In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter
Open accessAbstract
The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600 ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Restricted and hindered diffusion mechanisms coexist within each voxel, generating non-Gaussian and time-dependent diffusion behavior.
“These mechanisms coexist within each voxel, generating non-Gaussian and time-dependent diffusion behavior (Fieremans et al., 2016; Novikov et al., 2019).”
From 40 Years of diffusion MRI in the brain: From history to emerging frontiers (2026) · cites this paper as Fieremans et al., 2016
The Introduction links observed time dependence to non-Gaussian diffusion and argues that disordered hindrances and restrictions are likely contributors in human white matter. It does not establish that both mechanisms coexist within each voxel; the Discussion > Longitudinal Diffusion says the intra- and extra-axonal contributions cannot yet be separated. (LLM, conf=0.84)
Experimental — accuracy not yet measuredHuman white-matter diffusivity depends on diffusion time, supporting the idea that axonal packing, extra-axonal disorder, restrictions, and exchange contribute to the measured signal.
“Later work showed that human white-matter diffusivity depends on diffusion time, supporting the idea that axonal packing, extra-axonal disorder, restrictions, and exchange contribute to the measured signal (Fieremans et al., 2016).”
From 40 Years of diffusion MRI in the brain: From history to emerging frontiers (2026) · cites this paper as Fieremans et al., 2016
The Abstract and Conclusions report time-dependent diffusivity in human white matter and interpret it in terms of axonal packing, extra-axonal disorder, and restrictions along fibers. The Discussion’s “Potential confounding effects” section says exchange could affect the measured signal, but does not establish it as a contributor to the observed time dependence; the authors note that modeling this effect is beyond the study’s scope. (LLM, conf=0.86)
Experimental — accuracy not yet measuredFree-water correction, multi-shell acquisition, and joint structural-functional modeling are already making diffusion MRI less reliant on a few oversimplified scalar summaries.
“Free-water correction, multi-shell acquisition, and joint structural–functional modeling are already making diffusion MRI less reliant on a few oversimplified scalar summaries (Assaf et al., 2019; Fieremans et al., 2016).”
From 40 Years of diffusion MRI in the brain: From history to emerging frontiers (2026) · cites this paper as Fieremans et al., 2016
The Methods and Results describe varying diffusion time and fitting biophysical models to white-matter measurements, supporting the broader move beyond a few scalar summaries. But the Methods > In vivo measurements reports b = 0 and b = 500 s/mm² acquisitions, not multi-shell acquisition; the paper does not describe free-water correction or joint structural–functional modeling. Page numbers are unavailable in our copy. (LLM, conf=0.86)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Jenkinson, M., Bannister, P., Brady, M., & Smith, S. (2002) · NeuroImage · doi:10.1006/nimg.2002.1132 · Cited by 11,888 · see citing works
The basis of anisotropic water diffusion in the nervous system—A technical review.
