Medicine (St Vincent's) - Research Publications

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    Electrical Stimulation of Neural Tissue Modeled as a Cellular Composite: Point Source Electrode in an Isotropic Tissue
    Monfared, O ; Nesic, D ; Freestone, DR ; Grayden, DB ; Tahayori, B ; Meffin, H (IEEE, 2014-01-01)
    Standard volume conductor models of neural electrical stimulation assume that the electrical properties of the tissue are well described by a conductivity that is smooth and homogeneous at a microscopic scale. However, neural tissue is composed of tightly packed cells whose membranes have markedly different electrical properties to either the intra- or extracellular space. Consequently, the electrical properties of tissue are highly heterogeneous at the microscopic scale: a fact not accounted for in standard volume conductor models. Here we apply a recently developed framework for volume conductor models that accounts for the cellular composition of tissue. We consider the case of a point source electrode in tissue comprised of neural fibers crossing each other equally in all directions. We derive the tissue admittivity (that replaces the standard tissue conductivity) from single cell properties, and then calculate the extracellular potential. Our findings indicate that the cellular composition of tissue affects the spatiotemporal profile of the extracellular potential. In particular, the full solution asymptotically approaches a near-field limit close to the electrode and a far-field limit far from the electrode. The near-field and far-field approximations are solutions to standard volume conductor models, but differ from each other by nearly an order or magnitude. Consequently the full solution is expected to provide a more accurate estimate of electrical potentials over the full range of electrode-neurite separations.
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    A Neural Mass Model of Spontaneous Burst Suppression and Epileptic Seizures
    Freestone, DR ; Nesic, D ; Jafarian, A ; Cook, MJ ; Grayden, DB (IEEE, 2013-01-01)
    The paper presents a neural mass model that is capable of simulating the transition to and from various forms of paroxysmal activity such as burst suppression and epileptic seizure-like waveforms. These events occur without changing parameters in the model. The model is based on existing neural mass models, with the addition of feedback of fast dynamics to create slowly time varying parameters, or slow states. The goal of this research is to establish a link between system properties that modulate neural activity and the fast changing dynamics, such as membrane potentials and firing rates that can be manipulated using electrical stimulation. Establishing this link is likely to be a necessary component of a closed-loop system for feedback control of pathological neural activity.
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    A circle criterion observer for estimating the unmeasured membrane potential of neuronal populations
    Chong, M ; Postoyan, R ; Nešić, D ; Kuhlmann, L ; Varsavsky, A (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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    Parameter and state estimation for a class of neural mass models
    Postoyan, R ; Chong, M ; Nesic, D ; Kuhlmann, L (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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    INFERRING PATIENT-SPECIFIC PHYSIOLOGICAL PARAMETERS FROM INTRACRANIAL EEG: APPLICATION TO CLINICAL DATA
    Shmuely, S ; Freestone, DR ; Grayden, DB ; Nesic, D ; Cook, M (WILEY-BLACKWELL, 2012-09-01)
    Purpose: Intracranial EEG (iEEG) provides information regarding where and when seizures occur, whilst the underlying mechanisms are hidden. However physiologically plausible mechanisms for seizure generation and termination are explained by neural mass models, which describe the macroscopic neural dynamics. Fusion of models with patient-specific data allows estimation and tracking of the normally hidden physiological parameters. By monitoring changes in physiology, a new understanding of seizures can be achieved. This work addresses model-data fusion for iEEG for application in a clinical setting. Method: Data was recorded from three patients undergoing evaluation for epilepsy-related surgery at St. Vincent's Hospital, Melbourne. Using this data, we created patient-specific neural mass mathematical models based on the formulation of Jansen and Rit (1995). The parameters that were estimated include the synaptic gains, time constants, and the firing threshold. The estimation algorithm utilized the Unscented Kalman Filter (Julier and Uhlmann, 1997). Result: We demonstrate how parameters changed in relation to seizure initiation, evolution and termination. We also show within-patient (across different seizures) and between-patient specificity of the parameter estimates. Conclusion: The fusion of clinical data and mathematical models can be used to infer valuable information about the underlying mechanisms of epileptic seizure generation. This information could be used to develop novel therapeutic strategies
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    A nonlinear estimator for the activity of neuronal populations in the hippocampus
    Chong, M ; Postoyan, R ; Nešić, D ; Kuhlmann, L ; Varsavsky, A (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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    Analytic synchronization conditions for a network of Wilson and Cowan oscillators
    Ahmadizadeh, S ; Nesic, D ; Grayden, DB ; Freestone, DR (IEEE, 2015)
    We investigate the problem of synchronization in a network of homogeneous Wilson-Cowan oscillators with diffusive coupling. Such networks can be used to model the behavior of populations of neurons in cortical tissue, referred to as neural mass models. A new approach is proposed to address local synchronization for these types of neural mass models. By exploiting the linearized model around a limit cycle, we analyze synchronization within a network for weak, intermediate, and strong coupling. We use two-time scale averaging and the Chetaev theorem to analytically check the absence or presence of synchronization in the network with weak coupling. We also utilize the Chetaev theorem to analytically prove synchronization death in a network with strong coupling. For intermediate coupling, we use a recently proposed numerical approach to prove synchronization in the network. Simulation results confirm and illustrate our results.
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    State and parameter estimation of nonlinear systems: a multi-observer approach
    Chong, MS ; Nesic, D ; Postoyan, R ; Kuhlmann, L (IEEE, 2014-01-01)
    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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    Identification of a Neural Mass Model of Burst Suppression
    Jafarian, A ; Freestone, DR ; Nesic, D ; Grayden, D (IEEE, 2019)
    Burst suppression includes alternating patterns of silent and fast spike activities in neuronal activities observable in micro to macro scale recordings. Biological models of burst suppression are given as dynamical systems with slow and fast states. The aim of this paper is to give a method to identify parameters of a mesoscopic model of burst suppression that can provide insights into study underlying generators of intracranial electroencephalogram (iEEG) data. An optimisation technique based upon a genetic algorithm (GA) is employed to find feasible model parameters to replicate burst patterns in the iEEG data with paroxysmal transitions. Then, a continuous discrete unscented Kalman filter (CD-UKF) is used to infer hidden states of the model and to enhance the identification results from the GA. The results show promise in finding the model parameters of a partially observed mesoscopic model of burst suppression.