Vascular tumor growth and treatment: Consequences of polyclonality, competition and dynamic vascular support

Journal of Mathematical Biology

Volumn 44, Issue 3, 2002, Pages 201-226

  Jackson, Trachette L ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Mathematical model; Polyclonal tumors; Vascular support

Indexed keywords

ANTINEOPLASTIC AGENT; DOXORUBICIN;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BLOOD; CELL CULTURE; CELL DIVISION; DRUG EFFECT; DRUG RESISTANCE; HUMAN; KINETICS; MATHEMATICAL COMPUTING; NEOPLASM; NEOVASCULARIZATION (PATHOLOGY); PATHOLOGY; VASCULARIZATION;

ANIMALS; ANTINEOPLASTIC AGENTS; CELL DIVISION; DOXORUBICIN; DRUG RESISTANCE, NEOPLASM; HUMANS; KINETICS; MATHEMATICAL COMPUTING; MODELS, BIOLOGICAL; NEOPLASMS; NEOVASCULARIZATION, PATHOLOGIC; TUMOR CELLS, CULTURED;

EID: 0036516794     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s002850100118     Document Type: Article

References (46)

1. Adam, J.A.: A mathematical model of tumor growth. II Effects of geometry and spatial uniformity on stability, Math. Biosci. 86, 183 (1987)
2. Adam, J.A.: A mathematical model of tumor growth III: Comparison with experiment. Math. Biosci. 86, 213 (1987)
3. Adam, J.A., Maggelakis, S.A.: Diffusion regulated growth characteristics of a spherical prevascular carcinoma, Bull. Math. Biol. 52, 549 (1990)
4. Baxter, L.T., Yuan, F., Jain, R.K.: Pharmacokinetic analysis of the perivascular distribution of bifunctional antibodies and haptens: comparison with experimental data, Cancer Res. 52, 5838 (1992)
5. Birkhead, B.C., Rankin, E.M., Gallivan, S., Dones, L., Rubens, R.D.: A mathematical model of the development of drug resistance to cancer chemotherapy, Eur. J. Cancer Clin. Oncol. 23, 1421 (1987)
6. Byrne, H.M., Chaplain, M.A.J.: Growth of non-necrotic tumors in the presence and absence of inhibitors. Math. Biosci. 130, 151-181 (1995)
7. Byrne, H.M., Chaplain, M.A.J.: Growth of necrotic tumors in the presence and absence of inhibitors, Math. Biosci. 135, 187 (1996)
8. Byrne, H.M., Gourley, S.A.: The role of growth factors in avascular tumour growth, Math. Comput. Modelling 26, 83 (1997)
9. Byrne, H.M., Chaplain, M.A.J.: Free boundary value problems associated with the growth and development of multicellular spheroids, Eur. J. Appl. Math. 8, (1997) 639
10. Byrne, H.M., Chaplain, M.A.J.: Necrosis and apoptosis: distinct cell loss mechanisms in a mathematical model of avascular tumor growth, J. Theor. Med. 1, 223 (1998)
11. Byrne, H.M.: A weakly nonlinear analysis of a model of avascular solid tumour growth, J. Math. Bio. 39, 59 (1999)
12. Byrne, H.M., Chaplain, M.A.J.: Modelling the role of cell-cell adhesion in the growth and development of carcinoma Math. Comput. Model. 24( 12), 1 (1996)
13. Chaplain, M.A.J., Orme, M.E.: Travelling waves arising in mathematical models of tumour angiogenesis and invasion FORMA 10, 147 (1996)
14. Crank, J.: Free and moving boundary problems, O.U.P., 1988
15. Crowther, D.: A rational approach to the chemotherapy of human malignant disease - II, Brit. Med. J. 4, 216 (1974)
16. Curry, F.E., Mason, J.C., Michel, C.C.: Osmotic reflection of coefficients of capillary to low molecular weight hydrophilic solutes measures in single perfused capillaries of the frog mesentery, J. Physiol. London 261, 319 (1976)
17. Deen, W.M.: Hindered transport of large molecules in liquid-filled pores, AIChE J. 33, 1409 (1987)
18. Dordal, M.S., Winter, J.N., Atkinson, A.J.: Kinetic Analysis of P-glycoprotein-mediated Doxorubicin Efflux, J. Pharmacol. Exp. Ther. 263, 762 (1992)
19. Hahnfeldt, P., Panigrahy, D., Folkman, J., Hlatky, L.: Tumor development under angiogenic signaling: A dynamic theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 4770 (1999)
20. Folkman, J.: Fighting cancer by attacking its blood supply, Sci. Amer. Sept. 150 (1996)
