In recent years, the microscopy technology referred to as Polarized Light Imaging (3D-PLI) has successfully been established to study the brain’s nerve fiber architecture at the micrometer scale. The myelinated axons of the nervous tissue introduce optical birefringence that can be used to contrast nerve fibers and their tracts from each other. Beyond the generation of contrast, 3D-PLI renders the estimation of local fiber orientations possible. To do so, unstained histological brain sections of 70 μm thickness cut at a cryo-microtome were scanned in a polarimetric setup using rotating polarizing filter elements while keeping the sample unmoved. To address the fundamental question of brain connectivity, i. e., revealing the detailed organizational principles of the brain’s intricate neural networks, the tracing of fiber structures across volumes has to be performed at the microscale. This requires a sound basis for describing the in-plane and out-of-plane orientations of each potential fiber (axis) in each voxel, including information about the confidence level (uncertainty) of the orientation estimates. By this means, complex fiber constellations, e. g., at the white matter to gray matter transition zones or brain regions with low myelination (i. e., low birefringence signal), as can be found in the cerebral cortex, become quantifiable in a reliable manner. Unfortunately, this uncertainty information comes with the high computational price of their underlying Monte-Carlo sampling methods and the lack of a proper visualization. In the presented work, we propose a supervised machine learning approach to estimate the uncertainty of the inferred model parameters. It is shown that the parameter uncertainties strongly correlate with simple, physically explainable features derived from the signal strength. After fitting these correlations using a small sub-sample of the data, the uncertainties can be predicted for the remaining data set with high precision. This reduces the required computation time by more than two orders of magnitude. Additionally, a new visualization of the derived three-dimensional nerve fiber information, including the orientation uncertainty based on ellipsoids, is introduced. This technique makes the derived orientation uncertainty information visually interpretable.
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