Beaulieu, C. (2002) · NMR in Biomedicine · doi:10.1002/nbm.782 · Cited by 4,653 · see citing works
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Bouchaud, J.-P., & Georges, A. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90099-n · Cited by 4,162 · see citing works
Flagged first, then by citations
Research works printed but not linked: 66
- Aboitiz F Scheibel AB Fisher RS Zaidel E 1992 Fiber composition of the human corpus callosum Brain Research 598 143 153 1486477
- Alexander DC Hubbard PL Hall MG Moore EA Ptito M Parker GJM Dyrby TB 2010 Orientationally invariant indices of axon diameter and density from diffusion MRI Neuroimage 52 1374 1389 20580932
- Assaf Y Blumenfeld-Katzir T Yovel Y Basser PJ 2008 AxCaliber: A method for measuring axon diameter distribution from diffusion MRI Magnetic Resonance In Medicine 59 1347 1354 18506799 PMC4667732
- Assaf Y Cohen Y 2000 Assignment of the water slow-diffusing component in the central nervous system using q-space diffusion MRS: Implications for fiber tract imaging Magnetic Resonance In Medicine 43 191 199 10680682
- Assaf Y Freidlin RZ Rohde GK Basser PJ 2004 New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter Magnetic Resonance In Medicine 52 965 978 15508168
- Bar-Shir A Cohen Y 2008 High b-value q-space diffusion MRS of nerves: structural information and comparison with histological evidence NMR in Biomedicine 21 165 174 17492659
- Barazany D Basser PJ Assaf Y 2009 In vivo measurement of axon diameter distribution in the corpus callosum of rat brain Brain 132 1210 1220 19403788 PMC2677796
- Baron CA Beaulieu C 2014 Oscillating gradient spin-echo (OGSE) diffusion tensor imaging of the human brain Magnetic Resonance in Medicine 72 726 736 24142863
- Basser PJ 1995 Inferring microstructural features and the physiological state of tissues from diffusion-weighted images NMR in Biomedicine 8 333 344 8739270
- Beaulieu C Allen PS 1996 An in vitro evaluation of the effects of local magnetic-susceptibility-induced gradients on anisotropic water diffusion in nerve Magnetic Resonance in Medicine 36 39 44 8795018
- Behrens TEJ Woolrich MW Jenkinson M Johansen-Berg H Nunes RG Clare S Matthews PM Brady JM Smith SM 2003 Characterization and propagation of uncertainty in diffusion-weighted MR imaging Magn Reson Med 50 1077 1088 14587019
- Bjarnason TA Vavasour IM Chia CLL MacKay AL 2005 Characterization of the NMR behavior of white matter in bovine brain Magn Reson Med 54 1072 1081 16200557
- Budde MB Frank JA 2010 Neurite beading is sufficient to decrease the apparent diffusion coefficient after ischemic stroke PNAS 107 14472 14477 20660718 PMC2922529
- Burcaw LM Fieremans E Novikov DS 2015 Mesoscopic structure of neuronal tracts from time-dependent diffusion Neuroimage 114 18 37 25837598 PMC4446209
- Callaghan PT Stepišnik J 1995 Frequency-domain analysis of spin motion using modulated-gradient NMR Journal of Magnetic Resonance, Series A 117 118 122
- Clark C Hedehus M Moseley M 2001 Diffusion time dependence of the apparent diffusion tensor in healthy human brain and white matter disease Magnetic Resonance In Medicine 45 1126 1129 11378893
- Clark CA Le Bihan D 2000 Water diffusion compartmentation and anisotropy at high b values in the human brain Magn Reson Med 44 852 859 11108621
- Debanne D Campanac E Bialowas A Carlier E Alcaraz G 2011 Axon Physiology Physiol Rev 91 555 602 21527732
- Does MD Gore JC 2002 Compartmental study of T1 and T2 in rat brain and trigeminal nerve in vivo Magnetic Resonance in Medicine 47 274 283 11810670
- Does MD Parsons EC Gore JC 2003 Oscillating Gradient Measurements of Water Diffusion in Normal and Globally Ischemic Rat Brain Magnetic Resonance In Medicine 49 206 215 12541239
