Biomedical Engineering - Research Publications
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ItemElectrical Stimulation of Neural Tissue Modeled as a Cellular Composite: Point Source Electrode in an Isotropic Tissue(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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ItemA Neural Mass Model of Spontaneous Burst Suppression and Epileptic Seizures(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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ItemAnalytic synchronization conditions for a network of Wilson and Cowan oscillators(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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ItemSlow-Fast Duffing Neural Mass Model(IEEE, 2019)Epileptic seizures may be initiated by random neuronal fluctuations and/or by pathological slow regulatory dynamics of ion currents. This paper presents extensions to the Jansen and Rit neural mass model (JRNMM) to replicate paroxysmal transitions in intracranial electroencephalogram (iEEG) recordings. First, the Duffing NMM (DNMM) is introduced to emulate stochastic generators of seizures. The DNMM is constructed by applying perturbations to linear models of synaptic transmission in each neural population of the JRNMM. Then, the slow-fast DNMM is introduced by considering slow dynamics (relative to membrane potential and firing rate) of some internal parameters of the DNMM to replicate pathological evolution of ion currents. Through simulation, it is illustrated that the slow-fast DNMM exhibits transitions to and from seizures with etiologies that are linked either to random input fluctuations or pathological evolution of slow states. Estimation and optimization of a log likelihood function (LLF) using a continuous-discrete unscented Kalman filter (CD-UKF) and a genetic algorithm (GA) are performed to capture dynamics of iEEG data with paroxysmal transitions.