  The neuroimaging technique three-dimensional polarized light imaging (3D-PLI)
provides a high-resolution reconstruction of nerve fibres in human post-mortem
brains. The orientations of the fibres are derived from birefringence
measurements of histological brain sections assuming that the nerve fibres -
consisting of an axon and a surrounding myelin sheath - are uniaxial
birefringent and that the measured optic axis is oriented in direction of the
nerve fibres (macroscopic model). Although experimental studies support this
assumption, the molecular structure of the myelin sheath suggests that the
birefringence of a nerve fibre can be described more precisely by multiple
optic axes oriented radially around the fibre axis (microscopic model). In this
paper, we compare the use of the macroscopic and the microscopic model for
simulating 3D-PLI by means of the Jones matrix formalism. The simulations show
that the macroscopic model ensures a reliable estimation of the fibre
orientations as long as the polarimeter does not resolve structures smaller
than the diameter of single fibres. In the case of fibre bundles, polarimeters
with even higher resolutions can be used without losing reliability. When
taking the myelin density into account, the derived fibre orientations are
considerably improved.
