Simulation studies of biomagnetic computed tomography

Differential characterization of neural sources with the bimodal truncated SVD pseudo-inverse for EEG and MEG measurements

A method for obtaining a practical inverse for the distribution of neural activity in the human cerebral cortex is developed for electric, magnetic, and bimodal data to exploit their complementary aspects. Intracellular current is represented by current dipoles uniformly distributed on two parallel sulci joined by a gyrus. Linear systems of equations relate electric, magnetic, and bimodal data to unknown dipole moments. The corresponding lead-field matrices are characterized by singular value decomposition (SVD). The optimal reference electrode location for electric data is chosen on the basis of the decay behavior of the singular values. The singular values of these matrices show better decay behavior with increasing number of measurements, however, that property is useful depending on the noise in the measurements. The truncated SVD pseudo-inverse is used to control noise artifacts in the reconstructed images. Simulations for single-dipole sources at different depths reveal the relative contributions of electric and magnetic measures. For realistic noise levels the performance of both unimodal and bimodal systems do not improve with an increase in the number of measurements beyond approximately 100. Bimodal image reconstructions are generally superior to unimodal ones in finding the center of activity.

An iterative approach on magnetic source imaging within the human cortex--a simulation study

A simulation study on magnetic source imaging within the human brain from a synthetic evoked magnetic field is presented. An inhomogeneous boundary element (BE) head model (cortex cerebrospinal fluid) was built up from real magnetic resonance imaging (MRI) cross-sections. In the forward problem, one or two rotating primary current dipoles (PCDs) are located at arbitrary sites within the auditory cortices. The PCDs should represent focal and distributed neural activities, respectively. The reconstruction space (predefined by a priori morphological information) is defined as a surface within the three-dimensional cortical volume, with an averaged distance of 0.005 m to the outer cortex surface. The reconstructed pseudo primary current dipoles (PPCDs) are not restricted to any particular direction. The observation space consists of two concave surfaces closely above the scalp. Each observation surface contains 37 observation points. An iterative Wiener filter estimation (WFE) is applied in order to reconstruct PPCD distribution from simulated magnetic field data. This iterative WFE approach enables the simultaneous localization of focal and distributed activities. Aspects on the correlation between neural activities are not investigated within this paper.

An optimal constrained linear inverse method for magnetic source imaging

Magnetic source imaging is the reconstruction of the current source distribution inside an inaccessible volume from magnetic field measurements made outside the volume. It is possible in many applications to estimate, from prior physiological and anatomical knowledge, the source positions, amplitudes, and correlations, as well as the noise amplitudes and correlations. The optimal constrained linear inverse method (OCLIM) uses this prior knowledge to obtain a minimum mean-square error estimate of the current distribution. OCLIM can be efficiently computed using the Cholesky decomposition, taking about a second on a workstation-class computer for a problem with 64 sources and 144 detectors. Any source and detector configuration is allowed as long as their positions are fixed a priori. Correlations among source and noise amplitudes are permitted. OCLIM reduces to the optimally weighted pseudoinverse method of Shim and Cho if the source amplitudes are independent and identically distributed and to the minimum-norm least-squares estimate in the limit of no measurement noise or no prior knowledge of the source amplitudes. In the general case, OCLIM has better mean-square error than either previous method. OCLIM appears well suited to magnetic imaging, since it exploits prior information, provides the minimum reconstruction error, and is inexpensive to compute.

Resolution enhancement of biomagnetic images using the method of alternating protections

Resolution of biomagnetic images using the technique of the alternating projections is proposed. Our image reconstruction procedure is divided in two steps. First, the biomagnetic inverse problem is solved by use of the projection theorem to reconstruct an initial image of the current distribution from a given magnetic field profile. Although the current distribution thus obtained has poor resolution, it can resemble the original shape of the current distribution. The second step improves the resolution of the reconstructed image by using the method of alternating projections. The procedure assumes that images can be represented by line like elements and involves finding the line like elements based on the initial image and projecting back onto the original solution space. Simulation studies were performed on a set of parallel conductors and a shape of the conductors in the form of letters, UWB@. All conductors were of line like thickness. Restored images closely resemble the original shape of the conductors.