Studies of anomalous diffusion in the human brain using fractional order calculus
It is well known that diffusion‐induced MR signal loss deviates from monoexponential decay, particularly at high b‐values (e.g., >1500 sec/mm2 for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to ti...
Saved in:
| Published in | Magnetic resonance in medicine Vol. 63; no. 3; pp. 562 - 569 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken
Wiley Subscription Services, Inc., A Wiley Company
01.03.2010
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | It is well known that diffusion‐induced MR signal loss deviates from monoexponential decay, particularly at high b‐values (e.g., >1500 sec/mm2 for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to tissue structures. Recently, a new diffusion model was proposed by solving the Bloch‐Torrey equation using fractional order calculus with respect to time and space (Magin et al., J Magn Reson 2008;190:255‐270; Zhou et al., Proc Int'l Soc Magn Reson Med 2008). Using a spatial Laplacian ∇2β, this model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). In this study, we demonstrate that the fractional calculus model can be successfully applied to analyzing diffusion images of healthy human brain tissues in vivo. Five human volunteers were scanned on a commercial 3‐T scanner using a customized single‐shot echo‐planar imaging diffusion sequence with 15 b values ranging from 0 to 4700 sec/mm2. The set of images was analyzed using the fractional calculus model, producing spatially resolved maps of D, β, and μ. The β and μ maps showed notable contrast between white and gray matter. The contrast has been attributed to the varying degree of complexity of the underlying tissue structures and microenvironment. Although the biophysical basis of β and μ remains elusive, the potential utility of these parameters to characterize the environment for molecular diffusion, as a complement to apparent diffusion coefficient, may lead to a new way to investigate tissue structural changes in disease progression, intervention, and regression. Magn Reson Med 63:562–569, 2010. © 2010 Wiley‐Liss, Inc. |
|---|---|
| AbstractList | It is well known that diffusion‐induced MR signal loss deviates from monoexponential decay, particularly at high b‐values (e.g., >1500 sec/mm2 for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to tissue structures. Recently, a new diffusion model was proposed by solving the Bloch‐Torrey equation using fractional order calculus with respect to time and space (Magin et al., J Magn Reson 2008;190:255‐270; Zhou et al., Proc Int'l Soc Magn Reson Med 2008). Using a spatial Laplacian ∇2β, this model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space β, and a spatial parameter μ (in units of μm). In this study, we demonstrate that the fractional calculus model can be successfully applied to analyzing diffusion images of healthy human brain tissues in vivo. Five human volunteers were scanned on a commercial 3‐T scanner using a customized single‐shot echo‐planar imaging diffusion sequence with 15 b values ranging from 0 to 4700 sec/mm2. The set of images was analyzed using the fractional calculus model, producing spatially resolved maps of D, β, and μ. The β and μ maps showed notable contrast between white and gray matter. The contrast has been attributed to the varying degree of complexity of the underlying tissue structures and microenvironment. Although the biophysical basis of β and μ remains elusive, the potential utility of these parameters to characterize the environment for molecular diffusion, as a complement to apparent diffusion coefficient, may lead to a new way to investigate tissue structural changes in disease progression, intervention, and regression. Magn Reson Med 63:562–569, 2010. © 2010 Wiley‐Liss, Inc. It is well known that diffusion-induced MR signal loss deviates from monoexponential decay, particularly at high b-values (e.g., >1500 sec/mm(2) for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to tissue structures. