Simultaneous T₁, T₂, and T_1ρ Relaxation Mapping of the Lower Leg Muscle with MR-Fingerprinting (MRF)

Abstract

Purpose

To develop a novel MR-fingerprinting pulse sequence that is insensitive to B₁⁺ and B₀ imperfections for simultaneous T₁, T_2, and T_1ρ relaxation mapping.

Methods

We implemented a totally-balanced-spin-lock (TB-SL) module to encode T_1ρ relaxation into an existing MRF framework that encoded T₁ and T₂. The spin-lock module utilized two 180° pulses with compensatory phases to reduce T_1ρ sensitivity to B₁ and B₀ inhomogeneities. We compared T_1ρ measured using TB-SL MRF in Bloch simulations, model agar phantoms, and in-vivo experiments to those with a self-compensated spin-lock preparation module (SC-SL). TB-SL MRF repeatability was evaluated in maps acquired in the lower leg skeletal muscle of 12 diabetic peripheral neuropathy patients scanned two times each during visits separated by ~30 days.

Results

The phantom relaxation times measured with TB-SL and SC-SL MRF were in good agreement with reference values in regions with low B₁ inhomogeneities. Compared to SC-SL, TB-SL MRF showed in experiments greater robustness against severe B₁ inhomogeneities and in Bloch simulations greater robustness against B₁ and B₀. We measured with TB-SL MRF average of T₁=950.1±28.7ms, T₂=26.0±1.2ms, and T_1ρ=31.7±3.2ms in skeletal muscle across patients. Bland-Altman analysis demonstrated low bias between TB-SL and SC-SL MRF and between TB-SL MRF maps acquired in two visits. The coefficient of variation was less than 3% for all measurements.

Conclusion

The proposed TB-SL MRF sequence is fast and insensitive to B₁⁺ and B₀ imperfections. It can simultaneously map T₁, T₂, T_1ρ, and B₁⁺ in a single scan and could potentially be used to study muscle composition.

INTRODUCTION

Recent advancements in quantitative MRI have significantly expanded the potential to evaluate pathologic changes in muscle disorders, including composition, architecture, mechanical properties, perfusion, and function (1–5). Semi-quantitative methods can assess and grade the extension of compositional changes such as fatty degeneration (1). Moreover, has been shown that T₁ relaxation significantly decreased with fat infiltration and increased with edema (1,6,7). T₂ relaxation is sensitive to water binding (1, 8–10), enabling the detection of early pathologic changes in muscle integrity before deterioration (1). In subsequent pathologic stages, T₂ increases with free water content, fat infiltration, and edema (11).

Moreover, a small number of studies showed that both T₁ and T₂ relaxations changed after exercise (9,12,13). In addition to T₁ and T₂, the spin-lattice relaxation time in the rotating frame, T_1ρ, is shown to capture biochemical changes (14–17). Virta et al. (15) showed that T_1ρ is more sensitive to muscle composition than T₁. The sensitivity of T_1ρ to the change in muscle composition and accumulation of fibrotic tissue due to aging was shown by Wang et al. (16), while Lamminen et al. (17) showed that T_1ρ relaxation time is significantly different between healthy and diseased muscle tissue.

Conventional quantitative MRI approaches can be time-consuming and generally provide only a single parameter at a time. Given the diverse physiologic information represented by T₁, T₂, and T_1ρ, it is desirable to develop a technique to measure these parameters simultaneously. Magnetic resonance fingerprinting (MRF) is a newly developed method (18) to measure multiple MR parameters using dynamic signal patterns simultaneously.

MRF has demonstrated improved scan efficiency in several applications, including the knee (19), prostate (20), hip (21), abdomen (22,23), brain (24,25), liver (26), kidney (27), and heart (28). While most MRF implementations included the capability to measure only T₁ and T₂ (21), our group integrated an additional self-compensated spin-lock preparation module to encode T_1ρ as well, which is particularly interesting in musculoskeletal applications. One drawback of this method was its sensitivity to B₁⁺ and B₀ imperfections that can confound T_1ρ measurements. In this work, we implemented a totally balanced spin-lock module to improve robustness. To demonstrate proof-of-concept, we show results in phantom and in lower extremity skeletal muscle in a cohort of patients with diabetic peripheral neuropathy (DPN) - such patients are expected to have significant skeletal muscle deficits, including loss of strength, power, and endurance, and neurogenic muscle atrophy (29–32).

