A gradient-driven mathematical model of antiangiogenesis

In this paper, we present a mathematical model describing the angiogenic response of endothelial cells to a secondary tumour. It has been observed experimentally that while the primary tumour remains in situ, any secondary tumours that may be present elsewhere in the host can go undetected, whereas removal of the primary tumour often leads to the sudden appearance of these hitherto undetected metastases—so-called occult metastases. In this paper, a possible explanation for this suppression of secondary tumours by the primary tumour is given in terms of the presumed migratory response of endothelial cells in the neighbourhood of the secondary tumour. Our model assumes that the endothelial cells respond chemotactically to two opposing chemical gradients: a gradient of tumour angiogenic factor, set up by the secretion of angiogenic cytokines from the secondary tumour; and a gradient of angiostatin, set up in the tissue surrounding any nearby vessels. The angiostatin arrives there through the blood system (circulation), having been originally secreted by the primary tumour. This gradient-driven endothelial cell migration therefore provides a possible explanation of how secondary tumours (occult metastases) can remain undetected in the presence of the primary tumour yet suddenly appear upon surgical removal of the primary tumour.