Computational Approach to Optimal Transport

Abstract

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.