Outputs (86)

Pulsating fronts in periodically modulated neural field models (2011)
Journal Article
Coombes, S., & Laing, C. (in press). Pulsating fronts in periodically modulated neural field models. Physical Review E, Article 011912. https://doi.org/10.1103/PhysRevE.83.011912

We consider a coarse grained neural field model for synaptic activity in spatially extended cortical tissue that possesses an underlying periodicity in its microstructure. The model is written as an integro-differential equation with periodic modula... Read More about Pulsating fronts in periodically modulated neural field models.

Neural fields with sigmoidal firing rates: Approximate solutions (2010)
Journal Article
Coombes, S., & Schmidt, H. (2010). Neural fields with sigmoidal firing rates: Approximate solutions. Discrete and Continuous Dynamical Systems - Series A, 28(4), 1369-1379. https://doi.org/10.3934/dcds.2010.28.1369

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of... Read More about Neural fields with sigmoidal firing rates: Approximate solutions.

Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks (2010)
Journal Article
Hlinka, J., Hlinka, J., & Coombes, S. (2010). Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks. Physical Review Letters, 104(6), https://doi.org/10.1103/PhysRevLett.104.068101

Ultraslow fluctuations (0.01-0.1 Hz) are a feature of intrinsic brain activity of as yet unclear origin. We propose a candidate mechanism based on retrograde endocannabinoid signaling in a synaptically coupled network of excitatory neurons. This is k... Read More about Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks.

Large-scale neural dynamics: Simple and complex (2010)
Journal Article
Coombes, S. (2010). Large-scale neural dynamics: Simple and complex. NeuroImage, 52(3), 731-739. https://doi.org/10.1016/j.neuroimage.2010.01.045

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models... Read More about Large-scale neural dynamics: Simple and complex.

Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map (2010)
Journal Article
Laudanski, J., Sumner, C., & Coombes, S. (2010). Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map. Physical Review E, 82(1), Article e011924. https://doi.org/10.1103/PhysRevE.82.011924

Thalamocortical (TC) neurones are known to express the low-voltage activated, inactivating Ca2+ current IT. The triggering of this current underlies the generation of low threshold Ca2+ potentials that may evoke single or bursts of action potentials.... Read More about Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map.

Understanding cardiac alternans: a piecewise linear modeling framework (2010)
Journal Article
Thul, R., & Coombes, S. (2010). Understanding cardiac alternans: a piecewise linear modeling framework. Chaos, 20, https://doi.org/10.1063/1.3518362

Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium (Ca²⁺) cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of the... Read More about Understanding cardiac alternans: a piecewise linear modeling framework.

Delays in activity-based neural networks (2009)
Journal Article
Coombes, S., & Laing, C. (2009). Delays in activity-based neural networks. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 367(1891), 1117-1129. https://doi.org/10.1098/rsta.2008.0256

In this paper, we study the effect of two distinct discrete delays on the dynamics of a Wilson-Cowan neural network. This activity-based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discu... Read More about Delays in activity-based neural networks.

Mode locking in a spatially extended neuron model: Active soma and compartmental tree (2009)
Journal Article
Svensson, C. M., Svensson, C.-M., & Coombes, S. (2009). Mode locking in a spatially extended neuron model: Active soma and compartmental tree. International Journal of Bifurcation and Chaos, 19(8), 2597-2607. https://doi.org/10.1142/S0218127409024347

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example, it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a c... Read More about Mode locking in a spatially extended neuron model: Active soma and compartmental tree.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics (2009)
Journal Article
Thul, R., Coombes, S., & Smith, G. (2009). Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics. Physica D: Nonlinear Phenomena, 238, https://doi.org/10.1016/j.physd.2009.08.011

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitl... Read More about Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics.

Gap Junctions and Emergent Rhythms (2009)
Book Chapter
Coombes, S., & Zachariou, M. (2009). Gap Junctions and Emergent Rhythms. In J. Rubin, K. Josic, M. Matias, & R. Romo (Eds.), Coherent Behavior in Neuronal Networks. Springer

Gap junction coupling is ubiquitous in the brain, particularly between the dendritic trees of inhibitory interneurons. Such direct non-synaptic interaction allows for direct electrical communication between cells. Unlike spike-time driven synaptic ne... Read More about Gap Junctions and Emergent Rhythms.