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (Magin et al., J Magn Reson 2008;190:255-270; Zhou et al., Proc Int'l Soc Magn Reson Med 2008). Using a spatial Laplacian [symbol: see text], this model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space beta, and a spatial parameter mu (in units of microm). In this study, we demonstrate that the fractional calculus model can be successfully applied to analyzing diffusion images of healthy human brain tissues in vivo. Five human volunteers were scanned on a commercial 3-T scanner using a customized single-shot echo-planar imaging diffusion sequence with 15 b values ranging from 0 to 4700 sec/mm(2). The set of images was analyzed using the fractional calculus model, producing spatially resolved maps of D, beta, and mu. The beta and mu maps showed notable contrast between white and gray matter. The contrast has been attributed to the varying degree of complexity of the underlying tissue structures and microenvironment. Although the biophysical basis of beta and mu remains elusive, the potential utility of these parameters to characterize the environment for molecular diffusion, as a complement to apparent diffusion coefficient, may lead to a new way to investigate tissue structural changes in disease progression, intervention, and regression.It is well known that diffusion-induced MR signal loss deviates from monoexponential decay, particularly at high b-values (e.g., >1500 sec/mm(2) for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to tissue structures. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (Magin et al., J Magn Reson 2008;190:255-270; Zhou et al., Proc Int'l Soc Magn Reson Med 2008). Using a spatial Laplacian [symbol: see text], this model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space beta, and a spatial parameter mu (in units of microm). In this study, we demonstrate that the fractional calculus model can be successfully applied to analyzing diffusion images of healthy human brain tissues in vivo. Five human volunteers were scanned on a commercial 3-T scanner using a customized single-shot echo-planar imaging diffusion sequence with 15 b values ranging from 0 to 4700 sec/mm(2). The set of images was analyzed using the fractional calculus model, producing spatially resolved maps of D, beta, and mu. The beta and mu maps showed notable contrast between white and gray matter. The contrast has been attributed to the varying degree of complexity of the underlying tissue structures and microenvironment. Although the biophysical basis of beta and mu remains elusive, the potential utility of these parameters to characterize the environment for molecular diffusion, as a complement to apparent diffusion coefficient, may lead to a new way to investigate tissue structural changes in disease progression, intervention, and regression. It is well known that diffusion-induced MR signal loss deviates from monoexponential decay, particularly at high b-values (e.g., >1500 sec/mm(2) for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to tissue structures. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (Magin et al., J Magn Reson 2008;190:255-270; Zhou et al., Proc Int'l Soc Magn Reson Med 2008). Using a spatial Laplacian [symbol: see text], this model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space beta, and a spatial parameter mu (in units of microm). In this study, we demonstrate that the fractional calculus model can be successfully applied to analyzing diffusion images of healthy human brain tissues in vivo. Five human volunteers were scanned on a commercial 3-T scanner using a customized single-shot echo-planar imaging diffusion sequence with 15 b values ranging from 0 to 4700 sec/mm(2). The set of images was analyzed using the fractional calculus model, producing spatially resolved maps of D, beta, and mu. The beta and mu maps showed notable contrast between white and gray matter. The contrast has been attributed to the varying degree of complexity of the underlying tissue structures and microenvironment. Although the biophysical basis of beta and mu remains elusive, the potential utility of these parameters to characterize the environment for molecular diffusion, as a complement to apparent diffusion coefficient, may lead to a new way to investigate tissue structural changes in disease progression, intervention, and regression. It is well known that diffusion-induced MR signal loss deviates from monoexponential decay, particularly at high b-values (e.g., >1500 sec/mm2 for human brain tissues). A number of models have been developed to describe this anomalous diffusion behavior and relate the diffusion measurements to tissue structures. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (Magin et al., J Magn Reson 2008; 190:255-270; Zhou et al., Proc Int'l Soc Magn Reson Med 2008). Using a spatial Laplacian {nabla}2 Delta *b, this model yields a new set of parameters to describe anomalous diffusion: diffusion coefficient D, fractional order derivative in space Delta *b, and a spatial parameter Delta *m (in units of Delta *mm). In this study, we demonstrate that the fractional calculus model can be successfully applied to analyzing diffusion images of healthy human brain tissues in vivo. Five human volunteers were scanned on a commercial 3-T scanner using a customized single-shot echo-planar imaging diffusion sequence with 15 b values ranging from 0 to 4700 sec/mm2. The set of images was analyzed using the fractional calculus model, producing spatially resolved maps of D, Delta *b, and Delta *m. The Delta *b and Delta *m maps showed notable contrast between white and gray matter. The contrast has been attributed to the varying degree of complexity of the underlying tissue structures and microenvironment. Although the biophysical basis of Delta *b and Delta *m remains elusive, the potential utility of these parameters to characterize the environment for molecular diffusion, as a complement to apparent diffusion coefficient, may lead to a new way to investigate tissue structural changes in disease progression, intervention, and regression. Magn Reson Med 63:562-569, 2010. [copy 2010 Wiley-Liss, Inc. |
| Author | Magin, Richard L. Zhou, Xiaohong Joe Abdullah, Osama Gao, Qing |
| Author_xml | – sequence: 1 givenname: Xiaohong Joe surname: Zhou fullname: Zhou, Xiaohong Joe email: xjzhou@uic.edu organization: Department of Radiology, University of Illinois Medical Center, Chicago, Illinois, USA – sequence: 2 givenname: Qing surname: Gao fullname: Gao, Qing organization: Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, USA – sequence: 3 givenname: Osama surname: Abdullah fullname: Abdullah, Osama organization: Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, USA – sequence: 4 givenname: Richard L. surname: Magin fullname: Magin, Richard L. organization: Department of Bioengineering, University of Illinois at Chicago, Chicago, Illinois, USA |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/20187164$$D View this record in MEDLINE/PubMed |
| BookMark | eNqFkTlPAzEQhS0EgnAU_AHkjmrB59ouUbgJIC5RWo4PMOwR7F0B_54NAVqqmdH73kgzbx0sN23jAdjGaA8jRPbrVO8RQiRfAiPMCSkIV2wZjJBgqKBYsTWwnvMLQkgpwVbBGkFYClyyEbi563oXfYZtgKZpa1O1fYYuhtDn2DYwNrB79vC5r00Dp8kM8yA0TzAkY7uBMBVsk_MJWlPZvurzJlgJpsp-66dugIfjo_vxaTG5PjkbH0yKSGXJC2WdQoqK4JksA3dYWDJvXRmmiDkamDFEqjJQ45yaSq6clZYyw4W0Jcd0A-wu9s5S-9b73Ok6ZuuryjR-uEFLSdH8GexfUlBKiBKcD-TOD9lPa-_0LMXapE_9-68B2F8A77Hyn386RnoehB6C0N9B6Mvby-9mcBQLR8yd__hzmPSqS0EF149XJ_pmfKEOLybnWtEvLyqLkg |
| ContentType | Journal Article |
| Copyright | Copyright © 2010 Wiley‐Liss, Inc. (c) 2010 Wiley-Liss, Inc. |
| Copyright_xml | – notice: Copyright © 2010 Wiley‐Liss, Inc. – notice: (c) 2010 Wiley-Liss, Inc. |
| DBID | BSCLL CGR CUY CVF ECM EIF NPM 7X8 7QO 7TK 8FD FR3 P64 |
| DOI | 10.1002/mrm.22285 |
| DatabaseName | Istex Medline MEDLINE MEDLINE (Ovid) MEDLINE MEDLINE PubMed MEDLINE - Academic Biotechnology Research Abstracts Neurosciences Abstracts Technology Research Database Engineering Research Database Biotechnology and BioEngineering Abstracts |
| DatabaseTitle | MEDLINE Medline Complete MEDLINE with Full Text PubMed MEDLINE (Ovid) MEDLINE - Academic Engineering Research Database Biotechnology Research Abstracts Technology Research Database Neurosciences Abstracts Biotechnology and BioEngineering Abstracts |
| DatabaseTitleList | MEDLINE - Academic MEDLINE Engineering Research Database |
| Database_xml | – sequence: 1 dbid: NPM name: PubMed url: https://proxy.k.utb.cz/login?url=http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed sourceTypes: Index Database – sequence: 2 dbid: EIF name: MEDLINE url: https://proxy.k.utb.cz/login?url=https://www.webofscience.com/wos/medline/basic-search sourceTypes: Index Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Medicine Physics |
| EISSN | 1522-2594 |
| EndPage | 569 |
| ExternalDocumentID | 20187164 MRM22285 ark_67375_WNG_QCK9DKLJ_9 |
| Genre | shortCommunication Research Support, Non-U.S. Gov't Journal Article Research Support, N.I.H., Extramural |
| GrantInformation_xml | – fundername: NIH‐NIDDS funderid: R01 NS057514 – fundername: CCTS – fundername: University of Illinois at Chicago – fundername: NINDS NIH HHS grantid: R01 NS057514 |
