MR diffusion kurtosis imaging for neural tissue characterization

In conventional diffusion tensor imaging (DTI), water diffusion distribution is described as a 2nd‐order three‐dimensional (3D) diffusivity tensor. It assumes that diffusion occurs in a free and unrestricted environment with a Gaussian distribution of diffusion displacement, and consequently that diffusion weighted (DW) signal decays with diffusion factor (b‐value) monoexponentially. In biological tissue, complex cellular microstructures make water diffusion a highly hindered or restricted process. Non‐monoexponential decays are experimentally observed in both white matter and gray matter. As a result, DTI quantitation is b‐value dependent and DTI fails to fully utilize the diffusion measurements that are inherent to tissue microstructure. Diffusion kurtosis imaging (DKI) characterizes restricted diffusion and can be readily implemented on most clinical scanners. It provides a higher‐order description of water diffusion process by a 2nd‐order 3D diffusivity tensor as in conventional DTI together with a 4th‐order 3D kurtosis tensor. Because kurtosis is a measure of the deviation of the diffusion displacement profile from a Gaussian distribution, DKI analyses quantify the degree of diffusion restriction or tissue complexity without any biophysical assumption. In this work, the theory of diffusion kurtosis and DKI including the directional kurtosis analysis is revisited. Several recent rodent DKI studies from our group are summarized, and DKI and DTI compared for their efficacy in detecting neural tissue alterations. They demonstrate that DKI offers a more comprehensive approach than DTI in describing the complex water diffusion process in vivo. By estimating both diffusivity and kurtosis, it may provide improved sensitivity and specificity in MR diffusion characterization of neural tissues. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  J. E. Tanner,et al.  Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient , 1965 .

[2]  William H. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[3]  K. Balanda,et al.  Kurtosis: A Critical Review , 1988 .

[4]  D. LeBihan,et al.  Molecular diffusion nuclear magnetic resonance imaging. , 1991 .

[5]  D. Le Bihan Molecular diffusion nuclear magnetic resonance imaging. , 1991, Magnetic resonance quarterly.

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

[7]  D. Gadian,et al.  q‐Space imaging of the brain , 1994, Magnetic resonance in medicine.

[8]  C. Beaulieu,et al.  Water diffusion in the giant axon of the squid: Implications for diffusion‐weighted MRI of the nervous system , 1994, Magnetic resonance in medicine.

[9]  P. Basser,et al.  MR diffusion tensor spectroscopy and imaging. , 1994, Biophysical journal.

[10]  P. Basser Inferring microstructural features and the physiological state of tissues from diffusion‐weighted images , 1995, NMR in biomedicine.

[11]  P. Basser,et al.  Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. , 1996, Journal of magnetic resonance. Series B.

[12]  P. Basser,et al.  Toward a quantitative assessment of diffusion anisotropy , 1996, Magnetic resonance in medicine.

[13]  D. Norris,et al.  Biexponential diffusion attenuation in various states of brain tissue: Implications for diffusion‐weighted imaging , 1996, Magnetic resonance in medicine.

[14]  K. Go The normal and pathological physiology of brain water. , 1997, Advances and technical standards in neurosurgery.

[15]  Josef Pfeuffer,et al.  Restricted diffusion and exchange of intracellular water: theoretical modelling and diffusion time dependence of 1H NMR measurements on perfused glial cells , 1998, NMR in biomedicine.

[16]  Y. Cohen,et al.  Non-mono-exponential attenuation of water and N-acetyl aspartate signals due to diffusion in brain tissue. , 1998, Journal of magnetic resonance.

[17]  M. Solaiyappan,et al.  In vivo three‐dimensional reconstruction of rat brain axonal projections by diffusion tensor imaging , 1999, Magnetic resonance in medicine.

[18]  C. Westin,et al.  Multi‐component apparent diffusion coefficients in human brain † , 1999, NMR in biomedicine.

[19]  Y. Cohen,et al.  Assignment of the water slow‐diffusing component in the central nervous system using q‐space diffusion MRS: Implications for fiber tract imaging , 2000, Magnetic resonance in medicine.

[20]  E. Melhem,et al.  Diffusion tensor MR imaging of the brain: effect of diffusion weighting on trace and anisotropy measurements. , 2000, AJNR. American journal of neuroradiology.

[21]  Bruno Quesson,et al.  Magnetic resonance temperature imaging for guidance of thermotherapy , 2000, Journal of magnetic resonance imaging : JMRI.

[22]  D. Le Bihan,et al.  Water diffusion compartmentation and anisotropy at high b values in the human brain , 2000, Magnetic resonance in medicine.

