Orthogonal tensor invariants and the analysis of diffusion tensor magnetic resonance images
Abstract
This paper outlines the mathematical development and application of two analytically orthogonal tensor invariants sets. Diffusion tensors can be mathematically decomposed into shape and orientation information, determined by the eigenvalues and eigenvectors, respectively. The developments herein orthogonally decompose the tensor shape using a set of three orthogonal invariants that characterize the magnitude of isotropy, the magnitude of anisotropy, and the mode of anisotropy. The mode of anisotropy is useful for resolving whether a region of anisotropy is linear anisotropic, orthotropic, or planar anisotropic. Both tensor trace and fractional anisotropy are members of an orthogonal invariant set, but they do not belong to the same set. It is proven that tensor trace and fractional anisotropy are not mutually orthogonal measures of the diffusive process. The results are applied to the analysis and visualization of diffusion tensor magnetic resonance images of the brain in a healthy volunteer. The theoretical developments provide a method for generating scalar maps of the diffusion tensor data, including novel fractional anisotropy maps that are color encoded for the mode of anisotropy and directionally encoded colormaps of only linearly anisotropic structures, rather than of high fractional anisotropy structures.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
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?
MD and FA are not mutually mathematically orthogonal measures.
“For example, MD and FA are not mutually mathematically orthogonal measures (Ennis and Kindlmann, 2006).”
From Quantitative mapping of the brain’s structural connectivity using diffusion MRI tractography: A review (2022) · cites this paper as Ennis and Kindlmann, 2006
Cites
Diffusion tensor MR imaging of the human brain
Pierpaoli, C., Jezzard, P., Basser, P. J., Barnett, A., & Di Chiro, G. (1996) · Radiology · doi:10.1148/radiology.201.3.8939209 · Cited by 2,664 · see citing works
High angular resolution diffusion imaging reveals intravoxel white matter fiber heterogeneity
Tuch, D. S., Reese, T. G., Wiegell, M. R., Makris, N., Belliveau, J. W., & Wedeen, V. J. (2002) · Magnetic Resonance in Medicine · doi:10.1002/mrm.10268 · Cited by 1,548 · cited 1× · see citing works
“[10] and solve for d , recalling that dK1 I:dA and Eq.”
BackgroundBasser, P. J. (1995) · NMR in Biomedicine · doi:10.1002/nbm.1940080707 · Cited by 1,526 · see citing works
Processing and visualization for diffusion tensor MRI
Westin, C., Maier, S. E., Mamata, H., Nabavi, A., Jolesz, F. A., & Kikinis, R. (2002) · Medical Image Analysis · doi:10.1016/s1361-8415(02)00053-1 · Cited by 802 · see citing works
Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data
Alexander, D. C., Barker, G. J., & Arridge, S. (2002) · Magnetic Resonance in Medicine · doi:10.1002/mrm.10209 · Cited by 527 · see citing works
Water diffusion and acute stroke
van Gelderen, P., de Vleeschouwer, M. H. M., Despres, D., Pekar, J. J., van Zijl, P. C. M., & MOONEN, C. T. W. (1994) · Magnetic Resonance in Medicine · doi:10.1002/mrm.1910310209 · Cited by 407 · see citing works
Fiber Crossing in Human Brain Depicted with Diffusion Tensor MR Imaging
Wiegell, M. R., Larsson, H. B. W., & Wedeen, V. J. (2000) · Radiology · doi:10.1148/radiology.217.3.r00nv43897 · Cited by 376 · see citing works
Determining and visualizing uncertainty in estimates of fiber orientation from diffusion tensor MRI
Jones, D. K. (2002) · Magnetic Resonance in Medicine · doi:10.1002/mrm.10331 · Cited by 371 · see citing works
Characterization of White Matter Damage in Ischemic Leukoaraiosis with Diffusion Tensor MRI
Jones, D. K., Lythgoe, D. J., Horsfield, M. A., Simmons, A., Williams, S., & Markus, H. S. (1999) · Stroke · doi:10.1161/01.str.30.2.393 · Cited by 307 · see citing works
Donahue, K. M., Krouwer, H. G. J., Rand, S. D., Pathak, A. P., Marszalkowski, C. S., Censky, S. C., & Prost, R. W. (2000) · Magnetic Resonance in Medicine · doi:10.1002/1522-2594(200006)43:6 · Cited by 241 · see citing works
