Dynamics of tumor growth and combination of anti-angiogenic and cytotoxic therapies

Physics in Medicine and Biology

Volumn 52, Issue 13, 2007, Pages 3665-3677

  Kohandel, M ^a,b   Kardar, M ^c   Milosevic, M ^d,e   Sivaloganathan, S ^a,b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b FIELDS INSTITUTE   (Canada)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d PRINCESS MARGARET HOSPITAL   (Canada)

^e UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BLOOD VESSELS; CELLS; CHEMOTHERAPY; COMPUTER SIMULATION; CYTOTOXICITY; MATHEMATICAL MODELS; NUTRIENTS; OXYGEN; RADIOTHERAPY;

ANGIOGENIC; ANTI-ANGIOGENIC THERAPY; TREATMENT STRATEGIES; TUMOR VASCULATURE;

TUMORS;

ANGIOGENESIS INHIBITOR;

ARTICLE; CANCER RADIOTHERAPY; MATHEMATICAL MODEL; PRIORITY JOURNAL; TUMOR CELL; TUMOR GROWTH; TUMOR VASCULARIZATION;

ALGORITHMS; ANGIOGENESIS INHIBITORS; HUMANS; MODELS, STATISTICAL; MODELS, THEORETICAL; NEOPLASMS; NEOVASCULARIZATION, PATHOLOGIC; NORMAL DISTRIBUTION;

EID: 34250345272     PISSN: 00319155     EISSN: 13616560     Source Type: Journal    
DOI: 10.1088/0031-9155/52/13/001     Document Type: Article

References (45)

