Analysis of temporal encoding efficiency of MR fingerprinting sequences

Purpose: MR Fingerprinting (MRF) relies on highly-undersampled images to simultaneously estimate multiple tissue parameters of interest. While a good understanding of the encoding principle behind MRF exists, we want to shed light on the question of when parameters are encoded during an MRF acquisition. Theory and Methods: We analyze the importance of each time point by leaving it out during matching (leave-one-out, LOO) assuming linear reconstruction is applied and study its influence on the reconstructed parameter map. To accelerate the analysis, we treat LOO as a small perturbation (LOOP) to the full matching problem and derive an analytical formula by leveraging Stolk and Sbrizzi's analysis on the interplay of k-space sampling and transient state dynamics. To study the influence of geometry and parameter distribution, we deploy LOOP on randomly sliced 3D brain geometries with randomized T1/T2 values to identify primary encoding regions independent of geometry. Results: LOOP can be evaluated orders of magnitude faster than conventional matching and visualizes temporal encoding efficiency. We use the findings to accelerate an MRF sequence by truncation as well as to remove undersampling artifacts through an iterative omission scheme in an ill-working MRF sequence in both in-silico and in-vivo experiments. Conclusion: LOOP is an analytical approach to quantify and visualize parameter encoding in MRF. ; ISSN:0740-3194 ; ISSN:1522-2594