- Fieremans E Novikov DS Jensen JH Helpern JA 2010 Monte Carlo study of a two-compartment exchange model of diffusion NMR in Biomedicine 23 711 724 20882537 PMC2997614
- Henkelman RM Stanisz GJ Kim JK Bronskill MJ 1994 Anisotropy Of Nmr Properties Of Tissues Magn Reson Med 32 592 601 7808260
- Horsfield M Barker G Mcdonald W 1994 Self-Diffusion in Cns Tissue by Volume-Selective Proton NMR Magnetic Resonance In Medicine 31 637 644 8057816
- Innocenti GM Caminiti R Aboitiz F 2015 Comments on the paper by Horowitz et al. (2014) Brain Structure and Function 220 1789 1790 25579065
- Jenkinson M Smith S 2001 A global optimisation method for robust affine registration of brain images Medical Image Analysis 5 143 156 11516708
- Jespersen SN Kroenke CD Østergaard L Ackerman JJH Yablonskiy DA 2007 Modeling dendrite density from magnetic resonance diffusion measurements Neuroimage 34 1473 1486 17188901
- Kroenke CD Ackerman JJH Yablonskiy DA 2004 On the nature of the NAA diffusion attenuated MR signal in the central nervous system Magnetic Resonance in Medicine 52 1052 1059 15508157
- Kunz N Sizonenko SV Hueppi PS Gruetter R van de Looij Y 2013 Investigation of field and diffusion time dependence of the diffusion-weighted signal at ultrahigh magnetic fields NMR In Biomedicine 26 1251 1257 23533088
- Lancaster JL Andrews T Hardies LJ Dodd S Fox PT 2003 Three-pool model of white matter Journal of Magnetic Resonance Imaging 17 1 10 12500269
- Lavdas I Behan KC Papadaki A McRobbie DW Aboagye EO 2013 A phantom for diffusion-weighted MRI (DW-MRI) Journal of Magnetic Resonance Imaging 38 173 179 23576443
- Lundell H Alexander DC Dyrby TB 2014 High angular resolution diffusion imaging with stimulated echoes: compensation and correction in experiment design and analysis NMR in Biomedicine 27 918 925 24890716 PMC4312915
- Merboldt KD Hanicke W Frahm J 1985 Self-diffusion NMR imaging using stimulated echoes Journal of Magnetic Resonance (1969) 64 479 486
- Mitra PP Sen PN Schwartz LM Le Doussal P 1992 Diffusion Propagator as a Probe of the Structure of Porous Media Physical Review Letters 68 3555 3558 10045734
- Mori S 2005 MRI Atlas of Human White Matter Elsevier Amsterdam, The Netherlands
- Mulkern RV Zengingonul HP Robertson RL Bogner P Zou KH Gudbjartsson H Guttmann CR Holtzman D Kyriakos W Jolesz FA Maier SE 2000 Multi-component apparent diffusion coefficients in human brain: relationship to spin-lattice relaxation Magn Reson Med 44 292 300 10918329
- Murday JS Cotts RM 1968 Self-Diffusion Coefficient of Liquid Lithium The Journal of Chemical Physics 48 4938 4945
- Neuman CH 1974 Spin echo of spins diffusing in a bounded medium The Journal of Chemical Physics 60 4508 4511
- Nilsson M Latt J Nordh E Wirestam R Stahlberg F Brockstedt S 2009 On the effects of a varied diffusion time in vivo: is the diffusion in white matter restricted? Magnetic Resonance Imaging 27 176 187 18657924
- Nilsson M Lätt J Ståhlberg F van Westen D Hagslätt H 2012 The importance of axonal undulation in diffusion MR measurements: a Monte Carlo simulation study NMR in Biomedicine 25 795 805 22020832
- Novikov DS Jensen JH Helpern JA Fieremans E 2014 Revealing mesoscopic structural universality with diffusion Proceedings of the National Academy of Sciences of the United States of America 111 5088 5093 24706873 PMC3986157
- Ong HH Wright AC Wehrli SL Souza A Schwartz ED Hwang SN Wehrli FW 2008 Indirect measurement of regional axon diameter in excised mouse spinal cord with q-space imaging: Simulation and experimental studies Neuroimage 40 1619 1632 18342541 PMC2440917