1. Alarcon T, Byrne H M and Maini P K 2004 Towards whole-organ modelling of tumour growth Prog. Biophys. Mol. Biol. 85 451-72
2. Anderson A R A 2005 A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion Math. Med. Biol. 22 163-86
3. Anderson A R A and Chaplain M A J 1998 Continuous and discrete mathematical models of tumor-induced angiogenesis Bull. Math. Biol. 60 857-99
4. Baish J W and Jain R K 2000 Fractals and cancer Cancer Res. 60 3683-8
5. Bergers G and Benjamin L E 2003 Tumorigenesis and the angiogenic switch Nat. Rev. Cancer 3 401-10
6. Bristow R G and Hill R P 2005 Molecular and cellular basis of radiotherapy The Basic Science of Oncology 4th edn ed I F Tannock (New York: McGraw-Hill) pp 261-88
7. Bussink J, Kaanders J H, Rijken P F, Raleigh J A and Van der Kogel A J 2000 Changes in blood perfusion and hypoxia after irradiation of a human squamous cell carcinoma xenograft tumor line Radiat. Res. 153 398-404
8. Carmeliet P and Jain R K 2000 Angiogenesis in cancer and other diseases Nature 407 249-57
9. Clatz O et al 2005 Realistic simulation of the 3D growth of brain tumors in MR images coupling diffusion with biomechanical deformation IEEE Trans. Med. Imaging 24 1334-46
10. Fenton B M, Paoni S F and Ding I 2004 Effect of VEGF receptor-2 antibody on vascular function and oxygenation in spontaneous and transplanted tumors Radiol. Oncol. 72 221-30
11. Folkman J 1971 Tumor angiogenesis: therapeutic implications N. Engl. J. Med. 285 1182-86
12. Fuite J, Marsh R and Tuszynski J 2002 Fractal pharmacokinetics of the drug mibefradil in the liver Phys. Rev. E 66 021904
13. Halpin-Healy T and Zhang Y-C 1995 Kinetic roughening phenomena, stochastic growth, directed polymers and all that Phys. Rep. 254 215-414
14. Hicklin D J and Ellis L M 2005 Role of vascular endothelial growth factor pathway in tumor growth and angiogenesis J. Clin. Oncol. 23 1011-27
15. Jain R K 2001 Normalizing tumor vasculature with anti-angiogenic therapy: a new paradigm for combination therapy Nature Med. 7 987-89
16. Jain R K 2005 Normalizing tumor vasculature: an emerging concept in anti-angiogenic therapy Science 307 58-62
17. Karalis V and Macheras P 2004 Drug disposition viewed in terms of the fractal volume of distribution Pharm. Res. 19 696-703
18. Kennedy A S et al 1997 Proliferation and hypoxia in human squamous cell carcinoma of the cervix: first report of combined immunohistochemical assays Int. J. Radiat. Oncol. Biol. Phys. 37 897-905
19. Kerbel R S and Kamen B A 2004 The anti-angiogenic basis of metronomic chemotherapy Nature Rev. Cancer 4 423-36
20. Leo C, Giaccia A J and Denko N C 2004 The hypoxic tumor microenvironment and gene expression Semin. Radiat. Oncol. 14 207-14
21. Ma J, Pulfer S, Li S, Chu J, Reed K and Gallo J M 2001 Pharmacodynamic-mediated reduction of temozolomide tumor concentrations by the angiogenesis inhibitor TNP-470 Cancer Res. 61 5491-98
22. Macheras P 1996 A fractal approach to heterogeneous drug distribution: calcium pharmacokinetics Pharm. Res. 13 663-70
23. Manoussaki D, Lubkin S R, Vernon R B and Murray J D 1996 A mechanical model for the formation of vascular networks in vitro Acta Biotheor. 44 271-82
24. Mantzaris N V, Webb S and Othmer H G 2004 Mathematical modeling of tumor-induced angiogenesis J. Math. Biol. 49 111-87
25. McDougall S R, Anderson A R A and Chaplain M A J 2006 Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: clinical implications and therapeutic targeting strategies J. Theor. Biol. 241 564-89
26. McDougall S R, Anderson A R A, Chaplain M A J and Sherratt J A 2002 Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies Bull. Math. Biol. 64 673-702
27. Milosevic M, Fyles A, Hedley D and Hill R 2004 The human tumor microenvironment: invasive (needle) measurement of oxygen and interstitial fluid pressure Semin. Radiat. Oncol. 14 249-58
28. Murata R, Nishimura Y and Hiraoka M 1997 An antiangiogenic agent (TNP-470) inhibited reoxygenation during fractionated radiotherapy of murine mammary carcinoma Int. J. Radiat. Oncol. Biol. Phys. 37 1107-13
29. Murray J D 2003 Mathematical Biology 3rd edn (New York: Springer)
30. O'Reily M S 2006 Radiation combined with antiangiogenic and antivascular agents Semin. Radiat. Oncol. 16 45-50
31. Rofstad E K, Henriksen K, Galappathi K and Mathiesen B 2003 Antiangiogenic treatment with thrombospondin-1 enhances primary tumor radiation response and prevents growth of dormant pulmonary micrometastases after curative radiation therapy in human melanoma xenografts Cancer Res. 63 4055-61
32. Scalerandi M and Sansone B C 2002 Inhibition of vascularization in tumor growth Phys. Rev. Lett. 89 218101
33. Serini G, Ambrosi D, Giraudo E, Gamba A, Preziosi L and Bussolino F 2003 Modeling the early stages of vascular network assembly EMBO J. 22 1171-79
34. Stein A M, Demuth T, Mobley D, Berens M and Sander L M 2007 A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment Biophys. J. 92 356-65
35. Stéphanou A, McDougall S R, Anderson A R A and Chaplain M A J 2005 Mathematical modelling of flow in 2D and 3D vascular networks: applications to anti-angiogenic and chemotherapeutic drug strategies Math. Comput. Model 41 1137-56
36. Subarsky P and Hill R 2003 The hypoxic tumour microenvironment and metastatic progression Clin. Exp. Metastasis 20 237-50
37. Swanson K R, Bridge C, Murray J D and Alvord E C Jr 2003 Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion J Neurol. Sci. 216 1-10
38. Tannock I F 1968 The relation between cell proliferation and the vascular system in a transplanted mouse mammary tumour Br. J. Cancer 22 258-73
39. Teicher B A 1996 A systems approach to cancer Cancer Metastasis Rev. 15 247-72
40. Tong R T, Boucher Y, Kozin S V, Winkler F, Hicklin D J and Jain R K 2004 Vascular normalization by vascular endothelial growth factor receptor 2 blockade induces a pressure gradient across the vasculature and improves drug penetration in tumors Cancer Res. 64 3731-6
41. Vaupel P 1989 Blood flow, oxygen and nutrient supply, and metabolic microenvironment of human tumors: a review Cancer Res. 49 6449-65
42. Willett C G et al 2004 Direct evidence that the VEGF-specific antibody bevacizumab has antivascular effects in human rectal cancer Nature Med. 10 145-47
43. Winkler F et al 2004 Kinetics of vascular normalization by VEGFR2 blockade governs brain tumor response to radiation: role of oxygenation, angiopoietin-1, and matrix metalloproteinases Cancer Cell 6 553-63
44. Yancopoulos G D, Davis S, Gale N W, Rudge J S, Wiegand S J and Holash J 2000 Vascular-specific growth factors and blood vessel formation Nature 407 242-48
45. Zips D et al 2003 Experimental study on different combination schedules of VEGF-receptor inhibitor PTK787/ZK222584 and fractionated irradiation Anticancer Res. 23 3869-76