Generalized linear mixed models for branching probabilities of brain artery systems

Study of factors affecting the functioning of the human brain has been of considerable interest for more than a century. In this paper, we focus on the structure of brain arterial systems in humans and study how this might be related to factors such as age, gender or handedness (left or right handed). To facilitate this study we first represent brain arterial systems using tree-structured objects and construct stochastic systems whose realizations are such tree-structured objects. We show that the parameters of the stochastic system, primarily the branching probabilities, may be effectively studied using a logistic regression framework. This appears to be a fruitful approach for understanding tree-structured data. Applying this novel approach to actual data collected on 98 subjects, we are able to conclude that age and gender do seem to influence brain artery branching patterns. Most brain arteries have decreasing branching probabilities with increasing age, and brain arteries of females are slightly more likely to branch than those of males. In addition, we find an interesting phenomenon that, as age increases, branching probabilities of thick arteries decrease while those of thin arteries increase. Possible medical/biological interpretations of this finding are provided.