Multichannel EEG Methods to Improve the Spatial Resolution of Cortical Potential Distribution and the Signal Quality of Deep Brain Sources

............................................................................................................................... i ACKNOWLEDGEMENTS ......................................................................................................... iii LIST OF ORIGINAL PUBLICATIONS ........................................................................................ vii AUTHOR’S CONTRIBUTION ................................................................................................. viii LIST OF ABBREVIATIONS ....................................................................................................... ix LIST OF SYMBOLS ................................................................................................................... x 1 INTRODUCTION ....................................................................................................... 1 2 OBJECTIVES OF THE STUDY ...................................................................................... 3 3 REVIEW OF THE LITERATURE AND THEORETICAL BACKGROUND ............................. 5 3.1 ELECTROENCEPHALOGRAPHY (EEG) ............................................................................................... 5 3.1.1 Properties of EEG ........................................................................................................... 5 3.1.2 Genesis of EEG signals ................................................................................................... 6 3.1.3 EEG electrode systems ................................................................................................... 6 3.1.4 Noise in EEG measurements .......................................................................................... 8 3.1.5 SNR Improvement of EEG measurements ................................................................... 10 3.2 EEG INVERSE PROBLEMS ............................................................................................................ 11 3.2.1 Definition of an EEG inverse problem .......................................................................... 11 3.2.2 Discrete source localization methods .......................................................................... 11 3.2.3 Source imaging methods ............................................................................................. 12 3.2.4 Formulation of the EEG inverse problem ..................................................................... 14 3.2.5 Effect of noise in EEG inverse solutions ....................................................................... 15 3.3 VOLUME CONDUCTOR MODELS ................................................................................................... 18 3.3.1 Properties of volume conductor models ...................................................................... 18 3.3.2 Geometry of the model ............................................................................................... 18 3.3.3 Electrical properties of the model ............................................................................... 20 3.3.4 Skull resistivity ............................................................................................................. 20 3.4 IMPROVEMENT OF THE SPATIAL RESOLUTION OF EEG ..................................................................... 23 3.4.1 Spatial resolution of EEG ............................................................................................. 23 3.4.2 Distributed source models and cortical imaging ......................................................... 24 3.4.3 Number of EEG electrodes in improving spatial resolution ......................................... 27 3.5 SENSITIVITY DISTRIBUTION OF EEG MEASUREMENT LEADS ............................................................... 30 3.5.1 Lead field and reciprocity theorem .............................................................................. 30 3.5.2 Sensitivity distribution of two‐electrode EEG .............................................................. 32 3.5.3 Modifications of sensitivity distributions ..................................................................... 32 4 MATERIALS AND METHODS ................................................................................... 35 4.1 VOLUME CONDUCTOR MODEL..................................................................................................... 35 4.2 EEG ELECTRODE SYSTEMS .......................................................................................................... 35 4.3 SPATIAL RESOLUTION OF CORTICAL POTENTIAL DISTRIBUTION [I‐III] ................................................... 36 4.3.1 Setting up the system of equations ............................................................................. 36 4.3.2 Finite difference method ............................................................................................. 37 4.3.3 Analysis of the accuracy of cortical potential distribution .......................................... 37 4.4 IMPROVED SIGNAL QUALITY OF DEEP EEG SOURCES [IV‐VII] ............................................................ 38 4.4.1 Synthesisation of multielectrode EEG leads ................................................................ 38 4.4.2 Sensitivity distribution analysis ................................................................................... 40 4.4.3 Simulation study .......................................................................................................... 40 4.4.4 Experimental measurements ....................................................................................... 40