Sequential and synchronous growth models related to vertex analysis and branching ratios

✍ Scribed by K. Horsfield; M.J. Woldenberg; C.L. Bowes

• Publisher: Springer
• Year: 1987
• Tongue: English
• Weight: 850 KB
• Volume: 49
• Category: Article
• ISSN: 1522-9602
• DOI: 10.1016/s0092-8240(87)80004-6

✦ Synopsis

Two models of binary tree growth are examined in terms of the Strahler order branching ratio (Rb) and the types of vertex produced during growth, and their inter-relationship. The sequential growth model is that described by Van Pelt and Verwer (1985, Bull. math. Biol. 47, 323-336) in which random growth occurs according to attributed probabilities on terminal or internal segments, one branch at a time. This model generates values of Rb > 3. The synchronous growth model is new and permits more than one segment to branch at a time, again randomly with attributed probabilities. This model generates values of Rb > 2 and in particular, when only terminal branching is permitted, gives 2_< Rb < 3. Such a model might explain the branching in the human bronchial tree, in which 2.5 _< Rb < 2.8. Our synchronous model is an alternative to the centrifugal-order-dependent sequential model of Van Pelt and Verwer (1986, Bull. math. Biol. 48, 197-211).