  SABRE (Signal Amplification By Reversible Exchange) has become a widely used
method for hyper-polarizing nuclear spins, thereby enhancing their Nuclear
Magnetic Resonance (NMR) signals by orders of magnitude. In SABRE experiments,
non-equilibrium spin order is transferred from parahydrogen to a substrate in a
transient organometallic complex. Applicability of SABRE is expanded by the
methodology of SABRE-relay, in which polarization can be relayed to a second
substrate either by direct chemical exchange of hyperpolarized nuclei or by
polarization transfer between two substrates in a second organometallic
complex. To understand the mechanism of the polarization transfer and study the
transfer efficiency, we propose a theoretical approach to SABRE-relay, which
can treat both spin dynamics and chemical kinetics as well as the interplay
between them. The approach is based on a set of equations for the spin density
matrices of the spin systems involved (i.e., SABRE substrates and complexes),
which can be solved numerically. Using this method, we perform a detailed study
of polarization formation and analyse in detail the dependence of attainable
polarization level on various chemical kinetic and spin dynamic parameters. We
foresee applications of the present approach for optimizing SABRE-relay
experiments with the ultimate goal of achieving maximal NMR signal enhancements
for substrates of interest.
