Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.

We study numerically liquid-vapor phase separation in two-dimensional, nonisothermal, van der Waals (vdW) liquid drops using the method of smoothed particle hydrodynamics (SPH). In contrast to previous SPH simulations of drop formation, our approach is fully adaptive and follows the diffuse-interface model for a single-component fluid, where a reversible, capillary (Korteweg) force is added to the equations of motion to model the rapid but smooth transition of physical quantities through the interface separating the bulk phases. Surface tension arises naturally from the cohesive part of the vdW equation of state and the capillary forces. The drop models all start from a square-shaped liquid and spinodal decomposition is investigated for a range of initial densities and temperatures. The simulations predict the formation of stable, subcritical liquid drops with a vapor atmosphere, with the densities and temperatures of coexisting liquid and vapor in the vdW phase diagram closely matching the binodal curve. We find that the values of surface tension, as determined from the Young-Laplace equation, are in good agreement with the results of independent numerical simulations and experimental data. The models also predict the increase of the vapor pressure with temperature and the fitting to the numerical data reproduces very well the Clausius-Clapeyron relation, thus allowing for the calculation of the vaporization pressure for this vdW fluid.

The rapid evaporation and explosive boiling of a van der Waals (vdW) liquid drop in microgravity is simulated numerically in two-space dimensions using the method of smoothed particle hydrodynamics. The numerical approach is fully adaptive and incorporates the effects of surface tension, latent heat, mass transfer across the interface, and liquid-vapor interface dynamics. Thermocapillary forces are modeled by coupling the hydrodynamics to a diffuse-interface description of the liquid-vapor interface. The models start from a nonequilibrium square-shaped liquid of varying density and temperature. For a fixed density, the drop temperature is increased gradually to predict the point separating normal boiling at subcritical heating from explosive boiling at the superheat limit for this vdW fluid. At subcritical heating, spontaneous evaporation produces stable drops floating in a vapor atmosphere, while at near-critical heating, a bubble is nucleated inside the drop, which then collapses upon itself, leaving a smaller equilibrated drop embedded in its own vapor. At the superheat limit, unstable bubble growth leads to either fragmentation or violent disruption of the liquid layer into small secondary drops, depending on the liquid density. At higher superheats, explosive boiling occurs for all densities. The experimentally observed wrinkling of the bubble surface driven by rapid evaporation followed by a Rayleigh-Taylor instability of the thin liquid layer and the linear growth of the bubble radius with time are reproduced by the simulations. The predicted superheat limit $\left(T_s\approx 0.96\right)$ is close to the theoretically derived value of $T_s=1$ at zero ambient pressure for this vdW fluid.