The Non-Uniform Spatial Development of a Micrometastasis

This paper presents a mathematical model for the growth of a cancer micrometastasis in the form of a vascular cuff. The model postulates the possibility of a local imbalance between the rate of cell proliferation and the rate of cell death through apoptosis which is taken as dependent on the concentration of an angiogenesis-inhibitor such as angiostatin. This imbalance produces non-zero cell velocities within the micrometastasis. The local cell velocity is related to an interstitial pressure gradient through a Darcy′s Law type of equation, and the spatio-temporal development of the micrometastasis in an environment with a non-uniform nutrient concentration is followed by treating its outer boundary as an advancing front.