Acta Stereologica

0351-580X

 

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Jaap Van Pelt & Ronald W.H. Verwer

Growth models for topological binary branching patterns

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Abstract

Binary branching patterns have been studied from a topological point of view. The central question is how the frequency distributions of the topologies of observed branching patterns can be understood in terms of growth of these patterns. For this purpose techniques have been developed to analyze the topological properties and growth models have been worked out mathematically to calculate the expectation values for these properties. The topologies of the branching patterns are described by the set of partitions (degrees of subtree pairs) for all branching points in all the trees. The model defines for each segment in a growing tree the probability of branching which depends of the type of segment (intermediate or terminal) and of its order (topological distance to the root). Two parameters in the model define the strength of these dependencies. Good fits to sets of observed neuronal dendrites could be obtained on basis of maximum likelihood criteria.

Keywords : branching patterns, dendrites, growth models, maximum likelihood, topology

Pour citer cet article

Jaap Van Pelt & Ronald W.H. Verwer, «Growth models for topological binary branching patterns», Acta Stereologica [En ligne], Volume 4 (1985), Number 2 - Proceedings of the fourth European symposium for stereology - Dec. 1985, 159-164 URL : https://popups.ulg.ac.be/0351-580x/index.php?id=3121.

A propos de : Jaap Van Pelt

Netherlands Institute for Brain Research, Meibergdreef 33, 1105 AZ Amsterdam, The Netherlands

A propos de : Ronald W.H. Verwer

Netherlands Institute for Brain Research, Meibergdreef 33, 1105 AZ Amsterdam, The Netherlands