Canonical Cortical Field Theories

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.Comment: 19 pages, 1 figur

Hints of the Quantum Nature of the Universe in Classical Electrodynamics and Their Connection to the Electronic Charge and Dark Energy

The electromagnetic fields of linear radiating systems working without dispersive and dissipative losses are analyzed both in the time and the frequency domains. In the case of the time domain radiating system, the parameter studied is the action, A, associated with the radiation. The action is defined as the product of the energy and the duration of the radiation. In the case of the frequency domain radiating system, which produces radiation in bursts of duration T/2 where T is the period of oscillation, the parameter studied is the energy, U, dissipated in a single burst of radiation of duration T/2. In this paper, we have studied how A and U vary as a function of the charge associated with the current in the radiating system and the ratio of the length of the radiating system and its radius. We have observed remarkable results when this ratio is equal to the ratio of the radius of the universe to the Bohr radius. In the case of the time domain radiating system, we have observed that when the charge associated with the current propagating along the radiator reaches the electronic charge, the action associated with the radiation reduces to h/2*pi where h is the Planck constant. In the case of the frequency domain radiating system, we have observed that as the magnitude of the oscillating charge reduces to the electronic charge, the energy dissipated in a single burst of radiation reduces to h*v, where v is the frequency of oscillation. Interestingly, all these results are based purely on classical electrodynamics and general relativity. The importance of the findings is discussed. In particular, the fact that the minimum free charge that exists in nature is the electronic charge, is shown for the first time to be a direct consequence of the photonic nature of the electromagnetic fields. Furthermore, the presented findings allow to derive for the first time an expression for the dark energy density of the universe in terms of the other fundamental constants in nature, the prediction of which is consistent with experimental observations. This Equation, which combines together the dark energy, electronic charge and mass, speed of light, gravitational constant and Planck constant, creates a link between classical field theories (i.e., classical electrodynamics and general relativity) and quantum mechanics.Comment: 19 pages, 4 figure

Electromagnetic radiation field of an electron avalanche.

Electron avalanches are the main constituent of electrical discharges in the atmosphere. However, the electromagnetic radiation field generated by a single electron avalanche growing in different field configurations has not yet been evaluated in the literature. In this paper, the electromagnetic radiation fields created by electron avalanches were evaluated for electric fields in pointed, co-axial and spherical geometries. The results show that the radiation field has a duration of approximately 1-2 ns, with a rise time in the range of 0.25 ns. The wave-shape takes the form of an initial peak followed by an overshoot in the opposite direction. The electromagnetic spectrum generated by the avalanches has a peak around 10 9 Hz

Effect of Diabetes Mellitus on Human Brain Function

The following thesis contains four clinical studies. Study I, II and IV were based on a cross sectional investigation on subjects with type 1 diabetes (T1DM) studying the effect of the disease on CNS function through electrophysiological parameters coupled with neuropsychological tests. Study III was an interventional study investigating the effect of strict glycaemic control on subjects with type 2 diabetes (T2DM). Several new techniques were applied to the study of EEG in both studies giving a deeper understanding of the effect of diabetes on the brain. Paper I, II & IV: A cross-sectional study was performed in adult patients (N=150) with T1DM. Factors that are important for cognitive impairment in T1DM were identified. Furthermore, the effects of T1DM on auditory event-related potentials (ERP), spectral properties of resting EEG, connectivity between cortical regions and flow of information across the scalp of resting EEG were studied on a subgroup of 119 patients and compared to healthy controls (N=61). The strongest predictor of cognitive decline was found to be long diabetes duration and young age of diabetes onset, however, body mass index (BMI), height, age and compound muscle action potential (CMAP) were also found to predict cognitive decline. Moreover, patients had a significant decrease in auditory N100 amplitude, which correlated with a decrease in psychomotor speed. Furthermore, connectivity and information flow were reduced for patients as was EEG power. There were no significant correlations between the spectral, connectivity and information flow parameters and cognition. The influence of diabetes duration, BMI, height, age and CMAP may suggest that loss of the neuroprotective effects of insulin or insulin-like growth factors plays a role in the decline of cognitive function. Furthermore, the decline in ERP, connectivity and information flow may suggest conduction defects in the white matter and in the cortex. As the above mentioned parameters only had a partial relationship with each other we conclude that the tests measure different functions and are complementary to the cognitive tests and that several tests need to be performed to monitor the effect of T1DM on brain function. Paper III: The mild cognitive decline associated with T2DM has been suggested to be reversible with improved glycaemic control. In order to characterise this cognitive decline and study the effects of improved glycaemic control patients with T2DM (N=28) and healthy control subjects (N=21) were studied. One group of patients with diabetes (N=15) were given a 2-month treatment of intensified glycaemic control, whereas the other group (N=13) maintained their regular treatment. Cognitive function and electrophysiological variables were studied in the two groups of patients and in healthy control subjects before and after the 2-month trial period. There were significant differences at baseline and the change between 1st and 2nd investigation was significantly different in the three groups where patients receiving intensified treatment had an improvement of HbA1c and cerebral function. In conclusion, T2DM had a similar type of effect on brain function as T1DM and intensified therapy improved the function, suggesting that the negative effect of T2DM on the brain is partly reversible

