On the fractality of the biological tree-like structures

Abstract

The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension Ds:DsD, where D is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have Ds≥D. The notion of the self-overlapping exponent is introduced to characterise the trees with Ds>D. A model of the human blood-vessel system is proposed. The model is consistent with the processes governing the growth of the blood-vessels and yields Ds=3.4. The model is used to analyse the transport of passive component by blood.

Keywords

• Fractals
• Blood-vessels
• Tree-like structures
• Similarity dimension
• Advective diffusion.