Exchange-dependent relaxation in the rotating frame for slow and
intermediate exchange - modeling off-resonant spin-lock and chemical exchange
saturation transfer
Chemical exchange observed by NMR saturation transfer (CEST) and spin-lock
(SL) experiments provide an MRI contrast by indirect detection of exchanging
protons. The determination of the relative concentrations and exchange rates is
commonly achieved by numerical integration of the Bloch-McConnell equations. We
derive an analytical solution of the Bloch-McConnell equations that describes
the magnetization of coupled spin populations under radiofrequency
irradiation.As CEST and off-resonant SL are equivalent, their steady-state
magnetization and dynamics can be predicted by the same single eigenvalue: the
longitudinal relaxation rate in the rotating frame R1rho. For the case of
slowly exchanging systems, e.g. amide protons, the saturation of the small
proton pool is affected by transverse relaxation (R2b). It turns out, that R2b
is also significant for intermediate exchange, such as amine- or
hydroxyl-exchange or paramagnetic CEST agents, if pools are only partially
saturated. We propose a solution for R1rho that includes R2 of the exchanging
pool by extending existing approaches, and verify it by numerical simulations.
With the appropriate projection factors, we obtain an analytical solution for
CEST and SL for nonzero R2 of the exchanging pool, whilst considering the
dilution by direct water saturation across the entire Z-spectra. This allows
the optimization of irradiation parameters and the quantification of
pH-dependent exchange rates and metabolite concentrations. In addition, we
propose evaluation methods that correct for concomitant direct saturation
effects. It is shown that existing theoretical treatments for CEST are special
cases of this approach
