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Register a new userDynamical and Statistical Criticality in a Model of Neural Tissue
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For the nervous system to work at all, a delicate balance of excitation and inhibition must be achieved. However, when such a balance is sought by global strategies, only few modes remain balanced close to instability, and all other modes are strongly stable. Here we present a simple model of neural tissue in which this balance is sought locally by neurons following `anti-Hebbian behavior: {sl all} degrees of freedom achieve a close balance of excitation and inhibition and become critical in the dynamical sense. At long timescales, the modes of our model oscillate around the instability line, so an extremely complex breakout dynamics ensues in which different modes of the system oscillate between prominence and extinction. We show the system develops various anomalous statistical behaviours and hence becomes self-organized critical in the statistical sense.
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A powerful experimental approach for investigating computation in networks of biological neurons is the use of cultured dissociated cortical cells grown into networks on a multi-electrode array. Such preparations allow investigation of network development, activity, plasticity, responses to stimuli, and the effects of pharmacological agents. They also exhibit whole-culture pathological bursting; understanding the mechanisms that underlie this could allow creation of more useful cell cultures and possibly have medical applications.
Research showed that, the information transmitted in biological neurons is encoded in the instants of successive action potentials or their firing rate. In addition to that, in-vivo operation of the neuron makes measurement difficult and thus continuous data collection is restricted. Due to those reasons, classical mean square estimation techniques that are frequently used in neural network training is very difficult to apply. In such situations, point processes and related likelihood methods may be beneficial. In this study, we will present how one can apply certain methods to use the stimulus-response data obtained from a neural process in the mathematical modeling of a neuron. The study is theoretical in nature and it will be supported by simulations. In addition it will be compared to a similar study performed on the same network model.
Complex systems are typically characterized as an intermediate situation between a complete regular structure and a random system. Brain signals can be studied as a striking example of such systems: cortical states can range from highly synchronous and ordered neuronal activity (with higher spiking variability) to desynchronized and disordered regimes (with lower spiking variability). It has been recently shown, by testing independent signatures of criticality, that a phase transition occurs in a cortical state of intermediate spiking variability. Here, we use a symbolic information approach to show that, despite the monotonical increase of the Shannon entropy between ordered and disordered regimes, we can determine an intermediate state of maximum complexity based on the Jensen disequilibrium measure. More specifically, we show that statistical complexity is maximized close to criticality for cortical spiking data of urethane-anesthetized rats, as well as for a network model of excitable elements that presents a critical point of a non-equilibrium phase transition.
We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of many individual subsystems linked by a network of interactions. As a specific example of the general theory, a model of neural network, introduced to describe the electrical activity of the cerebral cortex, is analyzed in detail: on the basis of this analysis we propose a novel definition of neuronal cascade, a physiological phenomenon of primary importance. We derive extreme value laws for the statistics of these cascades, both from the point of view of exceedances (that satisfy critical scaling theory) and of block maxima.
Neurostimulation using weak electric fields has generated excitement in recent years due to its potential as a medical intervention. However, study of this stimulation modality has been hampered by inconsistent results and large variability within and between studies. In order to begin addressing this variability we need to properly characterise the impact of the current on the underlying neuron populations. To develop and test a computational model capable of capturing the impact of electric field stimulation on networks of neurons. We construct a cortical tissue model with distinct layers and explicit neuron morphologies. We then apply a model of electrical stimulation and carry out multiple test case simulations. The cortical slice model is compared to experimental literature and shown to capture the main features of the electrophysiological response to stimulation. Namely, the model showed 1) a similar level of depolarisation in individual pyramidal neurons, 2) acceleration of intrinsic oscillations, and 3) retention of the spatial profile of oscillations in different layers. We then apply alternative electric fields to demonstrate how the model can capture differences in neuronal responses to the electric field. We demonstrate that the tissue response is dependent on layer depth, the angle of the apical dendrite relative to the field, and stimulation strength. We present publicly available computational modelling software that predicts the neuron network population response to electric field stimulation.
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