Mark A. J. Chaplain

Learn More
Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial-cell migration, and organize themselves into a dendritic structure. Subsequent cell proliferation near the(More)
In this article a model for the evolution of a spherically symmetric, nonnecrotic tumor is presented. The effects of nutrients and inhibitors on the existence and stability of time-independent solutions are studied. With a single nutrient and no inhibitors present, the trivial solution, which corresponds to a state in which no tumor is present, persists for(More)
Angiogenesis, the growth of a network of blood vessels, is a crucial component of solid tumour growth, linking the relatively harmless avascular growth phase and the potentially fatal vascular growth phase. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration, proliferation; degradation of tissue; new(More)
In this paper, we present a theoretical investigation of the influence of blood flow through a tumour-induced capillary network, whereby the vascular architecture adapts as it grows to the associated haemodynamic forces resulting in what we describe as adaptive tumour-induced angiogenesis (ATIA). The network is generated in response to tumour angiogenic(More)
Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network. Subsequent cell proliferation near(More)
Solid tumours grow through two distinct phases: the avascular and the vascular phase. During the avascular growth phase, the size of the solid tumour is restricted largely by a diffusion-limited nutrient supply and the solid tumour remains localised and grows to a maximum of a few millimetres in diameter. However, during the vascular growth stage the(More)
Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven initially by endothelial cell migration, and organize themselves into a branched, connected network structure. Subsequent cell(More)
In this article, we present a new multiscale mathematical model for solid tumour growth which couples an improved model of tumour invasion with a model of tumour-induced angiogenesis. We perform nonlinear simulations of the multi-scale model that demonstrate the importance of the coupling between the development and remodeling of the vascular network, the(More)
Even after a tumor is established, it can early on enter a state of dormancy marked by balanced cell proliferation and cell death. Disturbances to this equilibrium may affect cancer risk, as they may cause the eventual lifetime clinical presentation of a tumor that might otherwise have remained asymptomatic. Previously, we showed that cell death,(More)
Gliomas are uniformly fatal forms of primary brain neoplasms that vary from low- to high-grade (glioblastoma). Whereas low-grade gliomas are weakly angiogenic, glioblastomas are among the most angiogenic tumors. Thus, interactions between glioma cells and their tissue microenvironment may play an important role in aggressive tumor formation and progression.(More)