Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV

Functional MRI data analysis : Detection, estimation and modelling

Ph.DDOCTOR OF PHILOSOPH

Neural activity inspired asymmetric basis function TV-NARX model for the identification of time-varying dynamic systems

Inspired by the unique neuronal activities, a new time-varying nonlinear autoregressive with exogenous input (TV-NARX) model is proposed for modelling nonstationary processes. The NARX nonlinear process mimics the action potential initiation and the time-varying parameters are approximated with a series of postsynaptic current like asymmetric basis functions to mimic the ion channels of the inter-neuron propagation. In the model, the time-varying parameters of the process terms are sparsely represented as the superposition of a series of asymmetric alpha basis functions in an over-complete frame. Combining the alpha basis functions with the model process terms, the system identification of the TV-NARX model from observed input and output can equivalently be treated as the system identification of a corresponding time-invariant system. The locally regularised orthogonal forward regression (LROFR) algorithm is then employed to detect the sparse model structure and estimate the associated coefficients. The excellent performance in both numerical studies and modelling of real physiological signals showed that the TV-NARX model with asymmetric basis function is more powerful and efficient in tracking both smooth trends and capturing the abrupt changes in the time-varying parameters than its symmetric counterparts

Detecting and tracking time-varying causality with applications to EEG data

This paper introduces a novel method called the ERR-Causality, or Error Reduction Ratio Causality test, that can be used to detect and track causal relationships between two signals using a new adaptive forward orthogonal least squares (Adaptive-Forward-OLS) algorithm. In comparison to the traditional Granger method, one advantage of the new ERR-Causality test is that it can effectively detect the time-varying direction of linear or nonlinear causality between two signals without fitting a complete model. Another important advantage is that the ERR-Causality test can detect both the direction of interactions and estimate the relative time shift between the two signals. Several numerical examples are provided to illustrate the effectiveness of the new method for causal relationship detection between two signals. An important real application, relating to the analysis of the causality of EEG signals from different cortical sites which can be very useful for understanding brain activity during an epileptic seizure by inspecting the high-resolution time varying directed information flow, is also discussed

Towards Bayesian System Identification: With Application to SHM of Offshore Structures

Within the offshore industry Structural Health Monitoring remains a growing area of interest. The oil and gas sectors are faced with ageing infrastructure and are driven by the desire for reliable lifetime extension, whereas the wind energy sector is investing heavily in a large number of structures. This leads to a number of distinct challenges for Structural Health Monitoring which are brought together by one unifying theme --- uncertainty. The offshore environment is highly uncertain, existing structures have not been monitored from construction and the loading and operational conditions they have experienced (among other factors) are not known. For the wind energy sector, high numbers of structures make traditional inspection methods costly and in some cases dangerous due to the inaccessibility of many wind farms. Structural Health Monitoring attempts to address these issues by providing tools to allow automated online assessment of the condition of structures to aid decision making. The work of this thesis presents a number of Bayesian methods which allow system identification, for Structural Health Monitoring, under uncertainty. The Bayesian approach explicitly incorporates prior knowledge that is available and combines this with evidence from observed data to allow the formation of updated beliefs. This is a natural way to approach Structural Health Monitoring, or indeed, many engineering problems. It is reasonable to assume that there is some knowledge available to the engineer before attempting to detect, locate, classify, or model damage on a structure. Having a framework where this knowledge can be exploited, and the uncertainty in that knowledge can be handled rigorously, is a powerful methodology. The problem being that the actual computation of Bayesian results can pose a significant challenge both computationally and in terms of specifying appropriate models. This thesis aims to present a number of Bayesian tools, each of which leverages the power of the Bayesian paradigm to address a different Structural Health Monitoring challenge. Within this work the use of Gaussian Process models is presented as a flexible nonparametric Bayesian approach to regression, which is extended to handle dynamic models within the Gaussian Process NARX framework. The challenge in training Gaussian Process models is seldom discussed and the work shown here aims to offer a quantitative assessment of different learning techniques including discussions on the choice of cost function for optimisation of hyperparameters and the choice of the optimisation algorithm itself. Although rarely considered, the effects of these choices are demonstrated to be important and to inform the use of a Gaussian Process NARX model for wave load identification on offshore structures. The work is not restricted to only Gaussian Process models, but Bayesian state-space models are also used. The novel use of Particle Gibbs for identification of nonlinear oscillators is shown and modifications to this algorithm are applied to handle its specific use in Structural Health Monitoring. Alongside this, the Bayesian state-space model is used to perform joint input-state-parameter inference for Operational Modal Analysis where the use of priors over the parameters and the forcing function (in the form of a Gaussian Process transformed into a state-space representation) provides a methodology for this output-only identification under parameter uncertainty. Interestingly, this method is shown to recover the parameter distributions of the model without compromising the recovery of the loading time-series signal when compared to the case where the parameters are known. Finally, a novel use of an online Bayesian clustering method is presented for performing Structural Health Monitoring in the absence of any available training data. This online method does not require a pre-collected training dataset, nor a model of the structure, and is capable of detecting and classifying a range of operational and damage conditions while in service. This leaves the reader with a toolbox of methods which can be applied, where appropriate, to identification of dynamic systems with a view to Structural Health Monitoring problems within the offshore industry and across engineering

