Abstract

Previous simulation studies by Menzel et al. [Phys. Rev. X 10, 021002 (2020)] have shown that scattering patterns of light transmitted through artificial nerve fiber constellations contain valuable information about the tissue substructure such as the individual fiber orientations in regions with crossing nerve fibers. Here, we present a method that measures these scattering patterns in monkey and human brain tissue using coherent Fourier scatterometry with normally incident light. By transmitting a non-focused laser beam (λ = 633 nm) through unstained histological brain sections, we measure the scattering patterns for small tissue regions (with diameters of 0.1–1 mm), and show that they are in accordance with the simulated scattering patterns. We reveal the individual fiber orientations for up to three crossing nerve fiber bundles, with crossing angles down to 25°.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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    [Crossref]
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  20. J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
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  21. N.-J. Jan, J. L. Grimm, H. Tran, K. L. Lathrop, G. Wollstein, R. A. Bilonick, H. Ishikawa, L. Kagemann, J. S. Schuman, and I. A. Sigal, “Polarization microscopy for characterizing fiber orientation of ocular tissues,” Biomed. Opt. Express 6(12), 4705–4718 (2015).
    [Crossref]
  22. M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
    [Crossref]
  23. M. Menzel, J. Reckfort, D. Weigand, H. Köse, K. Amunts, and M. Axer, “Diattenuation of brain tissue and its impact on 3D polarized light imaging,” Biomed. Opt. Express 8(7), 3163–3197 (2017).
    [Crossref]

2020 (1)

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

2019 (2)

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
[Crossref]

2017 (3)

M. Menzel, J. Reckfort, D. Weigand, H. Köse, K. Amunts, and M. Axer, “Diattenuation of brain tissue and its impact on 3D polarized light imaging,” Biomed. Opt. Express 8(7), 3163–3197 (2017).
[Crossref]

Y. Shi and A. W. Toga, “Connectome imaging for mapping human brain pathways,” Mol. Psychiatry 22(9), 1230–1240 (2017).
[Crossref]

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

2015 (3)

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

N.-J. Jan, J. L. Grimm, H. Tran, K. L. Lathrop, G. Wollstein, R. A. Bilonick, H. Ishikawa, L. Kagemann, J. S. Schuman, and I. A. Sigal, “Polarization microscopy for characterizing fiber orientation of ocular tissues,” Biomed. Opt. Express 6(12), 4705–4718 (2015).
[Crossref]

2014 (2)

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. 111(12), 4363–4368 (2014).
[Crossref]

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22(20), 24678–24688 (2014).
[Crossref]

2011 (3)

O. E. Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent optical scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[Crossref]

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

2010 (1)

K. Michielsen, H. de Raedt, and D. G. Stavenga, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi,” J. Roy. Soc. Interface 7(46), 765–771 (2010).
[Crossref]

2009 (1)

S. Herculano-Houzel, “The human brain in numbers: a linearly scaled-up primate brain,” Front. Hum. Neurosci. 3, 1–11 (2009).
[Crossref]

1964 (1)

A. Savitsky and M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36(8), 1627–1639 (1964).
[Crossref]

Amunts, K.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
[Crossref]

M. Menzel, J. Reckfort, D. Weigand, H. Köse, K. Amunts, and M. Axer, “Diattenuation of brain tissue and its impact on 3D polarized light imaging,” Biomed. Opt. Express 8(7), 3163–3197 (2017).
[Crossref]

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

M. Menzel, M. Huwer, P. Schlömer, K. Amunts, and M. Axer, “Light scattering measurements enable an improved reconstruction of nerve fiber crossings,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN), (Optical Society of America, 2020), p. BW2C.3.

Axer, H.

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

Axer, M.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
[Crossref]

M. Menzel, J. Reckfort, D. Weigand, H. Köse, K. Amunts, and M. Axer, “Diattenuation of brain tissue and its impact on 3D polarized light imaging,” Biomed. Opt. Express 8(7), 3163–3197 (2017).
[Crossref]

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

M. Menzel, M. Axer, H. De Raedt, and K. Michielsen, “Finite-Difference Time-Domain Simulation for Three-Dimensional Polarized Light Imaging,” Brain-Inspired Computing. BrainComp 2015. Lecture Notes in Computer Science, vol. 10087, K. Amunts, L. Grandinetti, T. Lippert, and N. Petkov, eds. (Springer International Publishing, Cham, 2016), chap. 6, pp. 73–85.

