Incorporating energy metabolism into a growth model of multicellular tumor spheroids

Journal of Theoretical Biology

Volumn 242, Issue 2, 2006, Pages 440-453

  Venkatasubramanian, Raja ^a   Henson, Michael A ^a   Forbes, Neil S ^a  

^a University of Massachusetts   (United States)

Author keywords

Diffusion; Energy metabolism; Hypoxia; Multicellular tumor spheroid; Quiescence; Tumor growth modeling

Indexed keywords

ADENOSINE TRIPHOSPHATE; GLUCOSE; LACTIC ACID; OXYGEN;

ENERGY; GLUCOSE; GROWTH RATE; METABOLISM; PHYSIOLOGY; TUMOR;

ARTICLE; CANCER CHEMOTHERAPY; CANCER RADIOTHERAPY; CELL DEATH; CELL GROWTH; CELL HYPOXIA; CELL PROLIFERATION; CELL SURVIVAL; CELLULAR DISTRIBUTION; CONCENTRATION (PARAMETERS); DIFFUSION; DRUG PENETRATION; ENERGY METABOLISM; GLUCOSE TRANSPORT; GROWTH RATE; MATHEMATICAL MODEL; OXYGEN TRANSPORT; PRIORITY JOURNAL; SENSITIVITY ANALYSIS; TUMOR GROWTH; TUMOR SPHEROID;

BIOLOGICAL TRANSPORT; CELL DEATH; CELL PROLIFERATION; CELL SURVIVAL; DIFFUSION; ENERGY METABOLISM; HUMANS; MODELS, BIOLOGICAL; OXYGEN CONSUMPTION; SPHEROIDS, CELLULAR; TUMOR CELLS, CULTURED;

EID: 33747162432     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2006.03.011     Document Type: Article

References (39)

