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

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

Tradeoffs between measurement residual and reconstruction error in inverse problems with prior information

In many inverse problems with prior information, the measurement residual and the reconstruction error are two natural metrics for reconstruction quality, where the measurement residual is defined as the weighted sum of the squared differences between the data actually measured and the data predicted by the reconstructed model, and the reconstruction error is defined as the sum of the squared differences between the reconstruction and the truth, averaged over some a priori probability space of possible solutions. A reconstruction method that minimizes only one of these cost functions may produce unacceptable results on the other. This paper develops reconstruction methods that control both residual and error, achieving the minimum residual for any fixed error or vice versa. These jointly optimal estimators can be obtained by minimizing a weighted sum of the residual and the error; the weights are determined by the slope of the tradeoff curve at the desired point and may be determined iteratively. These results generalize to other cost functions, provided that the cost functions are quadratic and have unique minimizers; some results are obtained under the weaker assumption that the cost functions are convex. This paper applies these results to a model problem from biomagnetic source imaging and exhibits the tradeoff curve for this problem

Detection geometry and reconstruction error in magnetic source imaging

A recently developed reconstruction algorithm for magnetic source imaging exploits prior knowledge about source location, source power density, detector geometry, and detector noise power to obtain an explicit estimate of the reconstruction error. This paper demonstrates the application of the new algorithm to the optimal design of practical detector arrays to minimize the reconstruction error in specific applications. For a representative configuration for magnetocardiography, the optimal array width (for minimum reconstruction error) varies from 19 to 28 cm depending on the assumed source depth, number of detectors, source power and noise power. The reconstruction accuracy ranges from 5% of the a priori standard deviation for the sources nearest the detector plane to 95% of the a priori deviation for the deepest sources. The reconstruction error was found to depend on accidental alignments between dipole sources and point detectors, indicating that a more sophisticated model is required for accurate estimates of reconstruction error. The error calculation is fast, taking about a second for this problem on a workstation-class computer. The availability of a method for rapidly computing the reconstruction error for any given source characteristics and detector geometry will facilitate the optimal design of magnetometer array size, element spacing, and orientation for specific applications in biomagnetic and geomagnetic source imaging