Criscione, J. C., Humphrey, J. D., Douglas, A. S., & Hunter, W. C. (2000) · Journal of the Mechanics and Physics of Solids · doi:10.1016/s0022-5096(00)00023-5 · Cited by 221 · see citing works
Clinical applications of diffusion tensor imaging
Dong, Q., Welsh, R. C., Chenevert, T. L., Carlos, R. C., Sundgren, P. C., Gomez‐Hassan, D. M., & Mukherji, S. K. (2003) · Journal of Magnetic Resonance Imaging · doi:10.1002/jmri.10424 · Cited by 210 · see citing works
Visualization of tensor fields using superquadric glyphs
Ennis, D. B., Kindlmann, G., Rodríguez, I., Helm, P. A., & McVeigh, E. R. (2004) · Magnetic Resonance in Medicine · doi:10.1002/mrm.20318 · Cited by 60 · see citing works
Self-citationInvariant and Orthonormal Scalar Measures Derived from Magnetic Resonance Diffusion Tensor Imaging
Bahn, M. M. (1999) · Journal of Magnetic Resonance · doi:10.1006/jmre.1999.1875 · Cited by 26 · see citing works
Seo, Y., Shinar, H., Morita, Y., & Navon, G. (1999) · Magnetic Resonance in Medicine · doi:10.1002/(sici)1522-2594(199909)42:3 · Cited by 19 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Multimodal population brain imaging in the UK Biobank prospective epidemiological study
Miller, K. L., Alfaro-Almagro, F., Bangerter, N. K., Thomas, D. L., Yacoub, E., Xu, J., Bartsch, A. J., Jbabdi, S., Sotiropoulos, S. N., Andersson, J. L. R., et al. (2016) · Nature Neuroscience · doi:10.1038/nn.4393 · Cited by 2,020 · see citing works
Dipy, a library for the analysis of diffusion MRI data
Garyfallidis, E., Brett, M., Amirbekian, B., Rokem, A., van der Walt, S., Descoteaux, M., Nimmo-Smith, I., & Contributors, D. (2014) · Frontiers in Neuroinformatics · doi:10.3389/fninf.2014.00008 · Cited by 1,371 · see citing works
Shenton, M. E., Hamoda, H. M., Schneiderman, J. S., Sylvain Bouix, A., Pasternak, O., Yogesh Rathi, A., Vu, M.-A. T., Purohit, M. P., Helmer, K. G., Koerte, I. K., et al. (2012) · Brain Imaging and Behavior · doi:10.1007/s11682-012-9156-5 · Cited by 942 · see citing works
An Introduction to Diffusion Tensor Image Analysis
O’Donnell, L. J., & Westin, C. (2011) · Neurosurgery Clinics of North America · doi:10.1016/j.nec.2010.12.004 · Cited by 533 · see citing works
Douaud, G., Jbabdi, S., Behrens, T. E. J., Menke, R. A., Gass, A., Monsch, A. U., Rao, A., Whitcher, B., Kindlmann, G., Matthews, P. M., et al. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2010.12.008 · Cited by 514 · see citing works
Self-citationDiffusion MRI at 25: exploring brain tissue structure and function
Le Bihan, D., & Johansen-Berg, H. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2011.11.006 · Cited by 498 · see citing works
Disconnected aging: Cerebral white matter integrity and age-related differences in cognition
Bennett, I. J., & Madden, D. J. (2013) · Neuroscience · doi:10.1016/j.neuroscience.2013.11.026 · Cited by 492 · see citing works
Alexander, A. L., Hurley, S. A., Samsonov, A. A., Adluru, N., Hosseinbor, A. P., Mossahebi, P., Tromp, D., Zakszewski, E., & Field, A. S. (2011) · Brain Connectivity · doi:10.1089/brain.2011.0071 · Cited by 450 · see citing works
Automatic Tractography Segmentation Using a High-Dimensional White Matter Atlas
O’Donnell, L. J., & Westin, C. (2007) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2007.906785 · Cited by 402 · see citing works
van Ewijk, H., Heslenfeld, D. J., Zwiers, M. P., Buitelaar, J. K., & Oosterlaan, J. (2012) · Neuroscience & Biobehavioral Reviews · doi:10.1016/j.neubiorev.2012.01.003 · Cited by 377 · see citing works
Linked independent component analysis for multimodal data fusion
Groves, A. R., Beckmann, C. F., Smith, S. M., & Woolrich, M. W. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2010.09.073 · Cited by 319 · see citing works
Zhang, F., Daducci, A., He, Y., Schiavi, S., Seguin, C., Smith, R. E., Yeh, C.-H., Zhao, T., & O’Donnell, L. J. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2021.118870 · Cited by 302 · see citing works
“For example, MD and FA are not mutually mathematically orthogonal measures [150].”