M. Menzel, M. Huwer, P. Schlömer, K. Amunts, and M. Axer, “Light scattering measurements enable an improved reconstruction of nerve fiber crossings,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN), (Optical Society of America, 2020), p. BW2C.3.

Bilonick, R. A.

Chamberland, M.

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

Coene, W. M. J.

Costantini, I.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

Côté, M.-A.

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

Dammers, J.

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

De Raedt, H.

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. 111(12), 4363–4368 (2014).
[Crossref]

K. Michielsen, H. de Raedt, and D. G. Stavenga, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi,” J. Roy. Soc. Interface 7(46), 765–771 (2010).
[Crossref]

M. Menzel, M. Axer, H. De Raedt, and K. Michielsen, “Finite-Difference Time-Domain Simulation for Three-Dimensional Polarized Light Imaging,” Brain-Inspired Computing. BrainComp 2015. Lecture Notes in Computer Science, vol. 10087, K. Amunts, L. Grandinetti, T. Lippert, and N. Petkov, eds. (Springer International Publishing, Cham, 2016), chap. 6, pp. 73–85.

H. De Raedt, “Advances in unconditionally stable techniques,” Computational Electrodynamics: The Finite-Difference Time-Domain Method, A. Taflove and S. C. Hagness, eds. (Artech House, MA USA, 2005), chap. 18, 3rd ed.

Dickscheid, T.

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

Dohmen, M.

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

Eiben, B.

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

Garyfallidis, E.

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

Gawhary, O. E.

Ginsburger, K.

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

Golay, M.

A. Savitsky and M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36(8), 1627–1639 (1964).
[Crossref]

Grässel, D.

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

Grimm, J. L.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.

Hanke, F.

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

Herculano-Houzel, S.

S. Herculano-Houzel, “The human brain in numbers: a linearly scaled-up primate brain,” Front. Hum. Neurosci. 3, 1–11 (2009).
[Crossref]

Houde, J.-C.

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

Hütz, T.

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

Huwer, M.

M. Menzel, M. Huwer, P. Schlömer, K. Amunts, and M. Axer, “Light scattering measurements enable an improved reconstruction of nerve fiber crossings,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN), (Optical Society of America, 2020), p. BW2C.3.

Ishikawa, H.

Jan, N.-J.

Kagemann, L.

Kleiner, M.

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

Köse, H.

Kumar, N.

Lathrop, K. L.

Maier-Hein, K. H.

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

Matuschke, F.

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

Menzel, M.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
[Crossref]

M. Menzel, J. Reckfort, D. Weigand, H. Köse, K. Amunts, and M. Axer, “Diattenuation of brain tissue and its impact on 3D polarized light imaging,” Biomed. Opt. Express 8(7), 3163–3197 (2017).
[Crossref]

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

M. Menzel, Finite-difference time-domain simulations assisting to reconstruct the brain’s nerve fiber architecture by 3D polarized light imaging, vol. 188 of, Schriften des Forschungszentrums Jülich, Reihe Schlüsseltechnologien (Forschungszentrum Jülich GmbH, Jülich, 2018).

M. Menzel, M. Huwer, P. Schlömer, K. Amunts, and M. Axer, “Light scattering measurements enable an improved reconstruction of nerve fiber crossings,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN), (Optical Society of America, 2020), p. BW2C.3.

M. Menzel and S. F. Pereira, “Dataset: Coherent Fourier scatterometry reveals nerve fiber crossings in the brain,” Mendeley Data V4, https://doi.org/10.17632/dp496jpd7h.4 (2020).

M. Menzel, M. Axer, H. De Raedt, and K. Michielsen, “Finite-Difference Time-Domain Simulation for Three-Dimensional Polarized Light Imaging,” Brain-Inspired Computing. BrainComp 2015. Lecture Notes in Computer Science, vol. 10087, K. Amunts, L. Grandinetti, T. Lippert, and N. Petkov, eds. (Springer International Publishing, Cham, 2016), chap. 6, pp. 73–85.

