A cellular Potts model analyzing differentiated cell behavior during in vivo vascularization of a hypoxic tissue

• An in vivo angiogenic process is modeled by a suitable version of the Cellular Potts Model.
• Vascular cells undergo phenotypic differentiations (i.e., from quiescent to stalk or tip).
• A fundamental mechanism is the chemotactic movement of tip cells.
• Stalk cells are characterized by a directionally preferential mitosis.
• The size of the hypoxic tissue only affects the duration of the process.

Angiogenesis, the formation of new blood vessel networks from existing capillary or post-capillary venules, is an intrinsically multiscale process occurring in several physio-pathological conditions. In particular, hypoxic tissue cells activate downstream cascades culminating in the secretion of a wide range of angiogenic factors, including VEGF isoforms. Such diffusive chemicals activate the endothelial cells (ECs) forming the external walls of the nearby vessels that chemotactically migrate toward the hypoxic areas of the tissue as multicellular sprouts. A functional network eventually emerges by further branching and anastomosis processes. We here propose a CPM-based approach reproducing selected features of the angiogenic progression necessary for the reoxygenation of a hypoxic tissue. Our model is able to span the different scale involved in the angiogenic progression as it incorporates reaction–diffusion equations for the description of the evolution of microenvironmental variables in a discrete mesoscopic cellular Potts model (CPM) that reproduces the dynamics of the vascular cells. A key feature of this work is the explicit phenotypic differentiation of the ECs themselves, distinguished in quiescent, stalk and tip. The simulation results allow identifying a set of key mechanisms underlying tissue vascularization. Further, we provide evidence that the nascent pattern is characterized by precise topological properties. Finally, we link abnormal sprouting angiogenesis with alteration in selected cell behavior.