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Volumn 3, Issue 3, 2013, Pages 432-441

Fractional order generalization of anomalous diffusion as a multidimensional extension of the transmission line equation

Author keywords

Anomalous diffusion; Bloch Torrey equation; fractional calculus; magnetic resonance imaging

Indexed keywords

ANOMALOUS DIFFUSION; BLOCH-TORREY EQUATION; CEREBRAL SPINAL FLUIDS; DIFFUSION-WEIGHTED MRI; FRACTIONAL CALCULUS; FRACTIONAL EXPONENT; PRINCIPAL DIRECTIONS; TRANSMISSION LINE EQUATIONS;

EID: 84884533346     PISSN: 21563357     EISSN: None     Source Type: Journal    
DOI: 10.1109/JETCAS.2013.2265795     Document Type: Article
Times cited : (32)

References (32)
  • 1
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler and J. Klafter, "The random walk's guide to anomalous diffusion: A fractional dynamics approach," Phys. Rep., vol. 339, pp. 1-77, 2000.
    • (2000) Phys. Rep , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 6
    • 36149003638 scopus 로고
    • Bloch equations with diffusion terms
    • H. C. Torrey, "Bloch equations with diffusion terms," Phys. Rev., vol. 104, pp. 563-565, 1956.
    • (1956) Phys. Rev , vol.104 , pp. 563-565
    • Torrey, H.C.1
  • 7
    • 0028398052 scopus 로고
    • Estimation of the effective self-diffusion tensor from the NMR spin echo
    • Mar.
    • P. J. Basser, J. Mattiello, and D. LeBihan, "Estimation of the effective self-diffusion tensor from the NMR spin echo," J.Magn. Reson. B, vol. 103, pp. 247-254, Mar. 1994.
    • (1994) J.Magn. Reson. B , vol.103 , pp. 247-254
    • Basser, P.J.1    Mattiello, J.2    Lebihan, D.3
  • 8
    • 0030162959 scopus 로고    scopus 로고
    • Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI
    • P. J. Basser and C. Pierpaoli, "Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI," J. Magn. Reson. B., vol. 111, pp. 209-219, June 1996. (Pubitemid 126758682)
    • (1996) Journal of Magnetic Resonance - Series B , vol.111 , Issue.3 , pp. 209-219
    • Basser, P.J.1    Pierpaoli, C.2
  • 9
    • 0022969218 scopus 로고
    • MR imaging of intravoxel incoherent motions: Application to diffusion and perfusion in neurologic disorders
    • D. Le Bihan, E. Breton, D. Lallemand, P. Grenier, E. Cabanis, andM. Laval-Jeantet, "MR imaging of intravoxel incoherent motions: Application to diffusion and perfusion in neurologic disorders," Radiology, vol. 161, pp. 401-407, Nov. 1986. (Pubitemid 17173295)
    • (1986) Radiology , vol.161 , Issue.2 , pp. 401-407
    • Le Bihan, D.1    Breton, E.2    Lallemand, D.3
  • 10
    • 0141506097 scopus 로고    scopus 로고
    • Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model
    • DOI 10.1002/mrm.10581
    • K. M. Bennett, K. M. Schmainda, R. T. Bennett, D. B. Rowe, H. Lu, and J. S. Hyde, "Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model," Magn. Reson. Med., vol. 50, pp. 727-734, Oct. 2003. (Pubitemid 37187837)
    • (2003) Magnetic Resonance in Medicine , vol.50 , Issue.4 , pp. 727-734
    • Bennett, K.M.1    Schmainda, K.M.2    Bennett, R.3    Rowe, D.B.4    Lu, H.5    Hyde, J.S.6
  • 11
    • 33646376290 scopus 로고
    • Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient
    • E. O. Stejskal and J. E. Tanner, "Spin diffusion measurements: Spin echoes in the presence of a time-dependent field gradient," J. Chem. Phys., vol. 42, pp. 288-292, 1965.
    • (1965) J. Chem. Phys , vol.42 , pp. 288-292
    • Stejskal, E.O.1    Tanner, J.E.2
  • 12
    • 77649174534 scopus 로고    scopus 로고
