An approximate fast-mapping approach to the surface NMR forward problem

A surface nuclear magnetic resonance (NMR) forward model based on the full-Bloch equation improves the accuracy of the forward response given an arbitrary excitation pulse and a wider range of relaxation conditions. However, the full-Bloch solution imposes a significant slowdown in inversion times compared to the traditional forward model. We present a fastmapping approach capable of dramatic increases in inversion speeds with minimal sacrifices in forward response accuracy.We show that the look-up tables used to calculate the transverse magnetization and the full surface NMR forward response are smoothly varying functions of the underlying T2 and T2 values. We exploit this smoothness to form a polynomial representation of the look-up tables and surfaceNMRforward responses,where a fast-mapping approximation of each are reduced to a simple matrix multiplication. Accurate approximations with less than 1 per cent error can be produced using 21 coefficient representations of the look-up tables for each B1 value and for the signal expected from a particular depth layer for a particular pulse moment. In essence, the proposed fast-mapping approach front-loads all expensive calculations and stores the results in a compressed form as a coefficient matrix containing less than a half a million elements. This allows all subsequent inversions to be performed at greatly improved speeds.