On the fractality of the biological tree-like structures
type: Item
instance of: scholarly article
title: On the fractality of the biological tree-like structures
zbMATH Open document ID: 0956.92016
DOI: 10.1155/S102602269900031X
author: Jaan Kalda
published in: Discrete Dynamics in Nature and Society
publication date: 2001-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/120838
review text: Summary: The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension \(D_s:D_s<D\), \(D_s=D\) and \(D_s>D\), where \(D\) is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have \(D_s\geq D\). The notion of the self-overlapping exponent is introduced to characterise the trees with \(D_s>D\). 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 yields \(D_s=3.4\). The model is used to analyse the transport of passive components by blood.
Mathematics Subject Classification ID: 92C30
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 1529594
zbMATH Keywords: fractals
zbMATH Keywords: blood-vessels
zbMATH Keywords: similarity dimension
zbMATH Keywords: advective diffusion
zbMATH Keywords: tree-like structures
MaRDI profile type: Publication
OpenAlex ID: W2147662630
description: scientific article; zbMATH DE number 1529594