186.92024 · doi:10.1142/S0218202510004313
[8] D. Wodarz, “Viruses as antitumor weapons: defining conditions for tumor remission,” Cancer Research, vol. 61, no. 8, pp. 3501-3507, 2001.
[9] D. Wodarz and N. Komarova, Computational Biology of Cancer: Lecture Notes And Mathematical Modelin, World Scientific, Singapour, 2005. · Zbl 1126.92029
[10] B. I. Camara, H. Mokrani, and E. Afenya, “Mathematical modelling of gliomas therapy using oncolytic viruses,” to appear. · Zbl 1268.92058
[11] W. Walter, “Differential inequalities and maximum principles: theory, new methods and applications,” vol. 30, no. 8, pp. 4695-4711, 1997. · Zbl 0893.35014 · doi:10.1016/S0362-546X(96)00259-3
[12] H. L. Smith, “Dynamics of competition,” in Mathematics Inspired by Biology, vol. 1714 of Lecture Notes in Math., pp. 191-240, Springer, Berlin, Germany, 1999. · Zbl 1002.92564
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.