| GroupedDBID | --- -DZ .3N .55 .GA .Y3 05W 0R~ 10A 1L6 1OB 1OC 1ZS 24P 31~ 33P 3O- 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52R 52S 52T 52U 52V 52W 52X 53G 5GY 5RE 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A01 A03 AAESR AAEVG AAHHS AANLZ AAONW AASGY AAXRX AAZKR ABCQN ABCUV ABDPE ABEML ABIJN ABJNI ABLJU ABPVW ABQWH ABXGK ACAHQ ACBWZ ACCFJ ACCZN ACFBH ACGFO ACGFS ACGOF ACIWK ACMXC ACPOU ACPRK ACSCC ACXBN ACXQS ADBBV ADBTR ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN AEEZP AEGXH AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFNX AFFPM AFGKR AFPWT AFRAH AFZJQ AHBTC AHMBA AIACR AIAGR AITYG AIURR AIWBW AJBDE ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN AMBMR AMYDB ASPBG ATUGU AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMXJE BROTX BRXPI BSCLL BY8 C45 CS3 D-6 D-7 D-E D-F DCZOG DPXWK DR2 DRFUL DRMAN DRSTM DU5 EBD EBS EJD EMOBN F00 F01 F04 FEDTE FUBAC G-S G.N GNP GODZA H.X HBH HDBZQ HF~ HGLYW HHY HHZ HVGLF HZ~ I-F IX1 J0M JPC KBYEO KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M65 MEWTI MK4 MRFUL MRMAN MRSTM MSFUL MSMAN MSSTM MXFUL MXMAN MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG OVD P2P P2W P2X P2Z P4B P4D PALCI PQQKQ Q.N Q11 QB0 QRW R.K RGB RIWAO RJQFR ROL RWI RX1 RYL SAMSI SUPJJ SV3 TEORI TUS TWZ UB1 V2E V8K W8V W99 WBKPD WHWMO WIB WIH WIJ WIK WIN WJL WOHZO WQJ WRC WUP WVDHM WXI WXSBR X7M XG1 XPP XV2 ZGI ZXP ZZTAW ~IA ~WT AAHQN AAIPD AAMNL AANHP AAYCA ACRPL ACYXJ ADNMO AFWVQ ALVPJ AAMMB AEFGJ AEYWJ AGHNM AGQPQ AGXDD AGYGG AIDQK AIDYY CGR CUY CVF ECM EIF NPM 7X8 7QO 7TK 8FD FR3 P64 |
| ID | FETCH-LOGICAL-i3865-9cd90937fe486f5d17c2e486d6fb04d3f4aa2896f3add9b859dc8c34a578c6513 |
| IEDL.DBID | DR2 |
| ISSN | 0740-3194 1522-2594 |
| IngestDate | Fri Jul 11 04:42:22 EDT 2025 Fri Jul 11 07:05:05 EDT 2025 Mon Jul 21 05:59:09 EDT 2025 Wed Jan 22 16:21:14 EST 2025 Wed Oct 30 09:51:25 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| License | (c) 2010 Wiley-Liss, Inc. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-i3865-9cd90937fe486f5d17c2e486d6fb04d3f4aa2896f3add9b859dc8c34a578c6513 |
| Notes | CCTS istex:5F9534ED18AE9A2503BAED6746EB0D6C4F375A56 ArticleID:MRM22285 ark:/67375/WNG-QCK9DKLJ-9 University of Illinois at Chicago NIH-NIDDS - No. R01 NS057514 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 ObjectType-Article-2 ObjectType-Feature-1 |
| PMID | 20187164 |
| PQID | 733229755 |
| PQPubID | 23479 |
| PageCount | 8 |
| ParticipantIDs | proquest_miscellaneous_883015224 proquest_miscellaneous_733229755 pubmed_primary_20187164 wiley_primary_10_1002_mrm_22285_MRM22285 istex_primary_ark_67375_WNG_QCK9DKLJ_9 |
| PublicationCentury | 2000 |
| PublicationDate | March 2010 |
| PublicationDateYYYYMMDD | 2010-03-01 |
| PublicationDate_xml | – month: 03 year: 2010 text: March 2010 |
| PublicationDecade | 2010 |
| PublicationPlace | Hoboken |
| PublicationPlace_xml | – name: Hoboken – name: United States |
| PublicationTitle | Magnetic resonance in medicine |
| PublicationTitleAlternate | Magn. Reson. Med |
| PublicationYear | 2010 |
| Publisher | Wiley Subscription Services, Inc., A Wiley Company |
| Publisher_xml | – name: Wiley Subscription Services, Inc., A Wiley Company |
| References | Özarslan E, Basser PJ, Shepherd TM, Thelwall PE, Vemuri BC, Blackband SJ. Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal. J Magn Reson 2006; 183: 315-323. Sorensen AG, Buonanno FS, Gonzalez RG, Schwamm LH, Lev MH, Huang-Hellinger FR, Reese TG, Weisskoff RM, Davis TL, Suwanwela N, Can U, Moreira JA, Copen WA, Look RB, Finklestein SP, Rosen BR, Koroshetz WJ. Hyperacute stroke: evaluation with combined multisection diffusion-weighted and hemodynamically weighted echo-planar MR imaging. Radiology 1996; 199: 391-401. Hilfer R. Applications of fractional calculus in physics. Singapore: World Scientific; 2000, 472. Sehy JV, Zhao L, Xu JQ, Rayala HJ, Ackerman JJH, Neil JJ. Effects of physiologic challenge on the ADC of intracellular water in the Xenopus oocyte. Magn Reson Med 2004; 52: 239-247. Moseley ME, Cohen Y, Montorovitch J. Early detection of regional cerebral ischemia in cats: comparison of diffusion and T2 weighted MRI and spectroscopy. J Magn Reson 1990; 14: 330-346. Jensen JH, Helpern JA, Ramani A, Lu HZ, Kaczynski K. Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 2005; 53: 1432-1440. Yablonskiy DA, Bretthorst GL, Ackerman JJH. Statistical model for diffusion attenuated MR signal. Magn Reson Med 2003; 50: 664-669. van Zijl PCM, Moonen CTW, Faustino P, Pekar J, Kaplan O, Cohen JS. Complete separation of intracellular and extracellular information in NMR spectra of perfused cells by diffusion weighted spectroscopy. Proc Natl Acad Sci U|S|A 1990; 88: 3228-3232. Hall MG, Barrick TR. From diffusion-weighted MRI to anomalous diffusion imaging. Magn Reson Med 2008; 59: 447-455. Pfeuffer J, Provencher S, Gruetter R. Water diffusion in rat brain in vivo as detected at very large b values is multicompartmental. MAGMA 1999; 8: 98-108. Sehy JV, Banks AA, Ackerman JJH, Neil JJ. Importance of intracellular water apparent diffusion to the measurement of membrane permeability. Biophys J 2002; 83: 2856-2863. Özarslan E, Basser PJ. MR diffusion-"diffraction" phenomenon in multi-pulse-field-gradient experiments. J Magn Reson 2007; 188: 285-294. Gao Q, Haldar JP, Rangwala N, Magin RL, Liang Z-P, Zhou XJ. Analysis of high b-value diffusion images using a fractional order diffusion model with denoising image reconstruction. Proc Int Soc Magn Reson Med 2009; 17: 1418. Magin RL, Abdullah O, Baleanu D, Zhou XJ. Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation. J Magn Reson 2008; 190: 255-270. Reese TG, Heid O, Weisskoff RM, Wedeen VJ. Reduction of eddy-current-induced distortion in diffusion MRI using a twice-refocused spin echo. Magn Reson Med 2003; 49: 177-182. Carr HY, Purcell EM. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys Rev 1954; 94: 630. Bennett KM, Schmainda KM, Bennett R, Rowe DB, Lu HB, Hyde JS. Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model. Magn Reson Med 2003; 50: 727-734. Sugahara T, Korogi Y, Kochi M, Ikushima I, Shigematu Y, Hirai T, Okuda T, Liang L, Ge Y, Komohara Y, Ushio Y, Takahashi M. Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas. J Magn Reson Imaging 1999; 9: 53-60. Le Bihan D. The "wet mind": water and functional neuroimaging. Phys Med Biol 2007; 52: R57-R90. Mulkern RV, Gudbjartsson H, Westin CF, Zengingonul HP, Gartner W, Guttmann CRG, Robertson RL, Kyriakos W, Schwartz R, Holtzman D, Jolesz FA, Maier SE. Multi-component apparent diffusion coefficients in human brain. NMR Biomed 1999; 12: 51-62. Inglis BA, Bossart EL, Buckley DL, Wirth ED, Mareci TH. Visualization of neural tissue water compartments using biexponential diffusion tensor MRI. Magn Reson Med 2001; 45: 580-587. Barboriak D. Imaging of brain tumors with diffusion-weighted and diffusion tensor MR imaging. Magn Reson Imaging Clin N Am 2003; 11: 379-401. Zhou XJ, Leeds NE, McKinnon GC, Kumar AJ. Characterization of benign and metastatic vertebral compression fractures with quantitative diffusion MR imaging. AJNR Am J Neuroradiol 2002; 23: 165-170. Sehy JV, Ackerman JJH, Neil JJ. Evidence that both fast and slow water ADC components arise from intracellular space. Magn Reson Med 2002; 48: 765-770. Clark CA, Hedehus M, Moseley ME. In vivo mapping of the fast and slow diffusion tensors in human brain. Magn Reson Med 2002; 47: 623-628. Clark CA, Le Bihan D. Water diffusion compartmentation and anisotropy at high b values in the human brain. Magn Reson Med 2000; 44: 852-859. Benveniste H, Hedlund LW, Johnson GA. Mechanism of detection of acute cerebral ischemia in rats by diffusion-weighted magnetic resonance microscopy. Stroke 1992; 23: 746-754. 2008; 190 1990; 14 2000; 44 2007; 188 2008; 59 2008 2007; 52 1999; 8 2001; 45 2003; 50 2003; 11 1999; 9 1999 2004; 52 2002; 47 1954; 94 2002; 48 1990; 88 2001 2000 2002; 83 2002; 23 1999; 12 2005; 53 2003; 49 1996; 199 2006; 183 1992; 23 2009; 17 |
| References_xml | – reference: Clark CA, Le Bihan D. Water diffusion compartmentation and anisotropy at high b values in the human brain. Magn Reson Med 2000; 44: 852-859. – reference: Sugahara T, Korogi Y, Kochi M, Ikushima I, Shigematu Y, Hirai T, Okuda T, Liang L, Ge Y, Komohara Y, Ushio Y, Takahashi M. Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas. J Magn Reson Imaging 1999; 9: 53-60. – reference: Jensen JH, Helpern JA, Ramani A, Lu HZ, Kaczynski K. Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med 2005; 53: 1432-1440. – reference: Le Bihan D. The "wet mind": water and functional neuroimaging. Phys Med Biol 2007; 52: R57-R90. – reference: Hall MG, Barrick TR. From diffusion-weighted MRI to anomalous diffusion imaging. Magn Reson Med 2008; 59: 447-455. – reference: Hilfer R. Applications of fractional calculus in physics. Singapore: World Scientific; 2000, 472. – reference: van Zijl PCM, Moonen CTW, Faustino P, Pekar J, Kaplan O, Cohen JS. Complete separation of intracellular and extracellular information in NMR spectra of perfused cells by diffusion weighted spectroscopy. Proc Natl Acad Sci U|S|A 1990; 88: 3228-3232. – reference: Gao Q, Haldar JP, Rangwala N, Magin RL, Liang Z-P, Zhou XJ. Analysis of high b-value diffusion images using a fractional order diffusion model with denoising image reconstruction. Proc Int Soc Magn Reson Med 2009; 17: 1418. – reference: Barboriak D. Imaging of brain tumors with diffusion-weighted and diffusion tensor MR imaging. Magn Reson Imaging Clin N Am 2003; 11: 379-401. – reference: Sorensen AG, Buonanno FS, Gonzalez RG, Schwamm LH, Lev MH, Huang-Hellinger FR, Reese TG, Weisskoff RM, Davis TL, Suwanwela N, Can U, Moreira JA, Copen WA, Look RB, Finklestein SP, Rosen BR, Koroshetz WJ. Hyperacute stroke: evaluation with combined multisection diffusion-weighted and hemodynamically weighted echo-planar MR imaging. Radiology 1996; 199: 391-401. – reference: Özarslan E, Basser PJ, Shepherd TM, Thelwall PE, Vemuri BC, Blackband SJ. Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal. J Magn Reson 2006; 183: 315-323. – reference: Mulkern RV, Gudbjartsson H, Westin CF, Zengingonul HP, Gartner W, Guttmann CRG, Robertson RL, Kyriakos W, Schwartz R, Holtzman D, Jolesz FA, Maier SE. Multi-component apparent diffusion coefficients in human brain. NMR Biomed 1999; 12: 51-62. – reference: Benveniste H, Hedlund LW, Johnson GA. Mechanism of detection of acute cerebral ischemia in rats by diffusion-weighted magnetic resonance microscopy. Stroke 1992; 23: 746-754. – reference: Reese TG, Heid O, Weisskoff RM, Wedeen VJ. Reduction of eddy-current-induced distortion in diffusion MRI using a twice-refocused spin echo. Magn Reson Med 2003; 49: 177-182. – reference: Inglis BA, Bossart EL, Buckley DL, Wirth ED, Mareci TH. Visualization of neural tissue water compartments using biexponential diffusion tensor MRI. Magn Reson Med 2001; 45: 580-587. – reference: Pfeuffer J, Provencher S, Gruetter R. Water diffusion in rat brain in vivo as detected at very large b values is multicompartmental. MAGMA 1999; 8: 98-108. – reference: Özarslan E, Basser PJ. MR diffusion-"diffraction" phenomenon in multi-pulse-field-gradient experiments. J Magn Reson 2007; 188: 285-294. – reference: Sehy JV, Zhao L, Xu JQ, Rayala HJ, Ackerman JJH, Neil JJ. Effects of physiologic challenge on the ADC of intracellular water in the Xenopus oocyte. Magn Reson Med 2004; 52: 239-247. – reference: Zhou XJ, Leeds NE, McKinnon GC, Kumar AJ. Characterization of benign and metastatic vertebral compression fractures with quantitative diffusion MR imaging. AJNR Am J Neuroradiol 2002; 23: 165-170. – reference: Magin RL, Abdullah O, Baleanu D, Zhou XJ. Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation. J Magn Reson 2008; 190: 255-270. – reference: Carr HY, Purcell EM. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys Rev 1954; 94: 630. – reference: Sehy JV, Banks AA, Ackerman JJH, Neil JJ. Importance of intracellular water apparent diffusion to the measurement of membrane permeability. Biophys J 2002; 83: 2856-2863. – reference: Clark CA, Hedehus M, Moseley ME. In vivo mapping of the fast and slow diffusion tensors in human brain. Magn Reson Med 2002; 47: 623-628. – reference: Sehy JV, Ackerman JJH, Neil JJ. Evidence that both fast and slow water ADC components arise from intracellular space. Magn Reson Med 2002; 48: 765-770. – reference: Yablonskiy DA, Bretthorst GL, Ackerman JJH. Statistical model for diffusion attenuated MR signal. Magn Reson Med 2003; 50: 664-669. – reference: Bennett KM, Schmainda KM, Bennett R, Rowe DB, Lu HB, Hyde JS. Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model. Magn Reson Med 2003; 50: 727-734. – reference: Moseley ME, Cohen Y, Montorovitch J. Early detection of regional cerebral ischemia in cats: comparison of diffusion and T2 weighted MRI and spectroscopy. J Magn Reson 1990; 14: 330-346. – volume: 83 start-page: 2856 year: 2002 end-page: 2863 article-title: Importance of intracellular water apparent diffusion to the measurement of membrane permeability publication-title: Biophys J – volume: 190 start-page: 255 year: 2008 end-page: 270 article-title: Anomalous diffusion expressed through fractional order differential operators in the Bloch‐Torrey equation publication-title: J Magn Reson – volume: 11 start-page: 379 year: 2003 end-page: 401 article-title: Imaging of brain