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Angiogenesis, the formation of blood vessels, is a process whereby capillary sprout are formed in response to external stimuli. We model the tumor induced angiogenesis on keys events such of migratory response of endothelial cells to tumor angiogenic factors and the local cell interaction with the extracellular matrix (ECM). We consider the ECM medium as a statistically inhomogeneous two-phase random medium. Numerical simulations of the model are presented. Using this model, we will compare the influence of ECM distribution on vascular network formation. By developing mathematical models of angiogenesis, we hope to provide a deeper insight into the mechanisms underlying angiogenesis.

Three quantitative and non-invasive techniques were used to monitor angiogenesis in Kaposi's sarcoma patients: thermography, laser Doppler imaging (LDI), and near-infrared spectroscopy. Before and after combination cytotoxic and anti-angiogenesis therapy, blood volume, oxygenated hemoglobin, temperature, and blood flow were analyzed. These three techniques are objective, easy to perform, and appear to be very sensitive in assessing changes in the lesions upon administration of therapy.

In this study we are investigating three infrared imaging techniques, thermography, multispectral imaging and Laser Doppler imaging (LDI) to assess parameters of vascularity in lesions of Kaposi's sarcoma (KS) and response to therapy. Thermography, multispectral imaging and LDI were recorded over the lesion and compare to normal skin either adjacent to the lesion or on the contralateral side. The KS lesions generally had increased temperature, blood volume (as measured by multispectral imaging) and blood flux (as measured by LDI) as compare to normal skin. After the treatment with experimental antiKS drug, temperature, blood volume and blood flow of the lesion were significantly reduced from the baseline. These techniques hold promise to assess physiological parameter in KS lesion and their changes with therapy.