Figure 8.

High IF velocity results in enhanced metastatic behavior. (a) The net cell velocity ${\mathbf{u}}_{\text{c}}$ has a strong upstream migration at the the rim of the primary tumor whereas at a certain distance away (at a “critical radius”) the tumor cells are guided outwardly. (b) Spreading due to dispersion. (c) The velocity component ${\mathbf{u}}_{c,\text{fluid}-\text{stress}}$ gives rise to some upstream migration at the primary tumor periphery. Note, however, that the same cell velocity component in fact also contributes to downstream migration of the small clusters that have broken loose. This must be understood in light of the positive slope of ${\widehat{f}}_{\text{c}}({\alpha }_{\text{c}})$ for very small cell volume fractions ${\alpha }_{\text{c}}$, see Fig. 1c. (d) The cell velocity due to autologous chemotaxis. The upstream migration is strong at the rim of the primary tumor due to the accumulation of chemokine in that region, see Fig. 7c.