[23]  M. Solaiyappan,et al.  Diffusion tensor imaging of the developing mouse brain , 2001, Magnetic resonance in medicine.

[24]  C. Beaulieu,et al.  The basis of anisotropic water diffusion in the nervous system – a technical review , 2002, NMR in biomedicine.

[25]  P. Hüppi,et al.  Diffusion tensor imaging of normal and injured developing human brain ‐ a technical review , 2002, NMR in biomedicine.

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

[27]  A. Wright,et al.  Magnetic resonance microimaging of intraaxonal water diffusion in live excised lamprey spinal cord , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[28]  S. Arridge,et al.  Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data , 2002, Magnetic resonance in medicine.

[29]  T. Hendler,et al.  High b value q-space-analyzed diffusion MRI in vascular dementia: A preliminary study , 2002, Journal of the Neurological Sciences.

[30]  Y. Cohen,et al.  High b‐value q‐space analyzed diffusion‐weighted MRS and MRI in neuronal tissues – a technical review , 2002, NMR in biomedicine.

[31]  T. Hendler,et al.  High b‐value q‐space analyzed diffusion‐weighted MRI: Application to multiple sclerosis , 2002, Magnetic resonance in medicine.

[32]  M. Hedehus,et al.  In vivo mapping of the fast and slow diffusion tensors in human brain , 2002, Magnetic resonance in medicine.

[33]  L. Frank Characterization of anisotropy in high angular resolution diffusion‐weighted MRI , 2002, Magnetic resonance in medicine.

[34]  John Russell,et al.  Dysmyelination Revealed through MRI as Increased Radial (but Unchanged Axial) Diffusion of Water , 2002, NeuroImage.

[35]  T. Mareci,et al.  Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging , 2003, Magnetic resonance in medicine.

[36]  T. Nakada,et al.  Absolute eigenvalue diffusion tensor analysis for human brain maturation , 2003, NMR in biomedicine.

[37]  J. Gore,et al.  Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain , 2003, Magnetic resonance in medicine.

[38]  Elna-Marie Larsson,et al.  Visualisation of displacement-distribution parameters in q-space imaging , 2003 .

[39]  Sheng-Kwei Song,et al.  Relative indices of water diffusion anisotropy are equivalent in live and formalin‐fixed mouse brains , 2003, Magnetic resonance in medicine.

[40]  Hao Huang,et al.  Three-dimensional anatomical characterization of the developing mouse brain by diffusion tensor microimaging , 2003, NeuroImage.

[41]  J. Hyde,et al.  Characterization of continuously distributed cortical water diffusion rates with a stretched‐exponential model , 2003, Magnetic resonance in medicine.

[42]  A. Alexander,et al.  Does fractional anisotropy have better noise immunity characteristics than relative anisotropy in diffusion tensor MRI? An analytical approach , 2004, Magnetic resonance in medicine.

[43]  Derek K. Jones,et al.  “Squashing peanuts and smashing pumpkins”: How noise distorts diffusion‐weighted MR data , 2004, Magnetic resonance in medicine.

[44]  M. Moseley,et al.  Magnetic Resonance in Medicine 51:924–937 (2004) Characterizing Non-Gaussian Diffusion by Using Generalized Diffusion Tensors , 2022 .

[45]  Christos Davatzikos,et al.  Spatiotemporal maturation patterns of murine brain quantified by diffusion tensor MRI and deformation-based morphometry , 2005, Proc. Natl. Acad. Sci. USA.

[46]  Kamil Ugurbil,et al.  How does DWI correlate with white matter structures? , 2005, Magnetic resonance in medicine.

[47]  Christian Beaulieu,et al.  Diffusion tensor imaging of neurodevelopment in children and young adults , 2005, NeuroImage.

[48]  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.

[49]  Hsiao-Fang Liang,et al.  Formalin fixation alters water diffusion coefficient magnitude but not anisotropy in infarcted brain , 2005, Magnetic resonance in medicine.

[50]  Roland Bammer,et al.  Limitations of apparent diffusion coefficient‐based models in characterizing non‐gaussian diffusion , 2005, Magnetic resonance in medicine.

[51]  Andre Obenaus,et al.  Magnetic resonance imaging and mathematical modeling of progressive formalin fixation of the human brain , 2005, Magnetic resonance in medicine.

[52]  Chih-Liang Chin,et al.  Ex vivo evaluation of ADC values within spinal cord white matter tracts. , 2005, AJNR. American journal of neuroradiology.

[53]  Liqun Qi,et al.  Eigenvalues of a real supersymmetric tensor , 2005, J. Symb. Comput..