tumors with diffusion‐weighted and diffusion tensor MR imaging publication-title: Magn Reson Imaging Clin N Am – volume: 44 start-page: 852 year: 2000 end-page: 859 article-title: Water diffusion compartmentation and anisotropy at high b values in the human brain publication-title: Magn Reson Med – year: 2001 – volume: 94 start-page: 630 year: 1954 article-title: Effects of diffusion on free precession in nuclear magnetic resonance experiments publication-title: Phys Rev – volume: 23 start-page: 165 year: 2002 end-page: 170 article-title: Characterization of benign and metastatic vertebral compression fractures with quantitative diffusion MR imaging publication-title: AJNR Am J Neuroradiol – volume: 183 start-page: 315 year: 2006 end-page: 323 article-title: Observation of anomalous diffusion in excised tissue by characterizing the diffusion‐time dependence of the MR signal publication-title: J Magn Reson – volume: 188 start-page: 285 year: 2007 end-page: 294 article-title: MR diffusion‐“diffraction” phenomenon in multi‐pulse‐field‐gradient experiments publication-title: J Magn Reson – volume: 14 start-page: 330 year: 1990 end-page: 346 article-title: Early detection of regional cerebral ischemia in cats: comparison of diffusion and T2 weighted MRI and spectroscopy publication-title: J Magn Reson – volume: 59 start-page: 447 year: 2008 end-page: 455 article-title: From diffusion‐weighted MRI to anomalous diffusion imaging publication-title: Magn Reson Med – volume: 199 start-page: 391 year: 1996 end-page: 401 article-title: Hyperacute stroke: evaluation with combined multisection diffusion‐weighted and hemodynamically weighted echo‐planar MR imaging publication-title: Radiology – volume: 53 start-page: 1432 year: 2005 end-page: 1440 article-title: Diffusional kurtosis imaging: the quantification of non‐gaussian water diffusion by means of magnetic resonance imaging publication-title: Magn Reson Med – volume: 45 start-page: 580 year: 2001 end-page: 587 article-title: Visualization of neural tissue water compartments using biexponential diffusion tensor MRI publication-title: Magn Reson Med – volume: 17 start-page: 1418 year: 2009 article-title: Analysis of high b‐value diffusion images using a fractional order diffusion model with denoising image reconstruction publication-title: Proc Int Soc Magn Reson Med – volume: 50 start-page: 727 year: 2003 end-page: 734 article-title: Characterization of continuously distributed cortical water diffusion rates with a stretched‐exponential model publication-title: Magn Reson Med – start-page: 472 year: 2000 – volume: 88 start-page: 3228 year: 1990 end-page: 3232 article-title: Complete separation of intracellular and extracellular information in NMR spectra of perfused cells by diffusion weighted spectroscopy publication-title: Proc Natl Acad Sci U|S|A – volume: 8 start-page: 98 year: 1999 end-page: 108 article-title: Water diffusion in rat brain in vivo as detected at very large b values is multicompartmental publication-title: MAGMA – volume: 48 start-page: 765 year: 2002 end-page: 770 article-title: Evidence that both fast and slow water ADC components arise from intracellular space publication-title: Magn Reson Med – volume: 49 start-page: 177 year: 2003 end-page: 182 article-title: Reduction of eddy‐current‐induced distortion in diffusion MRI using a twice‐refocused spin echo publication-title: Magn Reson Med – volume: 52 start-page: R57 year: 2007 end-page: R90 article-title: The “wet mind”: water and functional neuroimaging publication-title: Phys Med Biol – volume: 12 start-page: 51 year: 1999 end-page: 62 article-title: Multi‐component apparent diffusion coefficients in human brain publication-title: NMR Biomed – volume: 23 start-page: 746 year: 1992 end-page: 754 article-title: Mechanism of detection of acute cerebral ischemia in rats by diffusion‐weighted magnetic resonance microscopy publication-title: Stroke – volume: 52 start-page: 239 year: 2004 end-page: 247 article-title: Effects of physiologic challenge on the ADC of intracellular water in the oocyte publication-title: Magn Reson Med – volume: 47 start-page: 623 year: 2002 end-page: 628 article-title: In vivo mapping of the fast and slow diffusion tensors in human brain publication-title: Magn Reson Med – volume: 50 start-page: 664 year: 2003 end-page: 669 article-title: Statistical model for diffusion attenuated MR signal publication-title: Magn Reson Med – volume: 9 start-page: 53 year: 1999 end-page: 60 article-title: Usefulness of diffusion‐weighted MRI with echo‐planar technique in the evaluation of cellularity in gliomas publication-title: J Magn Reson Imaging – start-page: 36 year: 2008 – year: 1999 |
