Scaling laws and thermodynamic analysis for vascular branching of microvessels

When blood flows through small vessels, the two-phase nature of blood as a suspension of red cells (erythrocytes) in plasma cannot be neglected, and with decreasing vessel size, a homogeneous continuum model become less adequate in describing blood flow. Following the Haynes’ marginal zone theory, and viewing the flow as the result of concentric laminae of fluid moving axially, the present work provides models for fluid flow in dichotomous branching composed by larger and smaller vessels, respectively. Expressions for the branching sizes of parent and daughter vessels, that provides easier flow access, are obtained by means of a constrained optimization approach using the Lagrange multipliers. This study shows that when blood behaves as a Newtonian fluid, Hess – Murray law that states that the daughters-to-parent diameter ratio must equal to 2^(-1/3) is valid. However, when the nature of blood as a suspension becomes important, the expression for optimum branching diameters of vessels is dependent on the separation phase lengths. It is also shown that the same effect occurs for the relative lengths of daughters and parent vessels. For smaller vessels (e. g., arterioles and capillaries), it is found that the daughters-to-parent diameter ratio may varies from 0,741 to 0,849, and the daughters-to-parent length ratio varies from 0,260 to 2,42. For larger vessels (e. g., arteries), the daughters-to-parent diameter ratio and the daughters-to-parent length ratio range from 0,458 to 0,819, and from 0,100 to 6,27, respectively. In this paper, it is also demonstrated that the entropy generated when blood behaves as a single phase fluid (i. e., continuum viscous fluid) is greater than the entropy generated when the nature of blood as a suspension becomes important. Another important finding is that the manifestation of the particulate nature of blood in small vessels reduces entropy generation due to fluid friction, thereby maintaining the flow through dichotomous branching vessels at a relatively lower cost.

First report on Meloidogyne chitwoodi hatching inhibition activity of essential oils and essential oils fractions

The Columbia root-knot nematode (CRKN), Meloidogyne chitwoodi, is an EPPO A2 type quarantine pest since 1998. This nematode causes severe damage in economically important crops such as potato and tomato, making agricultural products unacceptable for the fresh market and food processing. Commonly used nematicidal synthetic chemicals are often environmentally unsafe. Essential oils (EOs) may constitute safer alternatives against RKN. EOs, isolated from 56 plant samples, were tested against CRKN hatching, in direct contact bioassays. Some of the most successful EOs were fractionated and the hydrocarbon molecules (HM) and oxygen-containing molecules (OCM) fractions tested separately. 24 EOs displayed very strong hatching inhibitions (≥90 %) at 2 µL mL−1 and were further tested at lower concentrations. Dysphaniaambrosioides, Filipendula ulmaria, Ruta graveolens, Satureja montana and Thymbra capitata EOs revealed the lowest EC50 values (<0.15 µL mL−1). The main compounds of these EOs, namely 2-undecanone, ascaridol, carvacrol, isoascaridol, methyl salicylate, p-cymene and/or γ-terpinene, were putatively considered responsible for CRKN hatching inhibition. S. montana and T. capitata OCM fractions showed hatching inhibitions higher than HM fractions. The comparison of EO and corresponding fractions EC50 values suggests interactions between OCM and HM fractions against CRKN hatching. These species EOs showed to be potential environmentally friendly CRKN hatching inhibitors; nonetheless, bioactivity should be considered globally, since its HM and OCM fractions may contribute, diversely, to the full anti-hatching activity.