Abstract.
The early development of solid tumours has been extensively studied, both experimentally via the multicellular spheroid assay, and theoretically using mathematical modelling. The vast majority of previous models apply specifically to multicell spheroids, which have a characteristic structure of a proliferating rim and a necrotic core, separated by a band of quiescent cells. Many previous models represent these as discrete layers, separated by moving boundaries. Here, the authors develop a new model, formulated in terms of continuum densities of proliferating, quiescent and necrotic cells, together with a generic nutrient/growth factor. The model is oriented towards an in vivo rather than in vitro setting, and crucially allows for nutrient supply from underlying tissue, which will arise in the two-dimensional setting of a tumour growing within an epithelium. In addition, the model involves a new representation of cell movement, which reflects contact inhibition of migration. Model solutions are able to reproduce the classic three layer structure familiar from multicellular spheroids, but also show that new behaviour can occur as a result of the nutrient supply from underlying tissue. The authors analyse these different solution types by approximate solution of the travelling wave equations, enabling a detailed classification of wave front solutions.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 28 January 2000 / Revised version: 7 November 2000 / Published online: 21 August 2001
Rights and permissions
About this article
Cite this article
Sherratt, J., Chaplain, M. A new mathematical model for avascular tumour growth. J Math Biol 43, 291–312 (2001). https://doi.org/10.1007/s002850100088
Issue Date:
DOI: https://doi.org/10.1007/s002850100088