21. Folkman, J., Hochberg, M.: Self-regulation of growth in three dimensions, J. Exp. Med. 138, 743 (1973)
22. Gerlowski, L.E., Jain, R.K.: Microvascular permeability of normal and neoplastic tissues, Micro. Vasc. Res. 31, 288 (1986)
23. Goldie, J.H., Coldman, AJ.: A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate, Cancer Treat. Rep. 63, 1727 (1971)
24. Greenspan, H.P.: Models for the growth of a solid tumor by diffusion, Stud. Appl. Math. 52, 317 (1972)
25. Greenspan, H.P.: On the growth and stability of cell cultures and solid tumors, J. Theor. Biol. 56, 229 (1976)
26. Hanahan, D., Folkman, J.: Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis, Cell 86, 353 (1996)
27. Helmlinger, G., Netti, P.A., Lichtenbeld, H.C., Melder, R.J., Jain, R.K.: Solid stress inhibits the growth of multicellular tumour spheroids, Nature Biotech 5, 778 (1997)
28. Jackson, T.L., 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, 17 (2000)
29. Jain, R.K.: Barriers to drug delivery in solid tumors, Sci. Amer. 271, 58 (1994)
30. Baxter, L.T., Jain, R.K.: Transport of fluid and macromolecules in tumors I. Role of interstitial pressure and convection, Microvasc. Res. 37, 77 (1989)
31. Jain, R.K.: Transport of Macromolecules Across Tumor Vasculature, Cancer Metastasis Rev. 6, 559 (1987)
32. Kerr, D.E., Schreiber, G.J., Vrudhula, V.M., Svensson, H.P., Hellstrom, K.E., Senter, P.D.: Regressions and cures of melanoma xenografts following treatment with monoclonal antibody β-lactamase conjugates in combination with anti-cancer prodrugs, Cancer Res. 55, 3558 (1995)
33. Kerr, J.F.R., Wyllie, A.H., Currie, A.R.: Apoptosis: a basic biological phenomenon with wide-ranging implications in tissue kinetics, Br. J. Cancer 26, 239 (1972)
34. Kunz-Schughart, L.A., Kreutz, M., Kneuchel, R.: Multicellular spheroids: a three-dimensional in vitro culture system to study tumor biology, Int. J. Eng. Path. 79, 1-23 (1998)
35. Liotta, L.A., Saidel, G.M., Kleinerman, J.: Diffusion model of tumor vascularization, Bull. Math. Biol. 39, 117 (1977)
36. Maggelakis, S.A., Adam, J. A.: Mathematical model of prevascular growth of a spherical carcinoma, Math. Comput. Modelling 13, 23-38 (1990)
37. Marusic, M., Bajzer, Z., Vuk-Pavlovic, S., Freyer, J.P., Tumor growth in vivo and as multicellular spheroids compared by mathematical models, Bull. Math. Biol. 56, 617 (1994)
38. Nugent, L.J., Jain, R.K.: Extravascular diffusion in normal and neoplastic tissues, Cancer Res. 44, 238 (1984)
39. O'Reilly, M.S., Boehm, T., Shing, Y., Fukai, N., Vasios, G., Lane, W.S., Flynn, E., Birkhead, J.R., Folkman, J.: Endostatin: An endogenous inhibitor of angiogenesis and tumor growth, Cell 88, 277 (1997)
40. Orme, M.E., Chaplain, M.A.J.: A mathematical model of vascular tumor growth and invasion, Math. Comp. Model. 23(10), 43 (1996)
41. Panetta, J.C., Adam, J.: A mathematical model of cycle-specific chemotherapy, Math. Comput. Modelling 22, 67 (1995)
42. Panetta, J.C.: A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competitive environment, Bull. Math. Biol. 88, 425 (1996)
43. Robert, J., Illiadia, A., Hoerni, B., Cano, J., Durand, M., Lagarde, C.: Pharmacokinetics of Adriamycin in Patients with Breast Cancer: Correlation Between Pharmacokinetic Parameters and Clinical Short-term Response, Eur. J. Cancer Clin. Oncol. 18, 739 (1982)
44. Sutherland, R.M., Durand, R.E.: Growth and cellular characteristics of multicell spheroids, Recent Results in Cancer Research 95, 24 (1984)
45. Siemers, N.O., Kerr, D.E., Yarnold, S., Stebbins, M., Vrudgyka, V.M., Hellstrom, I., Hellstrom, K.E., Senter, P.D.: L49-sFv-β-Lactamase, a single chain anti-p97 antibody fusion protein, Bioconjugate Chem. 8, 510 (1997)
46. Ward, J.P., King, J.R.: Mathematical modeling of avascular-tumor growth, IMA J. Math. Appl. Med. Biol. 14, 39 (1997)