A realistic representation of the dynamics of neurons should be based on dendritic trees characterized according to both their geometrical structure (i.e. the branching pattern) and metric structure (e.g. the length of branches and their time development).
The goals of our study are to quantify dendritic growth as it develops in time, to characterize growth patterns of dendrites in different culture conditions, and to be able to make predictions for dendritic development. The approach is to construct a mathematical model that describes the basic patterns of dendritic development and that can be used for statistical estimation of crucial growth parameters and for prediction of the quantitative development of neuronal cells. Our basic model for the geometric branching pattern is a Galton-Watson branching process in varying environment. Together with a parameter that measures denseness and sparseness of patterns, this model delivered excellent predictability for hippocampal neurons in young rats.
In the long run, we excpect applications of these studies to drug testing, environmental effects on brain development, and a better understanding of diseases like Alzheimer's. The figures above show a microscope picture of neuronal dendrites in vitro and most probable growth patterns for dendritic trees in different environments, according to our model. (Supported by NIH.)
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