Michielsen, K.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
[Crossref]

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. 111(12), 4363–4368 (2014).
[Crossref]

K. Michielsen, H. de Raedt, and D. G. Stavenga, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi,” J. Roy. Soc. Interface 7(46), 765–771 (2010).
[Crossref]

M. Menzel, M. Axer, H. De Raedt, and K. Michielsen, “Finite-Difference Time-Domain Simulation for Three-Dimensional Polarized Light Imaging,” Brain-Inspired Computing. BrainComp 2015. Lecture Notes in Computer Science, vol. 10087, K. Amunts, L. Grandinetti, T. Lippert, and N. Petkov, eds. (Springer International Publishing, Cham, 2016), chap. 6, pp. 73–85.

Neher, P. F.

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

Palm, C.

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

Pavone, F. S.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

Pereira, S. F.

N. Kumar, P. Petrik, G. K. P. Ramanandan, O. E. Gawhary, S. Roy, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Reconstruction of sub-wavelength features and nano-positioning of gratings using coherent Fourier scatterometry,” Opt. Express 22(20), 24678–24688 (2014).
[Crossref]

O. E. Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent optical scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[Crossref]

M. Menzel and S. F. Pereira, “Dataset: Coherent Fourier scatterometry reveals nerve fiber crossings in the brain,” Mendeley Data V4, https://doi.org/10.17632/dp496jpd7h.4 (2020).

Petrik, P.

Pietrzyk, U.

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

Poupon, C.

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

Raedt, H. D.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
[Crossref]

Ramanandan, G. K. P.

Reckfort, J.

M. Menzel, J. Reckfort, D. Weigand, H. Köse, K. Amunts, and M. Axer, “Diattenuation of brain tissue and its impact on 3D polarized light imaging,” Biomed. Opt. Express 8(7), 3163–3197 (2017).
[Crossref]

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

Reuter, J. A.

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

Roy, S.

Savitsky, A.

A. Savitsky and M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36(8), 1627–1639 (1964).
[Crossref]

Schlömer, P.

M. Menzel, M. Huwer, P. Schlömer, K. Amunts, and M. Axer, “Light scattering measurements enable an improved reconstruction of nerve fiber crossings,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN), (Optical Society of America, 2020), p. BW2C.3.

Schubert, N.

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

Schuman, J. S.

Shi, Y.

Y. Shi and A. W. Toga, “Connectome imaging for mapping human brain pathways,” Mol. Psychiatry 22(9), 1230–1240 (2017).
[Crossref]

Sigal, I. A.

Silvestri, L.

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

Stavenga, D. G.

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. 111(12), 4363–4368 (2014).
[Crossref]

K. Michielsen, H. de Raedt, and D. G. Stavenga, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi,” J. Roy. Soc. Interface 7(46), 765–771 (2010).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.

Toga, A. W.

Y. Shi and A. W. Toga, “Connectome imaging for mapping human brain pathways,” Mol. Psychiatry 22(9), 1230–1240 (2017).
[Crossref]

Tran, H.

Urbach, H. P.

Weigand, D.

Wiese, H.

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

Wilts, B. D.

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. 111(12), 4363–4368 (2014).
[Crossref]

Wollstein, G.

Zhong, J.

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

Zilles, K.

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

Anal. Chem. (1)

A. Savitsky and M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36(8), 1627–1639 (1964).
[Crossref]

Appl. Phys. B (1)

O. E. Gawhary, N. Kumar, S. F. Pereira, W. M. J. Coene, and H. P. Urbach, “Performance analysis of coherent optical scatterometry,” Appl. Phys. B 105(4), 775–781 (2011).
[Crossref]

Biomed. Opt. Express (2)

Front. Hum. Neurosci. (1)

S. Herculano-Houzel, “The human brain in numbers: a linearly scaled-up primate brain,” Front. Hum. Neurosci. 3, 1–11 (2009).
[Crossref]

Front. Neuroanat. (1)

J. Reckfort, H. Wiese, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “A multiscale approach for the reconstruction of the fiber architecture of the human brain based on 3D-PLI,” Front. Neuroanat. 9, 1–11 (2015).
[Crossref]

Front. Neuroinform. (1)

M. Axer, D. Grässel, M. Kleiner, J. Dammers, T. Dickscheid, J. Reckfort, T. Hütz, B. Eiben, U. Pietrzyk, K. Zilles, and K. Amunts, “High-resolution fiber tract reconstruction in the human brain by means of three-dimensional polarized light imaging,” Front. Neuroinform. 5, 1–13 (2011).
[Crossref]

