[30]][“I Inhibitor”

This idea is based on the assumption that the tip cells serve to guide the EC, which form the sprouts immediately behind the tip.This approach has several advantages: it can account for the experimental observation that EC proliferation occurs mainly near the tip of the vasculature and is rather infrequent in the main body of the growing vasculature, and have pursued this approach with a onedimensional model describing the density in the sprout.In this model the tumor is atx and the parent vessel is dynamics of TAF concentration, EC density at the tip of the vasculature, and EC atx. The governing equations for the tip densityn, measured in units of length per unit area, and the TAF concentrationc nt tct x D nnD x n x cxx c c aH ektktn n represents branching, the third describes proliferation, and the fourth describes the loss of tip cells to vessel anastomosis.Proliferation of the tip cells is supposed to stop when the TAF concentration is below the threshold. Note however that there is no conversion of tip cells to vessel cells; the vessel density changes only due to the motion of the tip N.In effect it is supposed that cells are added to a growing vessel only at the parent vessel at a rate which is specied at the boundary, and cells move outward at a rate dictated by the movement of the tip.Thus, vessel density will decrease if the tip speeds up.It is somewhat unrealistic to assume that the consumption of a unit of TAF produces precisely the same change in the tip density; more generally another proportionality coefcient expressing the yield per unit of TAF would be expected in the rst equation.In all cases, the TAF dynamics are very fast, and when the TAF decay rate is low the tumor becomes vascularized, as judged by the fact that tip cells reach the boundary.In contrast, when the TAF decay rate is high vascularization is prevented. Also, in both cases where vascularization is achieved, the maximum of the tip density leads that of the vessel density, which suggests that this model can capture the brushborder effect.Despite the fact that the model can correctly predict the effect of the TAF decay rate on vascularization, it also predicts that vascularization is possible even if EC proliferation is absent, which Atenolol contradicts experimental observations that show EC proliferation is necessary for the vasculature to reach the tumor.However there are difculties if the model is extended to two or three space dimensions.Firstly it is not clear how to generalize the source of new vessel cells, since the rst two terms in represent a ux in one Flumazenil dimension, but this would be replaced by a vector quantity in higher dimensions, projected onto a particular direction.Despite these shortcomings, this model has some rather unique features, since it is the only continuum model to explicitly account for branching as a process by which new sprouts are created from capillary cells, and anastomosis as a process by which tip cells from one sprout merge with capillary cells from another sprout.

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