METHODS

MRF-Sequence Design

Based on the method described in (21), we developed an MRF-sequence to estimate T_1, T_2, and T_1ρ in less than 5 minutes. Similar to a previous design (21), the proposed MRF-sequence started with an adiabatic inversion pulse followed by two fast imaging with steady-state precession (FISP) segments to mainly encode T₁/T₂, and two fast low-angle shot (FLASH) segments, which encode T₁ and B₁⁺. Each segment contains 250 radiofrequency (RF) excitations, with a time-bandwidth product of three and a flip angle that varies from 0° to 60° in the FISP and from 0° to 20° in the FLASH segments, followed by a single radial readout whose rotation is incremented between excitations by the golden angle (33). The flip angles change in a sinusoidal fashion to smoothly vary the transient state of the magnetization. There was a delay equal to 50 repetition times (TRs) between segments to allow partial recovery of the magnetization and to enhance T₁ encoding. Finally, spin-lock preparation modules with different spin-lock duration, including t_sl = 2, 3.75, 7, 13, 24, 45ms, were added at the end of the train to encode T_1ρ. Each of the preparation modules was followed by a FLASH segment with 125-RF excitations with a peak flip angle of 20°. The complete train of 1750 excitations constitutes one shot. We acquired four shots per slice, uniformly distributed within k-space (21).

The T_1ρ preparation module starts with a 90° RF pulse along the x-axis (90_x) to flip the magnetization to the transverse plane. Afterward, a continuous spin-lock pulse was applied along the y-axis (α_y) to lock the transverse magnetization. The magnetization will decay during the lock time (T_sl) according to T_1ρ relaxation time. Applying a second tip-up 90° RF pulse in the opposite direction of the first (90_-x) will tip the magnetization back to the longitudinal direction. Crusher gradients were then applied to destroy the remaining magnetization in the transverse plane before readout. In practice, the actual spin-lock field strength and direction is affected by field inhomogeneities dictated by factors such as the excitation coil and tissue properties (34). In our application to study muscle composition, we used an in-house built 8-channel lower extremity coil (35) comprised of degenerate mode transmit/receive birdcages, which have characteristic inhomogeneous B₁⁺ in the periphery that can affect T_1ρ encoding without proper compensation.

The B₁⁺ inhomogeneity causes a deviation of the magnetization from the transverse plane after applying the tip-down 90° pulse. As a result, the magnetization rotates with an angle (α) around the spin-lock RF pulse during T_sl, and the final longitudinal magnetizations become a complicated function of T_sl:

$$M(T_{sl})=M_0[\mathrm{s}\mathrm{i}\mathrm{n}(\theta )e^{-\frac{T_{sl}}{T_{1\rho }}}+\cos (\alpha )\cos (\theta )e^{-\frac{T_{sl}}{T_{2\rho }}}]$$ [1]

Where θ is the actual flip angle of the tip-up and tip-down RF pulses, α is the flip angle of the spin-lock pulse, and T_2ρ is the relaxation time in the plane orthogonal to the spin-lock pulse. The cos(α) term causes the spatial signal modulation, which appears as banding artifacts in the acquired scans (36). Several papers (37,38) showed that the net α angle becomes zero using the rotary spin-lock pulse, and the effect of B₁⁺ inhomogeneity will be eliminated. The B₀ inhomogeneity can be compensated by inserting a 180° pulse (39). Mitrea et al. (37) further improved this approach by replacing the two spin-lock pulses with rotary self-compensated pairs. However, our experiments showed that this technique is still sensitive to the severe B₁⁺ field inhomogeneities, such as found in our application. Hence, in this work, we applied a totally balanced T_1ρ preparation module (TB-SL), in which the single 180° pulse was replaced with two rotary 180° pulses. Hence, every pulse is compensated with a correspondent pulse of the opposite phase (40). We compared our proposed MRF sequence with prior work described in (19), which uses Mitrea’s (37) self-compensated spin-lock preparation modules (SC-SL).

Model Phantoms Study

A model phantom consisting of 3%, 4%, and 8% agarose gels were scanned on a 3T MRI scanner (MAGNETOM Prisma, Siemens Healthcare GmbH, Germany) with the in-house built 8-channel lower extremity coil using both TB-SL and SC-SL MRF sequences. The imaging parameters were FOV=140×140mm², 0.7×0.7mm² in-plane resolution, 4.0mm slice thickness, TE/TR=3.5/7.5ms, BW=420Hz/pixel, number of slices= 4, number of shots= 4, spin-lock power f_sl= 500Hz. The acquisition time was 4:44 min. The slices were acquired in a combination of sequential/interleaved fashion where two slices were interleaved at a time. There was no delay between each shot. The signal from each shot was averaged together to improve the signal to noise ratio. Moreover, the radial angle changes for each shot to reduce the undersampling artifacts. The model agar phantoms were also scanned with the MRF sequence proposed by Cloos et al. (21) for T₁ and T₂ comparisons and a customized turbo FLASH sequence (41) for T_1ρ comparison.

