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Abstract Field: A Python Module For Neural Field Modelling

Paula Sanz-Leon1, 2* and Stuart A. Knock3
  • 1 The University Of Sydney, School of Physics, Australia
  • 2 The University Of Sydney, Centre of Integrative Brain Function, Australia
  • 3 QIMR Berghofer, Systems Neuroscience Group, Australia

In this work we present two main contributions: the first one is a Python implementation of the discrete approximation of the Laplace-Beltrami operator (LBO) (Belkin et al., 2008) allowing us to solve Robinson's neural field model (Robinson et al., 2002) on a curved (cortical) surface; the second contribution is a generalised implementation of the aforementioned neural field model which we call Abstract Field Representation (AFR). With this simplified dynamical model one can also express the spatially homogeneous case presented in previous work (Robinson et al., 2003; Breakspear et al., 2006) where various brain states and diseases are studied (e. g., rest, sleep and epilepsy). Many other variants may be defined with the AFR thanks to vector operations and spatialization of parameters. These two components constitute an open-source module for neural field modelling that can be seamlessly integrated in the multiscale hierarchy of The Virtual Brain (TVB) simulator (Sanz-Leon et al., 2013; Sanz-Leon et al., 2015), which is an established user-ready software (Gewaltig and Cannon, 2014). From a systems neuroscience point of view, our contribution favours the integration of multiple approaches to large-scale brain modelling that may lead to more biophysically realistic explanations of how our brains work and interact with the world. From a neuroinformatics perspective, we think this is a valuable addition to the ecosystem of software for meso- and macroscopic brain modelling. Indeed, having different computational models under the same numerical framework is, mildly put, desirable. In simple words, this module represents a way to compare and validate a range of computational models for large scale brain modelling in a systematic way. Lastly, we hope it will assist in the creation of very much needed standard tests in computational neuroscience (Gewaltig and Cannon, 2014).

References

Belkin, M. and Wang, J. S. (2008). Discrete Laplace operator on meshed surfaces. Proc. 24th Ann Symp On Comp Geom. 278–287

Robinson, P.A, Rennie, C.J and Rowe, D.L. (2002). Dynamics of large-scale brain activity in normal arousal states and epileptic seizures, Phys Revi E. 65:4. 041924 (1-9)

Breakspear, M., Roberts, J.A, Terry, J.T, Rodrigues, S., Mahant, N. and Robinson, P.A. (2006). A unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cereb Cor. 16:9. 1296-1313

Robinson, P., Rennie, C., Rowe, D., O'Connor, S., Wright, J., Gordon, E., Whitehouse, R. (2003). Neurophysical Modeling of Brain Dynamics. Neuropsychopharmacology. 28. S74-S79.

Sanz-Leon, P., Knock, S. A, Spiegler, A. and Jirsa, V. K. (2015). Mathematical framework for large-scale brain network modeling in The Virtual Brain. NeuroIm. 111. 385-430.

Sanz-Leon, P., Knock, S.A, Woodman, M.M, Domide, L., Mersmann, J., McIntosh, A.R, Jirsa, V.K. (2013). The Virtual Brain: a simulator of primate brain network dynamics. Frontiers in Neuroinformatics. 7:10. doi: 10.3389/fninf.2013.00010

Gewaltig, M. O and Cannon, R. (2014). Current Practice in Software Development for Computational Neuroscience and How to Improve It. Plos Comp Bio. doi: 10.1371/journal.pcbi.1003376

Keywords: neural field model, large-scale modeling, python, virtual brain, Brain Network Models

Conference: Neuroinformatics 2015, Cairns, Australia, 20 Aug - 22 Aug, 2015.

Presentation Type: Poster, to be considered for oral presentation

Topic: Large-scale modeling

Citation: Sanz-Leon P and Knock SA (2015). Abstract Field: A Python Module For Neural Field Modelling. Front. Neurosci. Conference Abstract: Neuroinformatics 2015. doi: 10.3389/conf.fnins.2015.91.00039

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Received: 31 May 2015; Published Online: 05 Aug 2015.

* Correspondence: Dr. Paula Sanz-Leon, The University Of Sydney, School of Physics, Sydney, NSW, 2006, Australia, paula.sanz-leon@sydney.edu.au