Algorithms for biomagnetic source imaging with prior anatomical and physiological information

This dissertation derives a new method for estimating current source amplitudes in the brain and heart from external magnetic field measurements and prior knowledge about the probable source positions and amplitudes. The minimum mean square error estimator for the linear inverse problem with statistical prior information was derived and is called the optimal constrained linear inverse method (OCLIM). OCLIM includes as special cases the Shim-Cho weighted pseudoinverse and Wiener estimators but allows more general priors and thus reduces the reconstruction error. Efficient algorithms were developed to compute the OCLIM estimate for instantaneous or time series data. The method was tested in a simulated neuromagnetic imaging problem with five simultaneously active sources on a grid of 387 possible source locations; all five sources were resolved, even though the true sources were not exactly at the modeled source positions and the true source statistics differed from the assumed statistics

Variance and Autocorrelation of the Spontaneous Slow Brain Activity

Slow (<0.1 Hz) oscillatory activity in the human brain, as measured by functional magnetic imaging, has been used to identify neural networks and their dysfunction in specific brain diseases. Its intrinsic properties may also be useful to investigate brain functions. We investigated the two functional maps: variance and first order autocorrelation coefficient (r1). These two maps had distinct spatial distributions and the values were significantly different among the subdivisions of the precuneus and posterior cingulate cortex that were identified in functional connectivity (FC) studies. The results reinforce the functional segregation of these subdivisions and indicate that the intrinsic properties of the slow brain activity have physiological relevance. Further, we propose a sample size (degree of freedom) correction when assessing the statistical significance of FC strength with r1 values, which enables a better understanding of the network changes related to various brain diseases

An optimal constrained linear inverse method for magnetic source imaging

Magnetic source imaging is the reconstruction of the current distribution inside an inaccessible volume from magnetic field measurements made outside the volume. If the unknown current distribution is expressed as a linear combination of elementary current distributions in fixed positions, then the magnetic field measurements are linear in the unknown source amplitudes and both the least square and minimum mean square reconstructions are linear problems. This offers several advantages: The problem is well understood theoretically and there is only a single, global minimum. Efficient and reliable software for numerical linear algebra is readily available. If the sources are localized and statistically uncorrelated, then a map of expected power dissipation is equivalent to the source covariance matrix. Prior geological or physiological knowledge can be used to determine such an expected power map and thus the source covariance matrix. The optimal constrained linear inverse method (OCLIM) derived in this paper 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

Algorithms for biomagnetic source imaging with prior anatomical and physiological information

This dissertation derives a new method for estimating current source amplitudes in the brain and heart from external magnetic field measurements and prior knowledge about the probable source positions and amplitudes. The minimum mean square error estimator for the linear inverse problem with statistical prior information was derived and is called the optimal constrained linear inverse method (OCLIM). OCLIM includes as special cases the Shim-Cho weighted pseudoinverse and Wiener estimators but allows more general priors and thus reduces the reconstruction error. Efficient algorithms were developed to compute the OCLIM estimate for instantaneous or time series data. The method was tested in a simulated neuromagnetic imaging problem with five simultaneously active sources on a grid of 387 possible source locations; all five sources were resolved, even though the true sources were not exactly at the modeled source positions and the true source statistics differed from the assumed statistics