Mathematical modelling of tumour cords

• Autorzy: Bertuzzi A. , Fasano A. , Gandolfi A.
• Języki publikacji: EN

Abstrakty

EN

In some tumours, cylindrical arrangements of tumour cells growing around blood vessels (tumour cords) have been observed. In this paper we review some mathematical models aimed to describe the cell kinetics of the tumour cell population within a cord assumed to be at the steady state, and the dynamics of these structures, in particular after cytotoxic treatments. The models here considered view the cell population as a continuum and take into account cell motion.

Słowa kluczowe

EN

tumour growth; cell kinetics; mathematical models

PL

wzrost guza; kinetyka komórek; modele matematyczne

• Wydawca: University of Silesia, Institute of Informatics, Computer Systems Department
• Czasopismo: Journal of Medical Informatics & Technologies
• Rocznik: 2001
• Tom: Vol. 2, Part. 1
• Strony: IP23--IP31
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Bertuzzi A.

• Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185 Roma, Italy

autor

Fasano A.

• Dipartimento di Matematica "U. Dini", Univerisita di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy

autor

Gandolfi A.

• Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185 Roma, Italy

Bibliografia

• [1] BERTUZZI A., GANDOLFI A., Cell kinetics in a tumour cord, J. theor. Biol., Vol. 204, pp. 587-599, 2000.
• [2] BERTUZZI A., FASANO A., GANDOLFI A., A mathematical model for the growth of tumor cords incor-porating the dynamics of a nutrient. In: Free Boundary Problems: Theory and Applications. II (Kenmochi N., Ed.), pp. 31-46, Gakkotosho, Tokyo, 2000.
• [3] BERTUZZI A., FASANO A., GANDOLFI A., MARANGI D., Cell kinetics in tumour cords studied by a model with variable cell cycle length, International Conference DESTOBIO 2000, West Lafayette, IASI-CNR Report R. 536, 2000, submitted for publication.
• [4] BERTUZZI, A., FASANO, A., GANDOLFI, A., Analysis of a mathematical model for tumour cords including spatially distributed spontaneous or treatment-induced cell death, submitted for publication. [5] FOLKMAN J., Tumor angiogenesis, Adv. Cancer Res., Vol. 43, pp. 175-203, 1985.
• [6] HIRST D.G., DENEKAMP J., Tumour cell proliferation in relation to the vasculature, Cell Tissue Kinet., Vol. 12, pp. 31-42, 1979.
• [7] MOORE J.V., HOPKINS H.A., LOONEY W.B., Tumour-cord parameters in two rat hepatomas that differ in their radiobiological oxygenation status, Radiat. Environ. Biophys., Vol. 23, pp. 213-222, 1984.
• [8] MOORE J.V., HOPKINS H.A., LOONEY W.B., Response of cell populations in tumor cords to a single dose of cyclophosphamide or radiation, Eur. J. Cancer Clin. Oncol., Vol. 19, pp. 73-79, 1983.
• [9] TAKAHASHI, M., Theoretical basis for cell cycle analysis. II. Further studies on labelled mitosis wave method, J. Theor. Biol., Vol. 18, pp. 195-209, 1968.
• [10] TANNOCK I.F., The relation between cell proliferation and the vascular system in a transplanted mouse mammary tumour, Br. J. Cancer, Vol. 22, pp. 258-273, 1968.