Int. J. CARS (1)

J. A. Reuter, F. Matuschke, M. Menzel, N. Schubert, K. Ginsburger, C. Poupon, K. Amunts, and M. Axer, “FAConstructor: an interactive tool for geometric modeling of nerve fiber architectures in the brain,” Int. J. CARS 14(11), 1881–1889 (2019).
[Crossref]

J. Roy. Soc. Interface (1)

K. Michielsen, H. de Raedt, and D. G. Stavenga, “Reflectivity of the gyroid biophotonic crystals in the ventral wing scales of the Green Hairstreak butterfly, Callophrys rubi,” J. Roy. Soc. Interface 7(46), 765–771 (2010).
[Crossref]

Mol. Psychiatry (1)

Y. Shi and A. W. Toga, “Connectome imaging for mapping human brain pathways,” Mol. Psychiatry 22(9), 1230–1240 (2017).
[Crossref]

Nat. Commun. (1)

K. H. Maier-Hein, P. F. Neher, J.-C. Houde, M.-A. Côté, E. Garyfallidis, J. Zhong, and M. Chamberland, “The challenge of mapping the human connectome based on diffusion tractography,” Nat. Commun. 8(1), 1349 (2017).
[Crossref]

NeuroImage (2)

M. Axer, K. Amunts, D. Grässel, C. Palm, J. Dammers, H. Axer, U. Pietrzyk, and K. Zilles, “A novel approach to the human connectome: Ultra-high resolution mapping of fiber tracts in the brain,” NeuroImage 54(2), 1091–1101 (2011).
[Crossref]

M. Dohmen, M. Menzel, H. Wiese, J. Reckfort, F. Hanke, U. Pietrzyk, K. Zilles, K. Amunts, and M. Axer, “Understanding fiber mixture by simulation in 3D Polarized Light Imaging,” NeuroImage 111, 464–475 (2015).
[Crossref]

Opt. Express (1)

Phys. Rev. X (1)

M. Menzel, M. Axer, H. D. Raedt, I. Costantini, L. Silvestri, F. S. Pavone, K. Amunts, and K. Michielsen, “Toward a high-resolution reconstruction of 3D nerve fiber architectures and crossings in the brain using light scattering measurements and finite-difference time-domain simulations,” Phys. Rev. X 10(2), 021002 (2020).
[Crossref]

Proc. Natl. Acad. Sci. (1)

B. D. Wilts, K. Michielsen, H. De Raedt, and D. G. Stavenga, “Sparkling feather reflections of a bird-of-paradise explained by finite-difference time-domain modeling,” Proc. Natl. Acad. Sci. 111(12), 4363–4368 (2014).
[Crossref]

Sci. Rep. (1)

M. Menzel, M. Axer, K. Amunts, H. D. Raedt, and K. Michielsen, “Diattenuation Imaging reveals different brain tissue properties,” Sci. Rep. 9(1), 1939 (2019).
[Crossref]

Other (6)

M. Menzel and S. F. Pereira, “Dataset: Coherent Fourier scatterometry reveals nerve fiber crossings in the brain,” Mendeley Data V4, https://doi.org/10.17632/dp496jpd7h.4 (2020).

M. Menzel, M. Huwer, P. Schlömer, K. Amunts, and M. Axer, “Light scattering measurements enable an improved reconstruction of nerve fiber crossings,” in Biophotonics Congress: Biomedical Optics 2020 (Translational, Microscopy, OCT, OTS, BRAIN), (Optical Society of America, 2020), p. BW2C.3.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005), 3rd ed.

M. Menzel, M. Axer, H. De Raedt, and K. Michielsen, “Finite-Difference Time-Domain Simulation for Three-Dimensional Polarized Light Imaging,” Brain-Inspired Computing. BrainComp 2015. Lecture Notes in Computer Science, vol. 10087, K. Amunts, L. Grandinetti, T. Lippert, and N. Petkov, eds. (Springer International Publishing, Cham, 2016), chap. 6, pp. 73–85.

H. De Raedt, “Advances in unconditionally stable techniques,” Computational Electrodynamics: The Finite-Difference Time-Domain Method, A. Taflove and S. C. Hagness, eds. (Artech House, MA USA, 2005), chap. 18, 3rd ed.

