Applied Magnetic Resonance

, Volume 44, Issue 12, pp 1373–1379 | Cite as

Computationally Efficient Steady-State Solution of the Bloch Equations for Rapid Sinusoidal Scans Based on Fourier Expansion in Harmonics of the Scan Frequency

  • Mark Tseitlin
  • Gareth R. Eaton
  • Sandra S. EatonEmail author


A rapid-scan electron paramagnetic resonance has been shown to improve the signal-to-noise ratio relative to conventional continuous wave spectroscopy. Equations are derived for the steady-state solution to the Bloch equations as a Fourier expansion in the harmonics of the scan frequency. This simulation method is about two orders of magnitude faster than time-domain numerical integration.


Electron Paramagnetic Resonance Nitroxide Electron Paramagnetic Resonance Signal Bloch Equation Spin Packet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The support of this work by NIH EB000557, NIH 1K25EB016040-01A1 and NSF IDBR 0753018 are gratefully acknowledged. The experimental data for mHCTPO were obtained by Deborah Mitchell, University of Denver.


  1. 1.
    D.G. Mitchell, R.W. Quine, M. Tseitlin, S.S. Eaton, G.R. Eaton, J. Magn. Reson. 214, 221–226 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    D.G. Mitchell, G.M. Rosen, M. Tseitlin, B. Symmes, S.S. Eaton, and G.R. Eaton, Biophys. J. 105, 338–342 (2013)Google Scholar
  3. 3.
    D.G. Mitchell, M. Tseitlin, R.W. Quine, V. Meyer, M.E. Newton, A. Schnegg, B. George, S.S. Eaton, and G.R. Eaton, Mol. Phys. 111, 2664–2673 (2013)Google Scholar
  4. 4.
    J.P. Joshi, J.R. Ballard, G.A. Rinard, R.W. Quine, S.S. Eaton, G.R. Eaton, J. Magn. Reson. 175, 44–51 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    R.W. Quine, D.G. Mitchell, S.S. Eaton, G.R. Eaton, Conc. Magn. Reson. 41B, 95–110 (2012)CrossRefGoogle Scholar
  6. 6.
    M. Tseitlin, G.A. Rinard, R.W. Quine, S.S. Eaton, G.R. Eaton, J. Magn. Reson. 208, 279–283 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    M. Tseitlin, D.G. Mitchell, S.S. Eaton, G.R. Eaton, J. Magn. Reson. 223, 80–84 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    J.W. Stoner, D. Szymanski, S.S. Eaton, R.W. Quine, G.A. Rinard, G.R. Eaton, J. Magn. Reson. 170, 127–135 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    B.H. Robinson, C. Mailer, A.W. Reese, J. Magn. Reson. 138, 199–209 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    G. Engeln-Muellges, F. Uhlig, Linear Systems with Five-Diagonal Matrices, Numerical Algorithms with C (Springer-Verlag, New York, 1996), pp. 98–100CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Mark Tseitlin
    • 1
  • Gareth R. Eaton
    • 1
  • Sandra S. Eaton
    • 1
    Email author
  1. 1.Department of Chemistry and BiochemistryUniversity of DenverDenverUSA

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