BackgroundVoineskos, A. N., Rajji, T. K., Lobaugh, N. J., Miranda, D., Shenton, M. E., Kennedy, J. L., Pollock, B. G., & Mulsant, B. H. (2010) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2010.02.009 · Cited by 293 · see citing works
Common genetic variation influencing human white matter microstructure
Zhao, B., Li, T., Yang, Y., Wang, X., Luo, T., Shan, Y., Zhu, Z., Xiong, D., Hauberg, M. E., Bendl, J. M., et al. (2021) · Science · doi:10.1126/science.abf3736 · Cited by 217 · see citing works
Microstructural White Matter Abnormalities and Cognitive Functioning in Type 2 Diabetes
Reijmer, Y. D., Brundel, M., de Bresser, J., Kappelle, L. J., Leemans, A., Biessels, G. J., & on behalf of the Utrecht Vascular Cognitive Impairment Study Group (2012) · Diabetes Care · doi:10.2337/dc12-0493 · Cited by 223 · see citing works
Vos, S. B., Jones, D. K., Jeurissen, B., Viergever, M. A., & Leemans, A. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2011.09.086 · Cited by 214 · see citing works
Tract-specific white matter degeneration in aging. The Rotterdam Study
de Groot, M., Ikram, M. A., Akoudad, S., Krestin, G. P., Hofman, A., van der Lugt, A., Niessen, W. J., & Vernooij, M. W. (2015) · Alzheimer's & Dementia · doi:10.1016/j.jalz.2014.06.011 · Cited by 211 · see citing works
Relevance of Magnetic Resonance Imaging for Early Detection and Diagnosis of Alzheimer Disease
Teipel, S. J., Grothe, M. J., Lista, S., Toschi, N., Garaci, F., & Hampel, H. J. (2013) · Medical Clinics of North America · doi:10.1016/j.mcna.2012.12.013 · Cited by 192 · see citing works
Crossing fibres in tract-based spatial statistics
Jbabdi, S., Behrens, T. E. J., & Smith, S. M. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2009.08.039 · Cited by 187 · see citing works
Group analysis of DTI fiber tract statistics with application to neurodevelopment
Goodlett, C., Fletcher, P. T., Gilmore, J. H., & Gerig, G. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.10.060 · Cited by 184 · see citing works
Neural systems for speech and song in autism
Lai, G. Y.-C., Pantazatos, S. P., Schneider, H. D., & Hirsch, J. (2012) · Brain · doi:10.1093/brain/awr335 · Cited by 184 · see citing works
Revolution of Alzheimer Precision Neurology. Passageway of Systems Biology and Neurophysiology
Hampel, H. J., (APMI), F. T. A. P. M. I., Toschi, N., Babiloni, C., Baldacci, F., Black, K. L., Bokde, A. L. W., Bun, R. S., Cacciola, F., Cavedo, E., et al. (2018) · Journal of Alzheimer s Disease · doi:10.3233/jad-179932 · Cited by 181 · see citing works
Neuroimaging Evidence for the Deficit Subtype of Schizophrenia
Voineskos, A. N., Foussias, G., Lerch, J. P., Felsky, D., Remington, G. J., Rajji, T. K., Lobaugh, N. J., Pollock, B. G., & Mulsant, B. H. (2013) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2013.786 · Cited by 176 · see citing works
The physical and biological basis of quantitative parameters derived from diffusion MRI.
Winston, G. P. (2012) · Europe PMC (PubMed Central) · doi:10.3978/j.issn.2223-4292.2012.12.05 · Cited by 174 · see citing works
White matter abnormalities and illness severity in major depressive disorder
Cole, J. H., Chaddock, C. A., FARMER, A. E., Aitchison, K. J., Simmons, A., McGuffin, P., & Fu, C. H. Y. (2012) · The British Journal of Psychiatry · doi:10.1192/bjp.bp.111.100594 · Cited by 165 · see citing works
Inter-site and inter-scanner diffusion MRI data harmonization
Mirzaalian, H., Ning, L., Savadjiev, P., Pasternak, O., Sylvain Bouix, A., Michailovich, O., Grant, G. A., Marx, C. E., Morey, R. A., Flashman, L. A., et al. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.04.041 · Cited by 153 · see citing works
Diffusion tensor tractography findings in schizophrenia across the adult lifespan
