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

  • Miriam MenzelEmail author
  • Markus Axer
  • Hans De Raedt
  • Kristel Michielsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10087)

Abstract

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.

Keywords

Polarized Light Imaging Nerve fiber architecture Optics Birefringence Jones matrix calculus Maxwell solver Finite-Difference Time-Domain algorithm Computer simulation 

Notes

Acknowledgments

Our work has been supported by the Helmholtz Association portfolio theme ‘Supercomputing and Modeling for the Human Brain’, by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 604102 (Human Brain Project), and partially by the National Institutes of Health under grant agreement No. R01MH 092311.

We gratefully acknowledge the computing time granted by the JARA-HPC Vergabegremium and provided on the JARA-HPC Partition part of the supercomputer JUQUEEN [18] at Forschungszentrum Jülich.

We would like to thank M. Cremer, Ch. Schramm, and P. Nysten for the preparation of the histological brain sections.

References

  1. 1.
    Behrens, T.E.J., Sporns, O.: Human connectomics. Current Opin. Neurobiol. 22(1), 144–153 (2012). doi: 10.1016/j.conb.2011.08.005 CrossRefGoogle Scholar
  2. 2.
    Sporns, O., Tononi, G., Kötter, R.: The human connectome: a structural description of the human brain. PLoS Comput. Biol. 1(4), 245–251 (2005). doi: 10.1371/journal.pcbi.0010042 CrossRefGoogle Scholar
  3. 3.
    Sporns, O.: The human connectome: linking structure and function in the human brain. In: Johansen-Berg, H., Behrens, T.E.J. (eds.) Diffusion MRI: From Quantitative Measurement to in vivo Neuroanatomy, pp. 309–332, 1st edn. Academic Press, Amsterdam (2009). doi: 10.1371/journal.pcbi.0010042. Google Scholar
  4. 4.
    Axer, M., Amunts, K., Grässel, D., Palm, C., Dammers, J., Axer, H., Pietrzyk, U., Zilles, K.: A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain. NeuroImage 54(2), 1091–1101 (2011). doi: 10.1016/j.neuroimage.2010.08.075 CrossRefGoogle Scholar
  5. 5.
    Axer, M., Grässel, D., Kleiner, M., Dammers, J., Dickscheid, T., Reckfort, J., Hütz, T., Eiben, B., Pietrzyk, U., Zilles, K., Amunts, K.: High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging. Frontiers Neuroinform. 5(34), 1–13 (2011). doi: 10.3389/fninf.2011.00034 Google Scholar
  6. 6.
    Göthlin, G.F.: Die doppelbrechenden Eigenschaften des Nervengewebes - ihre Ursachen und ihre biologischen Konsequenzen. Kungl. Svenska Vetenskapskakademiens Handlingar. 51(1), 1–91 (1913)Google Scholar
  7. 7.
    Bear, R.S.: The structure of the myelin sheath. Optical studies. Neurosci. Res. Program Bull. 9(4), 507–510 (1971)Google Scholar
  8. 8.
    Quarles, R.H., Macklin, W.B., Morell, P.: Myelin formation, structure and biochemistry. In: Siegel, G., Albers, R.W., Brady, S., Price, D. (eds.) Basic Neurochemistry: Molecular, Cellular and Medical Aspects, pp. 51–71, 7th edn. Elsevier Academic Press, Burlington (2006)Google Scholar
  9. 9.
    Jones, R.C.: A new calculus for the treatment of optical systems. J. Optical Soc. Am. 31, 488–503 (1941). doi: 10.1364/JOSA.31.000488 CrossRefzbMATHGoogle Scholar
  10. 10.
    Jones, R.C.: A new calculus for the treatment of optical systems. iv. J. Optical Soc. Am. 32, 486–486 (1942). doi: 10.1364/JOSA.31.000488 CrossRefGoogle Scholar
  11. 11.
    Menzel, M., Michielsen, K., De Raedt, H., Reckfort, J., Amunts, K., Axer, M.: A Jones matrix formalism for simulating three-dimensional polarized light imaging of brain tissue. J. R. Soc. Interface 12, 20150734 (2015). doi: 10.1098/rsif.2015.0734 CrossRefGoogle Scholar
  12. 12.
    Glazer, A.M., Lewis, J.G., Kaminsky, W.: An automatic optical imaging system for birefringent media. Proc. R. Soc. A 452, 2751–2765 (1996). doi: 10.1098/rspa.1996.0145 CrossRefGoogle Scholar
  13. 13.
    Menzel, M., Dohmen, M., De Raedt, H., Michielsen, K., Amunts, K., Axer, M.: Simulation-based validation of the physical model in 3D polarized light imaging. Optics and the Life Sciences, OSA Technical Digest (online), JT3A.33 (2015) doi: 10.1364/BODA.2015.JT3A.33
  14. 14.
    Dohmen, M., Menzel, M., Wiese, H., Reckfort, J., Hanke, F., Pietrzyk, U., Zilles, K., Amunts, K., Axer, M.: Understanding fiber mixture by simulation in 3D Polarized Light Imaging. NeuroImage 111, 464–475 (2015). doi: 10.1016/j.neuroimage.2015.02.020 CrossRefGoogle Scholar
  15. 15.
    Taflove, A., Hagness, S.C.: Computational Electrodynamics: The Finite- Difference Time-Domain Method, 3rd edn. Artech House, Boston (2005)zbMATHGoogle Scholar
  16. 16.
    Yee, K.S.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14, 302–307 (1966). doi: 10.1109/TAP.1966.1138693 CrossRefzbMATHGoogle Scholar
  17. 17.
    De Raedt, H.: Advances in unconditionally stable techniques. In: Taflove, A., Hagness, S.C. (eds.) Computational Electrodynamics: The Finite-Difference Time-Domain Method, Chap. 18, 3rd edn. Artech House, Boston (2005)Google Scholar
  18. 18.
    Stephan, M., Docter, J.: JUQUEEN: IBM Blue Gene/Q supercomputer system at the Jülich supercomputing centre. J. Large-Scale Res. Facil. 1, A1 (2015). doi: 10.17815/jlsrf-1-18 CrossRefGoogle Scholar
  19. 19.
    De Raedt, H., Michielsen, K.: Unconditionally stable perfectly matched layer boundary conditions. Physica Status Solidi (b) 244(10), 3497–3505 (2007). doi: 10.1002/pssb.200743148 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Miriam Menzel
    • 1
    Email author
  • Markus Axer
    • 1
  • Hans De Raedt
    • 2
  • Kristel Michielsen
    • 3
  1. 1.Institute of Neuroscience and Medicine (INM-1)Forschungszentrum JülichJülichGermany
  2. 2.Zernike Institute for Advanced MaterialsUniversity of GroningenGroningenThe Netherlands
  3. 3.Jülich Supercomputing Centre (JSC)Forschungszentrum JülichJülichGermany

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