Considerations for using linear combinations of array elements in B1 mapping

Introduction: Accurate B1 mapping of transmit coil arrays is vital for parallel transmission MRI. Current mapping methods accommodate a limited range of B1 amplitude, but can be adapted for use with coil arrays by mapping B1 fields from linear combinations of coils and solving for individual elements [1,2]. Existing formulations can be represented by an encoding matrix A, with Ai,j = 1 for i≠j, and Ai,j = ε for i=j. Setting ε=0 gives [1]; ε=-1 gives [2] and ε very large gives the single driven coil case. The possibilities for choosing A are vast, and the optimal choice is likely related to the mapping technique as well as the coil array/loading in any particular case. In general we require that the resulting linear combination B1 maps have a low dynamic range of flip angles but also that the condition number of the transformation is low so that noise amplification upon inversion is minimised. We have studied the performance of the family of encoding matrices generated by varying the parameter ε using numerical simulations with real coil data from a parallel transmit system, when used with the AFI B1 mapping technique [3].