From Mutation to Metastasis: The Mathematical Modelling of the Stages of Tumour Development

摘要: Cancer is a complicated multi-stage process beginning at the intra-cellular level of genetic mutation processing to inter-cellular and then in some cases inter-organ (metastasis). There are three well-recognised carcinogenic agents which known directly cause tumour growth animals or induce cell transformation purposeless proliferation vitro-viruses, chemical carcinogens radiation. The mutations occurring single lead among other things transformed cells escaping normal control mechanisms. This turn, coupled with favourable local environment adequate nutrient supply, leads formation rapidly growing mass tissue — solid tumour. In case malignant tumour, such as carcinoma, this early remains avascular limited size few millimeters diameter (cf. multicellular spheroids). may secrete certain chemicals (angiogenic factors) neighbouring blood vessels form well-organised capillary network grows toward connects primary Once supplied its own micro-circulation invasive possible spread distant parts body via lymph systems. chapter presents mathematical models describing growth, angiogenesis pre-invasive growth.