    • Studies of anomalous diffusion in the human brain using fractional order calculus
    • Mar.
    • X. J. Zhou, Q. Gao, O. Abdullah, and R. L. Magin, "Studies of anomalous diffusion in the human brain using fractional order calculus," Magn. Reson. Med., vol. 63, pp. 562-569, Mar. 2010.
    • (2010) Magn. Reson. Med , vol.63 , pp. 562-569
    • Zhou, X.J.1    Gao, Q.2    Abdullah, O.3    Magin, R.L.4
  • 13
    • 84855987270 scopus 로고    scopus 로고
    • Two-step anomalous diffusion tensor imaging
    • Feb. 2012
    • M. G. Hall and T. R. Barrick, "Two-step anomalous diffusion tensor imaging," NMR Biomed., vol. 25, pp. 286-294, Feb. 2012.
    • NMR Biomed , vol.25 , pp. 286-294
    • Hall, M.G.1    Barrick, T.R.2
  • 14
    • 79952806370 scopus 로고    scopus 로고
    • Anisotropic anomalous diffusion assessed in the human brain by scalar invariant indices
    • Apr.
    • S. De Santis, A. Gabrielli,M. Bozzali, B. Maraviglia, E.Macaluso, and S. Capuani, "Anisotropic anomalous diffusion assessed in the human brain by scalar invariant indices," Magn. Reson. Med., vol. 65, pp. 1043-1052, Apr. 2011.
    • (2011) Magn. Reson. Med , vol.65 , pp. 1043-1052
    • De Santis, S.1    Gabrielli, A.2    Bozzali, M.3    Maraviglia, B.4    Macaluso, E.5    Capuani, S.6
  • 17
    • 0001062660 scopus 로고
    • Imagerie de diffusion in vivo par Résonance magnétique nucléaire
    • D. LeBihan and E. Breton, "Imagerie de diffusion In vivo par Résonance magnétique nucléaire," CR Académie des Sciences de Paris, vol. 301, pp. 1109-1112, 1985.
    • (1985) CR Académie des Sciences de Paris , vol.301 , pp. 1109-1112
    • Lebihan, D.1    Breton, E.2
  • 18
    • 38349041965 scopus 로고    scopus 로고
    • Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation
    • R. L. Magin, O. Abdullah, D. Baleanu, and X. J. Zhou, "Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation," J. Magn. Reson., vol. 190, pp. 255-270, 2008.
    • (2008) J. Magn. Reson , vol.190 , pp. 255-270
    • Magin, R.L.1    Abdullah, O.2    Baleanu, D.3    Zhou, X.J.4
  • 20
    • 36849127288 scopus 로고
    • Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow
    • E. O. Stejskal, "Use of spin echoes in a pulsed magnetic-field gradient to study anisotropic, restricted diffusion and flow," J. Chem. Phys., vol. 43, pp. 3597-3603, 1965.
    • (1965) J. Chem. Phys , vol.43 , pp. 3597-3603
    • Stejskal, E.O.1
  • 21
    • 77954316974 scopus 로고    scopus 로고
    • Fractional advection-dispersion equations for modeling transport at the Earth surface
    • Dec. 18
    • R. Schumer, M. M. Meerschaert, and B. Baeumer, "Fractional advection-dispersion equations for modeling transport at the Earth surface," J. Geophys. Res.-Earth Surface, vol. 114, Dec. 18, 2009.
    • (2009) J. Geophys. Res.-Earth Surface , vol.114
    • Schumer, R.1    Meerschaert, M.M.2    Baeumer, B.3
  • 22
    • 79955404865 scopus 로고    scopus 로고
    • Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: Analysis using fractional order calculus
    • May.
    • Q. Gao, G. Srinivasan, R. L. Magin, and X. J. Zhou, "Anomalous diffusion measured by a twice-refocused spin echo pulse sequence: Analysis using fractional order calculus," J. Magn. Reson. Imag., vol. 33, pp. 1177-1183, May 2011.
    • (2011) J. Magn. Reson. Imag , vol.33 , pp. 1177-1183
    • Gao, Q.1    Srinivasan, G.2    Magin, R.L.3    Zhou, X.J.4
  • 25
    • 33750942521 scopus 로고    scopus 로고
    • Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal
    • DOI 10.1016/j.jmr.2006.08.009, PII S1090780706002527