[54]  S. Blackband,et al.  Effects of temperature and aldehyde fixation on tissue water diffusion properties, studied in an erythrocyte ghost tissue model , 2006, Magnetic resonance in medicine.

[55]  Lucie Hertz-Pannier,et al.  Assessment of the early organization and maturation of infants' cerebral white matter fiber bundles: A feasibility study using quantitative diffusion tensor imaging and tractography , 2006, NeuroImage.

[56]  J. Helpern,et al.  Three‐dimensional characterization of non‐gaussian water diffusion in humans using diffusion kurtosis imaging , 2006, NMR in biomedicine.

[57]  Anomalous Diffusion and Non-Monoexponential b-decay , 2006 .

[58]  Hao Huang,et al.  White and gray matter development in human fetal, newborn and pediatric brains , 2006, NeuroImage.

[59]  q-Space imaging using small magnetic field gradient. , 2006, Magnetic resonance in medical sciences : MRMS : an official journal of Japan Society of Magnetic Resonance in Medicine.

[60]  P. Poulet,et al.  Brain dysmyelination and recovery assessment by noninvasive in vivo diffusion tensor magnetic resonance imaging , 2006, Journal of neuroscience research.

[61]  Shu-Wei Sun,et al.  Differential sensitivity of in vivo and ex vivo diffusion tensor imaging to evolving optic nerve injury in mice with retinal ischemia , 2006, NeuroImage.

[62]  K. Lim,et al.  Advances in white matter imaging: A review of in vivo magnetic resonance methodologies and their applicability to the study of development and aging , 2006, Neuroscience & Biobehavioral Reviews.

[63]  J. Dubois,et al.  Diffusion tensor imaging of brain development. , 2006, Seminars in fetal & neonatal medicine.

[64]  Alex J. de Crespigny,et al.  An approach to high resolution diffusion tensor imaging in fixed primate brain , 2007, NeuroImage.

[65]  Stephan E Maier,et al.  Developmental changes and injury induced disruption of the radial organization of the cortex in the immature rat brain revealed by in vivo diffusion tensor MRI. , 2007, Cerebral cortex.

[66]  Fahmeed Hyder,et al.  Neurodevelopment of C57B/L6 mouse brain assessed by in vivo diffusion tensor imaging , 2007, NMR in biomedicine.

[67]  Ludovico Minati,et al.  Biexponential and diffusional kurtosis imaging, and generalised diffusion-tensor imaging (GDTI) with rank-4 tensors: a study in a group of healthy subjects , 2007, Magnetic Resonance Materials in Physics, Biology and Medicine.

[68]  P. Khong,et al.  Diffusion tensor magnetic resonance imaging finding of discrepant fractional anisotropy between the frontal and parietal lobes after whole-brain irradiation in childhood medulloblastoma survivors: reflection of regional white matter radiosensitivity? , 2007, International journal of radiation oncology, biology, physics.

[69]  Guido Gerig,et al.  Diffusion tensor imaging: Application to the study of the developing brain. , 2007, Journal of the American Academy of Child and Adolescent Psychiatry.

[70]  Shu-Wei Sun,et al.  Selective vulnerability of cerebral white matter in a murine model of multiple sclerosis detected using diffusion tensor imaging , 2007, Neurobiology of Disease.

[71]  Jerry L Prince,et al.  Effects of signal‐to‐noise ratio on the accuracy and reproducibility of diffusion tensor imaging–derived fractional anisotropy, mean diffusivity, and principal eigenvector measurements at 1.5T , 2007, Journal of magnetic resonance imaging : JMRI.

[72]  Jean-Marie Bonny,et al.  In vivo analysis of the post‐natal development of normal mouse brain by DTI , 2007, NMR in biomedicine.

[73]  J. A. Helpern,et al.  Assessment of abnormalities in the cerebral microstructure of schizophrenia patients : a diffusional kurtosis imaging study , 2007 .

[74]  Li Wang,et al.  LINGO-1 antagonist promotes spinal cord remyelination and axonal integrity in MOG-induced experimental autoimmune encephalomyelitis , 2007, Nature Medicine.

[75]  Valerij G Kiselev,et al.  Is the “biexponential diffusion” biexponential? , 2007, Magnetic resonance in medicine.

[76]  Yin Wu,et al.  MR diffusion tensor imaging study of postinfarct myocardium structural remodeling in a porcine model , 2007, Magnetic resonance in medicine.

[77]  Alexander Leemans,et al.  Microstructural maturation of the human brain from childhood to adulthood , 2008, NeuroImage.

[78]  Markus Nilsson,et al.  In vivo visualization of displacement-distribution-derived parameters in q-space imaging. , 2008, Magnetic resonance imaging.

