The forward problem of electromagnetic source imaging has two components: a numerical model to solve the related integral equations and a model of the head geometry. This study is on the boundary element method (BEM) implementation for numerical solutions and realistic head modelling. The use of second-order (quadratic) isoparametric elements and the recursive integration technique increase the accuracy in the solutions. Two new formulations are developed for the calculation of the transfer matrices to obtain the potential and magnetic field patterns using realistic head models. The formulations incorporate the use of the isolated problem approach for increased accuracy in solutions. If a personal computer is used for computations, each transfer matrix is calculated in 2.2 h. After this pre-computation period, solutions for arbitrary source configurations can be obtained in milliseconds for a realistic head model. A hybrid algorithm that uses snakes, morphological operations, region growing and thresholding is used for segmentation. The scalp, skull, grey matter, white matter and eyes are segmented from the multimodal magnetic resonance images and meshes for the corresponding surfaces are created. A mesh generation algorithm is developed for modelling the intersecting tissue compartments, such as eyes. To obtain more accurate results quadratic elements are used in the realistic meshes. The resultant BEM implementation provides more accurate forward problem solutions and more efficient calculations. Thus it can be the firm basis of the future inverse problem solutions.

The abilities of infants to perceive basic acoustic differences, essential for language development, can be studied using auditory event-related potentials (ERPs). However, scalp-channel averaged ERPs sum volume-conducted contributions from many cortical areas, reducing the functional specificity and interpretability of channel-based ERP measures. This study represents the first attempt to investigate rapid auditory processing in infancy using independent component analysis (ICA), allowing exploration of source-resolved ERP dynamics and identification of ERP cortical generators. Here, we recorded 60-channel EEG data in 34 typically developing 6-month-old infants during a passive acoustic oddball paradigm presenting ‘standard’ tones interspersed with frequency-or duration-deviant tones. ICA decomposition was applied to single-subject EEG data. The best-fitting equivalent dipole or bilaterally symmetric dipole pair was then estimated for each resulting independent component (IC) process using a four-layer infant head model. Similar brain-source ICs were clustered across subjects. Results showed ERP contributions from auditory cortex and multiple extra-auditory cortical areas (often, bilaterally paired). Different cortical source combinations contributed to the frequency- and duration-deviant ERP peak sequences. For ICs in an ERP-dominant source cluster located in or near the mid-cingulate cortex, source-resolved frequency-deviant response N2 latency and P3 amplitude at 6 months-of-age predicted vocabulary size at 20 months-of-age. The same measures for scalp channel F6 (though not for other frontal channels) showed similar but weaker correlations. These results demonstrate the significant potential of ICA analyses to facilitate a deeper understanding of the neural substrates of infant sensory processing.

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Boundary element method (BEM) is one of the numerical methods which is commonly used to solve the forward problem (FP) of electro-magnetic source imaging with realistic head geometries. Application of BEM generates large systems of linear equations with dense matrices. Generation and solution of these matrix equations are time and memory consuming. This study presents a relatively cheap and effective solution for parallel implementation of the BEM to reduce the processing times to clinically acceptable values. This is achieved using a parallel cluster of personal computers on a local area network. We used eight workstations and implemented a parallel version of the accelerated BEM approach that distributes the computation and the BEM matrix efficiently to the processors. The performance of the solver is evaluated in terms of the CPU operations and memory usage for different number of processors. Once the transfer matrix is computed, for a 12,294 node mesh, a single FP solution takes 676 ms on a single processor and 72 ms on eight processors. It was observed that workstation clusters are cost effective tools for solving the complex BEM models in a clinically acceptable time.

The isolated problem approach (IPA) is a method used in the boundary element method (BEM) to overcome numerical inaccuracies caused by the high-conductivity difference in the skull and the brain tissues in the head. Hämäläinen and Sarvas (1989 IEEE Trans. Biomed. Eng. 36 165-71) described how the source terms can be updated to overcome these inaccuracies for a three-layer head model. Meijs et al (1989 IEEE Trans. Biomed. Eng. 36 1038-49) derived the integral equations for the general case where there are an arbitrary number of layers inside the skull. However, the IPA is used in the literature only for three-layer head models. Studies that use complex boundary element head models that investigate the inhomogeneities in the brain or model the cerebrospinal fluid (CSF) do not make use of the IPA. In this study, the generalized formulation of the IPA for multi-layer models is presented in terms of integral equations. The discretized version of these equations are presented in two different forms. In a previous study (Akalin-Acar and Gençer 2004 Phys. Med. Biol. 49 5011-28), we derived formulations to calculate the electroencephalography and magnetoencephalography transfer matrices assuming a single layer in the skull. In this study, the transfer matrix formulations are updated to incorporate the generalized IPA. The effects of the IPA are investigated on the accuracy of spherical and realistic models when the CSF layer and a tumour tissue are included in the model. It is observed that, in the spherical model, for a radial dipole 1 mm close to the brain surface, the relative difference measure (RDM*) drops from 1.88 to 0.03 when IPA is used. For the realistic model, the inclusion of the CSF layer does not change the field pattern significantly. However, the inclusion of an inhomogeneity changes the field pattern by 25% for a dipole oriented towards the inhomogeneity. The effect of the IPA is also investigated when there is an inhomogeneity in the brain. In addition to a considerable change in the scale of the potentials, the field pattern also changes by 15%. The computation times are presented for the multi-layer realistic head model.