Abstracts

Mathematical modelling

For a long-distance delivering of a fluid and matters and for a bringing out of metabolites plants and animals have special transport systems - branched arterial and venous systems in animal tissues, xylem and phloem - in plants. The xylem and phloem vessels are parallel and connected into the branched network of veins. The construction of arterial and venous systems has some peculiarities in different organs and tissues and is characterized by dependences between lengths, diameters and branching angles of vessels in generations. The principles of design of arterial beds were formulated by the rules of vascular systems organization and were in detail researched on fixed preparations of arterial and venous trees and angiograms.

Here some results of research of construction principles of transport systems in dicotyledonous leaves with different types of nervation are presented. The scanned images of leaves were studied with the help of computer methods of image analysis. The lengths, diameters, branching angles between main and daughter vessels in separate bifurcations, squares of different lobes of a leaf are measured. More than 500 images of 29 species 14 families are researched. The following dependences are revealed:

1. There is a dependence between a whole angle of branching and the diameter of the main vessel. These dependences are similar for all researched types of leaves, don't depend on a size of the leaf blade and are similar to dependences obtained earlier for arterial systems of brain, heart and lungs.

2. In bifurcations there are such rules: larger daughter?s vessel has a smaller branching angle, smaller vessel is situated practically at right angle to main one, the daughter's vessels with equal diameters have similar branching angles.

3. There is a dependence between a branching coefficient k (the ratio of total square of daughter?s vessels to square of a main one) and a diameter of the main vessel. There are two types of vessels: type I with k (with the delivery function) and type II (with the distributive function) with varying values for k.

4. The branching angle is connected with a diameter of the main vessel and close to an optimum angle providing minimum hydraulic resistance at fixed volume.

5. The ratio of length of the main vessel to the square of that area of a leaf, delivering of a fluid in which one is determined by this vessel, is constant. That provides a relation between inflow and consumption of the fluids in each separate lobe of a leaf.

On the basis of research outcomes it is possible to establish, that the principles of organization of the systems for a long-distance fluid transport in plants and animals are similar. These principles are connected with optimal transport systems providing fluid delivering at minimum cost. All dependences are discussed on the base of the Murrey, Lighthill and Rosen laws, are known in a theoretical biology and also on the base of mechanics of branched transport systems.

Full Text in Russian:

HTML

Note. Abstracts are published in author's edition

Comments

[Home] [Conference]

©2001, Siberian Branch of Russian Academy of Science, Novosibirsk
©2001, United Institute of Computer Science SB RAS, Novosibirsk
©2001, Institute of Computational Techologies SB RAS, Novosibirsk
©2001, A.P. Ershov Institute of Informatics Systems SB RAS, Novosibirsk
©2001, Institute of Mathematics SB RAS, Novosibirsk
©2001, Institute of Cytology and Genetics SB RAS, Novosibirsk
©2001, Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk
©2001, Novosibirsk State University
Last modified 06-Jul-2012 (11:45:21)