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Quantitative time- and frequency-domain analysis of the two-pulse COSY revamped by asymmetric Z-gradient echo detection NMR experiment: Theoretical and experimental aspects, time-zero data truncation artifacts, and radiation damping.

Kirsch S, Hull WE

Department of Medical Physics in Radiology, German Cancer Research Center (DKFZ), Neuenheimer Feld 280, D-69120 Heidelberg, Germany.

The two-pulse COSY revamped by asymmetric Z-gradient echo detection (CRAZED) NMR experiment has the basic form 90 degrees -Gdelta-t(rec)-beta-nGdelta-t(rec)-FID, with a phase-encoding gradient pulse G of length delta applied during the evolution time tau for transverse magnetization, readout pulse beta, rephasing gradient nGdelta, and recovery time t(rec) prior to acquisition of the free-induction decay. Based on the classical treatment of the spatially modulated dipolar demagnetizing field and without invoking intermolecular multiple-quantum coherence, a new formulation of the first-order approximation for the theoretical solution of the nonlinear Bloch equations has been developed. The nth-order CRAZED signal can be expressed as a simple product of a scaling function C(n)(beta,tau) and a signal amplitude function A(n)(t), where the domain t begins immediately after the beta pulse. Using a single-quantum coherence model, a generalized rf phase shift function has also been developed, which explains all known phase behavior, including nth-order echo selection by phase cycling. Details of the derivations are provided in two appendices as supplementary material. For n>1, A(n)(t) increases from zero to a maximum value at t=t(max) before decaying and can be expressed as a series of n exponential decays with antisymmetric binomial coefficients. Fourier transform gives an antisymmetric binomial series of Lorentzians, where the composite lineshape exhibits negative wings, zero integral, and a linewidth that decreases with n. Analytical functions are presented for t(max) and A(n)(t(max)) and for estimating the maximal percent error incurred for A(n)(t(max)) when using the first-order model. The preacquisition delay Delta=delta+t(rec) results in the loss of the data points for t=0 to Delta. Conventional Fourier transformation produces time-zero truncation artifacts (reduced negative wing amplitude, nonzero integral, and reduced effective T(2) ( *)), which can be avoided by time-domain fitting after right shifting the data by Delta. A doped water sample (9.93 mM NiSO(4), 10 mm sample tube) was used to study the behavior of the CRAZED signal for n=1-4 with beta=90 degrees at 7 T (300 MHz (1)H frequency) as a function of Delta, with and without radiation damping. Pulse-acquire experiments were used to determine the relaxation times (T(1)=61.8 ms and T(2) ( *)=29.7 ms), and the radiation damping time constant T(rd)=18.5 ms. When experimental CRAZED data sets were right shifted by Delta, excellent least-squares fits to the first-order model function were obtained for all n using a minimal set of free variables. Without radiation damping the fitted T(2) ( *)values (29.7-30.2 ms) agreed with the reference value. With radiation damping the fitted effective T(2) ( *) values were 16.2 ms for a 90 degrees pulse-acquire experiment and 18.8-20.2 ms for the CRAZED experiment with n=1-4 and signal amplitudes spanning a range of 10(5).

Published 6 August 2008 in J Chem Phys, 129(4): 044505.
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