The dynamics of market efficiency: testing the adaptive market hypothesis in South Africa

A thesis submitted to the School of Economic and Business Sciences, Faculty of Commerce, Law and Management, University of the Witwatersrand in fulfilment of the requirements for the degree of Doctor of Philosophy (Ph/D). Johannesburg, South Africa June 2016In recent years, the debate on market efficiency has shifted to providing alternate forms of the hypothesis, some of which are testable and can be proven false. This thesis examines one such alternative, the Adaptive Market Hypothesis (AMH), with a focus on providing a framework for testing the dynamic (cyclical) notion of market efficiency using South African equity data (44 shares and six indices) over the period 1997 to 2014. By application of this framework, stylised facts emerged. First, the examination of market efficiency is dependent on the frequency of data. If one were to only use a single frequency of data, one might obtain conflicting conclusions. Second, by binning data into smaller sub-samples, one can obtain a pattern of whether the equity market is efficient or not. In other words, one might get a conclusion of, say, randomess, over the entire sample period of daily data, but there may be pockets of non-randomness with the daily data. Third, by running a variety of tests, one provides robustness to the results. This is a somewhat debateable issue as one could either run a variety of tests (each being an improvement over the other) or argue the theoretical merits of each test befoe selecting the more appropriate one. Fourth, analysis according to industries also adds to the result of efficiency, if markets have high concentration sectors (such as the JSE), one might be tempted to conclude that the entire JSE exhibits, say, randomness, where it could be driven by the resources sector as opposed to any other sector. Last, the use of neural networks as approximators is of benefit when examining data with less than ideal sample sizes. Examining five frequencies of data, 86% of the shares and indices exhibited a random walk under daily data, 78% under weekly data, 56% under monthly data, 22% under quarterly data and 24% under semi-annual data. The results over the entire sample period and non-overlapping sub-samples showed that this model's accuracy varied over time. Coupled with the results of the trading strategies, one can conclude that the nature of market efficiency in South Africa can be seen as time dependent, in line with the implication of the AMH.MT201

Review of rational (total) nonlinear dynamic system modelling, identification, and control

© 2013 Taylor & Francis. This paper is a summary of the research development in the rational (total) nonlinear dynamic modelling over the last two decades. Total nonlinear dynamic systems are defined as those where the model parameters and input (controller outputs) are subject to nonlinear to the output. Previously, this class of models has been known as rational models, which is a model that can be considered to belong to the nonlinear autoregressive moving average with exogenous input (NARMAX) model subset and is an extension of the well-known polynomial NARMAX model. The justification for using the rational model is that it provides a very concise and parsimonious representation for highly complex nonlinear dynamic systems and has excellent interpolatory and extrapolatory properties. However, model identification and controller design are much more challenging compared to the polynomial models. This has been a new and fascinating research trend in the area of mathematical modelling, control, and applications, but still within a limited research community. This paper brings several representative algorithms together, developed by the authors and their colleagues, to form an easily referenced archive for promotion of the awareness, tutorial, applications, and even further research expansion

Time-varying nonlinear causality detection using regularized orthogonal least squares and multi-wavelets with applications to EEG

