The reflection of different levels of the regulation of human brain activity in spectrally coherent EEG parameters]

On the basis of clinico-anatomo-electroencephalographic studies it was shown, that in early terms of cerebral trauma, at gross disturbances of the cortical functions and safety in some cases of only vital regulation, the parameters of the EEG stability or variability are of distinct information value for estimation of the functional state of patients. It was established, that changes of stability of the frequency, power, and coherent EEG characteristics correlate with different parameters of changes of the structural-functional brain organization. At this stage the greatest connection with the disease outcome reveals the EEG coherence parameters of the cortical symmetrical points reflecting the state of predominantly median formations and general brain reactions to traumatic action. In the process of restoration of disturbed neuromental functions priority prognostic significance is acquired by parameters of intrahemispheric coherence as well as by frequency-regional properties of interhemispheric asymmetry of coherence of the brain electrical processes, characterizing functional features of the lesion focus.     

Travelling waves and EEG patterns during epileptic seizure: analysis with an integrate-and-fire neural network

Epilepsy is characterized by paradoxical patterns of neural activity. They may cause different types of electroencephalogram (EEG), which dynamically change in shape and frequency content during the temporal evolution of seizure. It is generally assumed that these epileptic patterns may originate in a network of strongly interconnected neurons, when excitation dominates over inhibition. The aim of this work is to use a neural network composed of 50 x 50 integrate-and-fire neurons to analyse which parameter alterations, at the level of synapse topology, may induce network instability and epileptic-like discharges, and to study the corresponding spatio-temporal characteristics of electrical activity in the network. We assume that a small group of central neurons is stimulated by a depolarizing current (epileptic focus) and that neurons are connected via a Mexican-hat topology of synapses. A signal representative of cortical EEG (ECoG) is simulated by summing the membrane potential changes of all neurons. A sensitivity analysis on the parameters describing the synapse topology shows that an increase in the strength and in spatial extension of excitatory vs. inhibitory synapses may cause the occurrence of travelling waves, which propagate along the network. These propagating waves may cause EEG patterns with different shape and frequency, depending on the particular parameter set used during the simulations. The resulting model EEG signals include irregular rhythms with large amplitude and a wide frequency content, low-amplitude high-frequency rapid discharges, isolated or repeated bursts, and low-frequency quasi-sinusoidal patterns. A slow progressive temporal variation in a single parameter may cause the transition from one pattern to another, thus generating a highly non-stationary signal which resembles that observed during ECoG measurements. These results may help to elucidate the mechanisms at the basis of some epileptic discharges, and to relate rapid changes in EEG patterns with the underlying alterations at the network level.     

Optimal structure of the connections of the electrical processes in the human cerebral cortex and its disorders in changes of state

In this paper the data are analyzed on the human EEG investigation. Significance is shown of parameters of correlative and spectral-coherent EEG functions for the estimation of the brain functional state of healthy people and patients with local cerebral lesions. In the norm, the parameter of the mean coherence is stable, its characteristics correspond to the optimum cortical tone, the most favourable for the performance of the cortical functions. In healthy people unstable, individual, different in different cortical areas changes of the spectrum details, coherence and phases reflect local processes, taking place at the optimum mean level of the coherence and form the cortical mosaic. These two sides of the intercentral relations of the electrical processes (optimum level of coherence and dynamic mosaic of connections of separate rhythms) reflect the most favourable conditions of the nervous processes development. In the brain pathology, different forms are noted of deviations from the system of intercentral relations and levels of coherence of cortical electrical processes.     

Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals

In the field of epilepsy, the analysis of stereoelectroencephalographic (SEEG, intra-cerebral recording) signals with signal processing methods can help to better identify the epileptogenic zone, the area of the brain responsible for triggering seizures, and to better understand its organization. In order to evaluate these methods and to physiologically interpret the results they provide, we developed a model able to produce EEG signals from “organized” networks of neural populations. Starting from a neurophysiologically relevant model initially proposed by Lopes Da Silva et al. [Lopes da Silva FH, Hoek A, Smith H, Zetterberg LH (1974) Kybernetic 15: 27–37] and recently re-designed by Jansen et al. [Jansen BH, Zouridakis G, Brandt ME (1993) Biol Cybern 68: 275–283] the present study demonstrates that this model can be extended to generate spontaneous EEG signals from multiple coupled neural populations. Model parameters related to excitation, inhibition and coupling are then altered to produce epileptiform EEG signals. Results show that the qualitative behavior of the model is realistic; simulated signals resemble those recorded from different brain structures for both interictal and ictal activities. Possible exploitation of simulations in signal processing is illustrated through one example; statistical couplings between both simulated signals and real SEEG signals are estimated using nonlinear regression. Results are compared and show that, through the model, real SEEG signals can be interpreted with the aid of signal processing methods. Received: 3 January 2000 / Accepted: 24 March 2000     

Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data

In this work we address the problem of the robust identification of unknown parameters of a cell population dynamics model from experimental data on the kinetics of cells labelled with a fluorescence marker defining the division age of the cell. The model is formulated by a first order hyperbolic PDE for the distribution of cells with respect to the structure variable x (or z) being the intensity level (or the log₁₀-transformed intensity level) of the marker. The parameters of the model are the rate functions of cell division, death, label decay and the label dilution factor. We develop a computational approach to the identification of the model parameters with a particular focus on the cell birth rate α(z) as a function of the marker intensity, assuming the other model parameters are scalars to be estimated. To solve the inverse problem numerically, we parameterize α(z) and apply a maximum likelihood approach. The parametrization is based on cubic Hermite splines defined on a coarse mesh with either equally spaced a priori fixed nodes or nodes to be determined in the parameter estimation procedure. Ill-posedness of the inverse problem is indicated by multiple minima. To treat the ill-posed problem, we apply Tikhonov regularization with the regularization parameter determined by the discrepancy principle. We show that the solution of the regularized parameter estimation problem is consistent with the data set with an accuracy within the noise level in the measurements.      

A model for dual channel segmentation of the EEG signal

Dual channel segmentation of the EEG signal has been developed. The purpose was to divide the signals into segments, according to information common for the two channels. The criterion for segmentation was based on the changes in the cross-spectrum of the two signals. It has been shown theoretically, as well as by simulation studies and by analysis of real EEG data that this method is sensitive to changes common for both channels, whereas segmentation does not occur as a result of changes in each channel separately.     

Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model

The objective of this paper is to propose and assess an estimation procedure—based on data assimilation principles—well suited to obtain some regional values of key biophysical parameters in a beating heart model, using actual Cine-MR images. The motivation is twofold: (1) to provide an automatic tool for personalizing the characteristics of a cardiac model in order to achieve predictivity in patient-specific modeling and (2) to obtain some useful information for diagnosis purposes in the estimated quantities themselves. In order to assess the global methodology, we specifically devised an animal experiment in which a controlled infarct was produced and data acquired before and after infarction, with an estimation of regional tissue contractility—a key parameter directly affected by the pathology—performed for every measured stage. After performing a preliminary assessment of our proposed methodology using synthetic data, we then demonstrate a full-scale application by first estimating contractility values associated with 6 regions based on the AHA subdivision, before running a more detailed estimation using the actual AHA segments. The estimation results are assessed by comparison with the medical knowledge of the specific infarct, and with late enhancement MR images. We discuss their accuracy at the various subdivision levels, in the light of the inherent modeling limitations and of the intrinsic information contents featured in the data.     

Modulation of EEG Rhythms and Changes in Spike Activity of Noradrenergic Neurons of the <Emphasis Type="Italic">Locus Coeruleus</Emphasis> Related to Feedback Sessions by EEG Characteristics

In chronic experiments on awake cats, we studied the dynamics of the spectral power density (SPD) of the α rhythm vs SPD of the θ rhythm ratio and also of the characteristics of impulse activity generated by supposedly noradrenergic (NA) neurons of the locus coeruleus in the course of feedback (FB) sessions by EEG characteristics (EEG-FB). Trainings were performed using a technique analogous to that in EEG-FB sessions for humans. The level of a sound noise signal presented to the animal decreased with increase in the α/θ SPD ratio in the occipital lead. Changes in the level of the sound signal did not depend on EEG modulation in the control series. The animals were trained to correlate changes in the loudness of the sound signal with the power of EEG rhythms and, in such a way, to control the latter. The α/θ SPD ratio in EEG-FB sessions changed mostly due to a significant increase in the α rhythm power. The frequency of the impulse activity of NA neurons increased in a parallel manner with such EEG modulation. Possible mechanisms of the involvement of the cerebral NA system in the formation of the effects of EEG-FB sessions are discussed.     

Maximum a posteriori estimation of change points in the EEG

A new approach for EEG segmentation is introduced. This is based on a methodology for optimal segmentation of non-stationary signals derived from the maximum a posteriori estimation principle. It is a model-based, not sequential approach that allows for segmentation at different resolution levels. The features of the methodology are illustrated by its application to EEG recordings containing several types of spectral changes due to normal and pathological variations of spontaneous brain rhythmic activities, as well as physiological artifacts.     