1. Acker H., Carlsson J., Holtermann G., Nederman T., and Nylen T. Influence of glucose and buffer capacity in the culture medium on growth and pH in spheroids of human thyroid carcinoma and human glioma origin. Cancer Res. 47 (1987) 3504-3508
2. Adam J.A., and Maggelakis S.A. Mathematical models of tumor growth. IV. Effects of a necrotic core. Math. Biosci. 97 (1989) 121-136
3. Adam J.A., and Maggelakis S.A. Diffusion regulated growth characteristics of a spherical prevascular carcinoma. Bull. Math. Biol. 52 (1990) 549-582
4. Araujo R.P., and McElwain D.L. A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol. 66 (2004) 1039-1091
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. Brizel D.M., Scully S.P., Harrelson J.M., Layfield L.J., Bean J.M., Prosnitz L.R., and Dewhirst M.W. Tumor oxygenation predicts for the likelihood of distant metastases in human soft tissue sarcoma. Cancer Res. 56 (1996) 941-943
7. Brizel D.M., Schroeder T., Scher R.L., Walenta S., Clough R.W., Dewhirst M.W., and Mueller-Klieser W. Elevated tumor lactate concentrations predict for an increased risk of metastases in head-and-neck cancer. Int. J. Radiat. Oncol. Biol. Phys. 51 (2001) 349-353
8. Brown P.N., Hindmarsh A.C., and Petzold L.R. Using Krylov methods in the solution of large-scale differential-algebraic systems. SIAM J. Sci. Comput. 15 (1994) 1467-1488
9. Brown, P.N., Hindmarsh, A.C., Petzold, L.R., 1995. DASPK, Santa Barbara, CA.
10. Byrne H.M., and Chaplain M.A. Growth of nonnecrotic tumors in the presence and absence of inhibitors. Math. Biosci. 130 (1995) 151-181
11. Casciari J.J., Sotirchos S.V., and Sutherland R.M. Glucose diffusivity in multicellular tumor spheroids. Cancer Res. 48 14 (1988) 3905-3909
12. Casciari, J., 1989. The effects of diffusion and reaction of nutrients and metabolic waste products on the growth and microenvironment of multicellular tumor spheroids. Ph.D. Dissertation, University of Rochester, Rochester.
13. Casciari J.J., Sotirchos S.V., and Sutherland R.M. Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids. Cell Proliferat. 25 (1992) 1-22
14. Chaplain M.A., and Britton N.F. On the concentration profile of a growth inhibitory factor in multicell spheroids. Math. Biosci. 115 (1993) 233-243
15. Crank J. Free and Moving Boundary Problems (1984), Clarendon Press, New York
16. Finlayson B.A. Nonlinear Analysis in Chemical Engineering (1980), McGraw-Hill International Book Co., New York
17. Freyer J.P. Role of necrosis in regulating the growth saturation of multicellular spheroids. Cancer Res. 48 (1988) 2432-2439
18. Freyer J.P., and Sutherland R.M. Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply. Cancer Res. 46 (1986) 3504-3512
19. Greenspan H.P. On the growth and stability of cell cultures and solid tumors. J. Theor. Biol. 56 (1976) 229-242
20. Helmlinger G., Sckell A., Dellian M., Forbes N.S., and Jain R.K. Acid production in glycolysis-impaired tumors provides new insights into tumor metabolism. Clin. Cancer Res. 8 (2002) 1284-1291
21. Hietanen P., Blomqvist C., Wasenius V.M., Niskanen E., Franssila K., and Nordling S. Do DNA ploidy and S-phase fraction in primary tumour predict the response to chemotherapy in metastatic breast cancer?. Br. J. Cancer 71 (1995) 1029-1032
22. Jackson T.L., and Byrne H.M. 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
23. Kunz-Schughart L.A. Multicellular tumor spheroids: intermediates between monolayer culture and in vivo tumor. Cell Biol. Int. 23 (1999) 157-161
24. Landry J., Freyer J.P., and Sutherland R.M. A model for the growth of multicellular spheroids. Cell Tissue Kinet. 15 (1982) 585-594
25. Mueller-Klieser W.F., and Sutherland R.M. Oxygen consumption and oxygen diffusion properties of multicellular spheroids from two different cell lines. Adv. Exp. Med. Biol. 180 (1984) 311-321
26. Newsholme A.E., and Leech A.R. Biochemistry for the Medical Sciences (1983), Wiley, Chichester
27. Pettet G.J., Please C.P., Tindall M.J., and McElwain D.L. The migration of cells in multicell tumor spheroids. Bull. Math. Biol. 63 (2001) 231-257
28. Sherratt J.A., and Chaplain M.A. A new mathematical model for avascular tumour growth. J. Math. Biol. 43 (2001) 291-312
29. Siu W.Y., Arooz T., and Poon R.Y. Differential responses of proliferating versus quiescent cells to adriamycin. Exp. Cell Res. 250 (1999) 131-141
30. Smallbone K., Gavaghan D.J., Gatenby R.A., and Maini P.K. The role of acidity in solid tumour growth and invasion. J. Theor. Biol. 235 (2005) 476-484
31. Sutherland R.M. Cell and environment interactions in tumor microregions: the multicell spheroid model. Science 240 (1988) 177-184
32. Vaupel P., Thews O., and Hoeckel M. Treatment resistance of solid tumors: role of hypoxia and anemia. Med. Oncol. 18 (2001) 243-259
33. Walenta S., Salameh A., Lyng H., Evensen J.F., Mitze M., Rofstad E.K., and Mueller-Klieser W. Correlation of high lactate levels in head and neck tumors with incidence of metastasis. Am. J. Pathol. 150 (1997) 409-415
34. Walenta S., Wetterling M., Lehrke M., Schwickert G., Sundfor K., Rofstad E.K., and Mueller-Klieser W. High lactate levels predict likelihood of metastases, tumor recurrence, and restricted patient survival in human cervical cancers. Cancer Res. 60 (2000) 916-921
35. Walenta S., Schroeder T., and Mueller-Klieser W. Metabolic mapping with bioluminescence: basic and clinical relevance. Biomol. Eng. 18 (2002) 249-262
36. Warburg O. Ist die aerobe Glykolyse spezifisch für die Turmoren. Biochem. Z. 204 (1929) 482-483
37. Ward J.P., and King J.R. Mathematical modelling of avascular-tumour growth. IMA J. Math. Appl. Med. Biol. 14 (1997) 39-69
38. Ward J.P., and King J.R. Mathematical modelling of avascular-tumour growth II. Modeling growth saturation. IMA J. Math. Appl. Med. Biol. 16 (1999) 171-211
39. Ward J.P., and King J.R. Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures. Math. Biosci. 181 (2003) 177-207