A free boundary problem modelling cancer radiovirotherapy

Mathematical Models and Methods in Applied Sciences

Volumn 17, Issue 8, 2007, Pages 1241-1259

  Tao, Youshan ^a,b   Guo, Qian ^a,b  

^a DONGHUA UNIVERSITY   (China)

^b SHANGHAI NORMAL UNIVERSITY   (China)

Author keywords

Free boundary problems; Radioiodide; Tumors; Virus

Indexed keywords

EID: 34547306670     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202507002261     Document Type: Article

References (38)

1. J. Adam and N. Bellomo, A Survey of Models for Tumor-Immune System Dynamics (Birkhäuser, 1997).
2. N. Bellomo, E. De Angelis and L. Preziosi, Multiscale modeling and mathematical problems related to tumor evolution and medical therapy, J. Theor. Med. 5 (2003) 111-136.
3. N. Bellomo, A. Bellouquid and M. Delitala, Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition, Math. Mod. Meth. Appl. Sci. 14 (2004) 1683-1733.
4. N. Bellomo and G. Forni, Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems, Math. Mod. Meth. Appl. Sci. 16 (2006) 1001-1029.
5. N. Bellomo and P. K. Maini, Preface, Math. Mod. Meth. Appl. Sci. 15 (2005) iii-viii.
6. A. Bellouquid and M. Delitala, Mathematical methods and tools of kinetic theory towards modelling complex biological system, Math. Mod. Meth. Appl. Sci. 15 (2005) 1639-1666.
7. A. Bertuzzi, A. Fasano and A. Gandolfi, A free boundary problem with unilateral constraints describing the evolution of a tumor cord under the influence of cell killing agents, SIAM J. Math. Anal. 36 (2004) 882-915.
8. A. Bertuzzi, A. Fasano and A. Gandolfi, A mathematical model for tumor cords incorporating the flow of interstitial fluids, Math. Mod. Meth. Appl. Sci. 15 (2005) 1735-1778.
9. H. M. Byrne, J. R. King, D. L. McElwain and L. Preziosi, A two-phase model of solid tumour growth, Appl. Math. Lett. 16 (2003) 567-573.
10. M. A. J. Chaplain, V. A. Kuznetsov, Z. H. James and L. A. Stepanova, Spatiotemporal dynamics of the immune system reponse to cancer, Proc. of the Mathematical Models in Medical and Health Sciences Conference (eds. M. A. Horn, G. Simonett and G. Webb (Vanderbilt Univ. Press, 1998).
11. M. A. J. Chaplain and G. Lolas, Mathematical modelling of cancer cell invasion of tissue: The role of urokinase plasminogen activation system, Math. Mod. Meth. Appl. Sci. 15 (2005) 1685-1734.
12. E. De Angelis and P. E. Jabin, Mathematical models of therapeutical actions related to tumour and immune system competition, Math. Meth. Appl. Sei. 28 (2005) 2061-2083.
13. D. Dingli, E. R. Bergert, Ž. Bajzer, M. K. O'Connor, S. J. Russell and J. C. Morris, Dynamic iodide trapping by tumor cells expressing the thyroidal sodium iodide symporter, Biochem. Biophys. Res. Comm. 325 (2004) 157-166.
14. D. Dingli, M. D. Cascino, K. Josić, S. J. Russell and Ž. Bajzer, Mathematical modeling of cancer radiovirotherapy, Math. Biosci. 199 (2006) 80-103.
15. D. Dingli, K. W. Peng, M. E. Harvey, P. R. Greipp, M. K. O'Connor, R. Cattaneo, J. C. Morris and S. J. Russell, Image-guided radiovirotherapy for multiple myeloma using a recombinant measles virus expressing the thyroidal sodium iodide symporter, Blood 103 (2004) 1641-1646.
16. S. O. Freytag, K. R. Rogulski, D. L. Paielli, J. D. Gilbert and J. H. Kirn, A novel threepronged approach to kill cancer cells selectively: Concomitant viral, double suicide gene, and radiotherapy (see comments), Hum. Gene Ther. 9 (1998) 1323-1333.
17. A. Friedman and G. Lolas, Analysis of a mathematical model of tumor lymphangiogenesis, Math. Mod. Meth. Appl. Sci. 15 (2005) 95-107.
