Chemical exchange effects during refocusing pulses in constant-time CPMG relaxation dispersion experiments

In the analysis of the constant-time Carr-Purcell-Meiboom-Gill (CT-CPMG) relaxation dispersion experiment, chemical exchange parameters, such as rate of exchange and population of the exchanging species, are typically optimized using equations that predict experimental relaxation rates recorded as a function of effective field strength. In this process, the effect of chemical exchange during the CPMG pulses is typically assumed to be the same as during the free-precession. This approximation may introduce systematic errors into the analysis of data because the number of CPMG pulses is incremented during the constant-time relaxation period, and the total pulse duration therefore varies as a function of the effective field strength. In order to estimate the size of such errors, we simulate the time-dependence of magnetization during the entire constant time period, explicitly taking into account the effect of the CPMG pulses on the spin relaxation rate. We show that in general the difference in the relaxation dispersion profile calculated using a practical pulse width from that calculated using an extremely short pulse width is small, but under certain circumstances can exceed 1 s(-1). The difference increases significantly when CPMG pulses are miscalibrated.