Axel Hutt

Breakdown of local information processing may underlie isoflurane anesthesia effects

The disruption of coupling between brain areas has been suggested as the mechanism underlying loss of consciousness in anesthesia. This hypothesis has been tested previously by measuring the information transfer between brain areas, and by taking reduced information transfer as a proxy for decoupling. Yet, information transfer is a function of the amount of information available in the information source—such that transfer decreases even for unchanged coupling when less source information is available. Therefore, we reconsidered past interpretations of reduced information transfer as a sign of decoupling, and asked whether impaired local information processing leads to a loss of information transfer. An important prediction of this alternative hypothesis is that changes in locally available information (signal entropy) should be at least as pronounced as changes in information transfer. We tested this prediction by recording local field potentials in two ferrets after administration of isoflurane in concentrations of 0.0%, 0.5%, and 1.0%. We found strong decreases in the source entropy under isoflurane in area V1 and the prefrontal cortex (PFC)—as predicted by our alternative hypothesis. The decrease in source entropy was stronger in PFC compared to V1. Information transfer between V1 and PFC was reduced bidirectionally, but with a stronger decrease from PFC to V1. This links the stronger decrease in information transfer to the stronger decrease in source entropy—suggesting reduced source entropy reduces information transfer. This conclusion fits the observation that the synaptic targets of isoflurane are located in local cortical circuits rather than on the synapses formed by interareal axonal projections. Thus, changes in information transfer under isoflurane seem to be a consequence of changes in local processing more than of decoupling between brain areas. We suggest that source entropy changes must be considered whenever interpreting changes in information transfer as decoupling.

Statistical Frequency-Dependent Analysis of Trial-to-Trial Variability in Single Time Series by Recurrence Plots

For decades, research in neuroscience has supported the hypothesis that brain dynamics exhibits recurrent metastable states connected by transients, which together encode fundamental neural information processing. To understand the systems dynamics it is important to detect such recurrence domains, but it is challenging to extract them from experimental neuroscience datasets due to the large trial-to-trial variability. The proposed methodology extracts recurrent metastable states in univariate time series by transforming datasets into their time-frequency representations and computing recurrence plots based on instantaneous spectral power values in various frequency bands. Additionally, a new statistical inference analysis compares different trial recurrence plots with corresponding surrogates to obtain statistically significant recurrent structures. This combination of methods is validated by applying it to two artificial datasets. In a final study of visually-evoked Local Field Potentials in partially anesthetized ferrets, the methodology is able to reveal recurrence structures of neural responses with trial-to-trial variability. Focusing on different frequency bands, the δ-band activity is much less recurrent than α-band activity. Moreover, α-activity is susceptible to pre-stimuli, while δ-activity is much less sensitive to pre-stimuli. This difference in recurrence structures in different frequency bands indicates diverse underlying information processing steps in the brain.

Anesthesia-related changes in information transfer may be caused by reduction in local information generation.

In anesthesia research it is an open question how general anesthetics lead to loss of consciousness (LOC). It has been proposed that LOC may be caused by the disruption of cortical information processing, preventing information integration. Therefore, recent studies investigating information processing under anesthesia focused on changes in information transfer, measured by transfer entropy (TE). However, often this complex technique was not applied rigorously, using time series in symbolic representation, or using TE differences without accounting for neural conduction delays, or without accounting for signal history.

Neural field simulator: two-dimensional spatio-temporal dynamics involving finite transmission speed

Neural Field models (NFM) play an important role in the understanding of neural population dynamics on a mesoscopic spatial and temporal scale. Their numerical simulation is an essential element in the analysis of their spatio-temporal dynamics. The simulation tool described in this work considers scalar spatially homogeneous neural fields taking into account a finite axonal transmission speed and synaptic temporal derivatives of first and second order. A text-based interface offers complete control of field parameters and several approaches are used to accelerate simulations. A graphical output utilizes video hardware acceleration to display running output with reduced computational hindrance compared to simulators that are exclusively software-based. Diverse applications of the tool demonstrate breather oscillations, static and dynamic Turing patterns and activity spreading with finite propagation speed. The simulator is open source to allow tailoring of code and this is presented with an extension use case.

Kernel Reconstruction for Delayed Neural Field Equations

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues.In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed-point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Fréchet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.

Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data

Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, their identification and modeling is a challenging task. The present work reviews briefly the literature and proposes a novel combination of their identification in experimental data and their modeling by dynamical systems. This combination applies recurrence structure analysis permitting the derivation of an optimal symbolic representation of metastable states and their dynamical transitions. To derive heteroclinic sequences of metastable attractors in various experimental conditions, the work introduces a Hausdorff clustering algorithm for symbolic dynamics. The application to brain signals (event-related potentials) utilizing neural field models illustrates the methodology.

Optimal Model Parameter Estimation from EEG Power Spectrum Features Observed during General Anesthesia

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ − (0 − 4 Hz) and α − (8 − 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.

Suppression of underlying neuronal fluctuations mediates EEG slowing during general anaesthesia

&NA; The physiological mechanisms by which anaesthetic drugs modulate oscillatory brain activity remain poorly understood. Combining human data, mathematical and computational analysis of both spiking and mean‐field models, we investigated the spectral dynamics of encephalographic (EEG) beta‐alpha oscillations, observed in human patients undergoing general anaesthesia. The effect of anaesthetics can be modelled as a reduction of neural fluctuation intensity, and/or an increase in inhibitory synaptic gain in the thalamo‐cortical circuit. Unlike previous work, which suggested the primary importance of gamma‐amino‐butryic‐acid (GABA) augmentation in causing a shift to low EEG frequencies, our analysis demonstrates that a non‐linear transition, triggered by a simple decrease in neural fluctuation intensity, is sufficient to explain the clinically‐observed appearance – and subsequent slowing – of the beta‐alpha narrowband EEG peak. In our model, increased synaptic inhibition alone, did not correlate with the clinically‐observed encephalographic spectral changes, but did cause the anaesthetic‐induced decrease in neuronal firing rate. Taken together, our results show that such a non‐linear transition results in functional fragmentation of cortical and thalamic populations; highly correlated intra‐population dynamics triggered by anaesthesia decouple and isolate neural populations. Our results are able to parsimoniously unify and replicate the observed anaesthetic effects on both the EEG spectra and inter‐regional connectivity, and further highlight the importance of neural activity fluctuations in the genesis of altered brain states.

Description and removal of background activity in EEG power spectra under general anesthesia using the Lorentzian curve

General anesthesia is an important medical procedure in todays hospital practice and comprises loss of consciousness, analgesia, amnesia and immobility. Our current work analyzes patient reaction on nociception stimuli during a surgical operation and differences in this reaction provided different anesthetic drugs, propofol and desflurane. The studied dataset comprises EEG-recordings before and after incision obtained from 115 patients [1]. The task is the identification of spectral EEG signal features reflecting the incision. This analysis will reveal a possible new marker of pain during deep anesthesia. n nThis work considers one of the approaches to the problem, namely spectral analysis. First, power spectral density (PSD) estimates were obtained using Welchs method. It is well known that EEG power spectrum decays with higher frequencies following ~1/f scaling [2-4]. We attribute this behavior to background activity [5], which takes place in the brain when no other activity is present. Background activity was describe by fitting regression curve P(f)~a/f b to each PSD estimate. However, the resulting goodness of fit was not satisfactory. It is due to rise of power in delta peak, which becomes prominent under general anesthesia and makes the process of curve fitting less reliable. Thus, the original model was substituted by the Lorentzian function P(f)=a/(f b + c), which resembles the shape of actual power spectrum quite well. Afterwards, regression curves were subtracted from each power spectrum to normalize it [3] and to analyze spectral power contained in delta and alpha peaks regardless of distinctions in patients. n nThe results of this work revealed small differences between propofol and desflurane. Power spectra of patients receiving desflurane have more regular shape than the ones from propofol group. It can also be seen that delta power remains more consistent, while alpha power varies greatly from patient to patient. Another result of this work is a trend in the distribution of Lorentzian curve parameters: the set of parameters remains compact for small values of b, but a and c scatters significantly when b (which corresponds to steepness of curve) is larger than three. Results of this work provide insights on underlying background activity. However, they do not allow to distinguish between pre- and post-incision and poorly between propofol and desflurane. This problem requires more complicated techniques. Future work will expand spectral analysis with time information (time-frequency representations) and investigate time structure by means of recurrence analysis. n n n nFigure 1 n nExample of power spectrum density estimate (solid black), with fitted Lorentzian curve (dashed orange), goodness of fit (R2), delta (green circle) and alpha peaks (blue circle).