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Volumn 209, Issue 2, 2011, Pages 183-194

Exact solution of the CPMG pulse sequence with phase variation down the echo train: Application to R2 measurements

Author keywords

Bloch equations; CPMG experiments; Fitting models; Lagrange interpolation; Measurements of transverse relaxations; Phase alternation; Phase cycling scheme; Projection operators; Rectangular pulses

Indexed keywords

BLOCH EQUATION; CPMG EXPERIMENTS; FITTING MODELS; LAGRANGE INTERPOLATION; PHASE ALTERNATION; PHASE CYCLING SCHEME; PROJECTION OPERATORS; RECTANGULAR PULSE;

EID: 79953232635     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2011.01.009     Document Type: Article
Times cited : (14)

References (58)
  • 2
    • 0003186638 scopus 로고
    • Analysis of Carr-Purcell spin-echo NMR experiments on multiple-spin systems. II. The effect of chemical exchange
    • A. Allerhand, and E. Thiele Analysis of Carr-Purcell spin-echo NMR experiments on multiple-spin systems. II. The effect of chemical exchange J. Chem. Phys. 45 1966 902 916
    • (1966) J. Chem. Phys. , vol.45 , pp. 902-916
    • Allerhand, A.1    Thiele, E.2
  • 5
    • 33748619206 scopus 로고    scopus 로고
    • An NMR perspective on enzyme dynamics
    • DOI 10.1021/cr050312q
    • D.D. Boehr, H.J. Dyson, and P.E. Wright An NMR perspective on enzyme dynamics Chem. Rev. 106 2006 3055 3079 (Pubitemid 44376926)
    • (2006) Chemical Reviews , vol.106 , Issue.8 , pp. 3055-3079
    • Boehr, D.D.1    Dyson, H.J.2    Wright, P.E.3
  • 6
    • 46949093335 scopus 로고    scopus 로고
    • Using relaxation dispersion NMR spectroscopy to determine structures of excited, invisible protein states
    • D.F. Hansen, P. Vallurupalli, and L.E. Kay Using relaxation dispersion NMR spectroscopy to determine structures of excited, invisible protein states J. Biomol. NMR 41 2008 113 120
    • (2008) J. Biomol. NMR , vol.41 , pp. 113-120
    • Hansen, D.F.1    Vallurupalli, P.2    Kay, L.E.3
  • 8
    • 33749622370 scopus 로고
    • Spin echoes
    • E.L. Hahn Spin echoes Phys. Rev. 80 1950 580 594
    • (1950) Phys. Rev. , vol.80 , pp. 580-594
    • Hahn, E.L.1
  • 9
    • 33847534249 scopus 로고
    • Effects of diffusion on free precession in nuclear magnetic resonance experiments
    • H.Y. Carr, and E.M. Purcell Effects of diffusion on free precession in nuclear magnetic resonance experiments Phys. Rev. 94 1954 630 638
    • (1954) Phys. Rev. , vol.94 , pp. 630-638
    • Carr, H.Y.1    Purcell, E.M.2
  • 10
    • 0002899752 scopus 로고
    • Modified spin-echo method for measuring nuclear relaxation times
    • S. Meiboom, and D. Gill Modified spin-echo method for measuring nuclear relaxation times Rev. Sci. Instrum. 29 1958 688 691
    • (1958) Rev. Sci. Instrum. , vol.29 , pp. 688-691
    • Meiboom, S.1    Gill, D.2
  • 11
    • 79953165442 scopus 로고    scopus 로고
    • Exact solution to the bloch equations and application to the Hahn echo
    • A.D. Bain, C.K. Anand, and Z. Nie Exact solution to the bloch equations and application to the Hahn echo J. Magn. Reson. 206 2010 227 240
    • (2010) J. Magn. Reson. , vol.206 , pp. 227-240
    • Bain, A.D.1    Anand, C.K.2    Nie, Z.3
  • 13
    • 39749145723 scopus 로고    scopus 로고
    • Accurately probing slow motions on millisecond timescales with a robust NMR relaxation experiment
    • DOI 10.1021/ja710477h
    • D. Long, M. Liu, and D. Yang Accurately probing slow motions on millisecond timescales with a robust NMR relaxation experiment J. Am. Chem. Soc. 130 2008 2432 2433 (Pubitemid 351304747)
    • (2008) Journal of the American Chemical Society , vol.130 , Issue.8 , pp. 2432-2433
    • Long, D.1    Liu, M.2    Yang, D.3
  • 14
    • 0033209812 scopus 로고    scopus 로고
    • Density Matrix Simulations of the Effects of J Coupling in Spin Echo and Fast Spin Echo Imaging
