(50)) is derived. The result is expressed as a linear correction to the Carver Richards equation (summarised in Appendix A), and algorithms based on this have advantages in both see more precision and speed over existing formulaic approaches ( Supplementary Section 8). In a CPMG experiment, transverse magnetisation

is first created, and then allowed to evolve through a series of spin echoes. In this work it is defined that each consists of two delays of duration of τcp, separated by a 180° pulse. A single CPMG element is two concatenated echoes, which in the absence of relaxation and chemical exchange, returns transverse magnetisation to an identical state to which it started. In the complete experiment, Ncyc CPMG elements are further concatenated, leading to a pulsing frequency, vCPMG = Ncyc/Trel and the total time of the CPMG element is Trel = 4τcpNcyc. The change in signal intensity and hence R2,eff due to the exchange process is then monitored as a function of vCPMG. In the case of two-site chemical exchange, in the absence VX809 of pulses, in-phase magnetisation will evolve at two distinct frequencies.

As a useful book keeping exercise, one frequency can be associated with an ensemble of molecules that are primarily (but not entirely) in the majorly populated (ground) state, and the second with an ensemble of molecules that are primarily (but not entirely) in the minorly populated (excited) state. Both ensembles are mixed states whose exact ground/excited ‘composition’ depends explicitly on the exchange parameters. It is shown here that a 180° pulse Vildagliptin does not simply invert the chemical shift, as it would a pure state. Instead, it further mixes these two ensembles. Consequently, after the second evolution period, four frequencies emerge from a spin echo, corresponding to magnetisation that started and finished on either the ground or excited states, and that which started on the ground and finished in the excited, or vice versa. While the first two pathways are entirely

refocused in terms of their chemical shift, the second two are not. The 180° pulse can therefore be considered ‘leaky’, as not all magnetisation is refocused. When multiple Hahn echoes are concatenated in a CPMG experiment, the number of discrete frequencies increases. The derivation of the CPMG signal intensity relies on determining how ‘leaky’ a single CPMG element is, identifying which frequencies are present at the end, evaluating their weighting factors and calculating how these depend on the details of the exchange process. Each of the discrete frequencies that emerge from a CPMG block can be associated with a mixture of ground and excited state ensembles. A higher proportion of time spend in the excited state leads to more efficient relaxation, and loss of signal intensity.