Localization of multiple deep epileptic sources in a realistic head model via independent component analysis

Journal ArticleEstimating the location and distribution of current sources within the brain from electroencephalographic (EEG) recordings is an ill-posed inverse problem. The ill-posedness of the problem is due to a lack of uniqueness in the solution; that is, different configurations of sources can generate identical external fields. Additionally, the existence of only a finite number of scalp measurements increases the under-determined nature of this problem. Most source localization algorithms attempt to solve the inverse problem by fitting the potenials created on the scalp from multiple dipoles to a single time step of EEG measurements. In this paper we consider a spatio-temporal model and exploit the assumption that the EEG signal is composed of contributions from statistically independent sources. Under this assumption, we can apply the recently derived blind source separation algorithm (BSS), also referred as to Independent Component Analysis (ICA). This algorithm separates multichannel EEG data into temporally independent activation maps due to stationary sources. For our study, we use a 64 channel EEG recording of a multi-focal epileptic event and a realistic geometric model of the cranial volume derived from MRI data. The original ICA algorithm required the number of sources to be equal to the number of recorded channels and becomes unstable otherwise. In this paper, we propose a novel approach for solving this problem through the reduction of the data subspace. Specifically, we discard eigenvectors with small eigenvalues from a PCA analysis of the data prior to ICA decomposition. Our results show that using these proposed subspace reduction methods, multi-focal epileptic data can be successfully decomposed into several independent activation maps. For each activation map we perform a separate source localization procedure, looking only for a single dipole using a multistart downhill simplex method. The localized sources are found to be located and oriented at physiologically appropriate positions within the brain

Mathematical Foundation of Electroencephalography

Electroencephalography (EEG) has evolved over the years to be one of the primary diagnostic technologies providing information concerning the dynamics of spontaneous and stimulated electrical brain activity. The core question of EEG is to acquire the precise location and strength of the sources inside the human brain by knowledge of an electrical potential measured on the scalp. But in what way is the source recovered? Leaving aside the biological mechanisms on the cellular level responsible for the recorded EEG signals, we pay attention to the mathematical aspects of the narrative. Our goal is to provide a brief and concise introduction of the mathematical terminology associated with the modality of EEG. We start from the very beginning, presenting step by step the mathematical formulation behind EEG in a simple and clear manner, keeping the mathematical notation to a minimum. Whilst we serve only the key relations for the described problems, we focus specifically on the limitations of each modelling approach. In this fashion, the reader can appreciate the beauty of the formulas presented and discover every single piece of information encoded within these formulas

NASA supported research programs

A summary of the scientific NASA grants and achievements accomplished by the University of California, Los Angles, is presented. The development of planetary and space sciences as a major curriculum of the University, and statistical data on graduate programs in aerospace sciences are discussed. An interdisciplinary approach to aerospace science education is emphasized. Various research programs and scientific publications that are a direct result of NASA grants are listed

The effects of noise on binocular rivalry waves: a stochastic neural field model

We analyse the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how multiplicative noise in the activity variables leads to a diffusive–like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. The multiplicative noise also renormalizes the mean speed of the wave. We use our analysis to calculate the first passage time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation leads to quenched disorder in the neural fields during propagation of a wave

Localizing Brain Activity from Multiple Distinct Sources via EEG

An important question arousing in the framework of electroencephalography (EEG) is the possibility to recognize, by means of a recorded surface potential, the number of activated areas in the brain. In the present paper, employing a homogeneous spherical conductor serving as an approximation of the brain, we provide a criterion which determines whether the measured surface potential is evoked by a single or multiple localized neuronal excitations. We show that the uniqueness of the inverse problem for a single dipole is closely connected with attaining certain relations connecting the measured data. Further, we present the necessary and sufficient conditions which decide whether the collected data originates from a single dipole or from numerous dipoles. In the case where the EEG data arouses from multiple parallel dipoles, an isolation of the source is, in general, not possible