ANZIAM J. 46(E) pp.C902--C917, 2005.
A numerical simulation of avascular tumour growth
Tan Liang Soon | Ang Keng Cheng |
Abstract
We develop and calibrate a mathematical model for avascular tumour growth. The model is formulated as a set of partial differential equations describing the spatio-temporal changes in cell concentrations based on reaction-diffusion dynamics and the law of mass conservation. Unlike existing models, the current model takes into account the dependence of the cell proliferation rate on the growth inhibiting factors secreted by necrotic cells; furthermore, the model incorporates an element of random variation to the mitotic rate and nutrient supply. The model is solved using standard finite difference techniques. Results obtained from the simulation compare well with published experimental data. The biological and clinical implications of these results are also discussed.
Download to your computer
- Click here for the PDF article (385 kbytes) We suggest printing 2up.
- Click here for its BiBTeX record
Authors
- Tan Liang Soon
- Ang Keng Cheng
- National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616. mailto:shan@ri.sch.edu.sg
Published September 7, 2005, amended September 8, 2005. ISSN 1446-8735
References
- Ang, K. C. and Tan, L. S.: An avascular tumour model with random variation, 8th ATCM conference proceedings, 1, 153--161 (2003). http://epatcm.any2any.net/EP/2003/2003C173/abstract.html
- Balazs, H., Andraz, C., Ilona, F., Tamas, M., Emilia, M. and Tamas, V.: Locomotion and proliferation of glioblastoma cells in vitro: statistical evaluation of videomicroscopic observations. J. Neurosurg., 92, 428--434 (2000). http://angel.elte.hu/pdf/glioma.pdf
- Chandrasekar, N., Jasti S. R., Arnout C. R., Lauren A. L.and Mandri, O.: Growth characteristics of glioblastoma spheroids, Int. J. Oncology, 19, 1109--1115 (2001).
- Freyer, J. P.: Role of necrosis in regulating the growth saturation of multicellular spheroids, Cancer Res., 48, 2432--2439 (1988). http://cancerres.aacrjournals.org/cgi/content/abstract/48/9/2432
- Helmlinger, G., Netti, P. A., Lichtenbeld, H. C., Melder, R. J. and Jain R. K.: Solid stress inhibits the growth of multicellular tumor spheroids, Nature Biotech, 15, 778--783 (1997). http://dx.doi.org/10.1038/nbt0897-778
- Hystad, M. E., Rofstad, E. K.: Oxygen consumption rate and mitochondrial density in human melanoma monolayer cultures and multicellular spheroids, Int. J. Cancer, 57, 532--537 (1994).
- Sherratt, J. A., Chaplain, M. A. J.: A new mathematical model for avascular tumour growth, J. Math. Biol., 43, 291--312 (2001). http://dx.doi.org/10.1007/s002850100088
- Sutherland, R. M.: Cell and environment interaction in tumour microregions: The multicell spheroid model, Science, 240, 177--184 (1988).
- Ward, J. P., King, J. R.: Mathematical modelling of avascular tumour growth, IMA J. Math. Appl. Med. Biol., 14, 39--70 (1997). http://dx.doi.org/10.1093/imammb/14.1.39
- Ward, J. P., King, J. R.: Mathematical modelling of avascular-tumour growth II: modelling growth saturation, IMA J. Math. Appl. Med. Biol., 16, 171--211 (1999). http://dx.doi.org/10.1093/imammb/16.2.171