- Perge JA Koch K Miller R Sterling P Balasubramanian V 2009 How the Optic Nerve Allocates Space, Energy Capacity, and Information The Journal of Neuroscience 29 7917 7928 19535603 PMC2928227
- Perrot R Lonchampt P Peterson AC Eyer J 2007 Axonal neurofilaments control multiple fiber properties but do not influence structure or spacing of nodes of Ranvier Journal of Neuroscience 27 9573 9584 17804618 PMC6672964
- Rioux JA Levesque IR Rutt BK 2015 Biexponential longitudinal relaxation in white matter: Characterization and impact on T1 mapping with IR-FSE and MP2RAGE Magnetic Resonance in Medicine n/a-n/a PMC4837078 26190230
- Ronen I Budde M Ercan E Annese J Techawiboonwong A Webb A 2014 Microstructural organization of axons in the human corpus callosum quantified by diffusion-weighted magnetic resonance spectroscopy of N-acetylaspartate and postmortem histology Brain Structure and Function 219 1773 1785 23794120
- Salvador R Peña A Menon DK Carpenter TA Pickard JD Bullmore ET 2005 Formal characterization and extension of the linearized diffusion tensor model Human Brain Mapping 24 144 155 15468122 PMC6871750
- Schain AJ Hill RA Grutzendler J 2014 Label-free in vivo imaging of myelinated axons in health and disease with spectral confocal reflectance microscopy Nat Med 20 443 449 24681598 PMC3981936
- Shemesh N Cohen Y 2011 Microscopic and compartment shape anisotropies in gray and white matter revealed by angular bipolar double-PFG MR Magnetic Resonance in Medicine 65 1216 1227 21305595
- Shepherd G Raastad M 2003 Axonal varicosity distributions along parallel fibers: a new angle on a cerebellar circuit The Cerebellum 2 110 113 12880178
- Shepherd GMG Raastad M Andersen P 2002 General and variable features of varicosity spacing along unmyelinated axons in the hippocampus and cerebellum PNAS 99 6340 6345 11972022 PMC122950
- Sigmund EE Sui D Ukpebor O Baete S Fieremans E Babb JS Mechlin M Liu K Kwon J Mcgorty K Hodnett PA Bencardino J 2013 Stimulated Echo Diffusion Tensor Imaging and SPAIR T-2-Weighted Imaging in Chronic Exertional Compartment Syndrome of the Lower Leg Muscles J Magn Reson Imaging 38 1073 1082 23440764 PMC3664655
- Stanisz GJ 2003 Diffusion MR in Biological Systems: Tissue Compartments and Exchange Israel Journal of Chemistry 43 33 44
- Stanisz GJ Kecojevic A Bronskill MJ Henkelman RM 1999 Characterizing white matter with magnetization transfer and T2 Magnetic Resonance in Medicine 42 1128 1136 10571935
- Stanisz GJ Odrobina EE Pun J Escaravage M Graham SJ Bronskill MJ Henkelman RM 2005 T1, T2 relaxation and magnetization transfer in tissue at 3T Magn Reson Med 54 507 512 16086319
- Stanisz GJ Szafer A Wright GA Henkelman RM 1997 An Analyitical Model of Restricted Diffusion in Bovine Optic Nerve Magnetic Resonance In Medicine 37 103 111 8978638
- Szafer A Zhong J Gore JC 1995 Theoretical model for water diffusion in tissues Magnetic Resonance in Medicine 33 697 712 7596275
- Tang Y Nyengaard JR 1997 A stereological method for estimating the total length and size of myelin fibers in human brain white matter J Neurosci Methods 73 193 200 9196291
- Tanner JE 1970 Use of the Stimulated Echo in NMR Diffusion Studies The Journal of Chemical Physics 52 2523 2526
- van Gelderen P Devleeschouwer M Despres D Pekar J Vanzijl P Moonen C 1994 Water Diffusion And Acute Stroke Magnetic Resonance in Medicine 31 154 163 8133751
- Veraart J Fieremans E Jelescu IO Knoll F Novikov DS 2015 Gibss Ringing in Diffusion MRI Magnetic Resonance in Medicine In press PMC4915073 26257388
- Veraart J Sijbers J Sunaert S Leemans A Jeurissen B 2013 Weighted linear least squares estimation of diffusion MRI parameters: Strengths, limitations, and pitfalls Neuroimage 81 335 346 23684865
