Mathematical modelling of the Warburg effect in tumour cords

Journal of Theoretical Biology

Volumn 258, Issue 4, 2009, Pages 578-590

  Astanin, Sergey ^a   Preziosi, Luigi ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Ghost fluid method; Mathematical model; Population dynamics; Tumour growth; Tumour metabolism; Warburg effect

Indexed keywords

ADENOSINE TRIPHOSPHATE;

MECHANICAL PROPERTY; NUMERICAL MODEL; NUTRIENT UPTAKE; POPULATION DYNAMICS; TUMOR;

AEROBIC METABOLISM; ANALYTIC METHOD; ARTICLE; CELL DEATH; CELL GROWTH; ENERGY COST; GLYCOLYSIS; MATHEMATICAL MODEL; NUTRIENT UPTAKE; POPULATION MODEL; PRIORITY JOURNAL; TUMOR; WARBURG EFFECT;

CELL COUNT; CELL LINE, TUMOR; CELL SURVIVAL; COMPUTER SIMULATION; DISEASE PROGRESSION; GLYCOLYSIS; HUMANS; MODELS, BIOLOGICAL; NEOPLASMS;

EID: 67349114307     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2009.01.034     Document Type: Article

References (28)

1. Ambrosi D., and Preziosi L. On the closure of mass balance models for tumor growth. Math. Models Methods Appl. Sci. 12 5 (2002) 737-754
2. Ambrosi, D., Preziosi, L., 2009. Cell adhesion mechanisms and elasto-viscoplastic mechanics of tumours. Biomech. Modelling Mechanobiol., in press, doi:10.1007/s10237-008-0145-y.
3. Astanin S., and Preziosi L. Multiphase models of tumour growth. In: Bellomo N., Chaplain M., and De Angelis E. (Eds). Selected Topics on Cancer Modelling: Genesis-Evolution-Immune Competition-Therapy (2008), Birkhäuser, Boston 223-253
4. Astanin S., and Tosin A. Mathematical model of tumour cord growth along the source of nutrient. Math. Model. Nat. Phenom. 2 3 (2007) 153-177
5. Bertuzzi A., D'Onofrio A., Fasano A., and Gandolfi A. Regression and regrowth of tumour cords following single-dose anticancer treatment. Bull. Math. Biol. 65 (2003) 903-931
6. Bertuzzi A., Fasano A., and Gandolfi A. A mathematical model for tumor cords incorporating the flow of interstitial fluid. Math. Models Methods Appl. Sci. 15 11 (2005) 1735-1777
7. Bertuzzi A., Fasano A., Gandolfi A., and Marangi D. Cell kinetics in tumour cords studied by a model with variable cell cycle length. Math. Biosci. 177-178 (2002) 103-125
8. Bertuzzi A., Fasano A., Gandolfi A., and Sinisgalli C. ATP production and necrosis formation in a tumour spheroid model. Math. Model. Nat. Phenom. 2 3 (2007) 30-46
9. Bertuzzi A., and Gandolfi A. Cell kinetics in a tumour cord. J. Theor. Biol. 204 (2000) 587-599
10. Breward C.J.W., Byrne H.M., and Lewis C.E. Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour. Eur. J. Appl. Math. 12 (2001) 529-556
11. Fedkiw R.P., Aslam T., Merriman B., and Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152 2 (1999) 457-492
12. Fedkiw, R.P., Liu, X.-D., 2002. The Ghost Fluid Method for Viscous Flows. World Scientific Publishers, Arcachon, River Edge, NJ, pp. 111-143.
13. Gatenby R.A., Gawlinski E.T., Gmitro A.F., Kaylor B., and Gillies R.J. Acid-meditated tumour invasion: a multidisciplinary study. Cancer Res. 66 (2006) 5216-5223
14. Gatenby R.A., Smallbone K., Maini P.K., Rose F., Averill J., Nagle R.B., Worrall L., and Gillies R.J. Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer. Br. J. Cancer 97 5 (2007) 646-653
15. Gerlee P., and Anderson A.R.A. A hybrid cellular automaton model of clonal evolution in cancer: the emergence of the glycolytic phenotype. J. Theor. Biol. 250 (2008) 705-722
16. Hannahan D., and Weinberg R.A. The hallmarks of cancer. Cell 100 (2000) 57-70
17. Kim J., and Dang C.V. Cancer's molecular sweet tooth and the Warburg effect. Cancer Res. 66 18 (2006) 8927-8930
18. Macklin P., and Lowengrub J. An improved geometry-aware curvature discretization for level set methods: application to tumour growth. J. Comput. Phys. 215 (2006) 293-401
19. Mathupala S.P., Colen C.B., Parajuli P., and Sloan A.E. Lactate and malignant tumors: a therapeutic target at the end stage of glycolysis. J. Bioenerg. Biomembrane 39 1 (2007) 73-77
20. Nelson D.L., and Cox M.M. Lehninger Principles of Biochemistry. third ed. (2000), W. H. Freeman, New York
21. Nguyen, D., Gibou, F., Fedkiw, R., 2002. A fully conservative ghost fluid method stiff detonation waves. In: 12th International Detonation Symposium, San Diego, CA.
22. Preziosi, L., Tosin, A. 2008. Multiphase modeling of tumor growth and extracellular matrix interaction: mathematical tools and applications. J. Math. Biol. 58 (4-5), 626-656.
23. Rich P.R. The molecular machinery of Keilin's respiratory chain. Biochem. Soc. Trans. 31 Pt 6 (2003) 1095-1105
24. Sethian, J., Osher, S.J., 1989. The design of algorithms for hypersurfaces moving with curvature-dependent speed. In: Nonlinear Hyperbolic Equations-Theory, Computation Methods, and Applications (Aachen, 1988), Notes in Numerical Fluid Mechanics, vol. 24, Vieweg Braunschweig, pp. 544-551.
25. Smallbone K., Gatenby R.A., Gillies R.J., Maini P.K., and Gavaghan D.J. Metabolic changes during carcinogenesis: potential impact on invasiveness. J. Theor. Biol. 244 (2007) 703-713
26. Smallbone, K., Gatenby, R.A., Maini, P.K., 2008. Mathematical modelling of tumour acidity. J. Theor. Biol. 255 (1), 106-112.
27. Venkatasubramanian R., Henson M., and Forbes N. Incorporating energy metabolism into a growth model of multicellular tumor spheroids. J. Theor. Biol. 242 (2006) 440-453
28. Warburg O. On the origin of cancer cells. Science 123 3191 (1956) 309-314