Nonlinear interactions in the thalamocortical loop in essential tremor: A model-based frequency domain analysis.

There is increasing evidence to suggest that essential tremor has a central origin. Different structures appear to be part of the central tremorogenic network, including the motor cortex, the thalamus and the cerebellum. Some studies using electroencephalogram (EEG) and magnetoencephalography (MEG) show linear association in the tremor frequency between the motor cortex and the contralateral tremor electromyography (EMG). Additionally, high thalamomuscular coherence is found with the use of thalamic local field potential (LFP) recordings and tremulous EMG in patients undergoing surgery for deep brain stimulation (DBS). Despite a well-established reciprocal anatomical connection between the thalamus and cortex, the functional association between the two structures during "tremor-on" periods remains elusive. Thalamic (Vim) LFPs, ipsilateral scalp EEG from the sensorimotor cortex and contralateral tremor arm EMG recordings were obtained from two patients with essential tremor who had undergone successful surgery for DBS. Coherence analysis shows a strong linear association between thalamic LFPs and contralateral tremor EMG, but the relationship between the EEG and the thalamus is much less clear. These measurements were then analyzed by constructing a novel parametric nonlinear autoregressive with exogenous input (NARX) model. This new approach uncovered two distinct and not overlapping frequency "channels" of communication between Vim thalamus and the ipsilateral motor cortex, defining robustly "tremor-on" versus "tremor-off" states. The associated estimated nonlinear time lags also showed non-overlapping values between the two states, with longer corticothalamic lags (exceeding 50ms) in the tremor active state, suggesting involvement of an indirect multisynaptic loop. The results reveal the importance of the nonlinear interactions between cortical and subcortical areas in the central motor network of essential tremor. This work is important because it demonstrates for the first time that in essential tremor the functional interrelationships between the cortex and thalamus should not be sought exclusively within individual frequencies but more importantly between cross-frequency nonlinear interactions. Should our results be successfully reproduced on a bigger cohort of patients with essential tremor, our approach could be used to create an on-demand closed-loop DBS device, able to automatically activate when the tremor is on

Performance of a Boussinesq model for shoaling and breaking waves : a comparison with large scale laboratory data

In this thesis, a nonlinear model predicting hydrodynamics data for waves shoaling and breaking on a beach is reproduced and extensively tested with laboratory data. The model is based on the 1D Boussinesq equations as derived by Madsen et al. (1991) and Madsen and Sorensen (1992), with the free surface elevation and the depth-integrated velocity as variables. It allows slowly varying bathymetries and contains additional high order terms to improve the frequency dispersion for shorter wave periods, and thus also to improve the shoaling properties of the model. Wave breaking is modelled using the concept of a surface roller as formulated by Schäffer et al. (1993). It is assumed that bottom friction is negligible. A large scale laboratory experiment (Supertank), designed in particular to obtain data to test the validity of wave propagation models, provides the wave and current data. Wave evolution over a complex bathymetry is examined for 4 cases. The data include conditions for long and short waves, and regular and irregular waves. During the model evaluation, emphasis is put on the study of parameters of importance to sediment transport, including (orbital) velocity, undertow and wave shape prediction. The latter encompasses velocity and elevation skewness, kurtosis and asymmetry. It is found that, despite an overestimation of the depth-averaged horizontal velocity in some cases, the predicted velocity moments and undertow are in good agreement with the data. Using a bispectral analysis, it is shown that the nonlinear transfers of energy amongst the low order harmonics are well reproduced, but that errors are introduced in the treatment of the high order super-harmonics. As a result, the short waves tests are found to yield better results than those for long waves. A sensitivity analysis on the free parameters introduced in the simulation of wave breaking is carried out. It appears that the results are mostly sensitive to the critical xv avve fi-ont slope OB , and in particular that the elevation and velocity skewness and kurtosis predictions are very sensitive to this parameter.the University of Plymouth

Identifying nonlinear wave interactions in plasmas using two-point measurements: a case study of Short Large Amplitude Magnetic Structures (SLAMS)

A framework is described for estimating Linear growth rates and spectral energy transfers in turbulent wave-fields using two-point measurements. This approach, which is based on Volterra series, is applied to dual satellite data gathered in the vicinity of the Earth's bow shock, where Short Large Amplitude Magnetic Structures (SLAMS) supposedly play a leading role. The analysis attests the dynamic evolution of the SLAMS and reveals an energy cascade toward high-frequency waves.Comment: 26 pages, 13 figure

New Optimised Estimators for the Primordial Trispectrum

Cosmic microwave background studies of non-Gaussianity involving higher-order multispectra can distinguish between early universe theories that predict nearly identical power spectra. However, the recovery of higher-order multispectra is difficult from realistic data due to their complex response to inhomogeneous noise and partial sky coverage, which are often difficult to model analytically. A traditional alternative is to use one-point cumulants of various orders, which collapse the information present in a multispectrum to one number. The disadvantage of such a radical compression of the data is a loss of information as to the source of the statistical behaviour. A recent study by Munshi & Heavens (2009) has shown how to define the skew spectrum (the power spectra of a certain cubic field, related to the bispectrum) in an optimal way and how to estimate it from realistic data. The skew spectrum retains some of the information from the full configuration-dependence of the bispectrum, and can contain all the information on non-Gaussianity. In the present study, we extend the results of the skew spectrum to the case of two degenerate power-spectra related to the trispectrum. We also explore the relationship of these power-spectra and cumulant correlators previously used to study non-Gaussianity in projected galaxy surveys or weak lensing surveys. We construct nearly optimal estimators for quick tests and generalise them to estimators which can handle realistic data with all their complexity in a completely optimal manner. We show how these higher-order statistics and the related power spectra are related to the Taylor expansion coefficients of the potential in inflation models, and demonstrate how the trispectrum can constrain both the quadratic and cubic terms.Comment: 19 pages, 2 figure

