Elsevier

Neurocomputing

Volume 70, Issues 1–3, December 2006, Pages 327-342
Neurocomputing

NeuGen: A tool for the generation of realistic morphology of cortical neurons and neural networks in 3D

https://doi.org/10.1016/j.neucom.2006.01.028Get rights and content

Abstract

We introduce the software package NeuGen for the efficient generation of anatomically accurate synthetic neurons and neural networks. NeuGen generates non-identical neurons of morphological classes of the cortex, e.g., pyramidal cells and stellate neurons, and synaptically connected neural networks in 3D. It is based on sets of descriptive and iterative rules which represent the axonal and dendritic geometry of neurons by inter-correlating morphological parameters. The generation algorithm stochastically samples parameter values from distribution functions induced by experimental data. The generator is adequate for the geometric modelling and for the construction of the morphology. The generated neurons can be exported into a 3D graphic format for visualization and into multi-compartment files for simulations with the program NEURON. NeuGen is intended for scientists aiming at simulations of realistic networks in 3D. The software includes a graphical user interface and is available at http://neugen.uni-hd.de.

Introduction

In the past decade, computer simulations of cellular behaviour of single neurons or small networks of neurons with an accurate dendritic and axonal morphology have become increasingly common. The complex morphology of the neurons is usually taken from experimental data resulting in anatomically precise compartmental models. The complex geometric morphology is important for the understanding of the neuronal integration, see e.g. [8], [28], [19], [16], [13], [7], [23].

However, the reconstruction of anatomically precise compartmental models of neurons from experiments either manually or automatically with the help of reconstruction software is rather tedious and time-consuming. Depending on dye and recording technique such a reconstruction is only feasible for one or a few neurons at a time. Hence a software program that is able to generate three-dimensional (3D) synthetic neuron geometries and neural networks in conformity with experimental findings is an invaluable tool. We present the software package NeuGen for the generation of realistic neurons and neural networks in 3D. NeuGen provides an easy way to construct not only single cells but also complex networks with a large number of neurons. The networks are interconnected by synapses. These synapses are created at axonal locations determined by a function of the distance to the dendrites of all other neurons.

The software L-Neuron introduced in [1], [2] is a modelling tool to generate anatomically accurate neuronal analogues. It is oriented towards single-cell generation and is an implementation of the algorithm in [9], [5]. While L-Neuron is based on recursive rules using a Lindenmayer-system formalism, i.e., looping rules given by a Lindenmayer-string, NeuGen implements a straightforward algorithm which utilizes forward-stepping rules. The key of the generative method lies in a tail-recursive, thus forward-stepping and not truly recursive, function to generate the sections of a cell. Further each neuron type builds an independent class in NeuGen. The algorithm directly maps anatomical fingerprints of the different neuron types onto a coordinate-based description for the three-dimensional neuron geometry. Therefore, NeuGen uses statistical distributions based on morphological parameters given by realistic data, see e.g. [21], [22], [6], [14], and some basic compartment model elements.

ArborVitae is another software for the reconstruction of networks by algorithmic amplification of morphological data [30]. It generates large-scale, anatomically accurate networks similar to NeuGen. ArborVitae develops brain circuits by given growth rules and subcellular informations whereas NeuGen generates neurons simply by morphological rules. However, the variables used to describe the generated structures, such as soma and dendrite locations, length, diameter and taper of segments are the same. While ArborVitae focuses on generating cells of the hippocampus and other brain regions [30], NeuGen primarily generates cells of the neocortex. NeuGen also does not consider competition in the neuronal generation process as it is done in [32]. The program A-Cell-3D [11] also models detailed three-dimensional neuron morphology which is able to model the calcium dynamics in spines, too. Unlike NeuGen it develops only single cell geometries.

In NeuGen geometric constraints are used to describe the different neuron classes. These constraints are characteristic features as well as morphological rules obtained from experimental findings. These rules correlate the morphological parameters to describe the axonal and dendritic geometry of the neurons. The basic description of a single dendrite, for instance, is given by a list of sections. Each section is represented as a series of connected, cylindrical or frustum-shaped segments, also termed compartments, containing a numerical tag, the spatial Cartesian coordinates, the start radius and the end radius. This structure is used to assemble an accurate description of the dendritic morphology. We additionally characterize the sections by morphological parameters, such as branch point angles and branching depth. Statistical distributions are associated with each of these parameters, i.e., the final value for the parameter is sampled from a distribution and then used to generate the morphology. In the literature, there are a few algorithms available that describe neuronal morphologies purely on the basis of such statistical distributions of geometrical parameters [9], [5], [17]. Unlike the description applied in NeuGen, the algorithm in [17] only yields information on an ensemble of neurons, i.e., the description is not sufficient to provide an explicit and precise map of the morphology. Whereas the implementation of the algorithms of [9], [5] in L-Neuron [1] can provide an explicit representation of complete, individual neurons.

