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Cancer dynamics are an evolutionary game between cellular phenotypes. A typical assumption in this modelling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard for local neighbourhood structure. We address this limitation by using the Ohtsuki-Nowak(More)
Since the discovery of tumour initiating cells (TICs) in solid tumours, studies focussing on their role in cancer initiation and progression have abounded. The biological interrogation of these cells continues to yield volumes of information on their pro-tumourigenic behaviour, but actionable generalised conclusions have been scarce. Further, new(More)
BACKGROUND Tumours are made up of a mixed population of different types of cells that include normal structures as well as ones associated with the malignancy, and there are multiple interactions between the malignant cells and the local microenvironment. These intercellular interactions, modulated by the microenvironment, effect tumour progression and(More)
Two models of circulating tumour cell (CTC) dynamics have been proposed to explain the phenomenon of tumour 'self-seeding', whereby CTCs repopulate the primary tumour and accelerate growth: primary seeding, where cells from a primary tumour shed into the vasculature and return back to the primary themselves; and secondary seeding, where cells from the(More)
Elderly patients have largely been excluded from randomized trials for glioblastoma multiforme (GBM). We reviewed the results of treatment approaches, which included surgery, chemotherapy, and radiation in this group of patients. Patients were treated during the period 1979-2007 and were 70 years of age and older with histologically confirmed GBM. Overall(More)
Metastatic castrate resistant prostate cancer (mCRPC) is responsible for the majority of prostate cancer deaths with the median survival after diagnosis being 2 years. The metastatic lesions often arise in the skeleton, and current treatment options are primarily palliative. Using guidelines set forth by the National Comprehensive Cancer Network (NCCN), the(More)
Intratumoural heterogeneity is known to contribute to poor therapeutic response. Variations in oxygen tension in particular have been correlated with changes in radiation response in vitro and at the clinical scale with overall survival. Heterogeneity at the microscopic scale in tumour blood vessel architecture has been described, and is one source of the(More)
The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we consider a simple model of evolution in asexually reproducing populations which considers adaptation as a biased random walk on a fitness landscape. This model associates the global properties of the fitness(More)
Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic,(More)