Related papers: Fighting seizures with seizures: diffusion and sta…
Focal epilepsy is a devastating neurological disorder that affects an overwhelming number of patients worldwide, many of whom prove resistant to medication. The efficacy of current innovative technologies for the treatment of these patients…
An implanted device for brain-responsive neurostimulation (RNS System) is approved as an effective treatment to reduce seizures in adults with medically-refractory focal epilepsy. Clinical trials of the RNS System demonstrate…
Epilepsy is a neurological disorder arising from anomalies of the electrical activity in the brain, affecting about 0.5--0.8\% of the world population. Several studies investigated the relationship between seizures and brainwave…
Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a…
Purpose: The understanding of brain activity, and in particular events such as epileptic seizures, lies on the characterisation of the dynamics of the neural networks. The theory of non-linear dynamics provides signal analysis techniques…
Epileptic seizures are characterised by abnormal brain dynamics at multiple scales, engaging single neurons, neuronal ensembles and coarse brain regions. Key to understanding the cause of such emergent population dynamics, is capturing the…
Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates…
We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is…
Recent advances in neurotechnologies and decades of scientific and clinical research have made closed-loop electrical neuromodulation one of the most promising avenues for the treatment of drug-resistant epilepsy (DRE), a condition that…
The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
Epilepsy is a neurological illness that is characterised by continuous spasms of shaking, sometimes known as convulsions. Although there are effective treatments for epilepsy, such as drugs and surgery, there is still a group of individuals…
Recent advances in control theory yield closed-loop neurostimulations for suppressing epileptiform seizures. These advances are illustrated by computer experiments which are easy to implement and to tune. The feedback synthesis is provided…
This review provides a dynamical systems perspective on psychiatric symptoms and disease, and discusses its potential implications for diagnosis, prognosis, and treatment. After a brief introduction into the theory of dynamical systems, we…
Epileptic seizures are considered as abnormally hypersynchronous neuronal activities of the brain. Do hypersynchronous neuronal activities in a brain region lead to seizure or the hypersynchronous activities take place due to the…
Neural mass models are used to simulate cortical dynamics and to explain the electrical and magnetic fields measured using electro- and magnetoencephalography. Simulations evince a complex phase-space structure for these kinds of models;…
Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Heuristic models of this process of synaptic plasticity can provide excellent fits to results from in-vitro experiments in which pre- and…
In neural circuits, synaptic strengths influence neuronal activity by shaping network dynamics, and neuronal activity influences synaptic strengths through activity-dependent plasticity. Motivated by this fact, we study a recurrent-network…