    • E. Ozarslan, P. J. Basser, T. M. Shepherd, P. E. Thelwall, B. C. Vemuri, and S. J. Blackband, "Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal," J. Magn. Reson., vol. 183, pp. 315-323, Dec. 2006. (Pubitemid 44739339)
    • (2006) Journal of Magnetic Resonance , vol.183 , Issue.2 , pp. 315-323
    • Ozarslan, E.1    Basser, P.J.2    Shepherd, T.M.3    Thelwall, P.E.4    Vemuri, B.C.5    Blackband, S.J.6
  • 26
    • 0026019687 scopus 로고
    • A fractal analysis of cultured rat optic nerve glial growth and differentiation
    • T. G. Smith Jr., T. N. Behar, G. D. Lange, W. B. Marks, and W. H. Sheriff Jr., "A fractal analysis of cultured rat optic nerve glial growth and differentiation," Neuroscience, vol. 41, pp. 159-166, 1991.
    • (1991) Neuroscience , vol.41 , pp. 159-166
    • Smith Jr., T.G.1    Behar, T.N.2    Lange, G.D.3    Marks, W.B.4    Sheriff Jr., W.H.5
  • 27
    • 40449088884 scopus 로고    scopus 로고
    • From diffusion-weighted MRI to anomalous diffusion imaging
    • DOI 10.1002/mrm.21453
    • M. G. Hall and T. R. Barrick, "From diffusion-weighted MRI to anomalous diffusion imaging," Magn. Reson. Med., vol. 59, pp. 447-455, Mar. 2008. (Pubitemid 351348213)
    • (2008) Magnetic Resonance in Medicine , vol.59 , Issue.3 , pp. 447-455
    • Hall, M.G.1    Barrick, T.R.2
  • 28
    • 84856851435 scopus 로고    scopus 로고
    • Temporal scaling characteristics of diffusion as a new MRI contrast: Findings in rat hippocampus
    • Apr. 2
    • E. Ozarslan, T. M. Shepherd, C. G. Koay, S. J. Blackband, and P. J. Basser, "Temporal scaling characteristics of diffusion as a new MRI contrast: Findings in rat hippocampus," Neuroimage, vol. 60, pp. 1380-1393, Apr. 2, 2012.
    • (2012) Neuroimage , vol.60 , pp. 1380-1393
    • Ozarslan, E.1    Shepherd, T.M.2    Koay, C.G.3    Blackband, S.J.4    Basser, P.J.5
  • 29
    • 84875270729 scopus 로고    scopus 로고
    • Spatio-temporal anomalous diffusion imaging: Results in controlled phantoms and in excised human meningiomas
    • Apr.
    • S. Capuani, M. Palombo, A. Gabrielli, A. Orlandi, B. Maraviglia, and F. S. Pastore, "Spatio-temporal anomalous diffusion imaging: Results in controlled phantoms and in excised human meningiomas," Magn. Reson. Imag., vol. 31, pp. 359-365, Apr. 2012.
    • (2012) Magn. Reson. Imag , vol.31 , pp. 359-365
    • Capuani, S.1    Palombo, M.2    Gabrielli, A.3    Orlandi, A.4    Maraviglia, B.5    Pastore, F.S.6
  • 30
    • 79960925404 scopus 로고    scopus 로고
    • Spatio-temporal anomalous diffusion in heterogeneous media by nuclear magnetic resonance
    • July 21
    • M. Palombo, A. Gabrielli, S. De Santis, C. Cametti, G. Ruocco, and S. Capuani, "Spatio-temporal anomalous diffusion in heterogeneous media by nuclear magnetic resonance," J. Chem. Phys., vol. 135, pp. 034504-, July 21, 2011.
    • (2011) J. Chem. Phys , vol.135 , pp. 034504
    • Palombo, M.1    Gabrielli, A.2    De Santis, S.3    Cametti, C.4    Ruocco, G.5    Capuani, S.6
  • 31
    • 84858337968 scopus 로고    scopus 로고
    • The gamma parameter of the stretched-exponential model is influenced by internal gradients: Validation in phantoms
    • Mar.
    • M. Palombo, A. Gabrielli, S. De Santis, and S. Capuani, "The gamma parameter of the stretched-exponential model is influenced by internal gradients: Validation in phantoms," J. Magn. Reson., vol. 216, pp. 28-36, Mar. 2012.
    • (2012) J. Magn. Reson , vol.216 , pp. 28-36
    • Palombo, M.1    Gabrielli, A.2    De Santis, S.3    Capuani, S.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.