Sensitivity regularization of the Cramér‐Rao lower bound to minimize B 1 nonuniformity effects in quantitative magnetization transfer imaging

Purpose To develop and validate a regularization approach of optimizing B 1 insensitivity of the quantitative magnetization transfer (qMT) pool‐size ratio ( F ). Methods An expression describing the impact of B 1 inaccuracies on qMT fitting parameters was derived using a sensitivity analysis. To simultaneously optimize for robustness against noise and B 1 inaccuracies, the optimization condition was defined as the Cramér‐Rao lower bound (CRLB) regularized by the B 1 ‐sensitivity expression for the parameter of interest ( F ). The qMT protocols were iteratively optimized from an initial search space, with and without B 1 regularization. Three 10‐point qMT protocols (Uniform, CRLB, CRLB+B 1 regularization) were compared using Monte Carlo simulations for a wide range of conditions (e.g., SNR, B 1 inaccuracies, tissues). Results The B 1 ‐regularized CRLB optimization protocol resulted in the best robustness of F against B 1 errors, for a wide range of SNR and for both white matter and gray matter tissues. For SNR = 100, this protocol resulted in errors of less than 1% in mean F values for B 1 errors ranging between −10 and 20%, the range of B 1 values typically observed in vivo in the human head at field strengths of 3 T and less. Both CRLB‐optimized protocols resulted in the lowest σ F values for all SNRs and did not increase in the presence of B 1 inaccuracies. Conclusion This work demonstrates a regularized optimization approach for improving the robustness of auxiliary measurements (e.g., B 1 ) sensitivity of qMT parameters, particularly the pool‐size ratio ( F ). Predicting substantially less B 1 sensitivity using protocols optimized with this method, B 1 mapping could even be omitted for qMT studies primarily interested in F .