In vivo Study

Our Institutional Review Board approved this Health Insurance Portability and Accountability Act study, and 12 participants diagnosed with DPN were scanned after obtaining their informed consent. The patients (age =57.5±6.4 years, 10 male, 2 female) were scanned two times each, with 31.4±10.4 days (range=21 to 60 days) between scans. Three healthy volunteers (age=30.6± 6.3 years, 1 male, 2 female) were also scanned with TB-SL and SC-SL MRF sequences in one session for comparison. The foot was enclosed in an MR compatible ergometer (56), and extensive foam padding between the calf and coil was used to reduce the motion. Four axial MRF images of the calf muscle were acquired with FOV=140×140mm², 0.6×0.6mm² in-plane resolution, 4.0 mm slice thickness, 224×224 matrix size, TE/TR=3.5/7.5ms, BW=420 Hz/pixel, number of shots=4, spin-lock power f_sl=500Hz. The acquisition time was 4:45min.

MRF-Dictionary Construction for Multiparametric Mapping

All algorithms were implemented in MATLAB (R2019a, The MathWorks Inc., Natick, MA, USA). A dictionary of simulated MR fingerprints for possible T_1, T_2, T_1ρ, and B₁⁺ values was computed based on the extended phase graphs (42). The longitudinal magnetization following the T_1ρ preparation module was simulated to undergo mono-exponential decay since the crusher gradients after the tip-up 90° pulse were assumed to destroy any remnant transverse magnetizations (19). Moreover, the effects of field inhomogeneities (B₀ and B₁) were not simulated in the dictionary.

The simulation was performed for T₁:50–3000 ms, T₂: 2–200ms, and T_1ρ 2–200ms. The maximum excitation flip angle varied between 30° and 90° with 5% increments to simulate ±50% B₁⁺ variations (target flip angle 60°). Afterward, the dictionary and the measured fingerprint signal were compressed using the singular value decomposition (SVD) method (22,43) and matched with each other using an iterative approach (43) to create a PD image and T₁, T₂, T_1ρ, and B₁⁺ maps, simultaneously.

Statistical Analysis

The mean and standard deviation for T_1, T_2, and T_1ρ relaxation times were measured in agarose gel model phantoms and in the lower leg of DPN patients, in which we manually segmented the tibialis anterior (TA), soleus (SOL), gastrocnemius medialis (GM), and gastrocnemius lateralis (GL) muscles.

The Bland-Altman analysis was performed to assess the repeatability in the model phantoms and DPN patients. Moreover, the mean and standard deviation (SD) of each parameter was calculated for each subject across the test-retest scan, and the coefficient of variation (CV) was calculated as CV = SD/Mean to assess intra-subject repeatability.

The inter-subject repeatability was evaluated using the root mean square CV:

$$\mathrm{r}\mathrm{m}\mathrm{s}\mathrm{C}\mathrm{V}=\sqrt{\frac{\sum _{i=1}^n{\mathrm{C}\mathrm{V}}_i^2}{n}}$$ [2]

Where CV_i is the CV of an individual subject, and n (=12) is the total number of subjects.

RESULTS

The simulation results based on Bloch equations (Supplementary Figure 1) showed both TB-SL and SC-SL preparation modules provide high T_1ρ accuracy when B₁ and B₀ are well matched to the expected values. However, TB-SL provides greater T_1ρ accuracy than SC-SL when B₁ is lower than expected, and B₀ is offset from the center frequency. This is in agreement with our experimental results, in which the TB-SL module provided reliable T_1ρ in peripheral regions in model agar phantoms and in-vivo in which B₁⁺ was lower than expected.

Figure 1 shows improved B₁⁺ robustness of the TB-SL spin-lock module compared to the SC-SL module in model agar gel phantoms. Specifically, T_1ρ maps acquired with the TB-SL MRF sequence are largely immune to B₁⁺ heterogeneity in the peripheries, whereas artifacts are present in maps acquired with the SC-SL MRF sequence.

Figure 1.

Comparison of the SC-SL (top row) and TB-SL (bottom row) preparation modules in phantoms consisting of 3%, 4%, and 8% agarose gel. As shown by arrows, the SC-SL T_1ρ map (fourth column) contains artifacts due to B₁⁺ inhomogeneities (last column), while the artifacts are significantly reduced with the TB-SL module.

An average (Mean ± SD) of T₁, T₂, and T_1ρ were measured in 3%, 4%, and 8% agar phantoms using the proposed TB-SL MRF technique. As shown in Table 1, the relaxation times are inversely related to agar concentration. The same trend was observed with SC-SL MRF and the reference techniques. Both TB-SL and SC-SL MRF techniques underestimated the T₁ values compared to the reference values, which could be due to neglecting the magnetization transfer effect in the dictionary (48).

Table 1.

Phantom relaxation times measurements (Mean ± SD) using MRF sequence with TB and SC-SL preparation modules and comparison with conventional T₁ (IR-SE), T₂(SE), and T_1ρ (T1ρTFL(65)) measurements.