M. Menzel, Finite-difference time-domain simulations assisting to reconstruct the brain’s nerve fiber architecture by 3D polarized light imaging, vol. 188 of, Schriften des Forschungszentrums Jülich, Reihe Schlüsseltechnologien (Forschungszentrum Jülich GmbH, Jülich, 2018).

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Figures (11)

Fig. 1.
Fig. 1. Scatterometry measurement vs. simulation: (a) Setup to measure scattering patterns of a brain section. Non-focused, normally incident laser light ($\lambda = 633$ nm) is transmitted through the sample. The diameter of the laser beam is determined by a pinhole (with diameter $\varnothing = 0.1$ mm or 1.12 mm); the sample can be moved with micrometer screws in the x/y-direction. Different objective lenses with different numerical apertures (NA = {0.14, 0.4, 0.8}) are available. A camera (CCD) in the back-focal plane records the Fourier transform of the image plane (scattering pattern) for a given exposure time $t$. (The focal length of the lens in front of the camera is $f = 8$ cm, the focal length of the tube lens is $2f = 16$ cm.) (b) Scattering pattern and normalized polar integral obtained from a scatterometry measurement of a tissue region ($\varnothing = 1.12$ mm, NA = 0.4, $t$ = 30 ms) containing two crossing sections of human optic tracts. The magenta and green lines around the scattering pattern (top image) indicate the positions of the peaks. The dark-field microscopy image of the sample (bottom image) shows the measured tissue region (blue circle) and the predominant orientations of the nerve fibers (green/magenta lines), which are perpendicular to the determined peak positions. (c) Generation of simulated scattering pattern. A plane, coherent light wave ($\lambda = 550$ nm) with circular polarization is transmitted through an artificial nerve fiber constellation (here: two crossing fiber bundles). The propagation of light is computed by an FDTD algorithm [8]. The scattering pattern (top image) shows the distribution of scattered light intensity on a hemisphere behind the sample, projected onto the xy-plane. In the measurement, the maximum scattering angle $\varTheta$ that can be measured is limited by the numerical aperture of the objective lens (NA = $\sin \varTheta$) so that only the central area of the scattering pattern can be recorded (indicated by the red circle). The rings in the scattering pattern indicate steps of $\Delta \theta = 10^{\circ }$ (from $0^{\circ }$ in the center to $90^{\circ }$ for the outer ring); for NA = 0.4, only scattering angles up to $\varTheta = 23.6^{\circ }$ are collected. (The simulated scattering pattern was taken from [8], Fig. 7(b), licensed under CC BY 4.0.)
Fig. 2.
Fig. 2. Localization of the laser point, shown exemplary for a coronal monkey brain section (vervet brain, section no. 458): (a) Photograph of the scan table during the scatterometry measurement ($\varnothing = 1.12$ mm, NA = 0.4). The position of the laser beam on the brain section can be roughly determined by rulers and a transparent foil with cross-lines. To record scattering patterns of different tissue regions, micrometer screws were used to move the sample in steps of 0.5 mm or 1 mm in the x/y-directions. (b) Right before the scatterometry measurement, the starting points were marked on the cover glass with a pen (black dots) and the brain section was scanned with a digital microscope for reference (with aligned x/y-axes). The red circles indicate the laser beam (with 1.12 mm diameter) used in the measurement. (c) To find the starting points, a bright-field image of the sample was recorded (with the setup shown in Appx. B, Fig. 8(a)) and the sample was moved until the image center (i. e. the center of the laser beam, blue cross) lies in the center of the marked point (yellow cross). (d) The dark-field microscopy image of the same brain section was aligned with the image of the digital microscope, and the initial laser point positions (red circles) were transferred. According to how the sample was moved during the scatterometry measurement, the initial circles were translated in steps of 0.5 mm or 1 mm in the x/y-direction (yellow circles).
Fig. 3.