Changes in EEG Rhythms and Spike Activity of Brainstem Dopaminergic Neurons Induced by Neurofeedback Sessions in Cats

We examined the dynamics of the ratios of spectral power densities (SPDs) of the alpha vs theta rhythms (α/θ ratio). of EEG and of the spiking frequency of supposedly dopaminergic (DA) neurons of the ventral tegmentum in the course of neurofeedback sessions directed toward changes in the EEG characteristics. Trainings were performed using techniques analogous to that used in neurofeedback sessions in humans. The level of the noise acoustic signal presented to the animal decreased with increase in the α/θ ratio in the occipital leads. In the control realizations, there were no dependences between the intensity of the acoustic signal and modulation of the current EEG. It was found that the animals learned, in a conditioned-reflex mode, to correlate changes in the intensity of the sound signal and power of the EEG rhythms and to control the latter; a high sound intensity was probably considered a factor of discomfort. The α/θ ratio in the course of neurofeedback sessions changed due to some increase in the SPD of the alpha EEG component and a noticeable drop in the SPD of theta oscillations. In a parallel manner with such modifications, augmentation of the spike activity of DA neurons was observed. Probable mechanisms of the involvement of the cerebral DA system in the formation of the effects of neurofeedback sessions are discussed.     

Calibration of dynamic models of biological systems with KInfer

Methods for parameter estimation that are robust to experimental uncertainties and to stochastic and biological noise and that require a minimum of a priori input knowledge are of key importance in computational systems biology. The new method presented in this paper aims to ensure an inference model that deduces the rate constants of a system of biochemical reactions from experimentally measured time courses of reactants. This new method was applied to some challenging parameter estimation problems of nonlinear dynamic biological systems and was tested both on synthetic and real data. The synthetic case studies are the 12-state model of the SERCA pump and a model of a genetic network containing feedback loops of interaction between regulator and effector genes. The real case studies consist of a model of the reaction between the inhibitor κB kinase enzyme and its substrate in the signal transduction pathway of NF-κB, and a stiff model of the fermentation pathway of Lactococcus lactis.     

Modelling the Dynamical Components of the Sugar Beet Crop

Many models have been constructed to describe the growth ofthe sugar beet crop up to harvesting. In general, these modelshave a complex physiological basis, requiring a large numberof parameters yet relying on empirical functions with no mechanisticbasis to partition assimilates within the crop. An importantfactor in considering the growth of the crop, both from an economicand environmental point of view, is the response of the cropto varying amounts of available nitrogen in the soil. In thispaper, a model is described for crop growth using soil nitrogencontent and solar radiation as driving functions. The parsimoniousapproach to construction resulted in a 14 parameter model, sevenof which are associated with the driving variables. This issubstantially fewer than for other crop models. The model containsa new dynamical way of describing partitioning of assimilatesbetween shoot, storage root and fibrous roots. The partitioningmodel is derived from observations on the effect of soil nitrogenon crop growth. Interception of light is determined by foliagecover, which makes the model suitable for use with data collectedfrom satellite imaging. The model fits well to three independentdata sets with estimated parameters lying within biologicallyreasonable bounds. The model is used to test the sensitivityof yield to changes in soil nitrogen. Modelling; partitioning; parameter estimation; sugar beet; Beta vulgarisL.; nitrogen; crop growth dynamics     

Some Neurophysiological Correlates of Changed Mental States after Delivery: I. EEG Characteristics

A group of parturient women was divided on the basis of a special psychological poll into subgroups with a high (changed mental state, CMS) and low (unchanged mental state, UMS) number of signs of changes in the mental state during and after delivery. The background EEG was recorded in 16 monopolar leads before and after delivery. EEG processing included the calculation of indices of the basic rhythms, the parameters of auto- and cross-correlation functions, and the conditional probabilities of the mutual transitions of the EEG wave components that belong to the basic rhythm components according to their duration. Statistical comparison of the EEG characteristics of the subgroups, as well as their comparison with similar characteristics of the reference group of healthy nulliparous women, showed that the subgroups differed significantly in some parameters; the difference were generalized by lead zones. As a rule, the EEG characteristics of the CMS subgroup differed from those of the reference group more than those of the UMS subgroup. The differences between the CMS and UMS subgroups testify to some imbalance of the regulatory mechanisms in the former with the predominance of excitation at the predelivery stage and a more manifest physiological cerebral reaction to the delivery.     