Voineskos, A. N., Lobaugh, N. J., Sylvain Bouix, A., Rajji, T. K., Miranda, D., Kennedy, J. L., Mulsant, B. H., Pollock, B. G., & Shenton, M. E. (2010) · Brain · doi:10.1093/brain/awq040 · Cited by 143 · see citing works
Atypical diffusion tensor hemispheric asymmetry in autism
Lange, N., DuBray, M. B., Lee, J. E., Froimowitz, M. P., Froehlich, A., Adluru, N., Wright, B., Ravichandran, C., Fletcher, P. T., Bigler, E. D., et al. (2010) · Autism Research · doi:10.1002/aur.162 · Cited by 142 · see citing works
Hampel, H. J., Lista, S., Teipel, S. J., Garaci, F., Nisticò, R., Blennow, K., Zetterberg, H., Bertram, L., Duyckaerts, C. J., Bakardjian, H., et al. (2013) · Biochemical Pharmacology · doi:10.1016/j.bcp.2013.11.009 · Cited by 141 · see citing works
Groves, A. R., Smith, S. M., Fjell, A. M., Tamnes, C. K., Walhovd, K. B., Douaud, G., Woolrich, M. W., & Westlye, L. T. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2012.06.038 · Cited by 140 · see citing works
Voineskos, A. N., Lerch, J. P., Felsky, D., Shaikh, S. A., Rajji, T. K., Miranda, D., Lobaugh, N. J., Mulsant, B. H., Pollock, B. G., & Kennedy, J. L. (2011) · Archives of General Psychiatry · doi:10.1001/archgenpsychiatry.2010.194 · Cited by 126 · see citing works
Mackey, A. P., Whitaker, K. J., & Bunge, S. A. (2012) · Frontiers in Neuroanatomy · doi:10.3389/fnana.2012.00032 · Cited by 125 · see citing works
Bergamino, M., Walsh, R. R., & Stokes, A. M. (2021) · Scientific Reports · doi:10.1038/s41598-021-86505-7 · Cited by 124 · see citing works
Chad, J. A., Pasternak, O., Salat, D. H., & Chen, J. J. (2018) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2018.07.018 · Cited by 110 · see citing works
Diffusion-MRI in neurodegenerative disorders
Goveas, J., O’Dwyer, L., Mascalchi, M., Cosottini, M., Diciotti, S., De Santis, S., Passamonti, L., Tessa, C., Toschi, N., & Giannelli, M. (2015) · Magnetic Resonance Imaging · doi:10.1016/j.mri.2015.04.006 · Cited by 104 · see citing works
Alnæs, D., Kaufmann, T., Doan, N. T., Córdova-Palomera, A., Wang, Y.-P., Bettella, F., Moberget, T., Andreassen, O., & Westlye, L. (2018) · JAMA psychiatry · doi:10.1001/jamapsychiatry.2017.4277 · Cited by 112 · see citing works
Broad, R. J., Gabel, M. C., Dowell, N. G., Schwartzman, D. J., Seth, A. K., Zhang, H., Alexander, D. C., Cercignani, M., & Leigh, P. N. (2019) · Journal of Neurology, Neurosurgery & Psychiatry · doi:10.1136/jnnp-2018-318830 · Cited by 105 · see citing works
Diffusion Tensor Cardiovascular Magnetic Resonance Imaging
Khalique, Z., Ferreira, P., Scott, A. D., Nielles‐Vallespin, S., Firmin, D. N., & Pennell, D. J. (2019) · JACC. Cardiovascular imaging · doi:10.1016/j.jcmg.2019.07.016 · Cited by 101 · see citing works
Linke, J. O., King, A. V., Poupon, C., Hennerici, M. G., Gass, A., & Wessa, M. (2013) · Biological Psychiatry · doi:10.1016/j.biopsych.2013.04.010 · Cited by 100 · see citing works
Reijmer, Y. D., Leemans, A., Heringa, S. M., Wielaard, I., Jeurissen, B., Koek, H. L., & Biessels, G. J. (2012) · PLoS ONE · doi:10.1371/journal.pone.0044074 · Cited by 91 · see citing works
Does diffusion MRI tell us anything about the white matter? An overview of methods and pitfalls
O’Donnell, L. J., & Pasternak, O. (2014) · Schizophrenia Research · doi:10.1016/j.schres.2014.09.007 · Cited by 90 · see citing works
Zalesky, A. (2011) · Magnetic Resonance Imaging · doi:10.1016/j.mri.2010.06.027 · Cited by 88 · see citing works
Dimensionality reduction of diffusion MRI measures for improved tractometry of the human brain
Chamberland, M., Raven, E. P., Genc, S., Duffy, K., Descoteaux, M., Parker, G. D., Tax, C. M. W., & Jones, D. K. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2019.06.020 · Cited by 88 · see citing works
Building proper invariants for eddy-viscosity subgrid-scale models
Trias, F. X., Folch, D., Gorobets, A. V., & Oliva, A. (2015) · Physics of Fluids · doi:10.1063/1.4921817 · Cited by 89 · see citing works
