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Models and Simulation of 3D Neuronal Dendritic Trees Using Bayesian Networks

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Abstract

Neuron morphology is crucial for neuronal connectivity and brain information processing. Computational models are important tools for studying dendritic morphology and its role in brain function. We applied a class of probabilistic graphical models called Bayesian networks to generate virtual dendrites from layer III pyramidal neurons from three different regions of the neocortex of the mouse. A set of 41 morphological variables were measured from the 3D reconstructions of real dendrites and their probability distributions used in a machine learning algorithm to induce the model from the data. A simulation algorithm is also proposed to obtain new dendrites by sampling values from Bayesian networks. The main advantage of this approach is that it takes into account and automatically locates the relationships between variables in the data instead of using predefined dependencies. Therefore, the methodology can be applied to any neuronal class while at the same time exploiting class-specific properties. Also, a Bayesian network was defined for each part of the dendrite, allowing the relationships to change in the different sections and to model heterogeneous developmental factors or spatial influences. Several univariate statistical tests and a novel multivariate test based on Kullback–Leibler divergence estimation confirmed that virtual dendrites were similar to real ones. The analyses of the models showed relationships that conform to current neuroanatomical knowledge and support model correctness. At the same time, studying the relationships in the models can help to identify new interactions between variables related to dendritic morphology.

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Notes

  1. The term “database” refers to the sets of 3D reconstructions of basal dendrites from each of the three cortical areas. The term “dataset” is used to refer to the values of the variables measured for each pair of sibling segments in those reconstructions.

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Acknowledgements

This work has been supported by Spanish Science and Innovation Ministry, Cajal Blue Brain Project (C080020-09), TIN2010-20900-C04-04 Project and Consolider Ingenio 2010-CSD2007-00018. PL-C is supported by a FPU Fellowship from the Spanish Education Ministry.

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  1. Departamento de Inteligencia Artificial, Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo sn, 28660, Boadilla del Monte, Madrid, Spain

    Pedro L. López-Cruz, Concha Bielza & Pedro Larrañaga

  2. Laboratorio Cajal de Circuitos Corticales, Universidad Politécnica de Madrid and Instituto Cajal (CSIC), Campus de Montegancedo sn, 28223, Pozuelo de Alarcón, Madrid, Spain

    Ruth Benavides-Piccione & Javier DeFelipe

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  1. Pedro L. López-Cruz
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Correspondence to Pedro L. López-Cruz.

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López-Cruz, P.L., Bielza, C., Larrañaga, P. et al. Models and Simulation of 3D Neuronal Dendritic Trees Using Bayesian Networks. Neuroinform 9, 347–369 (2011). https://doi.org/10.1007/s12021-011-9103-4

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