A modified stochastic Gompertz model for tumour cell growth

Computational and Mathematical Methods in Medicine

Volumn 11, Issue 1, 2010, Pages 3-11

  Lo, C F ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Bounded random process; Fokker Planck equation; Lie algebraic method

Indexed keywords

ALGEBRA; CELL GROWTH; CELL PROLIFERATION; CELLS; CYTOLOGY; FOKKER PLANCK EQUATION; GROWTH KINETICS; ITERATIVE METHODS; RANDOM PROCESSES; STOCHASTIC SYSTEMS; TUMORS;

ALGEBRAIC METHOD; CELL FISSION; EXACT ANALYTICAL SOLUTIONS; GOMPERTZ MODEL; ITERATIVE APPROACH; TUMOUR CELLS;

STOCHASTIC MODELS;

ARTICLE; CELL DENSITY; CELL FUNCTION; CELL GROWTH; CELL SIZE; CLINICAL DECISION MAKING; ENGINEERING; MALIGNANT NEOPLASTIC DISEASE; MATHEMATICAL ANALYSIS; PHYSICS; PRACTICE GUIDELINE; STOCHASTIC MODEL; TUMOR GROWTH;

EID: 76949093617     PISSN: 1748670X     EISSN: 17486718     Source Type: Journal    
DOI: 10.1080/17486700802545543     Document Type: Article

References (24)

1. G. Albano and V. Giorno, A stochastic model in tumor growth, J. Theor. Biol. 242 (2006), p. 329.
2. L. Bass, H.S. Green and H. Boxenbaum, Gompertzian mortality derived from competition between cell-types: congenial, toxicologic and biometric determinants of longevity, J. Theor. Biol. 140 (1989), p. 263.
3. B. Basse, G.C. Wake, D.J.N. Wall, and B. van Brunt, On a cell-growth model for plankton, IMA. J. Math. Med. Biol. 21 (2004a), p. 49.
4. B. Basse, B.C. Baguley, E.S. Marshall, G.C. Wake, and D.J.N. Wall, Modelling cell population growth with applications to cancer therapy in human tumour cell lines, Prog. Biophys. Mol. Biol. 85 (2004b), p. 353.
5. I.D. Bassukas, Comparative Gompertzian analysis of alterations of tumor-growth patterns, Cancer Res. 54 (1994), p. 4385.
6. J.A. Cardeal, M. de Montigny, F.C. Khanna, T.M.R. Filho, and A.E. Santana, Galilei-invariant gauge symmetries in Fokker-Planck dynamics with logarithmic diffusion and drift terms, J. Phys. A: Math. Theor. 40 (2007), p. 13467.
7. J.C. Cox and S.A. Ross, Valuation of options for alternative stochastic processes, J. Financial Econ. 3 (1976), p. 145.
8. L. Ferrante, S. Bompadre, L. Possati, and L. Leone, Parameter estimation in a Gompertzian stochastic model for tumor growth, Biometrics 56 (2000), p. 1076.
9. S.C. Ferreira Jr., M.L. Matrins, and M.J. Vilela, Morphology transitions induced by chemotherapy in carcinomas in situ, Phys. Rev. E 67 (2003), p. 051914.
10. P. Fuchshuber, M. Gunther, W. Feaux de Lacroix, and R. Fischer, A mathematical model for metastatic growth illustrated by invivo and invitro growth of a transplantable mammarycarcinoma in mice, Anticancer Res. 6 (1986), p. 819.
11. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd ed., Springer-Verlag, Berlin, 1985.
12. C. Guiot, P.G. Degiorgis, P.P. Delsanto, P. Gabriele, and T.S. Deisboeck, Does tumor growth follow a universal law?, J. Theor. Biol. 225 (2003), p. 147.
13. L.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals Series and Products, 5th ed., Academic Press, UK, 1994.
14. C.F. Lo, Exact propagator of the Fokker-Planck equation with logarithmic factors in diffusion and drift terms, Phys. Lett. 319 (2003), p. 110.
15. C.F. Lo, Stochastic Gompertz model of tumour cell growth, J. Theor. Biol. 248 (2007), p. 317.
16. K. Pesz, A class of Fokker-Planck equations with logarithmic factors in diffusion and drift terms, J. Phys. A: Math. Gen. 35 (2002), p. 1827.
17. L. Preziosi ed., Cancer Modelling and Simulation, Chapman & Hall, London, 2003.
18. A.S. Qi, X. Zheng, C.Y. Du, and B.S. An, A cellular automaton model of cancerous growth, J. Theor. Biol. 161 (1993), p. 1.
19. B. Ribba, T. Colin, and S. Schnell, A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies, Theor. Biol. Med. Model. 3 (2006), p. 7.
20. K. Rygaard and M. Spang-Thomsen, Quantitation and Gompertzian analysis of tumor growth, Breast Cancer: Res. Treat. 46 (1997), p. 303.
21. E.M. Silva, T.M.R. Filho, and A.E. Santana, Lie symmetries of Fokker-Planck equations with logarithmic diffusion and drift terms, J. Phys.: Conference Series 40 (2006), p. 150. N.Y.
22. Tyurin, A.Y. Yakovlev, J. Shi, and L. Bass, Testing a model of aging in animal experiments, Biometrics 51 (1995), p. 363.
23. J. Wei and E. Norman, Lie algebraic solution of linear differential equations, J. Math. Phys. 4 (1963), p. 575.
24. B.G. Wybourne, Classical Groups for Physicists, Wiley, New York, 1974.