Fig. 3. Noise measured for different tissue regions ($\varnothing = 1.12$ mm) in the corona radiata of a coronal vervet brain section (section no. 458, cr1, x = {2,3,4} mm, y = -1 mm; see Fig. 11(c)): (a) Polar integrals of the same tissue region measured at two different times $t_1$ and $t_2$ (blue/orange curves). The black curve shows the smoothed polar integral. The scatter plot on the right shows the noise (Eq. (2)) for $t_2$ plotted against $t_1$. (b) Polar integrals for two similar, neighboring tissue regions ((i) and (ii)). The scatter plot shows the noise for (ii) plotted against (i). corr = correlation coefficient: $\textrm {cov}(x,y)/(\sigma _x \sigma _y)$.
Fig. 4.
Fig. 4. Scattering patterns of four different tissue regions in two brain tissue samples (three crossing sections of optic tracts and a coronal vervet brain section, cf. Fig. 11(c)) measured with different laser beam diameters ($\varnothing$), numerical apertures (NA), and exposure times ($t$). The rings in the scattering patterns indicate steps of $\Delta \theta = 10^{\circ }$ on the hemisphere. The graphs underneath the scattering patterns show the corresponding (smoothed) polar integrals and the signal-to-noise ratio ($S/N$) computed with Eq. (3). The graphs in the blue box on the lower right show — for two of the tissue regions — the smoothed polar integrals for different numerical apertures and pinhole diameters in one plot (upper two rows), and the histograms of the noise computed with Eq. (2) (lower row).
Fig. 5.
Fig. 5. Measured vs. simulated scattering patterns for different crossing fiber layers: (a) Dark-field microscopy images of two and three crossing sections of optic tracts. The white circles show the tissue regions measured with scatterometry ($\varnothing = 1.12$ mm, NA = 0.4, $t =$ 30 ms), consisting of one ((i),(ii)), two (iii), and three (iv) crossing fiber layers. The outline of the optic tract sections is shown in different colors for better reference. The straight colored lines indicate the fiber orientations of the respective layers in the measured tissue region. (b) Measured scattering patterns and normalized (smoothed) polar integrals of the four tissue regions (i)–(iv) indicated in (a). The non-dashed, colored lines indicate the positions of the scattering peaks, the dashed colored lines (in (i),(ii)) the predominant orientation of the nerve fibers in the measured tissue region. (c) Simulated scattering patterns for parallel fibers oriented in the x-direction (i) and y-direction (ii), and two crossing fiber layers with $90^{\circ }$ crossing angle (iii). The graphs below show the normalized (smoothed) polar integral. (d) Artificial fiber constellations ($30 \times 30 \times 30$ µm$^{3}$) used to compute the simulated scattering patterns in (c). The scattering patterns in (c) and the fiber configurations in (d) were adapted from Menzel et al. (2020b) [19], Fig. 1(c), licensed under CC BY 4.0.
Fig. 6.
Fig. 6. In-plane, crossing, and out-of-plane nerve fibers of a coronal vervet brain section studied with scatterometry: (a) The image on the left was obtained from a dark-field microscopy measurement of the left upper corner of the brain section (the whole brain section is shown in Fig. 11(a) in the Appendix). The white circles show the tissue regions measured with scatterometry ($\varnothing = 1.12$ mm, NA = 0.4, $t =$ 30 ms) with in-plane parallel (i), crossing ((ii),(iii)), and out-of-plane nerve fibers (iv). The straight colored lines indicate the fiber orientations known from anatomical brain structures (cc = corpus callosum, cr = corona radiata, cg = cingulum). The image on the right shows the strength of birefringence for a zoomed-in region of the corona radiata, measured with polarization microscopy [4,5]. The fine yellow curves show the approximate pathways for different nerve fiber bundles, according to visible structures in the fiber architecture. (b) Measured scattering patterns and normalized (smoothed) polar integrals of the four regions (i)–(iv) indicated in (a). The non-dashed, colored lines indicate the positions of the scattering peaks, the dashed colored lines (in (i),(ii),(iv)) the in-plane orientation of the nerve fibers in the measured region. (c) Simulated scattering pattern and polar integral for nerve fibers with an out-of-plane angle of $\alpha = 60^{\circ }$ (adapted from [8], Supplementary Fig. S3, licensed under CC BY 4.0). The white circle indicates the area belonging to NA = 0.4.
Fig. 7.
