Medicine (St Vincent's) - Research Publications
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ItemA circle criterion observer for estimating the unmeasured membrane potential of neuronal populations(IEEE, 2011-12-01)A circle criterion observer is designed for estimating the unmeasured membrane potential of neuronal populations using the electroencephalogram (EEG) from a class of parameterised models that replicates patterns seen on the EEG. Compared to existing similar designs, we provide a less conservative linear matrix inequality (LMI) condition that is shown to be fulfilled for the neural models we consider. The designed observer is robust towards disturbances in the input and measurement, as well as model uncertainty. We show that the observer can be designed for a model that reproduces alpha rhythms in the EEG as an illustrative example.
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ItemParameter and state estimation for a class of neural mass models(IEEE, 2012-01-01)We present an adaptive observer which asymptotically reconstructs the parameters and states of a model of interconnected cortical columns. Our study is motivated by the fact that the considered model is able to realistically reproduce patterns seen on (intracranial) electroencephalograms (EEG) by varying its parameters. Therefore, by estimating its parameters and states, we could gain a better understanding of the mechanisms underlying neurological phenomena such as seizures, which might lead to the prediction of the onsets of epileptic seizures. Simulations are performed to illustrate our results.
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ItemPATIENT-SPECIFIC NEURAL MASS MODELING - STOCHASTIC AND DETERMINISTIC METHODS(WORLD SCIENTIFIC PUBL CO PTE LTD, 2013)Deterministic and stochastic methods for online state and parameter estimation for neural mass models are presented and applied to synthetic and real seizure electrocorticographic signals in order to determine underlying brain changes that cannot easily be measured. The first ever online estimation of neural mass model parameters from real seizure data is presented. It is shown that parameter changes occur that are consistent with expected brain changes underlying seizures, such as increases in postsynaptic potential amplitudes, increases in the inhibitory postsynaptic time-constant and decreases in the firing threshold at seizure onset, as well as increases in the firing threshold as the seizure progresses towards termination. In addition, the deterministic and stochastic estimation methods are compared and contrasted. This work represents an important foundation for the development of biologically-inspired methods to image underlying brain changes and to develop improved methods for neurological monitoring, control and treatment.
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ItemA nonlinear estimator for the activity of neuronal populations in the hippocampus(IFAC - International Federation of Automatic Control, 2011-01-01)We present an estimator design to reconstruct the mean membrane potential of individual neuronal populations from a single channel simulated electroencephalographic signal based on a model of the hippocampus. The robustness of the estimator against variations in the synaptic gains of the neuronal populations and disturbances in the input and measurement is studied. Our results are further illustrated in simulations.
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ItemEstimating the unmeasured membrane potential of neuronal populations from the EEG using a class of deterministic nonlinear filters(IOP PUBLISHING LTD, 2012-04)We present a model-based estimation method to reconstruct the unmeasured membrane potential of neuronal populations from a single-channel electroencephalographic (EEG) measurement. We consider a class of neural mass models that share a general structure, specifically the models by Stam et al (1999 Clin. Neurophysiol. 110 1801-13), Jansen and Rit (1995 Biol. Cybern. 73 357-66) and Wendling et al (2005 J. Clin. Neurophysiol. 22 343). Under idealized assumptions, we prove the global exponential convergence of our filter. Then, under more realistic assumptions, we investigate the robustness of our filter against model uncertainties and disturbances. Analytic proofs are provided for all results and our analyses are further illustrated via simulations.
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ItemElectrical probing of cortical excitability in patients with epilepsy(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011-12)Standard methods for seizure prediction involve passive monitoring of intracranial electroencephalography (iEEG) in order to track the 'state' of the brain. This paper introduces a new method for measuring cortical excitability using an electrical probing stimulus. Electrical probing enables feature extraction in a more robust and controlled manner compared to passively tracking features of iEEG signals. The probing stimuli consist of 100 bi-phasic pulses, delivered every 10 min. Features representing neural excitability are estimated from the iEEG responses to the stimuli. These features include the amplitude of the electrically evoked potential, the mean phase variance (univariate), and the phase-locking value (bivariate). In one patient, it is shown how the features vary over time in relation to the sleep-wake cycle and an epileptic seizure. For a second patient, it is demonstrated how the features vary with the rate of interictal discharges. In addition, the spatial pattern of increases and decreases in phase synchrony is explored when comparing periods of low and high interictal discharge rates, or sleep and awake states. The results demonstrate a proof-of-principle for the method to be applied in a seizure anticipation framework. This article is part of a Supplemental Special Issue entitled The Future of Automated Seizure Detection and Prediction.
