An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange

•An exact equation for two site exchange for use in analysing CPMG data.•A generalisation of a result derived by Carver and Richards in 1972.•Offers physical insights into how CPMG experiment work.•Provides a means for significantly more rapid analysis of experimental CPMG data.

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is widely used to quantitatively analyse the effects of chemical exchange on NMR spectra. In a CPMG experiment, the effective transverse relaxation rate, R2,eff, is typically measured as a function of the pulse frequency, νCPMG. Here, an exact expression for how R2,eff varies with νCPMG is derived for the commonly encountered scenario of two-site chemical exchange of in-phase magnetisation. This result, summarised in Appendix A, generalises a frequently used equation derived by Carver and Richards, published in 1972. The expression enables more rapid analysis of CPMG data by both speeding up calculation of R2,eff over numerical methods by a factor of ca. 130, and yields exact derivatives for use in data analysis. Moreover, the derivation provides insight into the physical principles behind the experiment.

Graphical abstractDownload high-res image (195KB)Download full-size image