Searching for the best model: ambiguity of inverse solutions and application to fetal magnetoencephalography.

Fetal brain signals produce weak magnetic fields at the maternal abdominal surface. In the presence of much stronger interference these weak fetal fields are often nearly indistinguishable from noise. Our initial objective was to validate these weak fetal brain fields by demonstrating that they agree with the electromagnetic model of the fetal brain. The fetal brain model is often not known and we have attempted to fit the data to not only the brain source position, orientation and magnitude, but also to the brain model position. Simulation tests of this extended model search on fetal MEG recordings using dipole fit and beamformers revealed a region of ambiguity. The region of ambiguity consists of a family of models which are not distinguishable in the presence of noise, and which exhibit large and comparable SNR when beamformers are used. Unlike the uncertainty of a dipole fit with known model plus noise, this extended ambiguity region yields nearly identical forward solutions, and is only weakly dependent on noise. The ambiguity region is located in a plane defined by the source position, orientation, and the true model centre, and will have a diameter approximately 0.67 of the modelled fetal head diameter. Existence of the ambiguity region allows us to only state that the fetal brain fields do not contradict the electromagnetic model; we can associate them with a family of models belonging to the ambiguity region, but not with any specific model. In addition to providing a level of confidence in the fetal brain signals, the ambiguity region knowledge in combination with beamformers allows detection of undistorted temporal waveforms with improved signal-to-noise ratio, even though the source position cannot be uniquely determined.