Global dynamics of neural mass models

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; including stationary points and limit cycles and the possibility for bifurcations and transitions among different modes of activity. This complexity allows neural mass models to describe the itinerant features of brain dynamics. However, expressive, nonlinear neural mass models are often difficult to fit to empirical data without additional simplifying assumptions: e.g., that the system can be modelled as linear perturbations around a fixed point. In this study we offer a mathematical analysis of neural mass models, specifically the canonical microcircuit model, providing analytical solutions describing slow changes in the type of cortical activity, i.e. dynamical itinerancy. We derive a perturbation analysis up to second order of the phase flow, together with adiabatic approximations. This allows us to describe amplitude modulations in a relatively simple mathematical format providing analytic proof-of-principle for the existence of semi-stable states of cortical dynamics at the scale of a cortical column. This work allows for model inversion of neural mass models, not only around fixed points, but over regions of phase space that encompass transitions among semi or multi-stable states of oscillatory activity. Crucially, these theoretical results speak to model inversion in the context of multiple semi-stable brain states, such as the transition between interictal, pre-ictal and ictal activity in epilepsy

Modelling cortical network dynamics

We have investigated the theoretical constraints of the interactions between coupled cortical columns. Each cortical column consists of a set of neural populations where each population is modelled as a neural mass. The existence of semi-stable states within a cortical column is dependent on the type of interaction between the neuronal populations, i.e., the form of the synaptic kernels. Current-to-current coupling has been shown, in contrast to potential-to-current coupling, to create semi-stable states within a cortical column. The interaction between semi-stable states of the cortical columns is studied where we derive the dynamics for the collected activity. For small excitations the dynamics follow the Kuramoto model; however, in contrast to previous work we derive coupled equations between phase and amplitude dynamics with the possibility of defining connectivity as a stationary and dynamic variable. The turbulent flow of phase dynamics which occurs in networks of Kuramoto oscillators would indicate turbulent changes in dynamic connectivity for coupled cortical columns which is something that has been recorded in epileptic seizures. We used the results we derived to estimate a seizure propagation model which allowed for inversions using the Laplace assumption (Dynamic Causal Modelling). The seizure propagation model was trialed on simulated data, and future work will investigate the estimation of the connectivity matrix from empirical data. This model can be used to predict changes in seizure evolution after virtual changes in the connectivity network, something that could be of clinical use when applied to epilepsy surgical cases

Dynamic causal modelling of electrographic seizure activity using Bayesian belief updating

AbstractSeizure activity in EEG recordings can persist for hours with seizure dynamics changing rapidly over time and space. To characterise the spatiotemporal evolution of seizure activity, large data sets often need to be analysed. Dynamic causal modelling (DCM) can be used to estimate the synaptic drivers of cortical dynamics during a seizure; however, the requisite (Bayesian) inversion procedure is computationally expensive. In this note, we describe a straightforward procedure, within the DCM framework, that provides efficient inversion of seizure activity measured with non-invasive and invasive physiological recordings; namely, EEG/ECoG. We describe the theoretical background behind a Bayesian belief updating scheme for DCM. The scheme is tested on simulated and empirical seizure activity (recorded both invasively and non-invasively) and compared with standard Bayesian inversion. We show that the Bayesian belief updating scheme provides similar estimates of time-varying synaptic parameters, compared to standard schemes, indicating no significant qualitative change in accuracy. The difference in variance explained was small (less than 5%). The updating method was substantially more efficient, taking approximately 5–10min compared to approximately 1–2h. Moreover, the setup of the model under the updating scheme allows for a clear specification of how neuronal variables fluctuate over separable timescales. This method now allows us to investigate the effect of fast (neuronal) activity on slow fluctuations in (synaptic) parameters, paving a way forward to understand how seizure activity is generated

Dynamic causal modelling of seizure activity in a rat model

This paper presents a physiological account of seizure activity and its evolution over time using a rat model of induced epilepsy. We analyse spectral activity recorded in the hippocampi of three rats who received kainic acid injections in the right hippocampus. We use dynamic causal modelling of seizure activity and Bayesian model reduction to identify the key synaptic and connectivity parameters that underlie seizure onset. Using recent advances in hierarchical modelling (parametric empirical Bayes), we characterise seizure onset in terms of slow fluctuations in synaptic excitability of specific neuronal populations. Our results suggest differences in the pathophysiology – of seizure activity in the lesioned versus the non-lesioned hippocampus – with pronounced changes in excitation-inhibition balance and temporal summation on the lesioned side. In particular, our analyses suggest that marked reductions in the synaptic time constant of the deep pyramidal cells and the self-inhibition of inhibitory interneurons (in the lesioned hippocampus) are sufficient to explain changes in spectral activity. Although these synaptic changes are consistent over rats, the resulting electrophysiological phenotype can be quite diverse

Detection of interictal epileptiform discharges: A comparison of on-scalp MEG and conventional MEG measurements

Objective: Conventional MEG provides an unsurpassed ability to, non-invasively, detect epileptic activity. However, highly resolved information on small neuronal populations required in epilepsy diagnostics is lost and can be detected only intracranially. Next-generation on-scalp magnetencephalography (MEG) sensors aim to retrieve information unavailable to conventional non-invasive brain imaging techniques. To evaluate the benefits of on-scalp MEG in epilepsy, we performed the first-ever such measurement on an epilepsy patient. Methods: Conducted as a benchmarking study focusing on interictal epileptiform discharge (IED) detectability, an on-scalp high-temperature superconducting quantum interference device magnetometer (high-Tc SQUID) system was compared to a conventional, low-temperature SQUID system. Coregistration of electroencephalopraphy (EEG) was performed. A novel machine learning-based IED-detection algorithm was developed to aid identification of on-scalp MEG unique IEDs. Results: Conventional MEG contained 24 IEDs. On-scalp MEG revealed 47 IEDs (16 co-registered by EEG, 31 unique to the on-scalp MEG recording). Conclusion: Our results indicate that on-scalp MEG might capture IEDs not seen by other non-invasive modalities. Significance: On-scalp MEG has the potential of improving non-invasive epilepsy evaluation. (C) 2020 International Federation of Clinical Neurophysiology. Published by Elsevier B.V