All Outputs (81)

Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves (2012)
Journal Article

Clusters of ryanodine receptors within atrial myocytes are confined to spatially separated layers. In many species, these layers are not juxtaposed by invaginations of the plasma membrane (transverse tubules; 'T-tubules'), so that calcium-induced-cal... Read More about Persistence of pro-arrhythmic spatio-temporal calcium patterns in atrial myocytes: a computational study of ping waves.

Interface dynamics in planar neural field models (2012)
Journal Article

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patt... Read More about Interface dynamics in planar neural field models.

Using evolutionary algorithms for fitting high-dimensional models to neuronal data (2012)
Journal Article

n the study of neurosciences, and of complex biological systems in general, there is frequently a need to fit mathematical models with large numbers of parameters to highly complex datasets. Here we consider algorithms of two different classes, gradi... Read More about Using evolutionary algorithms for fitting high-dimensional models to neuronal data.

Neuronal spike-train responses in the presence of threshold noise (2012)
Journal Article

The variability of neuronal firing has been an intense topic of study for many years. From a modelling perspective it has often been studied in conductance based spiking models with the use of additive or multiplicative noise terms to represent chan... Read More about Neuronal spike-train responses in the presence of threshold noise.

Subcellular calcium dynamics in a whole-cell model of an atrial myocyte (2012)
Journal Article

In this study, we present an innovative mathematical modeling approach that allows detailed characterization of Ca 2+ movement within the three-dimensional volume of an atrial myocyte. Essential aspects of the model are the geometrically realistic re... Read More about Subcellular calcium dynamics in a whole-cell model of an atrial myocyte.

Nonsmooth dynamics in spiking neuron models (2011)
Journal Article

Large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue. One approach in computational neuroscience has been to consider the detailed electrophysiological propertie... Read More about Nonsmooth dynamics in spiking neuron models.

Pulsating fronts in periodically modulated neural field models (2011)
Journal Article

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

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

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

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

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

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.

Mathematical Modeling of Glucose Homeostasis and Its Relationship With Energy Balance and Body Fat (2009)
Journal Article

Delays in activity-based neural networks (2009)
Journal Article

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

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

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.

Instabilities in threshold-diffusion equations with delay (2008)
Journal Article

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics, ranging from periodic solutions through to spatio-temporal chaos. In this paper, we consider a class of scal... Read More about Instabilities in threshold-diffusion equations with delay.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models (2008)
Journal Article

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of the... Read More about Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models.

Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis (2008)
Journal Article

Gating of sensory information can be assessed using an auditory conditioning-test paradigm which measures the reduction in the auditory evoked response to a test stimulus following an initial conditioning stimulus. Recording brainwaves from specific... Read More about Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis.

Democratization in a passive dendritic tree: An analytical investigation (2008)
Journal Article

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as "dendritic democr... Read More about Democratization in a passive dendritic tree: An analytical investigation.