| SSID | ssj0009974 |
| Score | 2.3965533 |
| Snippet | It is well known that diffusion‐induced MR signal loss deviates from monoexponential decay, particularly at high b‐values (e.g., >1500 sec/mm2 for human brain... It is well known that diffusion-induced MR signal loss deviates from monoexponential decay, particularly at high b-values (e.g., >1500 sec/mm(2) for human... It is well known that diffusion-induced MR signal loss deviates from monoexponential decay, particularly at high b-values (e.g., >1500 sec/mm2 for human brain... |
| SourceID | proquest pubmed wiley istex |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 562 |
| SubjectTerms | Algorithms anomalous diffusion Brain Brain - anatomy & histology Calculus Diffusion coefficient Diffusion Magnetic Resonance Imaging - methods diffusion model Echo-Planar Imaging - methods fractional order calculus high b value Humans Image Enhancement - methods Image Interpretation, Computer-Assisted - methods Mathematical models Microenvironments N.M.R Neuroimaging Reproducibility of Results Sensitivity and Specificity Substantia grisea |
| Title | Studies of anomalous diffusion in the human brain using fractional order calculus |
| URI | https://api.istex.fr/ark:/67375/WNG-QCK9DKLJ-9/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fmrm.22285 https://www.ncbi.nlm.nih.gov/pubmed/20187164 https://www.proquest.com/docview/733229755 https://www.proquest.com/docview/883015224 |
| Volume | 63 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1baxQxFD4sBcUXq23VrRfyIOLLbGdnkkmCT1KtS-sWtrjYByHkMlNK3dmyFyj-es9JdrdUKohvgUnITE5y5svJl-8AvJXSizq3ecZd8BkPVmUKgXOW-6L0vHSuiGTM4Wk1GPPjc3HegQ_ruzBJH2ITcKOVEf01LXDr5ge3oqGT2aRH4Qu6YE5cLQJEZ7fSUVonBWbJyc9ovlYVyouDTUsEpDSWN_ehy7tgNf5tjrbhx_o9E8nkqrdcuJ7_9YeE439-yBN4vEKh7GOaNk-hU7c78HC4OmffgQeRGOrnuzBaEQ3ZtGG2nU7sz-lyziitypLibOyyZQghWUz1xxzlm2BEpb9gzSxdmcBuorwnw8lAocb5HoyPPn87HGSrNAzZJSUEzbQPOkcU09RcVY0IfekLKoaqcTkPZcOtxW1b1ZToK7VTQgevfMktOgNfiX75DLbaaVu_ACZDrYL2iJH7gdvSOqkRYyDo5DqvlJBdeBcNYq6T1Iaxsytinklhvp9-MaPDE_3p5Oux0V1ga4sZXA90yGHbGgfAyBJdlJZC_L2KUujVEHfyLjxPxt70V1COQtxBduF9NNnmQVJ3Lgway0RjmeHZMBb2_73qS3iUyAdEYXsFW4vZsn6NmGbh3sTJ-xt_B_Ew |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1La9wwEB7SlD4ufaRtsn3qUEov3ji2ZEnQS0mabrPrhYSE5hKELNklJOsN-4CSX58ZaXdDSwulN4ElZGuk8afRp28A3kvpRJ3aNOGVdwn3ViUKgXOSuix3PK-qLJAxy2HRO-EHp-J0DT4t78JEfYhVwI1WRvDXtMApIL19qxo6moy6FL8Qd-AuZfQm5fy9o1vxKK2jBrPk5Gk0X-oKpdn2qilCUhrNn3_Cl7_C1fC_2X8MZ8s3jTSTi-58VnXd9W8ijv_7KU_g0QKIss9x5jyFtbrdgPvl4qh9A-4FbqibPoPDBdeQjRtm2_HIXo7nU0aZVeYUamPnLUMUyUK2P1ZRyglGbPofrJnEWxPYTVD4ZDgfKNo4fQ4n-1-Od3vJIhNDck45QRPtvE4RyDQ1V0Uj_I50GRV90VQp93nDrcWdW9Hk6C51pYT2TrmcW_QHDk2Tv4D1dtzWW8Ckr5XXDmHyjuc2t5XUCDMQd3KdFkrIDnwIFjFXUW3D2MkFkc-kMN-HX83hbl_v9QcHRneALU1mcEnQOYdtaxwAI3P0UloK8fcqSqFjQ-jJO7AZrb3qL6M0hbiJ7MDHYLPVgyjwnBk0lgnGMuVRGQov_73qO3jQOy4HZvBt2H8FDyMXgRhtr2F9NpnXbxDizKq3YSbfAJSQ9Uw |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LbxMxEB6VIiouPMorPH1AiMumm117bYsTagilaSJaUdEDkuXHLqpKNlUeEuLXM2MnqUAgIW6W1pZ3Pfbs5_HnbwBeSulFnds84y74jAerMoXAOct9UXpeOldEMuZoXB2c8sMzcbYFb9Z3YZI-xCbgRisj-mta4Jeh2bsSDZ3MJl0KX4hrcJ1Xuaa8Df2TK-0orZMEs-TkaDRfywrlxd6mKSJSGszvf4KXv6LV-LsZ3IYv6xdNLJOL7nLhuv7HbxqO__kld-DWCoayt2ne3IWtut2FndHqoH0XbkRmqJ_fg-MV05BNG2bb6cR-my7njPKqLCnQxs5bhhiSxVx_zFHCCUZc-q-smaU7E9hN1PdkOBso1ji_D6eDd5_2D7JVHobsnDKCZtoHnSOMaWquqkaEnvQFFUPVuJyHsuHW4r6takp0ltopoYNXvuQWvYGvRK98ANvttK0fAZOhVkF7BMm9wG1pndQIMhB1cp1XSsgOvIoGMZdJa8PY2QVRz6Qwn8fvzfH-UPeHR4dGd4CtLWZwQdAph21rHAAjS_RRWgrx9ypKoVtD4Mk78DAZe9NfQUkKcQvZgdfRZJsHSd65MGgsE41lRiejWHj871VfwM7H_sAcfRgPn8DNREQgOttT2F7MlvUzxDcL9zzO45_AtvP7 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Studies+of+anomalous+diffusion+in+the+human+brain+using+fractional+order+calculus&rft.jtitle=Magnetic+resonance+in+medicine&rft.au=Zhou%2C+Xiaohong+Joe&rft.au=Gao%2C+Qing&rft.au=Abdullah%2C+Osama&rft.au=Magin%2C+Richard+L&rft.date=2010-03-01&rft.issn=1522-2594&rft.eissn=1522-2594&rft.volume=63&rft.issue=3&rft.spage=562&rft_id=info:doi/10.1002%2Fmrm.22285&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0740-3194&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0740-3194&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0740-3194&client=summon |