Itahashi, T., Yamada, T., Nakamura, M., Watanabe, H., Yamagata, B., Jimbo, D., Shioda, S., Kuroda, M., Toriizuka, K., Kato, N., et al. (2014) · NeuroImage Clinical · doi:10.1016/j.nicl.2014.11.019 · Cited by 89 · see citing works
Shared white-matter dysconnectivity in schizophrenia and bipolar disorder with psychosis
Kumar, J., Iwabuchi, S. J., Oowise, S., Balain, V., Palaniyappan, L. K., & Liddle, P. F. (2014) · Psychological Medicine · doi:10.1017/s0033291714001810 · Cited by 86 · see citing works
Early limbic microstructural alterations in apathy and depression in de novo Parkinson's disease
Prange, S., Météreau, É., Maillet, A., Lhommée, E., Klinger, H., Pélissier, P., Ibarrola, D., Heckemann, R. A., Castrioto, A., Tremblay, L., et al. (2019) · Movement Disorders · doi:10.1002/mds.27793 · Cited by 86 · see citing works
Harris, N. G., Verley, D. R., Gutman, B. A., & Sutton, R. L. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.03.012 · Cited by 83 · see citing works
Whitford, T. J., Kubicki, M., Ghorashi, S., Schneiderman, J. S., Hawley, K. J., McCarley, R. W., Shenton, M. E., & Spencer, K. M. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2010.10.048 · Cited by 83 · see citing works
Thalamo‐frontal white matter alterations in chronic schizophrenia
Oh, J. S., Kubicki, M. R., Rosenberger, G., Sylvain Bouix, A., Levitt, J. J., McCarley, R. W., Westin, C., & Shenton, M. E. (2009) · Human Brain Mapping · doi:10.1002/hbm.20809 · Cited by 84 · see citing works
Oligodendrocyte Genes, White Matter Tract Integrity, and Cognition in Schizophrenia
Voineskos, A. N., Felsky, D., Kovacevic, N., Tiwari, A. K., Zai, C. C. H., Chakravarty, M. M., Lobaugh, N. J., Shenton, M. E., Rajji, T. K., Miranda, D., et al. (2012) · Cerebral Cortex · doi:10.1093/cercor/bhs188 · Cited by 83 · see citing works
Kung, G. L., Nguyen, T. C., Itoh, A., Skare, S. T., Ingels, N. B., Miller, D. C., & Ennis, D. B. (2011) · Journal of Magnetic Resonance Imaging · doi:10.1002/jmri.22725 · Cited by 82 · see citing works
Self-citationTeipel, S. J., the EDSD study group, Grothe, M. J., Filippi, M., Fellgiebel, A., Dyrba, M., Frisoni, G. B., Meindl, T., Bokde, A. L. W., Hampel, H., et al. (2014) · Journal of Alzheimer s Disease · doi:10.3233/jad-131829 · Cited by 82 · see citing works
Crespi, C., Cerami, C., Dodich, A., Canessa, N., Arpone, M., Iannaccone, S., Corbo, M., Lunetta, C., Scola, E., Falini, A., et al. (2014) · Cortex · doi:10.1016/j.cortex.2014.01.002 · Cited by 81 · see citing works
Squarcina, L., Bellani, M., Rossetti, M. G., Perlini, C., Delvecchio, G., Dusi, N., Barillari, M., Ruggeri, M., Altamura, C. A., Bertoldo, A., et al. (2017) · PLoS ONE · doi:10.1371/journal.pone.0178089 · Cited by 79 · see citing works
Dance and music training have different effects on white matter diffusivity in sensorimotor pathways
Giacosa, C., Karpati, F. J., Foster, N. E. V., Penhune, V. B., & Hyde, K. L. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.04.048 · Cited by 81 · see citing works
Wright, A. M., Wu, Y., Chen, N., & Wen, Q. (2023) · Journal of Magnetic Resonance Imaging · doi:10.1002/jmri.29203 · Cited by 72 · see citing works
Long-Term Abnormalities in the Corpus Callosum of Female Concussed Athletes
Chamard, É., Lefebvre, G., Lassonde, M. C., & Théoret, H. (2015) · Journal of Neurotrauma · doi:10.1089/neu.2015.3948 · Cited by 72 · see citing works
Moulin, K., Croisille, P., Feiweier, T., Delattre, B. M. A., Wei, H., Robert, B., Beuf, O., & Viallon, M. (2015) · Magnetic Resonance in Medicine · doi:10.1002/mrm.25852 · Cited by 69 · see citing works
Sahara, N., Perez, P. D., Lin, W.-L., Dickson, D. W., Ren, Y., Zeng, H., Lewis, J., & Febo, M. (2014) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2013.12.009 · Cited by 70 · see citing works
Advances in MR imaging for cervical spondylotic myelopathy
