Optimization of branching pipelines on basis

Structure of the optimal rectangular microcirculatory cell of a leaf is investigated on the model of liquid motion through the bifurcating tubes with permeable walls and its filtration into the cell filled with anisotropic porous biological medium. The relation between the diameters of the tubes in the bifurcation as well as coordinates of the bifurcation point at given width and length of the cell which provides minimum total energy consumptions are obtained

Analysis of stress distribution and leaf blade bending during

Mechanical factors play an important role in plant tissues growth and development. Plant growth is tightly connected with cell divisions, new cell walls appearing and cell volumes increasing caused by turgor pressure and cell walls loosening and yielding. In biomechanics the plant tissue is considered as integral porous deformable skeleton of cell walls filled with viscous incompressible liquid (intracellular liquid and contents of plant vessels). Xylem sap moves through the xylem vessels, delivers mineral and regulatory components into cells and provides increasing of mass of the solid skeleton. The rate of cell growth is controlled by wall loosening caused by biochemical factors and wall yielding under the influence of the turgor pressure. The tissues consist of elements with different geometry and mechanical properties which are arranged in regular patterns

Computational Approach to Optimal Transport

Long-distance liquid transport in biosystems is provided by special branching systems of tubes (arteries, veins, plant vessels). Geometry of the systems possesses similar patterns and can be investigated by computer methods of pattern recognition. Here some results on plant leaf venation investigation are presented. The lengths, diameters and branching angles are estimated for the leaves of different shape, size and venation type. The statistical distributions of the measured parameters are similar to the corresponding ones which have been obtained for arterial beds. The both correspond to the model of optimal branching pipeline which provide liquid delivering at minimum total energy consumptions. The biomechanical model of liquid motion in a system consisting of a long thin tube with permeable walls which is embedded into a biological porous medium is considered. The pressure distributions and velocity fields for different geometry of the system are obtained. The main result is when the delivering liquid is completely absorbed by the alive cells in the porous medium the relation between the diameter and the length of the tube and the total volume of the medium which correspond to the measured data is reached

Architecture of optimal transport networks

We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape of channels in such optimal networks and show that they must be straight with uniform cross-sectional areas. Then, we establish a relation between the cross-sectional areas of adjoining channels at each junction. Indeed, this relation is a generalization of Murray's law, originally established in the context of local optimization. Moreover, we establish a relation between angles and cross-sectional areas of adjoining channels at each junction, which can be represented as a vectorial force balance equation, where the force weight depends on the channel cross-sectional area. A scaling law between the minimal resistance value and the total volume or surface area value is also derived from the analysis. Furthermore, we show that no more than three or four channels meet in one junction of optimal bi-dimensional networks, depending on the flow profile (e.g.: Poiseuille-like or plug-like) and the considered constraint (fixed volume or surface area). In particular, we show that sources are directly connected to wells, without intermediate junctions, for minimal resistance networks preserving the total channel volume in case of plug flow regime. Finally, all these results are illustrated with a simple example, and compared with the structure of natural networks

Optimization of branching pipelines on basis of design principles of nature

Structure of the optimal rectangular microcirculatory cell of a leaf is investigated on the model of liquid motion through the bifurcating tubes with permeable walls and its filtration into the cell filled with anisotropic porous biological medium. The relation between the diameters of the tubes in the bifurcation as well as coordinates of the bifurcation point at given width and length of the cell which provides minimum total energy consumptions are obtained

Construction principles and control over transport systems organization in biological tissues

The main common principles of the long-range transport systems construction in animal and plant tissues are summarized. The results of measurement of conducting system geometry in Cotinus obovatus leaf are analyzed. It is shown that the principles of design of the conducting systems in animals and higher plants are the same and correspond to the model of optimal pipeline. The mathematical model of fluid motion in the conducting system of the leaf as a mo tion in a branching pipeline with permeable walls is investigated. The cost of a bifurcation of the vessels is analyzed. The hypothesis of the control principle of optimal transport system formation in the growing leaf is discussed. As an example the self-similar conducting system with loops is investigated and compared with some venation systems in plant leaves

Stability of erythrocyte sedimentation in a constant magnetic field

The stability of erythrocyte sedimentation in the presence of a transverse component of the ponderomotive force is investigated. The processes of erythrocyte aggregation lead to the sedimentation being unstable with respect to small variations of the uniform horizontal cell distribution in the sedimentation tube. If an axisymmetric cell distribution is assumed, the system of equations describing erythrocyte sedimentation in blood plasma can be reduced to two-dimensional form and the investigation of this system, both with and without allowance for the viscous components and inertial terms, has shown that it is unstable with respect to small perturbations. The instability may sometimes result in the widely employed ESR test not being exclusively determined by the theological characteristics of the blood modified, for example, by disease. Accidental shaking of the capillary containing the blood or some other mechanical influence may lead to aggregation of the erythrocytes at the top of the tube and a sharp acceleration of the, entire sedimentation process

Load transfer from the growing fibre into the growing medium: application to plant leaf growth

Biological materials change their mass, shape, and porosity during the growth and possess high strength and durability at general lightweight design. Biological tissues are considered to be inhomogeneous anisotropic multiphase composites reinforced by fibres. A 2D problem of the load transfer from the growing fibre into the growing plate with different own growth rates and viscosity is considered in this paper. Rheology of the growing biological tissue is described by a modified Maxwell model of viscoelastic media. Numerical calculations of the growth velocity and stress fields are carried out. The influence of rheological parameters of two media on the stress–strain state is investigated. It is shown that the stress field may provide local coordinated growth of the fibres and the plate when the rheological parameters of two materials are different and anisotropic growth is observed

A Detailed Digital Model of the Human Arterial System

A detailed model of the human circulation is developed. The large systemic arteries are presented by the branching system of straight viscoelastic tubes which corresponds topology of the human circulation. Terminal elements at the outlets of the system are presented by tree-like systems with a given topology (with/without anastomoses) and certain geometrical relations between the lengths and diameters of the vessels of different branching orders and the relation between the maximal total length of the vasculature and diameter of the feeding artery. The relations have been obtained by analysis of the morphometric data. They allow correct calculations of the hydraulic resistance and wave impedance of the arterial beds of different organs. The proposed outflow boundary conditions are more preferable then the Windkessels and the regular tree-like systems because they describe both resonant properties of the intraorgan vasculatures and the distributed sources of the reflected waves. The model describes realistic pressure and flow waves and pressure-flow dependences either in the aorta or in the feeding arteries of the inner organs. The latter underlies possibility of the novel noninvasive diagnostics of the state (normal or pathological) of the intraorgan circulation by noninvasive measuring the wall oscillations and blood flow velocity in any cross-section of the feeding artery of the organ