    • L.A. Stables, R.P. Kennan, A.W. Anderson, and J.C. Gore Density matrix simulations of the effects of J coupling in spin echo and fast spin echo imaging J. Magn. Reson. 140 1999 305 314 (Pubitemid 129608295)
    • (1999) Journal of Magnetic Resonance , vol.140 , Issue.2 , pp. 305-314
    • Stables, L.A.1    Kennan, R.P.2    Anderson, A.W.3    Gore, J.C.4
  • 16
    • 0001309197 scopus 로고
    • Modified Carr-Purcell-Meiboom-Gill sequence for NMR Fourier imaging applications
    • A.A. Maudsley Modified Carr-Purcell-Meiboom-Gill sequence for NMR Fourier imaging applications J. Magn. Reson. 69 1986 488 491
    • (1986) J. Magn. Reson. , vol.69 , pp. 488-491
    • Maudsley, A.A.1
  • 19
    • 44049117201 scopus 로고
    • 2 Measurements with the Carr-Purcell-Meiboom-Gill sequence in the inhomogeneous RF field of surface coils
    • 2 Measurements with the Carr-Purcell-Meiboom-Gill sequence in the inhomogeneous RF field of surface coils J. Magn. Reson. 96 1992 589 595
    • (1992) J. Magn. Reson. , vol.96 , pp. 589-595
    • Ziegler, A.1    Decorps, M.2    Remy, C.3
  • 20
    • 0006663486 scopus 로고
    • Errors in measurements of transverse relaxation rates
    • R.L. Vold, R.R. Vold, and H.E. Simon Errors in measurements of transverse relaxation rates J. Magn. Reson. 11 1973 283 298
    • (1973) J. Magn. Reson. , vol.11 , pp. 283-298
    • Vold, R.L.1    Vold, R.R.2    Simon, H.E.3
  • 21
    • 0000117157 scopus 로고
    • Effect of RF field inhomogeneities on spin-echo measurements
    • T.E. Bull Effect of RF field inhomogeneities on spin-echo measurements Rev. Sci. Instrum. 45 1974 232 242
    • (1974) Rev. Sci. Instrum. , vol.45 , pp. 232-242
    • Bull, T.E.1
  • 22
    • 0040089010 scopus 로고
    • 2 values measured with the Carr-Purcell-Meiboom- Gill pulsed NMR sequence
    • 2 values measured with the Carr-Purcell-Meiboom-Gill pulsed NMR sequence J. Magn. Reson. 26 1977 481 489
    • (1977) J. Magn. Reson. , vol.26 , pp. 481-489
    • Hughes, D.G.1
  • 23
    • 49449126599 scopus 로고
    • Baseline drift in the Carr-Purcell-Meiboom-Gill pulsed NMR experiment
    • D.G. Hughes, and G. Lindblom Baseline drift in the Carr-Purcell-Meiboom- Gill pulsed NMR experiment J. Magn. Reson. 26 1977 469 479
    • (1977) J. Magn. Reson. , vol.26 , pp. 469-479
    • Hughes, D.G.1    Lindblom, G.2
  • 25
    • 0022930453 scopus 로고
    • 2 using multiple-echo techniques. II. Effects of static field inhomogeneity
    • DOI 10.1002/mrm.1910030410
    • 2 using multiple-echo MRI techniques. II. Effects of static field inhomogeneity Magn. Reson. Med. 3 1986 562 574 (Pubitemid 17171953)
    • (1986) Magnetic Resonance in Medicine , vol.3 , Issue.4 , pp. 562-574
    • Majumdar, S.1    Orphanoudakis, S.C.2    Gmitro, A.3
  • 26
    • 0009685329 scopus 로고
    • Suppression of artifacts in multiple-echo magnetic resonance
    • G.J. Barker, and T.H. Mareci Suppression of artifacts in multiple-echo magnetic resonance J. Magn. Reson. 83 1989 11 28
    • (1989) J. Magn. Reson. , vol.83 , pp. 11-28
    • Barker, G.J.1    Mareci, T.H.2
  • 27
    • 0000252605 scopus 로고
    • Analysis of Carr-Purcell sequences with nonideal pulses
    • J. Simbrunner, and R. Stollberger Analysis of Carr-Purcell sequences with nonideal pulses J. Magn. Reson., Ser. B 109 1995 301 309
    • (1995) J. Magn. Reson., Ser. B , vol.109 , pp. 301-309
    • Simbrunner, J.1    Stollberger, R.2
  • 28
    • 0035743530 scopus 로고    scopus 로고
    • Carr-Purcell sequences with composite pulses
    • M.D. Hürlimann Carr-Purcell sequences with composite pulses J. Magn. Reson. 152 2001 109 123
    • (2001) J. Magn. Reson. , vol.152 , pp. 109-123
    • Hürlimann, M.D.1
  • 29
    • 0034919209 scopus 로고    scopus 로고
    • Optimization of timing in the Carr-Purcell-Meiboom-Gill sequence
    • DOI 10.1016/S0730-725X(01)00251-X, PII S0730725X0100251X
    • M.D. Hürlimann Optimization of timing in the Carr-Purcell-Meiboom- Gill sequence Magn. Reson. Imaging 19 2001 375 378 (Pubitemid 32692198)
