Numerical study of a cylinder model of the diffusion MRI signal for neuronal dendrite trees.

We study numerically how the neuronal dendrite tree structure can affect the diffusion magnetic resonance imaging (dMRI) signal in brain tissue. For a large set of randomly generated dendrite trees, synthetic dMRI signals are computed and fitted to a cylinder model to estimate the effective longitudinal diffusivity D(L) in the direction of neurites. When the dendrite branches are short compared to the diffusion length, D(L) depends significantly on the ratio between the average branch length and the diffusion length. In turn, D(L) has very weak dependence on the distribution of branch lengths and orientations of a dendrite tree, and the number of branches per node. We conclude that the cylinder model which ignores the connectivity of the dendrite tree, can still be adapted to describe the apparent diffusion coefficient in brain tissue.

[1]  Denis S Grebenkov,et al.  Exploring diffusion across permeable barriers at high gradients. II. Localization regime. , 2014, Journal of magnetic resonance.

[2]  Concha Bielza,et al.  Branching angles of pyramidal cell dendrites follow common geometrical design principles in different cortical areas , 2014, Scientific Reports.

[3]  H. Seldon.  Structure of human auditory cortex. III. Statistical analysis of dendritic trees , 1982, Brain Research.

[4]  Hui Zhang,et al.  Axon diameter mapping in the presence of orientation dispersion with diffusion MRI , 2011, NeuroImage.

[5]  J. Frank,et al.  Neurite beading is sufficient to decrease the apparent diffusion coefficient after ischemic stroke , 2010, Proceedings of the National Academy of Sciences.

[6]  H. Pfeifer.  Principles of Nuclear Magnetic Resonance Microscopy , 1992 .

[7]  P. Basser,et al.  New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter , 2004, Magnetic resonance in medicine.

[8]  Dmitriy A Yablonskiy,et al.  Quantitative in vivo assessment of lung microstructure at the alveolar level with hyperpolarized 3He diffusion MRI , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[9]  K. Hayamizu,et al.  A model for diffusive transport through a spherical interface probed by pulsed-field gradient NMR. , 1998, Biophysical journal.

[10]  V. Wedeen,et al.  Diffusion MRI of Complex Neural Architecture , 2003, Neuron.

[11]  A. Sukstanskii,et al.  Probing lung microstructure with hyperpolarized 3He gradient echo MRI , 2014, NMR in biomedicine.

[12]  B. Sapoval,et al.  Restricted diffusion in a model acinar labyrinth by NMR: theoretical and numerical results. , 2007, Journal of magnetic resonance.

[13]  Ioannis Lavdas,et al.  A phantom for diffusion‐weighted MRI (DW‐MRI) , 2013, Journal of magnetic resonance imaging : JMRI.

[14]  Denis S. Grebenkov,et al.  NMR survey of reflected brownian motion , 2007 .

[15]  M. Mallar Chakravarty,et al.  Neurite density from magnetic resonance diffusion measurements at ultrahigh field: Comparison with light microscopy and electron microscopy , 2010, NeuroImage.

[16]  J. Morrison,et al.  Quantitative analysis of the dendritic morphology of corticocortical projection neurons in the macaque monkey association cortex , 2002, Neuroscience.

[17]  Denis S Grebenkov,et al.  Pulsed-gradient spin-echo monitoring of restricted diffusion in multilayered structures. , 2010, Journal of magnetic resonance.

[18]  Els Fieremans,et al.  Revealing mesoscopic structural universality with diffusion , 2014, Proceedings of the National Academy of Sciences.

[19]  J. Gore,et al.  Theoretical Model for Water Diffusion in Tissues , 1995, Magnetic resonance in medicine.

[20]  Christopher D. Kroenke,et al.  Determination of Axonal and Dendritic Orientation Distributions Within the Developing Cerebral Cortex by Diffusion Tensor Imaging , 2012, IEEE Transactions on Medical Imaging.

[21]  Heidi Johansen-Berg,et al.  Diffusion MRI at 25: Exploring brain tissue structure and function , 2012, NeuroImage.

[22]  C. H. Neuman.  Spin echo of spins diffusing in a bounded medium , 1974 .

[23]  Dmitriy A Yablonskiy,et al.  Theoretical models of the diffusion weighted MR signal , 2010, NMR in biomedicine.

[24]  Peter J Basser,et al.  Modeling diffusion in white matter in the brain: a composite porous medium. , 2005, Magnetic resonance imaging.

[25]  B. Sapoval,et al.  Diffusion-reaction in branched structures: theory and application to the lung acinus. , 2005, Physical review letters.

[26]  Leif Østergaard,et al.  Modeling dendrite density from magnetic resonance diffusion measurements , 2007, NeuroImage.

[27]  J. Helpern,et al.  Diffusional kurtosis imaging: The quantification of non‐gaussian water diffusion by means of magnetic resonance imaging , 2005, Magnetic resonance in medicine.

[28]  Denis S Grebenkov,et al.  Exploring diffusion across permeable barriers at high gradients. I. Narrow pulse approximation. , 2014, Journal of magnetic resonance.

[29]  Joseph A. Helpern,et al.  Random walk with barriers , 2010, Nature physics.

[30]  D. Yablonskiy,et al.  On the nature of the NAA diffusion attenuated MR signal in the central nervous system , 2004, Magnetic resonance in medicine.

[31]  J. Baudewig,et al.  Advances in functional MRI of the human brain , 2004 .

[32]  R. Edelman,et al.  A Phantom for diffusion‐weighted imaging of acute stroke , 1998, Journal of magnetic resonance imaging : JMRI.

[33]  V. Kiselev.  The Cumulant Expansion: An Overarching Mathematical Framework For Understanding Diffusion NMR , 2010 .

[34]  F. Chollet,et al.  Water Diffusion in q-space Imaging as a Probe of Cell Local Viscosity and Anomalous Diffusion in Grey and White Matter , 2010 .

[35]  A S Verkman,et al.  Low viscosity in the aqueous domain of cell cytoplasm measured by picosecond polarization microfluorimetry , 1991, The Journal of cell biology.

[36]  Christopher D. Kroenke,et al.  Using diffusion anisotropy to characterize neuronal morphology in gray matter: the orientation distribution of axons and dendrites in the NeuroMorpho.org database , 2013, Front. Integr. Neurosci..

[37]  Denis Le Bihan,et al.  A finite elements method to solve the Bloch-Torrey equation applied to diffusion magnetic resonance imaging , 2014, J. Comput. Phys..

[38]  A. Mastro,et al.  Diffusion of a small molecule in the cytoplasm of mammalian cells. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[39]  Daniel C. Alexander,et al.  NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain , 2012, NeuroImage.

[40]  Jim M Wild,et al.  The influence of lung airways branching structure and diffusion time on measurements and models of short-range 3He gas MR diffusion. , 2012, Journal of magnetic resonance.

[41]  J. E. Tanner,et al.  Restricted Self‐Diffusion of Protons in Colloidal Systems by the Pulsed‐Gradient, Spin‐Echo Method , 1968 .

[42]  A. Szafer,et al.  An analytical model of restricted diffusion in bovine optic nerve , 1997, Magnetic resonance in medicine.

[43]  Paul C. Bressloff,et al.  A `sum-over-paths' approach to diffusion on trees , 1996 .