NeuGen is intended to generate neural networks as cortical columns connecting layer 5 (L5) and layer 4 (L4) with layer 2/3 (L2/3) in the cortex; see Fig. 1 (middle) for the layers. These model columns are found in the somatosensory barrel cortex in rodents [22]. In the following we use the classification of neurons in the cortex due to their anatomical shape, i.e., the classes of pyramidal cells, star pyramidal cells, and stellate neurons. NeuGen is based on this classification, that is, NeuGen provides the generation of L2/3 pyramidal cells, L5 A and L5 B pyramidal cells, L4 star pyramidal cells, and L4 stellate neurons. The different cell types are arranged automatically in their associated layers. The generated three-dimensional networks are then represented by an object-oriented data structure and can be applied for visualizations and for numerical studies with the simulation program NEURON [10].

NeuGen is written in ANSI C++ and Java. It runs on Linux, MS Windows and MacOS X platforms, and it is available at http://neugen.uni-hd.de.

Section snippets

Methods

The NeuGen neuron generator is intended to produce realizations of neural networks in 3D where the geometry and morphology are modelled as realistic as possible. To this end we use appropriate probability density functions to describe the distributions of the morphological parameters. The morphological data is extracted from the morphometric analysis of the columnar innervation domain, as done e.g. in [28], [13], [15], [21]. The neuroanatomical parameters used by NeuGen are obtained from the

Object-oriented class design for the morphological description

We briefly describe the object-oriented class design that represents the neurons in NeuGen.

The classes Net and Neuron construct networks and neurons, respectively, based on the classes for the axon, the dendrites, and the soma, see Fig. 3.

The soma of each neuron is constructed by an instance of the class Cellipsoid. It represents an ellipsoid which approximates the shape and volume of the soma as set in the configuration. The ellipsoidal shape given by the lengths of the semi-axes of the

Discussion and results

The presented generation of the neuron morphology with NeuGen is intuitive and brings all the benefits of the object-oriented paradigm, which include portability, extensibility, and re-usability. Building on the two basic classes—Segment and Cellipsoid—we have developed a seven class model in NeuGen which can be used as a general framework for numerical studies on realistic morphology. With the additional classes for the net and the synapses (Net and Cons) the significant morphological

Conclusion and outlook

We present the software NeuGen for the efficient generation of anatomically accurate neurons and neural networks. NeuGen is intended for scientists aiming at simulations of morphologically realistic networks in 3D. It is based on sets of descriptive rules that represent the axonal and dendritic geometry by morphological parameters. The generator stochastically samples parameter values from statistical distributions induced by experimental data. The range of the parameter values is given by the

Jens P. Eberhard obtained a Diploma degree in Physics in 2001 and his Ph.D. in Mathematics in 2003 from the University of Heidelberg, Germany. He was a scholarship holder of the international graduate college “Complex Processes: Modelling, Simulation and Optimization”. He works currently as a post-doc at the Interdisciplinary Center for Scientific Computing of the University of Heidelberg. His research interests include numerics of multiscale processes, upscaling, modelling and simulation of

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    Jens P. Eberhard obtained a Diploma degree in Physics in 2001 and his Ph.D. in Mathematics in 2003 from the University of Heidelberg, Germany. He was a scholarship holder of the international graduate college “Complex Processes: Modelling, Simulation and Optimization”. He works currently as a post-doc at the Interdisciplinary Center for Scientific Computing of the University of Heidelberg. His research interests include numerics of multiscale processes, upscaling, modelling and simulation of signal processing in neural networks, and software engineering.

    Alexander Wanner is an undergraduate student of the faculty of mathematics at the University of Heidelberg, Germany. He currently works as a programmer for the NeuGen project, and he is working on his Diploma thesis about neuronal signal processing. His study interests are applied mathematics and software engineering.

    Gabriel Wittum is professor of computational science at the University of Heidelberg. He holds a chair for Simulation in Technology. He received a doctoral degree in mathematics from Kiel University. His research focuses on modelling and simulation of problems from applied sciences and engineering. In particular he develops methods and software tools for the solution of problems from life sciences as well as engineering. He published about 100 scientific publications.

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