On the fractality of the biological tree-like structures
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.
scientific article; zbMATH DE number 1529594