Finite-Difference Time-Domain Simulation for Three-Dimensional Polarized Light Imaging

Three-dimensional Polarized Light Imaging (3D-PLI) is a promising technique to reconstruct the nerve fiber architecture of human post-mortem brains from birefringence measurements of histological brain sections with micrometer resolution. To better understand how the reconstructed fiber orientations are related to the underlying fiber structure, numerical simulations are employed. Here, we present two complementary simulation approaches that reproduce the entire 3D-PLI analysis: First, we give a short review on a simulation approach that uses the Jones matrix calculus to model the birefringent myelin sheaths. Afterwards, we introduce a more sophisticated simulation tool: a 3D Maxwell solver based on a Finite-Difference Time-Domain algorithm that simulates the propagation of the electromagnetic light wave through the brain tissue. We demonstrate that the Maxwell solver is a valuable tool to better understand the interaction of polarized light with brain tissue and to enhance the accuracy of the fiber orientations extracted by 3D-PLI.

[1]  Beardsley Rs The structure of the myelin sheath. Optical studies. , 1971 .

[2]  Jutta Docter,et al.  JUQUEEN: IBM Blue Gene/Q® Supercomputer System at the Jülich Supercomputing Centre , 2015 .

[3]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[4]  De Raedt,et al.  Unconditionally stable perfectly matched layer boundary conditions , 2007 .

[5]  Olaf Sporns,et al.  The Human Connectome: Linking Structure and Function in the Human Brain , 2009 .

[6]  K. Yee Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[7]  R. Bear,et al.  The structure of the myelin sheath. Optical studies. , 1971, Neurosciences Research Program bulletin.

[8]  Werner Kaminsky,et al.  An automatic optical imaging system for birefringent media , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[9]  Katrin Amunts,et al.  Simulation-based validation of the physical model in 3D Polarized Light Imaging , 2015 .

[10]  Christoph Palm,et al.  A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain , 2011, NeuroImage.

[11]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[12]  H. De Raedt,et al.  Advances in unconditionally stable techniques , 2005 .

[13]  K Amunts,et al.  A Jones matrix formalism for simulating three-dimensional polarized light imaging of brain tissue , 2015, Journal of the Royal Society Interface.

[14]  R. Jones,et al.  A New Calculus for the Treatment of Optical SystemsII. Proof of Three General Equivalence Theorems , 1941 .

[15]  Timothy E. J. Behrens,et al.  Human connectomics , 2012, Current Opinion in Neurobiology.

[16]  Timo Dickscheid,et al.  High-Resolution Fiber Tract Reconstruction in the Human Brain by Means of Three-Dimensional Polarized Light Imaging , 2011, Front. Neuroinform..

[17]  Melinda Piket-May,et al.  9 – Computational Electromagnetics: The Finite-Difference Time-Domain Method , 2005 .

[18]  R. Jones A New Calculus for the Treatment of Optical Systems. IV. , 1942 .

[19]  Katrin Amunts,et al.  Understanding fiber mixture by simulation in 3D Polarized Light Imaging , 2015, NeuroImage.

[20]  R. Jones A New Calculus for the Treatment of Optical SystemsI. Description and Discussion of the Calculus , 1941 .

[21]  P. Morell,et al.  Myelin Formation, Structure and Biochemistry , 1999 .