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a small amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention

Imaging the spatial-temporal neuronal dynamics using dynamic causal modelling

Oscillatory brain activity is a ubiquitous feature of neuronal dynamics and the synchronous discharge of neurons is believed to facilitate integration both within functionally segregated brain areas and between areas engaged by the same task. There is growing interest in investigating the neural oscillatory networks in vivo. The aims of this thesis are to (1) develop an advanced method, Dynamic Causal Modelling for Induced Responses (DCM for IR), for modelling the brain network functions and (2) apply it to exploit the nonlinear coupling in the motor system during hand grips and the functional asymmetries during face perception. DCM for IR models the time-varying power over a range of frequencies of coupled electromagnetic sources. The model parameters encode coupling strength among areas and allows the differentiations between linear (within frequency) and nonlinear (between-frequency) coupling. I applied DCM for IR to show that, during hand grips, the nonlinear interactions among neuronal sources in motor system are essential while intrinsic coupling (within source) is very likely to be linear. Furthermore, the normal aging process alters both the network architecture and the frequency contents in the motor network. I then use the bilinear form of DCM for IR to model the experimental manipulations as the modulatory effects. I use MEG data to demonstrate functional asymmetries between forward and backward connections during face perception: Specifically, high (gamma) frequencies in higher cortical areas suppressed low (alpha) frequencies in lower areas. This finding provides direct evidence for functional asymmetries that is consistent with anatomical and physiological evidence from animal studies. Lastly, I generalize the bilinear form of DCM for IR to dissociate the induced responses from evoked ones in terms of their functional role. The backward modulatory effect is expressed as induced, but not evoked responses

Exploring the pharmacodynamics of multidrug combinations and using the advances in technology to individualise anaesthetic drug titration

In current practice, pharmacokinetic-dynamic (PK/PD) models are frequently used to describe the combined relationship between the time course of drug plasma concentrations (PK) and the time independent relationship between the drug concentration at the receptor site and the clinical effect (PD). This thesis contributes to the knowledge in anaesthetic pharmacology and explores the dose-response relationships of propofol and sevoflurane (with and without the coadministration of remifentanil) in greater detail using PK/PD models. Our studies show that PK/PD models are useful in clinical practice. The concept of neural inertia could have an influence on these models, but is still controversial in humans and it does not break down the essence and applicability of these PK/PD models. Subsequently, we used these models to compare the pharmacodynamics of propofol and sevoflurane (with and without remifentanil) at both a population level as well as at an individual level. This comparison let us describe potency ratios between both hypnotics which is very helpful for anaesthetist when switching between these drugs for any reason during a case. We applied the same PK/PD models and similar potency ratios in clinical practice using the SmartPilot® View, a drug advisory system, to guide anaesthetic drug titration, and we assessed its clinical utility. Finally, we evaluated a novel method to analyse the cerebral drug effect on the EEG using Artificial Intelligence in order to explore the feasibility of whether a single index can quantify the hypnotic effect in a drug-independent way

CLOSED-LOOP CONTROLLED TOTAL INTRA VENOUS ANAESTHESIA

Anaesthesia is important for both surgery and intensive care and intravenous anaesthetics are widely used to provide rapid onset, stable maintenance, and rapid recovery compared with inhaled anaesthetics. The aim of the project on which this thesis is based was to investigate a reliable and safe methodology for delivering total intravenous anaesthesia using closed-loop control technology and bispectral analysis of human electroencephalogram (EEG) waveform. In comparison with Target Controlled Infusion (TCI), drug effect is measured during drug infusion in closed loop anaesthesia (CLAN). This may provide superior safety, better patient care, and better quality of anaesthesia whilst relieving the clinician of the need to make recurrent and minor alterations to drug administration. However, the development of a CLAN system has been hindered by the Jack of a 'gold standard' for anaesthetic states and difficulties with patient variability in pharmacokinetic and pharmacodynamic modelling, and a new and generic mathematical model of a closed-loop anaesthesia system was developed for this investigation. By using this CLAN model, investigations on pharmacokinetic and pharmacodynamic variability existing in patients were carried out. A new control strategy that combines a Proportional, Integral, Derivative (PID) controller, bispectral analysis of EEG waveform and pharmacokinetic/ pharmacodynamic models was investigated. Based on the mathematical model, a prototype CLAN system, the first CLAN system capable of delivering both hypnotics and analgesics simultaneously for total intravenous anaesthesia, was developed. A Bispectral Index (BIS), derived from power spectral and bispectral analysis on EEG waveform, is used to measure depth of anaesthesia. A supervision system with built-in digital signal processing techniques was developed to compensate the non-linear characteristics inherent in the system while providing a comprehensive protection mechanism for patient safety. The CLAN system was tested in 78125 virtual patients modelled using published data. Investigations on intravenous anaesthesia induction and maintenance with the CLAN system were carried out in various clinical settings on 21 healthy volunteers and 15 patients undergoing surgery. Anaesthesia targets were achieved quickly and well maintained in all volunteers/patients except for 2 patients with clinically satisfactory anaesthesia quality.Derriford Hospita