Ellingson, B. M., Salamon, N., & Holly, L. T. (2013) · European Spine Journal · doi:10.1007/s00586-013-2915-1 · Cited by 70 · see citing works
Specific Patterns of White Matter Alterations Help Distinguishing Alzheimer's and Vascular Dementia
Palesi, F., Rinaldis, A. D., Vitali, P., Castellazzi, G., Casiraghi, L., Germani, G., Bernini, S., Anzalone, N., Ramusino, M. C., Denaro, F. M., et al. (2018) · Frontiers in Neuroscience · doi:10.3389/fnins.2018.00274 · Cited by 71 · see citing works
A strain energy filter for 3D vessel enhancement with application to pulmonary CT images
Xiao, C., Staring, M., Shamonin, D. P., Reiber, J. H. C., Stolk, J. N., & Stoel, B. C. (2010) · Medical Image Analysis · doi:10.1016/j.media.2010.08.003 · Cited by 69 · see citing works
Neurodevelopment of C57B/L6 mouse brain assessed by in vivo diffusion tensor imaging
Chahboune, H., Ment, L. R., Stewart, W. B., Jr., Ma, X., Rothman, D. L., & Hyder, F. (2007) · NMR in Biomedicine · doi:10.1002/nbm.1130 · Cited by 67 · see citing works
Wilde, E. A., Sylvain Bouix, A., Tate, D. F., Lin, A. P., Newsome, M. R., Taylor, B. A., Stone, J. R., Montier, J., Gandy, S., Biekman, B. D., et al. (2015) · Brain Imaging and Behavior · doi:10.1007/s11682-015-9444-y · Cited by 67 · see citing works
Diffusion Tensor Analysis With Invariant Gradients and Rotation Tangents
Kindlmann, G., Ennis, D. B., Whitaker, R., & Westin, C. (2007) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2007.907277 · Cited by 67 · see citing works
Self-citationGeodesic-Loxodromes for Diffusion Tensor Interpolation and Difference Measurement
Kindlmann, G., Estépar, R. S. J., Niethammer, M., Haker, S. J., & Westin, C. (2007) · Springer eBooks · doi:10.1007/978-3-540-75757-3_1 · Cited by 67 · see citing works
Self-citationScott, A. D., Nielles‐Vallespin, S., Ferreira, P., Khalique, Z., Gatehouse, P. D., Kilner, P. J., Pennell, D. J., & Firmin, D. N. (2018) · Journal of Cardiovascular Magnetic Resonance · doi:10.1186/s12968-017-0425-8 · Cited by 67 · see citing works
White matter abnormalities in first-episode schizophrenia: A combined structural MRI and DTI study
Chan, W., Yang, G.-L., Chia, M., Lau, I. Y., Sitoh, Y., Nowinski, W. L., & Sim, K. (2010) · Schizophrenia Research · doi:10.1016/j.schres.2009.12.012 · Cited by 65 · see citing works
Mollink, J., Smith, S. M., Elliott, L. T., Kleinnijenhuis, M., Hiemstra, M., Alfaro‐Almagro, F., Marchini, J., van Walsum, A. V. C., Jbabdi, S., & Miller, K. L. (2019) · Nature Neuroscience · doi:10.1038/s41593-019-0379-2 · Cited by 59 · see citing works
Chahboune, H., Ment, L. R., Stewart, W. B., Jr., Rothman, D. L., Vaccarino, F. M., Hyder, F., & Schwartz, M. L. (2009) · Cerebral Cortex · doi:10.1093/cercor/bhp068 · Cited by 63 · see citing works
Mapping track density changes in nigrostriatal and extranigral pathways in Parkinson's disease
Ziegler, E., Rouillard, M., André, E., Coolen, T., Stender, J., Balteau, E., Phillips, C. L. M., & Garraux, G. (2014) · NeuroImage · doi:10.1016/j.neuroimage.2014.06.033 · Cited by 62 · see citing works
Altered brain morphometry in carpal tunnel syndrome is associated with median nerve pathology
Maeda, Y., Kettner, N. W., Sheehan, J., Kim, J., Cina, S., Malatesta, C., Gerber, J. A., McManus, C., Mezzacappa, P., Morse, L. R., et al. (2013) · NeuroImage Clinical · doi:10.1016/j.nicl.2013.02.001 · Cited by 62 · see citing works
Diffusion magnetic resonance imaging in preterm brain injury
Pandit, A. S., Ball, G., Edwards, A. D., & Counsell, S. J. (2013) · Neuroradiology · doi:10.1007/s00234-013-1242-x · Cited by 61 · see citing works
The ZNF804A Gene: Characterization of a Novel Neural Risk Mechanism for the Major Psychoses
Voineskos, A. N., Lerch, J. P., Felsky, D., Tiwari, A. K., Rajji, T. K., Miranda, D., Lobaugh, N. J., Pollock, B. G., Mulsant, B. H., & Kennedy, J. L. (2011) · Neuropsychopharmacology · doi:10.1038/npp.2011.72 · Cited by 61 · see citing works