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ItemA robust circle criterion observer with application to neural mass models(PERGAMON-ELSEVIER SCIENCE LTD, 2012-11-01)A robust circle criterion observer is designed and applied to neural mass models. At present, no existing circle criterion observers apply to the considered models, i.e. the required linear matrix inequality is infeasible. Therefore, we generalise available results to derive a suitable estimation algorithm. Additionally, the design also takes into account input uncertainty and measurement noise. We show how to apply the observer to estimate the mean membrane potential of neuronal populations of a popular single cortical column model from the literature.
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ItemState and parameter estimation of nonlinear systems: a multi-observer approach(IEEE, 2014)We present a multi-observer approach for the parameter and state estimation of continuous-time nonlinear systems. For nominal parameter values in the known parameter set, state observers are designed with a robustness property. At any time instant, one observer is selected by a given criterion to provide its state estimate and its corresponding nominal parameter value. Provided that a persistency of excitation condition holds, we guarantee the convergence of state and parameter estimates up to a given margin of error which can be reduced by increasing the number of observers. The potential computational burden of the scheme is eased by introducing a dynamic parameter re-sampling technique, where the nominal parameter values are iteratively updated using a zoom-in procedure on the parameter set. We illustrate the efficacy of the algorithm on a model of neural dynamics.
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ItemParameter and State Estimation of Nonlinear Systems Using a Multi-Observer Under the Supervisory Framework(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2015-09)We present a hybrid scheme for the parameter and state estimation of nonlinear continuous-time systems, which is inspired by the supervisory setup used for control. State observers are synthesized for some nominal parameter values and a criterion is designed to select one of these observers at any given time instant, which provides state and parameter estimates. Assuming that a persistency of excitation condition holds, the convergence of the parameter and state estimation errors to zero is ensured up to a margin, which can be made as small as desired by increasing the number of observers. To reduce the potential computational complexity of the scheme, we explain how the sampling of the parameter set can be dynamically updated using a zoom-in procedure. This strategy typically requires a fewer number of observers for a given estimation error margin compared to the static sampling policy. The results are shown to be applicable to linear systems and to a class of nonlinear systems. We illustrate the applicability of the approach by estimating the synaptic gains and the mean membrane potentials of a neural mass model.
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ItemPostictal suppression and seizure durations: A patient-specific, long-term iEEG analysis(WILEY, 2018-05)OBJECTIVE: We report on patient-specific durations of postictal periods in long-term intracranial electroencephalography (iEEG) recordings. The objective was to investigate the relationship between seizure duration and postictal suppression duration. METHODS: Long-term recording iEEG from 9 patients (>50 seizures recorded) were analyzed. In total, 2310 seizures were recorded during a total of 13.8 years of recording. Postictal suppression duration was calculated as the duration after seizure termination until total signal energy returned to background levels. The relationship between seizure duration and postictal suppression duration was quantified using the correlation coefficient (r). The effects of populations of seizures within patients, on correlations, were also considered. Populations of seizures within patients were distinguished by seizure duration thresholds and k-means clustering along the dimensions of seizure duration and postictal suppression duration. The effects of bursts of seizures were also considered by defining populations based on interseizure interval (ISI). RESULTS: Seizure duration accounted for 40% of postictal suppression duration variance, aggregated across all patients and seizures. Seizure duration accounted for more than 25% of the variance in postictal suppression duration in 2 patients and accounted for less than 25% in the remaining 7. In 3 patients, heat maps showed multiple distinct postictal patterns indicating multiple populations of seizures. When accounting for these populations, seizure duration accounted for less than 25% of the variance in postictal duration in all populations. Variance in postictal suppression duration accounted for less than 10% of ISI variance in all patients. SIGNIFICANCE: We have previously demonstrated that some patients have multiple seizure populations distinguishable by seizure duration. This article shows that different seizure populations have distinct and consistent postictal behaviors. The existence of multiple populations in some patients has implications for seizure management and forecasting, whereas the distinct postictal behaviors may have implications for sudden unexpected death in epilepsy (SUDEP) prediction and prevention.