Modeling neural mass action in brain networks using differential equations

July 22, 2009 - Berlin, Germany

A satellite workshop of the CNS 2009: Eighteenth Annual Computational Neuroscience Meeting, 18-23 July 2009, Berlin, Germany.


Fatihcan M. Atay (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)
Thomas Knösche (Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany)

Information processing in the brain is largely based on dynamic interaction within a complex network of neurons. Neural mass action plays an important role in this process and is, in contrast to single neuron activity, accessible to non-invasive measurement by EEG, MEG and fMRI. Therefore, mathematical models for the dynamic behaviour of interconnected neural masses are suitable for the description of the relationship between neural activity, brain measurements and psychological functions. The finite transmission speed within these networks causes time delays and creates special challenges for the mathematical treatment. In this workshop, techniques will be presented and discussed, which (1) describe masses of neurons by their mean membrane potentials and firing rates, (2) model interactions between these masses, in particular under consideration of time delays, (3) incorporate biological knowledge into the models, (3) solve the resulting systems of differential equations effectively and (4) analyze the dynamic properties of the models, in particular through bifurcation diagrams.  


13:30-13:35   Fatihcan Atay, Introduction

13:35-14:10   Stephen Coombes (University of Nottingham), Neural field models with space-dependent axonal delay.

14:10-14:45   Axel Hutt (LORIA, France), The activity dynamics of spatially extended neural populations subject to additive noise.

14:45-15:15   Break

15:15-15:50   Hecke Schrobsdorff (BCCN Göttingen), Localized activity in two dimensional neural fields.

15:50-16:25   Thomas Knösche (MPI for Human Cognitive & Brain Sciences, Leipzig), Bifurcations in neural mass models.

16:25-18:00   Break

18:00-18:35   Fatihcan Atay (MPI for Mathematics in the Sciences, Leipzig), Stability and complex dynamics in neural fields with propagation delays.

18:35-19:10   Thomas Wennekers (University of Plymouth), Neural field models of spatio-temporal receptive fields.

19:10-19:40   David Liley (Swinburne University of Technology, Australia), Mass action approaches to modeling the genesis and dynamics of the human alpha rhythm.

19:40-20:15   General discussion


F.M. Atay and A. Hutt. Stability and bifurcations in neural fields with finite propagation speed and general connectivity. SIAM J. Applied Math., 65(2):644-666 (2005)

S. Coombes, N.A. Venkov, L. Shiau, I. Bojak, D.T.J. Liley and C.R. Laing. Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E 76, 051901 (2007)

F. Grimbert and O. Faugeras. Bifurcation Analysis of Jansen's Neural Mass Model. Neural Computation 18(12): 3052-3068 (2006)

J. M. Herrmann, H. Schrobsdorff, T. Geisel. Localized Activations in a simple neural field model. Neurocomputing 65-66 (2005)

R. Moran, S.J. Kiebel, K.E. Stephan, R.B. Reilly, J. Daunizeau, and K.J. Friston. A neural mass model of spectral responses in electrophysiology. NeuroImage, 37(3):706-720 (2007)

A. Spiegler and T.R. Knösche. Considering Afferent Pathways on Interneurons in the Jansen and Rit Neural Mass Model. Proc. 15th Annual Meeting of the Organization of Human Brain Mapping, San Francisco (2009)

N.A. Venkov, S. Coombes, and P.C. Matthews. Dynamic instabilities in scalar neural field equations with space-dependent delays. Physica D, 232: 1-15 (2007)

T. Wennekers. Dynamic approximation of spatio-temporal receptive fields in nonlinear neural field models. Neural Computation 14 (8): 1801-1825 (2002)