Zhang, R., Zhang, B., Shen, C., Sahakian, B. J., Li, Z., Zhang, W., Zhao, Y., Li, Y., Feng, J., & Cheng, W. (2024) · Nature Mental Health · doi:10.1038/s44220-024-00226-0 · Cited by 61 · see citing works
White matter and memory in healthy adults: Coupled changes over two years
Bender, A. R., Prindle, J., Brandmaier, A. M., & Raz, N. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.10.085 · Cited by 59 · see citing works
Annen, J., Heine, L., Ziegler, E., Frasso, G., Bahri, M. A., Perri, C. D., Stender, J., Martial, C., Wannez, S., D’Ostilio, K., et al. (2016) · Human Brain Mapping · doi:10.1002/hbm.23269 · Cited by 60 · see citing works
Cardiac Diffusion: Technique and Practical Applications
Nielles‐Vallespin, S., Scott, A. D., Ferreira, P., Khalique, Z., Pennell, D. J., & Firmin, D. N. (2019) · Journal of Magnetic Resonance Imaging · doi:10.1002/jmri.26912 · Cited by 57 · see citing works
Neuroanatomical correlates of verbal fluency in early Alzheimer’s disease and normal aging
Rodríguez‐Aranda, C., Waterloo, K. K., Johnsen, S. H., Eldevik, P., Sparr, S., Wikran, G., Herder, M., & Vangberg, T. R. (2016) · Brain and Language · doi:10.1016/j.bandl.2016.03.001 · Cited by 53 · see citing works
Simulation Methods and Validation Criteria for Modeling Cardiac Ventricular Electrophysiology
Krishnamoorthi, S., Perotti, L. E., Borgstrom, N. P., Ajijola, O. A., Frid, A. A., Ponnaluri, A. V. S., Weiss, J. N., Qu, Z., Klug, W. S., Ennis, D. B., et al. (2014) · PLoS ONE · doi:10.1371/journal.pone.0114494 · Cited by 56 · see citing works
Self-citationKratz, A., Auer, C., Stommel, M., & Hotz, I. (2012) · Computer Graphics Forum · doi:10.1111/j.1467-8659.2012.03231.x · Cited by 56 · see citing works
Invariant Crease Lines for Topological and Structural Analysis of Tensor Fields
Tricoche, X., Kindlmann, G., & Westin, C. (2008) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2008.148 · Cited by 56 · see citing works
Self-citationKing, A. V., Linke, J. O., Gass, A., Hennerici, M. G., Tost, H., Poupon, C., & Wessa, M. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2011.09.008 · Cited by 54 · see citing works
White Matter Integrity and Depressive Symptoms in Cerebral Small Vessel Disease: The RUN DMC Study
van Uden, I. W. M., Tuladhar, A. M., de Laat, K. F., van Norden, A. G. W., Norris, D. G., van Dijk, E. J., Tendolkar, I., & de Leeuw, F. (2014) · American Journal of Geriatric Psychiatry · doi:10.1016/j.jagp.2014.07.002 · Cited by 53 · see citing works
Lista, S., Molinuevo, J. L., Cavedo, E., Rami, L., Amouyel, P., Teipel, S. J., Garaci, F., Toschi, N., Habert, M.-O., Blennow, K., et al. (2015) · Journal of Alzheimer's Disease · doi:10.3233/jad-150202 · Cited by 53 · see citing works
Dementia resulting from traumatic brain injury
Ramalho, J., & Castillo, M. (2015) · Dementia & Neuropsychologia · doi:10.1590/1980-57642015dn94000356 · Cited by 53 · see citing works
The DELCODE Study Group, Brueggen, K., Dyrba, M., Cardenas-Blanco, A., Schneider, A., Fliessbach, K., Buerger, K., Janowitz, D., Peters, O., Menne, F., et al. (2019) · Journal of Neurology · doi:10.1007/s00415-019-09429-3 · Cited by 51 · see citing works
Voineskos, A. N., O’Donnell, L. J., Lobaugh, N. J., Markant, D. B., Ameis, S. H., Niethammer, M., Mulsant, B. H., Pollock, B. G., Kennedy, J. L., Westin, C., et al. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.12.028 · Cited by 51 · see citing works
Zekelman, L., Zhang, F., Makris, N., He, J., Chen, Y., Xue, T., Liera, D., Drane, D. L., Yogesh Rathi, A., Golby, A. J., et al. (2021) · NeuroImage · doi:10.1016/j.neuroimage.2021.118739 · Cited by 50 · see citing works
Structural network differences in chronic muskuloskeletal pain: Beyond fractional anisotropy