A new transient Granger causality detection method is proposed based on a time-varying parametric modelling framework, and is applied to real EEG signals to reveal the causal information flow during motor imagery (MI) tasks. The time-varying parametric modelling approach employs a nonlinear autoregressive with external input (NARX) model, whose parameters are approximated by a set of multiwavelet basis functions. A regularized orthogonal least squares (ROLS) algorithm is then used to produce a parsimonious or sparse regression model and estimate the associated model parameters. The time-varying Granger causality between nonstationary signals can be detected accurately by making use of both the good approximation properties of multi-wavelets and the good generalization performance of the ROLS in the presence of high-level noise. Two simulation examples are presented to demonstrate the effectiveness of the proposed method for both linear and nonlinear causal detection respectively. The proposed method is then applied to real EEG signals of MI tasks. It follows that transient causal information flow over the time course between various sensorimotor related channels can be successfully revealed during the whole reaction processes. Experiment results from these case studies confirm the applicability of the proposed scheme and show its utility for the understanding of the associated neural mechanism and the potential significance for developing MI tasks based brain-computer interface (BCI) systems

A parametric time frequency-conditional Granger causality method using ultra-regularized orthogonal least squares and multiwavelets for dynamic connectivity analysis in EEGs

Objective: This study proposes a new para-metric TF-CGC (time-frequency conditional Granger causality) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source EEG signals to reveal dynamic interaction patterns in oscillatory neo-cortical sensorimotor networks. Methods: The Geweke's spectral measure is combined with the TVARX (time-varying autoregressive with exogenous input) model-ling approach, which uses multiwavelet-based ul-tra-regularized orthogonal least squares (UROLS) algo-rithm aided by APRESS (adjustable prediction error sum of squares), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems. Re-sults: The proposed method is validated on two simulations and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cor-tical networks. Conclusion: Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks. Significance: The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition

Closed-Loop Brain-Computer Interfaces for Memory Restoration Using Deep Brain Stimulation

The past two decades have witnessed the rapid growth of therapeutic brain-computer interfaces (BCI) targeting a diversity of brain dysfunctions. Among many neurosurgical procedures, deep brain stimulation (DBS) with neuromodulation technique has emerged as a fruitful treatment for neurodegenerative disorders such as epilepsy, Parkinson\u27s disease, post-traumatic amnesia, and Alzheimer\u27s disease, as well as neuropsychiatric disorders such as depression, obsessive-compulsive disorder, and schizophrenia. In parallel to the open-loop neuromodulation strategies for neuromotor disorders, recent investigations have demonstrated the superior performance of closed-loop neuromodulation systems for memory-relevant disorders due to the more sophisticated underlying brain circuitry during cognitive processes. Our efforts are focused on discovering unique neurophysiological patterns associated with episodic memories then applying control theoretical principles to achieve closed-loop neuromodulation of such memory-relevant oscillatory activity, especially, theta and gamma oscillations. First, we use a unique dataset with intracranial electrodes inserted simultaneously into the hippocampus and seven cortical regions across 40 human subjects to test for the presence of a pattern that the phase of hippocampal theta oscillation modulates gamma oscillations in the cortex, termed cross-regional phase-amplitude coupling (xPAC), representing a key neurophysiological mechanism that promotes the temporal organization of interregional oscillatory activities, which has not previously been observed in human subjects. We then establish that the magnitude of xPAC predicts memory encoding success along with other properties of xPAC. We find that strong functional xPAC occurs principally between the hippocampus and other mesial temporal structures, namely entorhinal and parahippocampal cortices, and that xPAC is overall stronger for posterior hippocampal connections. Next, we focus on hippocampal gamma power as a `biomarker\u27 and use a novel dataset in which open-loop DBS was applied to the posterior cingulate cortex (PCC) during the encoding of episodic memories. We evaluate the feasibility of modulating hippocampal power by a precise control of stimulation via a linear quadratic integral (LQI) controller based on autoregressive with exogenous input (ARX) modeling for in-vivo use. In the simulation framework, we demonstrate proposed BCI system achieves effective control of hippocampal gamma power in 15 out of 17 human subjects and we show our DBS pattern is physiologically safe with realistic time scales. Last, we further develop the PCC-applied binary-noise (BN) DBS paradigm targeting the neuromodulation of both hippocampal theta and gamma oscillatory power in 12 human subjects. We utilize a novel nonlinear autoregressive with exogenous input neural network (NARXNN) as the plant paired with a proportional–integral–derivative (PID) controller (NARXNN-PID) for delivering a precise stimulation pattern to achieve desired oscillatory power level. Compared to a benchmark consisted of a linear state-space model (LSSM) with a PID controller, we not only demonstrate that the superior performance of our NARXNN plant model but also show the greater capacity of NARXNN-PID architecture in controlling both hippocampal theta and gamma power. We outline further experimentation to test our BCI system and compare our findings to emerging closed-loop neuromodulation strategies