Nonlinear EEG analysis based on a neural mass model

The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics. Received: 11 August 1997 / Accepted in revised form: 20 April 1999     

Minimal output sets for identifiability

Ordinary differential equation models in biology often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not uniquely structurally identifiable with the given set of outputs selected as measurements. In designing an experiment for the purpose of parameter estimation, given a set of feasible but resource-consuming measurements, it is useful to know which ones must be included in order to obtain an identifiable system, or whether the system is unidentifiable from the feasible measurement set. We have developed an algorithm that, from a user-provided set of variables and parameters or functions of them assumed to be measurable or known, determines all subsets that when used as outputs give a locally structurally identifiable system and are such that any output set for which the system is structurally identifiable must contain at least one of the calculated subsets. The algorithm has been implemented in Mathematica and shown to be feasible and efficient. We have successfully applied it in the analysis of large signalling pathway models from the literature.     

Nonlinear parameter estimation applied to a model of smooth pursuit eye movements

We present a procedure that optimally adjusts specified parameters of a mathematical model to describe a set of measured data. The technique integrates a dynamic systems-simulation language with a robust algorithm for nonlinear parameter estimation, and it can be implemented on a microcomputer. Sensitivity functions are generated that indicate how the operation of the model is affected by each updated parameter. This procedure offers a greater resolution of optimal parameter values than other, less rigorous methods. To illustrate this technique we have applied it to the model of human smooth pursuit eye movements proposed by D.A. Robinson and colleagues (1986).     

Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach

A new measure of dissimilarity between two EEG segments is proposed. It is derived from the application of the mathematical concept of distance between series of one-step predictions according to the estimated non-linear autoregressive functions. The non-linear autoregressive estimation is performed by non-parametric regression using kernel estimators. The possibility of applying this measure for automatic classification of EEG segments is explored. For this purpose multidimensional scaling and cluster analyses are applied on the basis of the calculated dissimilarity measures. In particular, its application to different EEG segments with delta activity and also with alpha waves reveals high agreement with visual classification by EEG specialists.     

Analysis of phase-locking is informative for studying event-related EEG activity

 A new method is presented for quantitative evaluation of single-sweep phase and amplitude electroencephalogram (EEG) characteristics that is a more informative approach in comparison with conventional signal averaging. In the averaged potential, phase-locking and amplitude effects of the EEG response cannot be separated. To overcome this problem, single-trial EEG sweeps are decomposed into separate presentations of their phase relationships and amplitude characteristics. The stability of the phase-coupling to stimulus is then evaluated independently by analyzing the single-sweep phase presentations. The method has the following advantages: information about stability of the phase-locking can be used to assess event-related oscillatory activity; the method permits evaluation of the timing of event-related phase-locking; and a global assessment and comparison of the phase-locking of ensembles of single sweeps elicited in different processing conditions is possible. The method was employed to study auditory alpha and theta responses in young and middle-aged adults. The results showed that whereas amplitudes of frequency responses tended to decrease, the phase-locking increased significantly with age. The synchronization with stimulus (phase-locking) was the only parameter reliably to differentiate the brain responses of the two age groups, as well as to reveal specific age-related changes in frontal evoked alpha activity. Thus, the present approach can be used to evaluate dynamic brain processes more precisely. Received: 12 February 1996 / Accepted in revised form: 11 October 1996     

Comparative efficiencies of different methods for removing blink artifacts in analyzing quantitative electroencephalogram and event-related potentials

Different methods for blink artifact correction in multichannel electoencephalogram (EEG) have been compared with respect to their efficiency and the relative systemic error of the estimation of the parameters of EEG spectra and event-related potentials (ERPs). Three methods of blink artifact correction have been used: distraction of the electrooculogram (EOG) signals from EEG signals, zeroing independent EEG components associated with vertical eye movement, and zeroing the principal EEG components related to blinking. The results have shown that these correction methods can substantially improve the accuracy of the estimation of quantitative EEG parameters while only slightly distorting signals from most EEG sites. It is concluded that wide use of these methods for EEG processing in fundamental and applied studies would be advisable.     

Non-linear and linear forecasting of the EEG time series

The method of non-linear forecasting of time series was applied to different simulated signals and EEG in order to check its ability of distinguishing chaotic from noisy time series. The goodness of prediction was estimated, in terms of the correlation coefficient between forecasted and real time series, for non-linear and autoregressive (AR) methods. For the EEG signal both methods gave similar results. It seems that the EEG signal, in spite of its chaotic character, is well described by the AR model.