Abstract:
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Complex branching structures such as a blood vessel network, the root system of a tree or the dendritic network of a neural cell can be represented as trees. Advances in imaging, segmentation and line tracking now enable biologists to automatically collect data on multiple copies of such networks, allowing the study of their variation. Modelling tree valued random variables represents a statistical challenge, because of their hierarchical structure and resulting dependencies. A natural probabilistic framework to study trees is as a branching process. Substantial simplification of analysis is possible under the assumption that the branching probabilities and associated properties (marks) are only dependent on the branching order or level. Under this assumption, we demonstrate that the topology and other properties of trees can be analysed in a regression modelling framework. We apply this methodology to a dataset comprising the brain blood vessel network for 98 subjects. Our analysis shows significant differences in branching topology and properties such as thickness and length in the front of the brain relative to the back or two sides. We show that there is also a strong log-line
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