Bishop, J. H., Shpaner, M., Kubicki, A., Clements, S., Watts, R., & Naylor, M. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.12.021 · Cited by 46 · see citing works
Glyph-Based Comparative Visualization for Diffusion Tensor Fields
Zhang, C., Schultz, T., Lawonn, K., Eisemann, E., & Vilanova, A. (2015) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2015.2467435 · Cited by 48 · see citing works
Brain Changes within the Visuo-Spatial Attentional Network in Posterior Cortical Atrophy
Cerami, C., Crespi, C., Rosa, P. A. D., Dodich, A., Marcone, A., Magnani, G., Coppi, E., Falini, A., Cappa, S. F., & Perani, D. (2014) · Journal of Alzheimer s Disease · doi:10.3233/jad-141275 · Cited by 48 · see citing works
Auditory verbal hallucinations and the interhemispheric auditory pathway in chronic schizophrenia
Wigand, M. C. C., Kubicki, M. R., von Hohenberg, C. C., Leicht, G., Karch, S., Eckbo, R., Pelavin, P. E., Hawley, K. J., Rujescu, D., Sylvain Bouix, A., et al. (2014) · The World Journal of Biological Psychiatry · doi:10.3109/15622975.2014.948063 · Cited by 46 · see citing works
Doan, N. T., Engvig, A., Persson, K., Alnæs, D., Kaufmann, T., Rokicki, J., Córdova‐Palomera, A., Moberget, T., Brækhus, A., Barca, M. L., et al. (2017) · Scientific Reports · doi:10.1038/srep45131 · Cited by 48 · see citing works
The effects of noise in cardiac diffusion tensor imaging and the benefits of averaging complex data
Scott, A. D., Nielles‐Vallespin, S., Ferreira, P., McGill, L., Pennell, D. J., & Firmin, D. N. (2016) · NMR in Biomedicine · doi:10.1002/nbm.3500 · Cited by 46 · see citing works
Curran, K. M., Emsell, L., & Leemans, A. (2015) · Springer eBooks · doi:10.1007/978-1-4939-3118-7_5 · Cited by 45 · see citing works
White Matter Indices of Medication Response in Major Depression: A Diffusion Tensor Imaging Study
Davis, A. D., Hassel, S., Arnott, S. R., Harris, J. K., Lam, R. W. M., Milev, R. V., Rotzinger, S., Zamyadi, M., Frey, B. N., Minuzzi, L., et al. (2019) · Biological Psychiatry Cognitive Neuroscience and Neuroimaging · doi:10.1016/j.bpsc.2019.05.016 · Cited by 46 · see citing works
Linke, J. O., Witt, S. H., King, A. V., Nieratschker, V., Poupon, C., Gass, A., Hennerici, M. G., Rietschel, M., & Wessa, M. (2011) · NeuroImage · doi:10.1016/j.neuroimage.2011.10.083 · Cited by 46 · see citing works
Matthews, P. M., Filippini, N., & Douaud, G. (2012) · Journal of Alzheimer s Disease · doi:10.3233/jad-2012-129012 · Cited by 44 · see citing works
- Authors
- Ennis, D. B., & Kindlmann, G.
- Affiliations
- Stanford University (US)
- Harvard University (US)
- Corresponding author
- Ennis, Daniel B.
- ORCID
- Ennis, Daniel B.
- Venue
- Magnetic Resonance in Medicine
- Publisher
- Wiley
- Published
- 2005-12-09
- Volume
- 55
- Issue
- 1
- Pages
- 136-146
- ISSN
- 0740-3194 (ISSN-L)
- 1522-2594
- OpenAlex
- W2106841463
- Cited by
- 276
- References
- 15
- Citations by year
- 2026: 11 · 2025: 8 · 2024: 10 · 2023: 13 · 2022: 8 · 2021: 17 · 2020: 13 · 2019: 12 · 2018: 15 · 2017: 11 · 2016: 19 · 2015: 23 · 2014: 26 · 2013: 22 · 2012: 20
- FWCI
- 3.83
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Magnetic Resonance in Medicine (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Cancer Institute (T32CA09695, T32CA009695)
- National Institute of Biomedical Imaging and Bioengineering (T32EB002177)
- Topics
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced MRI Techniques and Applications
- Physical Sciences › Mathematics › Computational Mathematics › Tensor decomposition and applications
- Keywords
- diffusion tensor imaging, tensor invariants, anisotropy, fractional anisotropy, linear anisotropy, orthotropic anisotropy, easy-plane anisotropy
- MeSH terms
- Brain Mapping, Humans, Image Processing, Computer-Assisted, Linear Models, Anisotropy, Diffusion Magnetic Resonance Imaging
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