The Lamellar Structure of the Brain Fiber Pathways

We present a quantitative statistical analysis of pairwise crossings for all fibers obtained from whole brain tractography that confirms with high confidence that the brain grid theory (Wedeen et al., 2012a) is not supported by the evidence. The overall fiber tracts structure appears to be more consistent with small angle treelike branching of tracts rather than with near-orthogonal gridlike crossing of fiber sheets. The analysis uses our new method for high-resolution whole brain tractography that is capable of resolving fibers crossing of less than 10 degrees and correctly following a continuous angular distribution of fibers even when the individual fiber directions are not resolved. This analysis also allows us to demonstrate that the whole brain fiber pathway system is very well approximated by a lamellar vector field, providing a concise and quantitative mathematical characterization of the structural connectivity of the human brain.

[1]  L. Frank,et al.  Information pathways in a disordered lattice. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Alan Connelly,et al.  Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution , 2007, NeuroImage.

[3]  Y. Jan,et al.  Branching out: mechanisms of dendritic arborization , 2010, Nature Reviews Neuroscience.

[4]  Steen Moeller,et al.  The Human Connectome Project: A data acquisition perspective , 2012, NeuroImage.

[5]  Dmitri B Chklovskii,et al.  Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors , 2009, Proceedings of the National Academy of Sciences.

[6]  Terrence J Sejnowski,et al.  Communication in Neuronal Networks , 2003, Science.

[7]  Max A. Viergever,et al.  Mapping the brain's "sheet probability index" (SPI) with diffusion MRI: sheet happens?! , 2016 .

[8]  Susanne Schnell,et al.  Global fiber reconstruction becomes practical , 2011, NeuroImage.

[9]  B.W. Kreher,et al.  Connecting and merging fibres: Pathway extraction by combining probability maps , 2008, NeuroImage.

[10]  J. Polimeni,et al.  Blipped‐controlled aliasing in parallel imaging for simultaneous multislice echo planar imaging with reduced g‐factor penalty , 2012, Magnetic resonance in medicine.

[11]  H. Fernández-morán.  Fine Structure of Biological Lamellar Systems , 1959 .

[12]  M. Raichle,et al.  Tracking neuronal fiber pathways in the living human brain. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Le Ma,et al.  Developmental regulation of axon branching in the vertebrate nervous system , 2011, Development.

[14]  Douglas L. Rosene,et al.  The Geometric Structure of the Brain Fiber Pathways , 2012, Science.

[15]  L. Wald,et al.  A 64‐channel 3T array coil for accelerated brain MRI , 2013, Magnetic resonance in medicine.

[16]  N. Makris,et al.  High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity , 2002, Magnetic resonance in medicine.

[17]  Paul Suetens,et al.  Global tractography of multi-shell diffusion-weighted imaging data using a multi-tissue model , 2015, NeuroImage.

[18]  P. Basser,et al.  In vivo fiber tractography using DT‐MRI data , 2000, Magnetic resonance in medicine.

[19]  Kaoru Sugimura,et al.  Self-organizing Mechanism for Development of Space-filling Neuronal Dendrites , 2007, PLoS Comput. Biol..

[20]  Andrea Fuster,et al.  Robust assessment of the brain's sheet structure using normalized convolution , 2016 .

[21]  M. Affolter,et al.  Branching morphogenesis: from cells to organs and back. , 2012, Cold Spring Harbor perspectives in biology.

[22]  L. Gordon,et al.  Tutorial on large deviations for the binomial distribution , 1989 .

[23]  Lawrence R. Frank,et al.  Simultaneous Multi-Scale Diffusion Estimation and Tractography Guided by Entropy Spectrum Pathways , 2015, IEEE Transactions on Medical Imaging.

[24]  Heidi Johansen-Berg,et al.  Tractography: Where Do We Go from Here? , 2011, Brain Connect..

[25]  James Serrin,et al.  Mathematical Principles of Classical Fluid Mechanics , 1959 .

[26]  Max A. Viergever,et al.  Towards quantification of the brain's sheet structure : evaluation of the discrete Lie bracket , 2014 .

[27]  Andrea Fuster,et al.  Towards quantification of the brain’s sheet structure in diffusion MRI data , 2015 .

[28]  Susumu Mori,et al.  Fiber tracking: principles and strategies – a technical review , 2002, NMR in biomedicine.

[29]  Steve Weiner,et al.  Materials design in biology , 2000 .

[30]  G. Mitchison.  Neuronal branching patterns and the economy of cortical wiring , 1991, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[31]  Flavio Dell'Acqua,et al.  Comment on “The Geometric Structure of the Brain Fiber Pathways” , 2012, Science.

[32]  Timothy Edward John Behrens,et al.  Effects of image reconstruction on fiber orientation mapping from multichannel diffusion MRI: Reducing the noise floor using SENSE , 2013, Magnetic resonance in medicine.

[33]  Jeremy D. Schmahmann,et al.  Diffusion spectrum magnetic resonance imaging (DSI) tractography of crossing fibers , 2008, NeuroImage.

[34]  J. Kaas,et al.  Response to Comment on “The Geometric Structure of the Brain Fiber Pathways” , 2012, Science.

[35]  Julien Cohen-Adad,et al.  Pushing the limits of in vivo diffusion MRI for the Human Connectome Project , 2013, NeuroImage.

[36]  Dmitry S. Novikov,et al.  MesoFT: Unifying Diffusion Modelling and Fiber Tracking , 2014, MICCAI.

[37]  Jean-Francois Mangin,et al.  A Novel Global Tractography Algorithm Based on an Adaptive Spin Glass Model , 2009, MICCAI.

[38]  Christophe Lenglet,et al.  Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity , 2009, MICCAI.