Branching ratio and growth of tree-like structures

Respiration Physiology
K Horsfield, M J Woldenberg

Abstract

Dichotomously branching trees were generated by computer using random terminal and random segmental growth. The branching ratio (Rb) of such a tree during growth oscillates periodically as new branches are added. The magnitude of the oscillations diminishes as the tree enlarges and Rb converges towards an expected value. This phenomenon was investigated using the reverse of the growth process, that is by terminal or segmental subtraction of branches from existing trees. These were either computer generated trees or mammalian bronchial tree data. The oscillations of Rb thus obtained were similar to those obtained during growth and were used to calculate convergent values of Rb. In addition, an estimate of convergent Rb was obtained from the mean of the maximum and minimum Rb of the first oscillation occurring when the least number of branches had been subtracted. Values of Rb obtained by these methods were compared with those obtained by taking the antilogarithm of the slope of the regression of log number of branches against order. With large trees the results are similar, but with smaller trees a more reliable Rb is given by the means of the oscillations. We find that Rb values from the bronchial trees are different from those...Continue Reading

References

May 8, 1975·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·T Hollingworth, M Berry
Jan 1, 1985·Bulletin of Mathematical Biology·J Van Pelt, R W Verwer
Jun 1, 1967·The Bulletin of Mathematical Biophysics·K Horsfield, G Cumming
Aug 1, 1983·Journal of Neuroscience Methods·R W Verwer, J van Pelt
Jan 1, 1983·Bulletin of Mathematical Biology·J Van Pelt, R W Verwer
Dec 21, 1980·Journal of Theoretical Biology·K Horsfield
Jan 1, 1981·Bulletin of Mathematical Biology·K Horsfield, A Thurlbeck

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Citations

Jan 1, 1987·Bulletin of Mathematical Biology·K HorsfieldC L Bowes
Aug 1, 1986·Respiration Physiology·K Horsfield, M J Woldenberg
Mar 18, 2004·The American Naturalist·Juan Armando SánchezMichael J Woldenberg
Oct 28, 2008·The Anatomical Record : Advances in Integrative Anatomy and Evolutionary Biology·Daniel R EinsteinRichard A Corley
Sep 1, 1992·Bulletin of Mathematical Biology·J Van PeltM J Woldenberg
Feb 1, 1993·Pediatric Pulmonology·E A MassoudW M Thurlbeck

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