Mathematical modeling of prostate tumor growth under intermittent androgen suppression with partial differential equations

International Journal of Bifurcation and Chaos

Volumn 18, Issue 12, 2008, Pages 3789-3797

  Guo, Qian ^a   Tao, Youshan ^b   Aihara, Kazuyuki ^c,d  

^a SHANGHAI NORMAL UNIVERSITY   (China)

^b DONGHUA UNIVERSITY   (China)

^c INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

^d JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

Androgen independent cells; Intermittent androgen suppression; PDE model; Prostate cancer

Indexed keywords

ANTIGENS; CELLS; CYTOLOGY; DISEASES; PARTIAL DIFFERENTIAL EQUATIONS; TUMORS; UROLOGY;

ANDROGEN SUPPRESSION; ANDROGEN-DEPENDENT; MIXED ASSEMBLIES; OPTIMAL PROTOCOLS; PARTIAL DIFFERENTIAL EQUATIONS (PDE); PDE MODEL; PROSTATE CANCERS; PROSTATE SPECIFIC ANTIGEN;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 60749116929     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127408022743     Document Type: Article

References (26)

1. Bhandari, M. S., Crook, J. & Hussain, M. [2005] "Should intermittent androgen deprivation be used in routine clinical practice?" J. Clin. Oncol. 23, 8212-8218.
2. Bruchovsky, N., Klotz, L., Sadar, M., Crook, J., Hoffart, D., Godwin, L., Warkentin, M., Cleave, M. E. & Goldenberg, S. L. [2000] "Intermittent androgen suppression for prostate cancer: Canadian prospective trial and related observations," Mol. Urol. 4, 191-199.
3. Bruchovsky, N., Klotz, L., Crook, J., Malone, S., Ludgate, C., Morris, W. J., Gleave, M. E. & Goldenberg, S. L. [2006] "Final results of the Canadian prospective phase II trial of intermitten androgen suppression for men in biochemical recurrence after radiotherapy for locally advanced prostate cancer," Cancer 107, 389-395.
4. Bruchovsky, N., Klotz, L., Crook, J., Larry, S. & Goldenberg, S. L. [2007] "Locally advanced prostate cancer - biochemical results from a prospective phase II study of intermitten androgen suppression for men with evidence of psa relapse after radiotherapy," Cancer 109, 858-867.
5. Byrne, H. M. & Chaplain, M. A. J. [1996] "Modelling the role of cell-cell adhesion in the growth and development of carcinoma," Math. Comput. Model 12, 1-17.
6. Greenspan, H. [1976] "On the growth and stability of cell cultures and solid tumors," J. Theor. Biol. 56, 229-235.
7. Holland, J. F. & Frei, E. [2001] Cancer Medicine, 5th edition (Harcourt asia Pte Ltd).
8. Huggins, C. & Hodges, C. [1941] "Studies of prostate cancer: I. The effects of castration, oestrogen and androgen injections on serum phosphates in metastatic carcinoma of the prostate," Cancer Res. 1, 293-207.
9. Ideta, A., Tanaka, G., Takeuchi, T. & Aihara, K. [2008] "A mathematical model of intermitten androgen suppression for prostate cancer," J. Nonlin. Sci. 18, 593-614.
10. Igawa, T., Lin, F. F., Lee, M. S., Karan, D., Batra, S. K. & Lin, M. F. [2002] "Establishment and characterization of androgen-independent human prostate cancer LNCaP cell model," Prostate 50, 222-235.
11. Jackson, T. L. & Byrne, H. M. [2000] "A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy," Math. Biosci, 164, 17-38.
12. Jackson, T. L. [2002] "Vascular tumor growth and treatment: Consequence of polyclonality, competition and dynamic vascular support," J. Math. Biol. 44, 201-226.
13. Jackson, T. L. [2004a] "A mathematical model of prostate tumor growth and androgen-independent relapse," Discr. Contin. Dyn. Syst. B 4, 187-201.
14. Jackson, T. L. [2004b] "A mathematical investigation of multiple pathways to recurrent prostate cancer: Comparion with experimental data," Neoplasia 6, 697-704.
15. Kamradt, J. M. & Pienta, K. J. [1999] "Novel molecular targets for prostate cancer therapy," Semin, Oncol. 26, 234-243.
16. Kip1 in androgen-induced cell cycle arrest," Mol. Endocrinol. 12, 941-953.
17. Kokontis, J. M., Hsu, S., Chuu, C., Dang, M., Pukuchi, J., Hiipakka, It. A. & Liao, S. [2005] "Role of androgen receptor in the progression of human prostate tumor cells to androgen independence and insensitivity," The Prostate 65, 287-298.
18. Macri, E. & Loda, M. [1998] "Role of p27 in prostate carcinogenesis," Cancer Metastasis Rev. 17, 337-344.
19. Nelson, W. G., Marzo, A. M. De & Isaacs, W. B. [2003] "Mechanisms of disease: Prostate cancer," N. Engl. J. Med. 349, 366-381.
20. Shimada, T. & Aihara, K. [2008] "A nonlinear model with competition between prostate tumor cells and its application to intermittent androgen suppression therapy of prostate cancer," Math. Biosci. 214, 134-139.
21. Simon, C., Everitt, H., Birtwistle, J. & Stevenson, B. [2002] Oxford Handbook of General Practice (Oxford University Press, Oxford).
22. Swanson, K. R., True, L. D., Lin, D. W., Buhler, K. R., Vessella, R. & Murray J. D. [2001] "A quantitative model for the dynamics of serum prostate-specific antigen as a marker for cancerous growth: An explanation for medical anomaly," Am. J. Pathol. 158, 2195-2199.
23. Tao, Y. & Chen, M. [2006] "An elliptic-hyperbolic free boundary problem modelling cancer therapy," Non-linearity 19, 419-440.
24. Tao, Y., Guo, Q. & Aihara, K. [2008] "A mathematical model of prostate tumor growth with mutation under hormone therapy," Technical Report, Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, METR 2008-28.
25. Ward, J. P. & King, J. R. [2003] "Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures," Math. Biosci. 181, 177-207.
26. Ware, J. L. [1993] "Growth factors and their receptors as determinants in the proliferation and metastasis of human prostate cancer," Cancer Metastasis Rev. 12, 287-301.