Parameter map error due to normal noise and aliasing artifacts in MR fingerprinting

Abstract

Purpose To introduce a quantitative tool that enables rapid forecasting of T1 and T2 parameter map errors due to normal and aliasing noise as a function of the MR fingerprinting (MRF) sequence, which can be used in sequence optimization. Theory and Methods The variances of normal noise and aliasing artifacts in the collected signal are related to the variances in T1 and T2 maps through derived quality factors. This analytical result is tested against the results of a Monte‐Carlo approach for analyzing MRF sequence encoding capability in the presence of aliasing noise, and verified with phantom experiments at 3 T. To further show the utility of our approach, our quality factors are used to find efficient MRF sequences for fewer repetitions. Results Experimental results verify the ability of our quality factors to rapidly assess the efficiency of an MRF sequence in the presence of both normal and aliasing noise. Quality factor assessment of MRF sequences is in agreement with the results of a Monte‐Carlo approach. Analysis of MRF parameter map errors from phantom experiments is consistent with the derived quality factors, with T1 (T2) data yielding goodness of fit R2 ≥ 0.92 (0.80). In phantom and in vivo experiments, the efficient pulse sequence, determined through quality factor maximization, led to comparable or improved accuracy and precision relative to a longer sequence, demonstrating quality factor utility in MRF sequence design. Conclusion The here introduced quality factor framework allows for rapid analysis and optimization of MRF sequence design through T1 and T2 error forecasting.

Flexible and efficient optimization of quantitative sequences using automatic differentiation of Bloch simulations

“…Additional characterizations of the bias of the CRLB optimized sequence are provided in Supporting Information Figures S8 and S9. The presence of a bias between different schedules is in line with other works performing pattern matching after changing the flip angle, TR or TE schedules …”

“…Zhao et al selected flip angles and TRs to minimize the CRLB of the MRF IR‐FISP sequence calculated using analytical differentiation. Kara et al selected flip angles to maximize a quality factor dependent on the variance of the and estimates. Assländer et al minimized the CRLB of a balanced pseudo steady‐state free precession (pSSFP) MRF sequence over the flip angles.…”

Magnetic resonance fingerprinting review part 2: Technique and directions

“…In Optimized I, upper and lower bounds are placed on FA and TR, whereas in in Optimized II, changes in neighboring FA values are additionally constrained. In (c) is the FA pattern from Kara et al, which is calculated using the genetic algorithm to optimize T 1 and T 2 quality factors. The FA and TR patterns used in MRF‐FISP are shown in (d) .…”

“…Figures reprinted with permission. 49,52,53 for the relaxation values estimated with DESPOT. 11,51 A rigorous derivation of a cost function to characterize the signal to noise ratio (SNR) efficiency of the MRF sequence is presented in Zhao et al, 52 using the Cramér-Rao lower bound.…”

“…The calculated FA patterns are considerably different from the sinusoidal FA pattern. 5 In Kara et al, 53 a cost function and optimization metric are derived in terms of a quality factor for each tissue property in MRF-FISP. The quality factors relate the variance from noise and aliasing artifacts to the variance of the computed tissue properties.…”