Introduction

T_1ρ relaxation time is a tissue property that can be probed in order to assess tissue composition, e.g. glycosaminoglycan content in cartilage and fiber type proportion in skeletal muscle¹. T_1ρ characterizes longitudinal relaxation during the application of a “spin-locking” radiofrequency excitation magnetic (B₁) pulse². T_1ρ is influenced by interactions of large biomolecules and water and is dependent on the spin-lock frequency (FSL) of the applied B₁ field. T_1ρ dispersion across FSL values is an additional magnetic property beyond single-frequency T_1ρ that is sensitive to chemical exchange and diffusion or diffusive exchange³.
T_1ρ relaxation can be quantified via multiple spin-lock magnetization preparation pulses at a given FSL with varied spin-lock times (TSL) to acquire T_1ρ-weighted images. Typically, curve-fitting of T_1ρ-weighted images is performed using an exponential decay equation². By quantifying T_1ρ at multiple FSL values, the T_1ρ dispersion of a tissue can be characterized. However, this approach can be prohibitively time consuming as it requires multiple scans at different FSL and can also require prohibitively high energy deposition rates at relatively high FSL values.
MR Fingerprinting (MRF) is a flexible, rapid imaging technique that can allow simultaneous quantification of multiple tissue properties⁴. In this work, we demonstrate the use of MRF for T_1ρ dispersion characterization in simulation and physical phantom.

Methods

The T_1ρ dispersion MRF method in this work is based on a previously reported T_1ρ-MRF sequence⁵. Whereas the previous T_1ρ-MRF sequence used spin-lock preparations at a single, fixed FSL, this method used variable FSL. TSL values were fixed to 40 ms for each spin-lock pulse. Variable flip angle, fixed repetition time, and fixed echo time were used. Spatial encoding used a Cartesian spiral undersampling pattern⁶.
A model of T_1ρ dispersive effects across FSL was used as part of dictionary generation, given by³
$$T_{1\rho}(\omega)=\frac{(q^2D)^2+\omega^2}{\gamma^2g^2D}=T_2+a^2\omega^2$$
which relates T_1ρ, FSL ($$$\omega$$$), Hydrogen gyromagnetic ratio ($$$\gamma$$$), self-diffusion coefficient ($$$D$$$), spatial frequency of local magnetic field variation ($$$q$$$), and related mean gradient strength ($$$g$$$)³. The quantities $$$g^2D$$$ and $$$q^2D$$$ are related to T₂ by $$$T_2=\frac{(q^2D)^2}{\gamma^2g^2D}$$$ and $$$a^2=\frac{1}{\gamma^2g^2D}$$$. Note that at FSL=0, T_1ρ=T₂. The dictionary is generated containing three parameters that characterize the relevant magnetic characteristics, namely: $$$T_1$$$, $$$T_2$$$, and $$$a$$$. After acquisition of T_1ρ dispersion MRF data, a 3D spatial total variation-regularized, temporal low rank reconstruction was employed to suppress noise and undersampling artifacts and obtain tissue property maps.
A digital cylindrical phantom with known ground truth T₁, T₂, and T_1ρ dispersion values was used for in silico implementation of the T_1ρ dispersion MRF sequence. A 500 frame MRF sequence was used with acceleration factor R=60 and matrix size 192x192x16.
An agarose gel phantom with glucose addition was used to assess T_1ρ dispersion using T_1ρ dispersion MRF as compared to a reference method. The scanner was a Prisma 3T (Siemens Healthineers) and a 15-channel Tx/Rx knee coil was used. The reference method used MAPSS at matrix size 192x192x16 with T_1ρ quantification at FSL=50, 100, 200, and 500 Hz. Four echoes were acquired for each FSL, with TSL=0, 10, 30, 70 ms. The total scan time was 10 min. The aforementioned T_1ρ dispersion model was fitted to MAPSS T_1ρ values for comparison with MRF. T_1ρ dispersion MRF used the same sequence settings as in simulation but with matrix size 96x96x16 and a 2.5 minute scan time.

Results

Simulation results (Figures 1-3) show strong agreement between MRF and the ground truth reference values for T₁, T₂, and T_1ρ dispersion ($$$a$$$). Phantom results (Figures 4-5) show similar trends as compared to the reference method, MAPSS, for T₂ and T_1ρ dispersion. Greater errors were observed at the high dispersion values for both simulation and physical phantom.

Discussion

The feasibility of direct characterization of T_1ρ dispersion by MRF was demonstrated. In simulation, strong agreement between ground truth and MRF estimated parameters was observed, however errors were greater for high T_1ρ dispersion values. In phantom, generally good agreement between T_1ρ dispersion maps derived from conventional T_1ρ mapping and T_1ρ dispersion MRF was observed, but with the highest dispersion values showing substantial errors for MRF, suggesting that sequence optimization would be needed depending on the range of values under investigation. T_1ρ dispersion MRF may significantly reduce the required acquisition time as compared to conventional T_1ρ dispersion collection at different spin-lock frequencies, and has the benefit of providing T₁ and T₂ maps in addition to T_1ρ dispersion model parameters. The MRF T_1ρ dispersion method will also enable reductions in radiofrequency pulse energy deposition or amplifier requirements as compared to conventional T_1ρ dispersion acquisition methods. Thus, MRF may enable T_1ρ dispersion characterization for a broader range of applications and system hardware. Dictionary size requirements pose memory and computational challenges given the wide range of T₁, T₂, and T_1ρ dispersion values anticipated in practice. Deep learning-based dictionary generation⁷ and randomized SVD compression⁸ may address such dictionary related challenges. Further evaluation, including in vivo study and refinement of sequence and reconstruction parameters, is needed.

Conclusion

A novel method for T_1ρ dispersion characterization based on MR Fingerprinting was developed and feasibility was demonstrated in simulation and phantom. T_1ρ dispersion MRF enables simultaneous quantification of T₁, T₂, and T_1ρ dispersion as well as retrospective generation of T_1ρ maps at any spin-lock frequency.

References

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