    • (2001) Magnetic Resonance Imaging , vol.19 , Issue.3-4 , pp. 375-378
    • Hurlimann, M.D.1
  • 30
    • 0000698894 scopus 로고    scopus 로고
    • Systematic Errors Associated with the CPMG Pulse Sequence and Their Effect on Motional Analysis of Biomolecules
    • A. Ross, M. Czisch, and G.C. King Systematic errors associated with the CPMG pulse sequence and their effect on motional analysis of biomolecules J. Magn. Reson. 124 1997 355 365 (Pubitemid 127451800)
    • (1997) Journal of Magnetic Resonance , vol.124 , Issue.2 , pp. 355-365
    • Ross, A.1    Czisch, M.2    King, G.C.3
  • 33
    • 28844450707 scopus 로고    scopus 로고
    • Rectifying system-specific errors in NMR relaxation measurements
    • DOI 10.1016/j.jmr.2005.08.017, PII S1090780705002946
    • N.H. Pawley, M.D. Clark, and R. Michalczyk Rectifying system-specific errors in NMR relaxation measurements J. Magn. Reson. 178 2006 77 87 (Pubitemid 41774014)
    • (2006) Journal of Magnetic Resonance , vol.178 , Issue.1 , pp. 77-87
    • Pawley, N.H.1    Clark, M.D.2    Michalczyk, R.3
  • 35
    • 49549172665 scopus 로고
    • Calculation of response in nuclear magnetic resonance: II. Pulsed experiments
    • B.W. Goodwin, and R. Wallace Calculation of response in nuclear magnetic resonance: II. Pulsed experiments J. Magn. Reson. 9 1973 280 290
    • (1973) J. Magn. Reson. , vol.9 , pp. 280-290
    • Goodwin, B.W.1    Wallace, R.2
  • 36
    • 84948615230 scopus 로고
    • Superoperators in magnetic resonance
    • J. Jeener Superoperators in magnetic resonance Adv. Magn. Reson. 10 1982 1 51
    • (1982) Adv. Magn. Reson. , vol.10 , pp. 1-51
    • Jeener, J.1
  • 37
    • 0001900963 scopus 로고    scopus 로고
    • The Complete Homogeneous Master Equation for a Heteronuclear Two-Spin System in the Basis of Cartesian Product Operators
    • P. Allard, M. Helgstrand, and T. Härd The complete homogeneous master equation for a heteronuclear two-spin system in the basis of Cartesian product operators J. Magn. Reson. 134 1998 7 16 (Pubitemid 128451251)
    • (1998) Journal of Magnetic Resonance , vol.134 , Issue.1 , pp. 7-16
    • Allard, P.1    Helgstrand, M.2    Hard, T.3
  • 38
    • 36149027317 scopus 로고
    • Transient nutations in nuclear magnetic resonance
    • H.C. Torrey Transient nutations in nuclear magnetic resonance Phys. Rev. 76 1949 1059 1068
    • (1949) Phys. Rev. , vol.76 , pp. 1059-1068
    • Torrey, H.C.1
  • 39
    • 0027411977 scopus 로고
    • The general solution to the Bloch equation with constant rf and relaxation terms: Application to saturation and slice selection
    • DOI 10.1118/1.597063
    • R.V. Mulkern, and M.L. Williams The general solution to the Bloch equation with constant RF and relaxation terms: application to saturation and slice selection Med. Phys. 20 1993 5 13 (Pubitemid 23069852)
    • (1993) Medical Physics , vol.20 , Issue.1 , pp. 5-13
    • Mulkern, R.V.1    Williams, M.L.2
  • 40
    • 0000921534 scopus 로고
    • General analytical solutions of the Bloch equations
    • G.A. Morris, and P.B. Chilvers General analytical solutions of the Bloch equations J. Magn. Reson., Ser. A 107 1994 236 238
    • (1994) J. Magn. Reson., Ser. A , vol.107 , pp. 236-238
    • Morris, G.A.1    Chilvers, P.B.2
  • 41
    • 43949156397 scopus 로고
    • Erratum: 107 (2) series A (1994) in the note
    • General analytical solutions of the Bloch equations, by Gareth A. Morris, Paul B. Chilvers 232-232
    • G.A. Morris, P.B. Chilvers, Erratum: 107 (2) series A (1994) in the note, General analytical solutions of the Bloch equations, by Gareth A. Morris, Paul B. Chilvers, pp. 236-238, J. Magn. Reson., Ser. A 111 (1994) 232-232.
    • (1994) J. Magn. Reson., Ser. A , vol.111 , pp. 236-238
    • Morris, G.A.1    Chilvers, P.B.2
  • 42
    • 0001376398 scopus 로고