[79]  Yoram Cohen,et al.  High b‐value q‐space diffusion MRS of nerves: structural information and comparison with histological evidence , 2008, NMR in biomedicine.

[80]  P. Basser,et al.  Axcaliber: A method for measuring axon diameter distribution from diffusion MRI , 2008, Magnetic resonance in medicine.

[81]  Ed X. Wu,et al.  Comparison of directional diffusion kurtoses and diffusivities in EAE-induced spinal cord , 2008 .

[82]  Ed X. Wu,et al.  Towards better MR characterization of neural tissues using directional diffusion kurtosis analysis , 2008, NeuroImage.

[83]  Xiaohong Joe Zhou,et al.  Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation. , 2008, Journal of magnetic resonance.

[84]  Adriana Di Martino,et al.  Age‐related non‐Gaussian diffusion patterns in the prefrontal brain , 2008, Journal of magnetic resonance imaging : JMRI.

[85]  Joong Hee Kim,et al.  Axonal injury detected by in vivo diffusion tensor imaging correlates with neurological disability in a mouse model of multiple sclerosis , 2008, NMR in biomedicine.

[86]  Liang Xuan,et al.  Estimation of the orientation distribution function from diffusional kurtosis imaging , 2008, Magnetic resonance in medicine.

[87]  P A Narayana,et al.  Early postnatal development of rat brain: In vivo diffusion tensor imaging , 2008, Journal of neuroscience research.

[88]  Liqun Qi,et al.  D-eigenvalues of diffusion kurtosis tensors , 2008 .

[89]  Peter J Basser,et al.  The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: experiments and simulations. , 2008, Journal of magnetic resonance.

[90]  Pearson set of distributions as improved signal model for diffusion kurtosis imaging , 2009 .

[91]  Kevin C. Chan,et al.  Does diffusion kurtosis imaging lead to better neural tissue characterization? A rodent brain maturation study , 2009, NeuroImage.

[92]  Silun Wang,et al.  Longitudinal diffusion tensor magnetic resonance imaging study of radiation-induced white matter damage in a rat model. , 2009, Cancer research.

[93]  Maher Moakher,et al.  The Algebra of Fourth-Order Tensors with Application to Diffusion MRI , 2009 .

[94]  Timothy Edward John Behrens,et al.  Training induces changes in white matter architecture , 2009, Nature Neuroscience.

[95]  Sheng-Kwei Song,et al.  Axial Diffusivity Is the Primary Correlate of Axonal Injury in the Experimental Autoimmune Encephalomyelitis Spinal Cord: A Quantitative Pixelwise Analysis , 2009, The Journal of Neuroscience.

[96]  In vivo Imaging of Kurtosis Tensor Eigenvalues in the Brain at 3 T , 2009 .

[97]  Detection of brain maturation - DTI with different B-values versus diffusion kurtosis imaging , 2009 .

[98]  E. Hui,et al.  In vivo DTI assessment of hepatic ischemia reperfusion injury in an experimental rat model , 2009, Journal of magnetic resonance imaging : JMRI.

[99]  Yoram Cohen,et al.  QSI and DTI of excised brains of the myelin-deficient rat , 2009, NeuroImage.

[100]  F. Ståhlberg,et al.  Diffusion‐weighted MRI measurements on stroke patients reveal water‐exchange mechanisms in sub‐acute ischaemic lesions , 2009, NMR in biomedicine.

[101]  P. Basser,et al.  In vivo measurement of axon diameter distribution in the corpus callosum of rat brain. , 2009, Brain : a journal of neurology.

[102]  Lutz Jäncke,et al.  White matter plasticity in the corticospinal tract of musicians: A diffusion tensor imaging study , 2009, NeuroImage.

[103]  L. Qi,et al.  Principal invariants and inherent parameters of diffusion kurtosis tensors , 2009 .

[104]  L. Qi,et al.  The measure of diffusion skewness and kurtosis in magnetic resonance imaging , 2010 .

[105]  M. Moseley,et al.  In vivo generalized diffusion tensor imaging (GDTI) using higher‐order tensors (HOT) , 2010, Magnetic resonance in medicine.

[106]  Eric Achten,et al.  Optimal Experimental Design for Diffusion Kurtosis Imaging , 2010, IEEE Transactions on Medical Imaging.

[107]  Derek K. Jones,et al.  Diffusion tensor imaging. , 2011, Methods in molecular biology.

[108]  Josef Pfeuffer,et al.  Water diffusion in rat brain in vivo as detected at very large b values is multicompartmental , 2022 .