On the fractality of the biological tree-like structures. Issue 4 (1999)

• Record Type: Journal Article
• Authors: Kalda, Jaan
• Is Part Of: Discrete dynamics in nature and society. Volume 3:Issue 4(1999)
• Page Start: 297
• Page End: 306
• Publication Date: 1999
• Subjects: Fractals -- Blood-vessels -- Tree-like structures -- Similarity dimension -- Advective diffusion; System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/S102602269900031X
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimensionD s : D s < D, D s = D andD s > D, whereD is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures haveD s ≥ D . The notion of the self-overlapping exponent is introduced to characterise the trees withD s > 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 yieldsD s = 3.4 . The model is used to analyse the transport of passive component by blood.