Fluid transport in vascularized tumours and metastasis

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 15, Issue 1, 1998, Pages 53-63

  Sleeman, B D ^a   Nimmo, H R ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Intestitial pressure; Transport of drugs; Vascularized tumours

Indexed keywords

ARTICLE; FLUID TRANSPORT; MATHEMATICAL MODEL; METASTASIS; NEOVASCULARIZATION (PATHOLOGY); PRESSURE VOLUME CURVE; SOLID TUMOR; TISSUE PRESSURE; TUMOR GROWTH;

TRANSPORT PROPERTIES;

BAXTER MODELS; CONDITION; FLUID TRANSPORT; GIBBS-THOMSON; INTERSTITIALS; INTESTITIAL PRESSURE; PERTURBATION ANALYSIS; TRANSPORT OF DRUG; TUMOR GROWTH; VASCULARIZED TUMOR;

TUMORS;

EID: 0031777161     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb15.1.53     Document Type: Article

References (27)

1. ADAM, J. A., & NOREN, R. D. 1993 Equilibrium model of a vascularized spherical carcinoma with central necrosis - Some properties of the solution. J. Math. Biol. 31, 735-45.
2. ASTARITA, G. 1967 Mass Transfer with Chemical Reactions. Amsterdam: Elsevier.
3. BAXTER, L. T., & JAIN, R. K. 1989 Transport of fluid and macromolecules in tumours. I, Role of interstitial pressure and convection. Microvasc. Res. 37, 77-104.
4. BAXTER, L. T., & JAIN, R. K. 1990 Transport of fluid and macromolecules in tumours. II, Role of heterogeneous perfusion and lymphatics. Microvasc. Res. 40, 246-63.
5. BURN, D. S. 1994 Modelling of tumour angiogenesis in solid tumours. M.Sc. thesis University of Dundee.
6. CHAPLAIN, M. A. J., & SLEEMAN, B. D. 1993 Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory J. Math. Biol. 31, 431-73.
7. CHAPLAIN, M. A. J., & STUART, A. M. 1991 A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue. IMA J. Math. Appl. Med. Biol. 8, 191-220.
8. CHAPLAIN, M. A. J., GILES, S., SLEEMAN, B. D., & JARVIS, R. J. A. 1995 Mathematical analysis of a model of tumour angiogenesis. J. Math. Biol. 33, 744-70.
9. CURRY, F. E. (1984) Mechanics and thermodynamics of transcapillary exchange. In: Handbook of Physiology, Section 2: The cardiovascular system (E. M. Renkin & C. C. Michel, eds.), pp. 309-74. Bethesda, MD: American Physiology Society.
10. EPENETOS, A. A., SNOOK, D., DURBIN, H., JOHNSON, P. H., & TAYLOR-PAPADMITRIOU, J. 1986 Limitations of radio labeled monoclonal antibodies for localization of human neoplasms. Cancer Res. 46, 3183-91.
11. FOLKMAN, J. 1974 Tumour angiogenesis. Adv. Cancer Res. 19, 331-8.
12. GREENSPAN, H. P. 1972 Models of the growth of a solid tumour by diffusion. Stud. Appl. Math. 51, 317-40.
13. GROSS, J. F., & POPEL, A. S. 1979 Mathematical models of transport phenomena in normal and neoplastic tissue. In: Tumour Blood Circulation (H. I. Peterson, ed.), pp. 169-183. Boca Raton, FL: CRC Press.
14. JAIN, R. K. 1987a Transport of molecules in the tumour interstitium. Rev. Cancer Res. 47, 3039-51.
15. JAIN, R. K. 1987b Transport of molecules across tumour vasculature. Cancer Metastasis Rev. 6, 559-94.
16. JAIN, R. K. 1988 Determinants of tumour blood flow. Rev. Cancer Res. 48, 2641-58.
17. JAIN, R. K. 1994 Barrier to drug delivery in solid tumours. Sci. Am. 271, 58-65.
18. JAIN, R. K., & BAXTER, L. T. 1988 Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumour: Significance of elevated interstitial pressure. Cancer Res. 48, 7022-32.
19. JAIN, R. K., & WARD-HARTLEY, K. 1984 Tumour blood-flow characterization modifications and role in hyperthermia. IEEE. Trans. Sonics Ultrason. 31, 504-26.
20. JONES, P. K., GALLAGHER, B. M., & SANDS, H. 1986 Autoradiographic analysis of monoclonal antibody distribution in human colon and breast tumour xenografts. Cancer Immunol. Immunother. 22, 139-43.
21. KOHLER, M., & MILSTEIN, C. 1975 Continuous cultures of the fused cells secreting antibody of predefined specifity. Nature 256, 494-7.
22. NIMMO, H. R. 1996 Modelling of tumour vascularization and internal pressure in solid tumours, M.Sc. thesis. University of Dundee.
23. SANDS, H., JONES, P. K., SHAH, S. A., PLAME, D., VESSELLA, R. L., & GALLAGHER, B. M. 1988 Correlation of vascular permeability and blood flow with monoclonal antibody uptake by human clouser and renol cell xenografts. Cancer Res. 48, 188-93.
24. SLEEMAN, B. D., BURN, D. S., & NIMMO, H. R. 1996 Endothelial cell response to tumour angiogenesis. Submitted.
25. STARLING, E. H. 1896 On the absorption of fluids from the convective tissue spaces. J. Physiol. 19, 312-26.
26. SUTHERLAND, R. M. 1988 Cell and environment interactions in tumour micro-regions: The multicell spherical model. Science 240, 177-84.
27. SUTHERLAND, R., BUCHEGGER, F., SCHREYER, M., VACCA, A., & MACH, J. P. 1987 Penetration and binding of radio labelled anti-carcinoembryonic antigen monoclonal antibodies and their antigen binding fragments in human colon multicellular tumour spheriods. Cancer Res. 47, 1627-33.