Product operator analysis of the influence of chemical exchange on relaxation rates

On-resonance low B1 pulses for imaging of the effects of PARACEST agents

“…Under the conditions when the WALTZ-16* irradiation is cyclic (e.g., exactly on-resonance or when t p x 1 = p/2), the behavior of the Z magnetization at the end of the WALTZ-16* train will be governed by T 1q . Based on the theoretical treatments of exchange in the presence of CW [28,29,32] and adiabatic pulses [20], it can be assumed that the T 1q will contain contributions from T 2 , exchange lifetimes, and T 1 . Hence, the effective decrease will be determined not only by exchange parameters but also by the T 2a and T 1a of bulk water.…”

“…For instance, in the WEX experiment, van Zijl et al [18,19] used a water-exchange filter to detect mobile and exchanging protons. Recently, Michaeli and coworkers [20] studied the effects of exchange on the rotating frame relaxation under the influence of adiabatic pulses and showed that the contribution of exchange to T 1q can be varied by changing pulse parameters. It has also been demonstrated that fast exchanging agents can reduce the T 2 of bulk water protons by chemical exchange [17,21].…”

Exchange-induced relaxation in the presence of a fictitious field

“…Finally, in Figure 3 the calculations performed with Eqs. (28–31) are shown in comparison with the results obtained with the invariant trajectory approach [8] and with the Bloch-McConnell formalism (Figure 5 of ref. [5]).…”

“…In this work, the analytical solution for anisocronous two site exchange (2SX) (i.e., exchange between sites with different chemical shifts) in the fast exchange regime (FXR) during RAFF2 was derived. The validity of the analytical solution was verified by comparing with Bloch-McConnell and product operator formalisms [5, 8]. The relaxation rates were derived for the case of a fictitious field in the 2 nd rotating frame (SRF).…”

Generalized treatment of NMR spectra for rapid chemical reactions

“…Although pseudo first-order conditions sometimes can be accomplished by manipulations of experimental conditions, simulation of NMR spectra in the presence of reactions following any arbitrary rate law would be more useful. Recently, Idiyatullin has commented that extension of HHA's method to nonfirst order kinetic scenarios should be possible ''by increasing the number and complexity of the differential equations'' (55). We describe a general solution that combines the matrix formulation described by HHA with numeric integration routines to evaluate the modified Bloch equations for a wide variety of kinetic scenarios.…”