18. A. Friedman and Y. Tao, Analysis of a model of a virus that replicates selectively in tumor cells, J. Math. Biol. 47 (2003) 391-423.
19. C. Heise, A. Sampson-Johannes, A. Williams, F. McCormick, D. D. Von Hoff and D. H. Kirn, ONYX-015, an EIB gene-attenuated adenovirus, causes tumor-specific cytolysis and antitumoral efficacy that can be augmented by standard chemotherapeutic agents, Nature Med. 3 (1997) 639-645.
20. R. K. Hobbie, Intermediate Physics for Medicine and Biology (Springer, 1997).
21. T. L. Jackson and H. M. Byrne, A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy, Math. Biosci. 164 (2000) 17-38.
22. R. Jain, Barriers to drug delivery in solid tumors, Sci. Am. 271 (1994) 58-65.
23. J. Nemunaitis, C. Cunningham, A. Buchanan, A. Blackburn, G. Edelman, P. Maples, G. Netto, A. Tong, B. Randley, S. Olson and D. Kirn, Intravenous infusion of a replication-selective adenovirus (ONYX-015) in cancer patients: safety, feasibility and biological activity, Gene Ther. 8 (2001) 746-759.
24. J. Nemunaitis, I. Ganly, F. Khuri, J. Arseneau, J. Kuhn, T. McCarty, S. Landers, P. Maples, L. Romel, B. Randley, T. Reid, S. Kaye and D. Kirn, Selective replication and oncolysis in p53 mutant tumors with ONYX-015, an E1B-55kD gene-deleted adenovirus, in patients with advanced head and neck cancer: a phase II trial, Cancer Res. 60 (2000) 6359-6366.
25. M. R. Owen, H. M. Byrne and C. E. Lewis, Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites, J. Theor. Biol. 226 (2004) 377-391.
26. K. R. Rogulski, S. Q. Freytag, K. Zhang, J. D. Gilbert, D. L. Paielli, J. H. Kim, C. C. Heise and D. H. Kirn, In vivo antitumor activity of ONYX-015 is influenced by p53 status and is augmented by radiotherapy, Cancer Res. 60 (2000) 1193-1196.
27. M. A. Savageau, Allometric morphogenesis of complex systems: a derivation of the basic equations from the first principles, Proc. Natl. Acad. Sci. 76 (1979) 6023-6025.
28. Y. Tao and M. Chen, An elliptic-hyperbolic free boundary problem modelling cancer therapy, Nonlinearity 19 (2006) 419-440.
29. Y. Tao and Q. Guo, The competitive dynamics between tumor cells, a replication-competent virus and an immune response, J. Math. Biol. 51 (2005) 37-74.
30. Y. Tao, N. Yoshida and Q. Guo, Nonlinear analysis of a model of vascular tumour growth and treatment, Nonlinearity 17 (2004) 867-895.
31. Y. Tao and H. Zhang, A parabolic-hyperbolic free boundary problem modelling tumor treatment with virus, Math. Mod. Meth. Appl. Sci. 17 (2007) 63-80.
32. H. P. de Vladar and J. A. Gonzalez, Dynamic response of cancer under the influence of immunological activity and therapy, J. Theor. Biol. 227 (2004) 335-348.
33. J. P. Ward and J. R. King, Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures, Math. Biosci. 181 (2003) 177-207.
34. L. M. Wein, J. T. Wu and D. H. Kirn, Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: implications for virus design and delivery, Cancer Res. 63 (2003) 1317-1324.
35. D. Wodarz, Viruses as antitumor weapons: defining conditions for tumor remission, Cancer Res. 61 (2001) 3501-3507.
36. D. Wodarz, Gene therapy for killing p53-negative cancer cells: use of replicating versus nonreplicating agents, Human Gene Ther. 14 (2003) 153-159.
37. J. T. Wu, H. M. Byrne, D. H. Kirn and L. M. Wein, Modeling and analysis of a virus that replicates selectively in tumor cells, Bull. Math. Biol. 63 (2001) 731-768.
38. J. T. Wu, D. H. Kirn and L. M. Wein, Analysis of a three-way race between tumor growth, a replication-competent virus and an immune response, Bull. Math. Biol. 66 (2004) 605-625.