Validation of single reference variable flip angle (SR-VFA) dynamic T1 mapping with T2 * correction using a novel rotating phantom

PURPOSE

To validate single reference variable flip angle (SR-VFA) dynamic T1 mapping with and without T2 * correction against inversion recovery (IR) T1 measurements.

METHODS

A custom cylindrical phantom with three concentric compartments was filled with variably doped agar to produce a smooth spatial gradient of the T1 relaxation rate as a function of angle across each compartment. IR T1 , VFA T1 , and B1 + measurements were made on the phantom before rotation, and multi-echo stack-of-radial dynamic images were acquired during rotation via an MRI-compatible motor. B1 + -corrected SR-VFA and SR-VFA-T2 * T1 maps were computed from the sliding window reconstructed images and compared against rotationally registered IR and VFA T1 maps to determine the percentage error.

RESULTS

Both VFA and SR-VFA-T2 * T1 maps fell within 10% of IR T1 measurements for a low rotational speed, with a mean accuracy of 2.3% ± 2.6% and 2.8% ± 2.6%, respectively. Increasing rotational speed was found to decrease the accuracy due to increasing temporal smoothing over ranges where the T1 change had a nonconstant slope. SR-VFA T1 mapping was found to have similar accuracy as the SR-VFA-T2 * and VFA methods at low TEs (˜<2 ms), whereas accuracy degraded strongly with later TEs. T2 * correction of the SR-VFA T1 maps was found to consistently improve accuracy and precision, especially at later TEs.

CONCLUSION

SR-VFA-T2 * dynamic T1 mapping was found to be accurate against reference IR T1 measurements within 10% in an agar phantom. Further validation is needed in mixed fat-water phantoms and in vivo.

Effects of T2 * on accuracy and precision of dynamic T1 measurements using the single reference variable flip angle method - a simulation study

PURPOSE

To study in simulation and in theory the accuracy and precision of dynamic T₁ measurements obtained using the previously published single-reference variable flip angle (SR-VFA) technique, with a focus on the effects of dynamic changes in T₂ * on the calculation.

METHODS

Monte Carlo simulations were performed over 1000 noisy iterations for the VFA method, the SR-VFA method, and a proposed method, SR-VFA with a T₂ * correction (SR-VFA-T₂ *). Dynamic T₁ estimates were calculated analytically for each method, with signals modeled by the steady-state spoiled gradient echo equation. The mean and standard deviation of these estimates were calculated and compared to truth, while varying repetition time (TR), baseline and dynamic T₁ , echo time (TE), baseline and dynamic T₂ *, flip angles, and the number of averages on baseline scans. Additionally, the variance of T₁ in the SR-VFA and SR-VFA-T₂ * methods was derived analytically based on the theory of propagation of errors. This equation was used to produce an inverse-variance weighted linear combination to improve T₁ mapping precision in the SR-VFA-T₂ * method. Flip angle sensitivity of dynamic T₁ precision in the SR-VFA and SR-VFA-T₂ * methods was also performed.

RESULTS

Substantial bias can be produced by the SR-VFA method when the ratio of the T₂ * decay of the dynamic signal versus that of the baseline signals deviates from 1, with a 0.01 deviation leading to approximately a 1% bias in cases of high SNR and TR ≫ T₁ . This bias can be corrected by estimating the baseline and dynamic T₂ * values in this ratio via multi-echo measurements. The bias and precision of the SR-VFA-T₂ * method, when normalized to scan time, is found to rival and sometimes improve upon the two flip angle VFA method when an inverse variance weighted linear combination is applied across its multi-echo T₁ maps. The analytic variance equation presented is found to be accurate within 1% relative to the Monte Carlo simulations over a broad parameter space. Flip angle ranges that maximize SR-VFA and SR-VFA-T₂ * T₁ precision over a broad parameter space are given, and each is defined relative to TR and T₁ .

CONCLUSIONS

Multi-echo SR-VFA-T₂ * T₁ mapping is found in simulation and theory to be a promising alternative to the VFA method that maintains speed of the SR-VFA method with accuracy and precision similar to the VFA method. This article is protected by copyright. All rights reserved.