, Volume 9, Issue 4, pp 347–369 | Cite as

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

  • Pedro L. López-Cruz
  • Concha Bielza
  • Pedro Larrañaga
  • Ruth Benavides-Piccione
  • Javier DeFelipe


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.


Pyramidal cells Virtual dendrites Morphology simulation Dendritic structure Bayesian networks 



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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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Pedro L. López-Cruz
    • 1
  • Concha Bielza
    • 1
  • Pedro Larrañaga
    • 1
  • Ruth Benavides-Piccione
    • 2
  • Javier DeFelipe
    • 2
  1. 1.Departamento de Inteligencia Artificial, Facultad de InformáticaUniversidad Politécnica de MadridMadridSpain
  2. 2.Laboratorio Cajal de Circuitos CorticalesUniversidad Politécnica de Madrid and Instituto Cajal (CSIC)MadridSpain

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