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Published on Oct 26, 2010
Tumour growing in a 1 cm x 1 cm section of simulated brain tissue, including white matter, grey matter, cerebrospinal fluid (black), and cranium (white). There is extensive nonlinear feedback between the extracellular matrix density and its degradation by the tumour, the tissue's biomechanical properties, the resulting tumour growth profile, and the distribution of oxygen and hypoxia in and around the tumour. Note the preferential growth of the tumour along regions of least biomechanical resistance.
Upper left: red = viable tumour region. blue = hypoxic tumour cells. brown = necrotic tumour cells.
Upper middle: Extracellular matrix (ECM) density. Note the growing hole (blue) in the ECM, due to the secretion of matrix degrading enzymes (MDEs) by the tumour (lower middle).
Upper right: Oxygen is released by the pre-existing vasculature in non-degraded tissue, which perfuses through the tissue domain.
Lower left: Distribution of biomechanical pressure generated by the growing tumor (bright red peaks in regions of rapid proliferation correlating with high oxygen). Necrosis provides a mechanical stress relief (blue regions in interior). The tissue's mechanical compliance (Darcy coefficient) is directly dependent upon the ECM density.
Lower middle: Secretion of matrix metalloproteinases by the tumour, which degrade the nearby tissue and any pre-existing vessels contained therein.
Lower right: Hypoxic regions of the tumour secrete tumour-angiogenic growth factors (TAFs), such as VEGF. These stimulate angiogenesis (not included in this simulation).
Method: Level set representation of moving sharp tumor-microenvironment interface, with a Darcy's law representation of the biomechanics. Oxygen transport governed by nonlinear quasi-steady reaction-diffusion equation.