    • Direct Cartesian-space solutions of generalized Bloch equations in the rotating frame
    • P.K. Madhu, and A. Kumar Direct Cartesian-space solutions of generalized Bloch equations in the rotating frame J. Magn. Reson., Ser. A 114 1995 201 211
    • (1995) J. Magn. Reson., Ser. A , vol.114 , pp. 201-211
    • Madhu, P.K.1    Kumar, A.2
  • 43
    • 0031287981 scopus 로고    scopus 로고
    • Bloch equations revisited: New analytical solutions for the generalized Bloch equations
    • P.K. Madhu, and A. Kumar Bloch equations revisited: new analytical solutions for the generalized Bloch equations Concepts Magn. Reson. 9 1997 1 12
    • (1997) Concepts Magn. Reson. , vol.9 , pp. 1-12
    • Madhu, P.K.1    Kumar, A.2
  • 45
    • 0032110618 scopus 로고    scopus 로고
    • An Adiabatic Multiple Spin-Echo Pulse Sequence: Removal of Systematic Errors Due to Pulse Imperfections and Off-Resonance Effects
    • M. Zweckstetter, and T.A. Holak An adiabatic multiple spin-echo pulse sequence: removal of systematic errors due to pulse imperfections and off-resonance effects J. Magn. Reson. 133 1998 134 147 (Pubitemid 128450620)
    • (1998) Journal of Magnetic Resonance , vol.133 , Issue.1 , pp. 134-147
    • Zweckstetter, M.1    Holak, T.A.2
  • 46
    • 0041993710 scopus 로고    scopus 로고
    • CPMG relaxation by diffusion with constant magnetic field gradient in a restricted geometry: Numerical simulation and application
    • G.Q. Zhang, and G.J. Hirasaki CPMG relaxation by diffusion with constant magnetic field gradient in a restricted geometry: numerical simulation and application J. Magn. Reson. 163 2003 81 91
    • (2003) J. Magn. Reson. , vol.163 , pp. 81-91
    • Zhang, G.Q.1    Hirasaki, G.J.2
  • 49
    • 33947578726 scopus 로고    scopus 로고
    • Analytical derivation of multiple spin echo amplitudes with arbitrary refocusing angle
    • DOI 10.1016/j.jmr.2006.11.010, PII S1090780706003922
    • N.N. Lukzen, and A.A. Savelov Analytical derivation of multiple spin echo amplitudes with arbitrary refocusing angle J. Magn. Reson. 185 2007 71 76 (Pubitemid 46484402)
    • (2007) Journal of Magnetic Resonance , vol.185 , Issue.1 , pp. 71-76
    • Lukzen, N.N.1    Savelov, A.A.2
  • 51
    • 33947130227 scopus 로고    scopus 로고
    • Keeping a quantum bit alive by optimized π-pulse sequences
    • G.S. Uhrig Keeping a quantum bit alive by optimized π-pulse sequences Phys. Rev. Lett. 98 2007 100504-1-4
    • (2007) Phys. Rev. Lett. , vol.98
    • Uhrig, G.S.1
  • 52
    • 77950392958 scopus 로고    scopus 로고
    • Near-optimal dynamical decoupling of a Qubit
    • J.R. West, B.H. Fong, and D.A. Lidar Near-optimal dynamical decoupling of a Qubit Phys. Rev. Lett. 104 2010 130501-1-4
    • (2010) Phys. Rev. Lett. , vol.104
    • West, J.R.1    Fong, B.H.2    Lidar, D.A.3
  • 53
    • 0000682534 scopus 로고
    • The normal constants of motion in quantum mechanics treated by projection technique
    • P.-O. Löwdin The normal constants of motion in quantum mechanics treated by projection technique Rev. Modern Phys. 34 1962 520 530
    • (1962) Rev. Modern Phys. , vol.34 , pp. 520-530
    • Löwdin, P.-O.1
  • 56
    • 0001415052 scopus 로고
    • A modeling language for mathematical programming
    • R. Fourer, D.M. Gay, and B.W. Kernighan A modeling language for mathematical programming Manage. Sci. 36 1990 519 554
    • (1990) Manage. Sci. , vol.36 , pp. 519-554
    • Fourer, R.1    Gay, D.M.2    Kernighan, B.W.3
  • 57
    • 29144523061 scopus 로고    scopus 로고
    • On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
    • DOI 10.1007/s10107-004-0559-y
    • A. Wächter, and L.T. Biegler On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Math. Program., Ser. A 106 2006 25 57 (Pubitemid 41813168)
    • (2006) Mathematical Programming , vol.106 , Issue.1 , pp. 25-57
    • Wachter, A.1    Biegler, L.T.2


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