Spatial Regularization for Head Models using EEG and MRI Antonio Quintero Rinc´ on 1 , Alberto Tabl´ on 1 , Marcelo Pereyra 2 , 1,3 Marcelo Risk 1
Buenos Aires Institute of Technology, Bioengineering Department, Av. Eduardo Madero 399, Buenos Aires, 1106, Argentine 3 University of Bristol, Department of Maths, Clifton, Bristol BS8 1TW, U.K. 4 National Council of Scientific and Technical Research, Argentine. E-mail:
[email protected] Abstract. The brain is divided into a large number of regions, each of which, when active, generates a local magnetic field or synaptic electric current. The brain activities can be considered to constitute signals which are either spontaneous and correspond to the normal rhythms of the brain, a result of brain stimulation, or related to physical movements. Localization of brain signal sources solely from EEGs are necessary for the study of different parts of the brain and such source localization is necessary to study brain physiological, mental, pathological, and functional abnormalities, and even problems related to various body disabilities, and ultimately to specify the sources of abnormalities, such as tumours and epilepsy. In the brain activity image reconstruction there are several ways and solutions that can suit the same problem and its constrains. In this work we estimate the unknown variable in the inverse problem through regularization techniques, the implementation of the realistic head model with BEM was obtained using Spatial and Spatio-Temporal regularization, the results were evaluated by medical specialists and it showed a good performance, the source activity was correctly localized and the image was satisfactory. We suggest that the regularization techniques are accurate for indicating both the time course and the number of sources.
1. Introducction Many electrical activity can be measured on the surface of the body non-invasively, such as ECG can be measured on the surface of the thorax, the EMG in the muscles and the scalp EEG. The question that confronts the physician is to determine the source of the measured signal, in order to decide whether the source is normal or abnormal. The problem in which the field and the conductor are known but the source is unknown, is called the inverse problem, the first theoretical paper, which stated that the inverse problem does not have a unique solution, was written by Hermann von Helmholtz (1853) [26]. The brain is composed of excitable nerve tissue, whose study is of great interest given the critical role played by this organ in the human function. The electrical activity can be measured easily in the scalp by an EEG. In brain tissue are the locations of the electrical sources (Sources) and the volume conductor including the skull and scalp (section 2). The brain cortex can be modeled as a fixed number of vertices NS from which a cortex surface can be represented. In each vertex an electric dipole is placed characterizing a source point which may be a vector with three unknown components (i.e., the three dipole moments), or a scalar
SABI 2013 - XIX Argentine Congress of Bioengineering- Tucum´ an September 4,5 and 6 Septiembre - Volume 2013 Number 142
(unknown dipole amplitude, known orientation). The way these source points generate the scalp electric potential at each one of the NE points of measurements is modeled by a matrix called Lead Field Matrix, this matrix embodies the anatomy of the subject including shape, number of interfaces in which the source signals go through and also the volume conductivities; in other words, the matrix is a bridge between the current density distribution and the EEG’s measurements. The estimation of the sources commonly involves a dimensional problem where NE
