121 research outputs found
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
Numerical methods in blood flow modelling in the complex systems of distensible tubes with arbitrary geometry.
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
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