| dc.description.abstract | The human brain comprises of neurons that connect with each other via electrical signals. One can record and measure these activities using an electroencephalogram (EEG). An essential use of the EEG is in locating the generating source of these signals, usually approximated by dipoles. This is important because, in some particular circumstances, neurons may not function optimally and could make the equivalent dipole generate abnormal signals. This could be a result of seizures or other brain disorders. In order to isolate such disorders, the challenge is to find a non-invasive way to locate the anomalous source.
This research aims to introduce an algorithm that not only can precisely detect the source location of an EEG-like signal but also estimate all other characteristic signal features, such as orientation and magnitude. In general, any source identification problem is solved in two steps. The first step is called the Forward Problem, where the measured signal is simulated mathematically. In the Forward Problem, it is assumed that all the parameters, such as the location of the sensors on the scalp, the properties of the source (location, orientation, and magnitude), and the head model conductivity, are known. All the mentioned
properties are passed to a proper mathematical model that can simulate the signal measured by each sensor.
The second step is the Inverse Problem, which aims to predict the source properties. This problem starts in the opposite direction to the Forward Problem. In this case, it is assumed that the collected signals from the sensors are available, and by utilizing the present mathematical model, one should be able to find the source location and other features. Among different methods to solve the Inverse Problem, a Least Squares error-based Source Localization algorithm is used. This algorithm enables us to add both linear and non-linear constraints, which optimize solving the source identification problem.
Given the absence of the physical source in the EEG-like signal, the actual values of source properties are unknown. Thus, to evaluate the accuracy of the proposed source identification algorithm and compare the estimation results to the actual values, one can use three main approaches. First, one can use the Forward Problem to generate synthetic data where it is assumed that all the dipole features are known. Hence, the estimation result can be compared to these available source properties. Second, comparing the estimation result to one of the available and well-known software is recommended. This study uses the popular MATLAB-based software called EEGLAB to evaluate the proposed estimation.
The third approach to assess the estimation accuracy of the presented method is to use an experimental setup and generate EEG-like signals. In this case, the source is visible, unlike the EEG signals, and all the source properties are known. Since a realistic head phantom is complicated to make and unavailable in many laboratories, a simple experimental setup, including a bucket filled with salt and water, is used to generate the EEG-like signals. This setup is very common for fundamental EEG signal tests. In this experiment, the electrical sources generate a sine wave with different frequencies to make the test more complicated and challenge the least squares error based source identification algorithm. The proposed algorithm uses the measured data from different oscillatory signal sources and solves an inverse problem by minimizing a cost function to estimate all the signal properties, including the locations, frequencies, and phases. To increase the overall signal accuracy for a wide range of initial guess frequencies, we have utilized the Lomb-Scargle spectral analysis along with the Least Squares error optimization method. We observed that our algorithm can identify the source location within 10 mm from the actual source immersed inside the bucket of radius $=\sim$ 90 mm. Moreover, the frequency estimation error is nearly zero, which justifies the effectiveness of our proposed method.
Finally, we have introduced a novel head model which considered different conductivities without using Finite Element Method (FEM). This approach is based on random conductivity distribution and is computationally less expensive than FEM while providing an acceptable result to generate EEG signals using Forward Model. | |
