Sensitivity regularization of the Cramér-Rao lower bound to minimize B1 nonuniformity effects in quantitative magnetization transfer imaging

Abstract

Purpose: To develop and validate a regularization approach of optimizing B₁ insensitivity of the quantitative magnetization transfer (qMT) pool-size ratio (F).

Methods: An expression describing the impact of B₁ inaccuracies on qMT fitting parameters was derived using a sensitivity analysis. To simultaneously optimize for robustness against noise and B₁ inaccuracies, the optimization condition was defined as the Cramér-Rao lower bound (CRLB) regularized by the B₁ -sensitivity expression for the parameter of interest (F). The qMT protocols were iteratively optimized from an initial search space, with and without B₁ regularization. Three 10-point qMT protocols (Uniform, CRLB, CRLB+B₁ regularization) were compared using Monte Carlo simulations for a wide range of conditions (e.g., SNR, B₁ inaccuracies, tissues).

Results: The B₁ -regularized CRLB optimization protocol resulted in the best robustness of F against B₁ 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 B₁ errors ranging between -10 and 20%, the range of B₁ 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 B₁ inaccuracies.

Conclusion: This work demonstrates a regularized optimization approach for improving the robustness of auxiliary measurements (e.g., B₁ ) sensitivity of qMT parameters, particularly the pool-size ratio (F). Predicting substantially less B₁ sensitivity using protocols optimized with this method, B₁ mapping could even be omitted for qMT studies primarily interested in F.