A generalized optimization principle for asymmetric branching in fluidic networks

In silico analysis of a hierarchical microfluidic vascular network: Detecting the location of angiogenic sprouting

Lack of oxygen is one of the leading causes of failure in engineered tissue. Therefore, angiogenesis will be necessary for the survival of larger tissues in vivo. In addition, a proper lymphatic system that plays an essential role in relieving inflammation and maintaining tissue homeostasis is of great importance for tissue regeneration and repair. Many biomechanical parameters are involved in controlling angiogenesis and capillary network generation, which are challenging to study and control in experimental studies or in vitro. In the present study, using numerical modeling, the effect of various geometric and biomechanical parameters in creating suitable conditions for angiogenesis was investigated. Furthermore, sprouting points were predicted using flow dynamics. For this purpose, a porous scaffold, flow channels with parametric geometry that followed Murray's law, and a drainage channel were considered. Results suggested that the geometry of the microfluidic channels and the characteristics of the vessel wall and scaffold plays a complementary role in determining the transmural pressure. It was found that a twofold increase in the vascular hydraulic conductivity can reduce the minimum transmural pressure by up to 28% and increase the drainage flow rate by 44%. In addition, the minimum magnitude of transmural pressure tends to zero for scaffold's hydraulic conductivity values smaller than 10^-11  m³ s kg^-1 . The results of this study can be used in optimizing the design of the relevant microfluidic systems to induce angiogenesis and avoid leakage in the constructed implantable tissue.

Vessel scaling in evergreen angiosperm leaves conforms with Murray's law and area-filling assumptions: implications for plant size, leaf size and cold tolerance

Water transport in leaf vasculature is a fundamental process affecting plant growth, ecological interactions and ecosystem productivity, yet the architecture of leaf vascular networks is poorly understood. Although Murray's law and the West-Brown-Enquist (WBE) theories predict convergent scaling of conduit width and number, it is not known how conduit scaling is affected by habitat aridity or temperature. We measured the scaling of leaf size, conduit width and conduit number within the leaves of 36 evergreen Angiosperms spanning a large range in aridity and temperature in eastern Australia. Scaling of conduit width and number in midribs and 2° veins did not differ across species and habitats (P > 0.786), and did not differ from that predicted by Murray's law (P = 0.151). Leaf size was strongly correlated with the hydraulic radius of petiole conduits (r²  = 0.83, P < 0.001) and did not differ among habitats (P > 0.064), nor did the scaling exponent differ significantly from that predicted by hydraulic theory (P = 0.086). The maximum radius of conduits in petioles was positively correlated with the temperature of the coldest quarter (r²  = 0.67; P < 0.001), suggesting that habitat temperature restricts the occurrence of wide-conduit species in cold habitats.