Fig. 7. Reconstructed nerve fiber orientations for (a) two crossing sections of human optic tracts and (b) a coronal vervet monkey brain section. The images were obtained by dark-field microscopy; the sections of optic tracts in (a) were surrounded by a magenta/green outline for better reference. Different tissue regions were measured with scatterometry ($\varnothing = 1.12$ mm, NA = 0.4, $t =$ 30 ms), see white circles. The peak positions were determined from the smoothed polar integrals of the resulting scattering patterns, as shown in Figs. 5 and 6. The (in-plane) fiber orientations were computed from the arithmetic mean values of the peak pair positions with approx. $180^{\circ }$ distance (cf. dashed green/blue lines in Fig. 6(b)(ii)), and marked in the images by green, magenta, and yellow lines. (c) Sketch of crossing nerve fiber pathways in the corona radiata of the vervet brain section, known from polarization microscopy studies. (cr = corona radiata, cg = cingulum, cc = corpus callosum, f = fornix)
Fig. 8.
Fig. 8. Schematic drawing of the setup used for the scatterometry measurements: (a) Setup used to record a bright-field image of the sample plane. (b) Setup used to record the Fourier transform of the image plane (scattering pattern). (CCD = charge-coupled device)
Fig. 9.
Fig. 9. Evaluation of scattering patterns, shown exemplary for a region with three crossing sections of optic tracts (see Fig. 5(iv)): (a) azimuthal integral, (b) polar integral. The red circle with radius $R$ corresponds to the maximum scattering angle $\varTheta$ that is collected by the objective lens with numerical aperture NA. The green circle with radius $R'$ is the largest possible circle that can still be evaluated. To compute the azimuthal integral for a certain polar angle $\theta$, the intensity values of the scattering pattern are integrated over a concentric circle with radius $\sin (\theta )$ (see lower image in (a)). To compute the polar integral for a certain azimuthal angle $\phi$, the intensity values of the scattering pattern are multiplied by the distance $r$ to the center (upper image in (b)) and integrated from the center ($r=0$) to the outer circle ($r=R'$) for the corresponding $\phi$ (see lower image in (b)). The graphs show the azimuthal integral $I(\theta )$ and the polar integral $I(\phi )$, computed with Eqs. (4) and (5).
Fig. 10.
Fig. 10. Study of polarization effects. (a) Polar plot of the average transmitted light intensity for different rotation angles {$0^{\circ }$, $30^{\circ }$, $\dots$, $330^{\circ }$} of a linear polarizer placed directly behind the 1.12 mm pinhole. The measurement was repeated four times (colored curves) and fitted by an elliptical shape (black dashed curve). (b) Azimuthal and polar integrals of a scattering pattern measured with 1.12 mm pinhole, NA = 0.4, and linearly polarized light (blue: polarization along the x-axis, orange: polarization along the y-axis).
Fig. 11.
Fig. 11. Investigated brain tissue samples. (a) Transmittance image of the coronal vervet monkey brain section (no. 458). The corresponding region shown in (c) is marked by a yellow rectangle. (b) Transmittance image of the human optic chiasm (section no. 36) for the whole section (left) and the two sections of the optic tracts crossing each other (right). (ot = optic tract, on = optic nerve) (c) Dark-field microscopy images of all investigated brain tissue samples. The colored circles and points show the tissue regions that were measured with scatterometry (using different pinhole diameters, numerical apertures (NA), and exposure times ($t$), refer to legend). The asterisk ($\ast$) marks the starting point of the measurement from which the sample (laser point position) was moved in steps of 0.5 mm and 1 mm (cf. Fig. 2). (cr = corona radiata, cg = cingulum, cc = corpus callosum, f = fornix)

Tables (1)

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Table 1. List of sample properties and measurement parameters for the investigated brain tissue samples: sample, section number, section thickness ( T ), dates of dark-field microscopy and scatterometry (scatt.) measurements [in days after tissue embedding], pinhole diameter ( ), numerical aperture (NA), and exposure time ( t ) used for the scatterometry measurements.

Equations (5)

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I N ( ϕ ) = I ( ϕ ) I ( ϕ ) min I ( ϕ ) ¯ .
N = I ( ϕ ) I ~ ( ϕ ) I ~ ( ϕ ) max I ~ ( ϕ ) min .
S / N = σ { I ~ ( ϕ ) max I ~ ( ϕ ) min I ( ϕ ) I ~ ( ϕ ) } .
I ( θ ) = I ( r ) = 0 2 π I ( r , ϕ ) d ϕ ,
I ( ϕ ) = 0 R I ( r , ϕ ) r d r ,