A surface NMR forward in a dot product

Abstract

SUMMARY The computation required to simulate surface nuclear magnetic resonance (SNMR) data increases proportionally with the number of sequences and number of pulses in each sequence. This poses a particular challenge to modelling steady-state SNMR, where suites of sequences are acquired, each of which require modelling 10–100 s of pulses. To model such data efficiently, we have developed a reformulation of surface NMR forward model, where the geometry of transmit and receive fields are encapsulated into a vector (or set of vectors), which we call B1-volume-receive (BVR) curves. Projecting BVR curve(s) along complimentary magnetization solutions for a particular sequence amounts to computing the full SNMR forward model. The formulation has the additional advantage that computations for increased transmitter current amounts to a relative translation between the BVR and magnetization solutions. We generate 1-D kernels using BVR curves and standard integration techniques and find the difference is within 2 per cent. Using BVR curves, a typical suite of steady-state kernels can be computed two orders of magnitude faster than previous approaches.