- Wang L Dong J Cull G Fortune B Cioffi GA 2003 Varicosities of Intraretinal Ganglion Cell Axons in Human and Nonhuman Primates Investigative Ophthalmology and Visual Science 44 2 9 12506048
- Whittall KP MacKay AL Graeb DA Nugent RA Li DK Paty DW 1997 In vivo measurement of T2 distributions and water contents in normal human brain Magn Reson Med 37 34 43 8978630
- Xu J Li H Harkins KD Jiang X Xie J Kang H Does MD Gore JC 2014 Mapping mean axon diameter and axonal volume fraction by MRI using temporal diffusion spectroscopy Neuroimage 103 10 19 25225002 PMC4312203
- Zhang H Hubbard PL Parker GJM Alexander DC 2011 Axon diameter mapping in the presence of orientation dispersion with diffusion MRI Neuroimage 56 1301 1315 21316474
- Zhang Y Brady M Smith S 2001 Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm IEEE Transactions on Medical Imaging 20 45 57 11293691
Cited by
Sorted by citations
Jelescu, I. O., de Skowronski, A., Geffroy, F., Palombo, M., & Novikov, D. S. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119277 · Cited by 177 · see citing works
Self-citationThe role of diffusion MRI in neuroscience
Assaf, Y., Johansen‐Berg, H., & Thiebaut de Schotten, M. (2019) · NMR in Biomedicine · doi:10.1002/nbm.3762 · Cited by 158 · see citing works
Promise and pitfalls of g-ratio estimation with MRI
Campbell, J. S. W., Leppert, I. R., Narayanan, S., Boudreau, M., Duval, T., Cohen-Adad, J., Pike, G. B., & Stikov, N. (2018) · NeuroImage · doi:10.1016/j.neuroimage.2017.08.038 · Cited by 129 · see citing works
Diffusion time dependence, power‐law scaling, and exchange in gray matter
Olesen, J. L., Østergaard, L., Shemesh, N., & Jespersen, S. N. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.118976 · Cited by 125 · see citing works
40 Years of diffusion MRI in the brain: From history to emerging frontiers
Le Bihan, D. (2026) · Imaging Neuroscience · doi:10.1162/imag.a.1365
“These mechanisms coexist within each voxel, generating non-Gaussian and time-dependent diffusion behavior ( Fieremans et al., 2016; Novikov et al., 2019).”
- Authors
- Fieremans, E., Burcaw, L. M., Lee, H.-H., Lemberskiy, G., Veraart, J., & Novikov, D. S.
- Affiliations
- New York University (US)
- University of Antwerp (BE)
- Corresponding author
- Fieremans, Els
- Venue
- NeuroImage
- Publisher
- Elsevier BV
- Published
- 2016-04
- Volume
- 129
- Pages
- 414-427
- ISSN
- 1053-8119 (ISSN-L)
- PMC
- PMC4803645
- OpenAlex
- W2282437794
- Cited by
- 181
- References
- 3
- Citations by year
- 2026: 9 · 2025: 13 · 2024: 18 · 2023: 9 · 2022: 16 · 2021: 19 · 2020: 27 · 2019: 16 · 2018: 23 · 2017: 24 · 2016: 7
- FWCI
- 20.26
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- NeuroImage (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- Christopher Glielmi
- Thorsten Feiweier
- Raymond and Beverly Sackler Laboratories for Convergence of Physical, Engineering, and Biomedical Sciences
- Litwin Foundation for Alzheimer's Research
- National Institute of Neurological Disorders and Stroke of the National Institutes of Health (R01NS088040)
- Fund for Scientific Research-Flanders (12S1615N)
- Topics
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › NMR spectroscopy and applications
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
- Keywords
- time-dependent diffusion, diffusion tensor imaging, stimulated echo, diffusion coefficient, structural disorder, confined diffusion, diffusion in disordered media
- MeSH terms
- Adult, Brain, Brain Mapping, Female, Humans, Image Processing, Computer-Assisted, Male, Diffusion Tensor Imaging, White Matter
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review