Propagation of uncertainty from coregistration to source estimates

The uncertainty in MEG-to-MRI co-registrations propagates through the forward model to uncertainty in source reconstruction results of MEG data. However, the common tools for source reconstruction in MEG or EEG analysis do not account for that source of uncertainty and usually only the variance of the noise is considered in the assessment of the standard error or covariance of source parameters. For realistic head models, the computational costs of forward modeling are unfeasible for straightforward Monte Carlo simulations. To overcome this problem, a polynomial expansion of the forward model is constructed as a function of the co-registration parameters. The six-dimensional co-registration space of three rotation and three translation parameters is sampled using a Metropolis algorithm. The eigen-decomposition of the Metropolis sample covariance matrix provides a map to a six-dimensional uncorrelated parameter space. Based on the uncorrelated parameters, the forward model matrix is expanded in terms of Hermite polynomials. The number of polynomial terms is limited using an adaptive expansion with an error tolerance of 1% resulting in 61 terms for our demonstration model. For this expansion, the forward model is evaluated at 97 different co-registration parameterizations. The polynomial expansion is used as a computationally cheap surrogate of the forward model construction. We demonstrate the benefit of the expansion by drawing 10000 independent samples of the linearly constrained minimum variance beamformer for 42 target sources. Our methods provide a computationally feasible assessment of the distribution of source estimates, e.g. the beamformer activation maxima, based on the uncertainty in MEG-to-MRI co-registrations