	MRF-TBSL			MRF-SCSL			Conventional
	T1 (ms)	T2(ms)	T1ρ(ms)	T1 (ms)	T2(ms)	T1ρ(ms)	T1 (ms)	T2(ms)	T1ρ(ms)
AGAR 3%	1516.6 ± 164.6	42.0 ± 11.7	47.8 ± 10.2	1429.5 ± 141.2	46.1 ± 12.1	40.0 ± 12.1	1683.2 ± 54.1	46.1 ± 3.8	45.7 ± 1.4
AGAR 4%	1002.0 ± 125.8	26.6 ± 2.1	25.5 ± 2.8	977.8 ± 115.3	28.3 ± 2.6	24.5 ± 5.5	1656.3 ± 233.5	28.0 ± 2.7	23.2 ± 0.6
AGAR 8%	766.3 ± 44	15.9 ± 4.1	14.2 ± 2.6	746.1 ± 44.5	17.0 ± 4.0	11.1 ± 3.5	987.6 ± 64.2	17.8 ± 2.0	17.1 ± 0.4

Figure 2 shows the comparison between SC-SL and TB-SL modules in the in-vivo experiment and representative examples of the acquired signals and their respective dictionary matches in positions with low and high (periphery) B₁⁺ inhomogeneities. In sequence with the SC-SL preparation module, the higher B₁⁺ inhomogeneities caused a faster drop in the signal, which leads to a severe underestimation of T_1ρ. We measured an average of T₁=909.9±43.4, and 898.4±37.9ms, T₂ =22.1±1.6, and 21.7±1.7ms, and T_1ρ = 27.11±3.1, and 26.1±2.4ms across three healthy volunteers using TB-SL and SC-SL technique, respectively.

Figure 2.

In-vivo comparison of the (a) SC-SL and (b) TB-SL preparation modules in the presence of B₁⁺inhomogeneities. As shown by arrows, the T_1ρ is affected using the SC-SL module, while the TB-SL-MRF sequence is robust against the inhomogeneities. (c, d) a representative example of the acquired signals using two sequences and their respective dictionary match in a position with (c) low and (d) high B₁⁺ inhomogeneities. In sequence with the SC-SL preparation module, the higher inhomogeneities caused a faster drop in the signal, which leads to a smaller T_1ρ value.

The regression and Bland-Altman plots (Figure 3) show excellent agreement between T₁, T₂, and T_1ρ measured with SC-SL and TB-SL MRF in the part of the gastrocnemius medialis, gastrocnemius lateral, and soleus ROIs that were not affected by B₁⁺ inhomogeneities. In the parts with high inhomogeneities, there is a drop in the estimated T_1ρ, which leads to a lower overall mean value in the ROIs.

Figure 3.

Regression (top row) and Bland-Altman plots (bottom row) to assess the differences in T₁, T₂, and T_1ρ measured using SC-SL and the proposed TB-SL MRF sequence. There is a good agreement between the measured relaxation times from the two experiments.

Figure 4a demonstrates representative T₁, T₂, T_1ρ, and B₁⁺ maps in the lower leg of a DPN patient acquired in two separate visits. In gastrocnemius medialis, gastrocnemius lateral and soleus muscles, we measured an average of T₁ = 950.1±28.7 ms, T₂ =26.0±1.2 ms, and T_1ρ = 31.7±3.2 across 12 DPN patients. Analysis of the Bland-Altman plots (Figure 4b) demonstrated an average difference of −6.40ms, −0.23ms, and 0.69ms between two visits for T₁, T₂, and T_1ρ, respectively. Our in vivo study showed excellent repeatability (Figure 4c) with rmsCV smaller than 3% across all ROIs for T₁, T₂, and T_1ρ.

Figure 4.

(a) Representative PD, T₁, T₂, and T_1ρ and B₁⁺ maps of the calf muscle of a DPN patient acquired in two sessions one month apart. (B) Bland-Altman plots and (c) coefficient of variation in different muscle groups for T₁, T₂, and T_1ρ measured during visits 1 (V1) and 2 (V2). The experiment showed low rmsCV (<3%) for all relaxation parameters in all ROIs.

DISCUSSION

In this work, we implemented an MRF sequence that showed the feasibility of rapid simultaneous acquisition of accurate PD image and T₁, T₂, B₁^+, and T_1ρ maps of the skeletal muscle. The proposed TB-SL MRF method is fast, reproducible, and less sensitive to field inhomogeneities than SC-SL MRF. By integrating the T_1ρ module into the MRF framework, we measured voxel-wise the three different relaxation times that may provide more comprehensive insight on skeletal muscle properties than T₁ and T₂ alone (22). The simultaneous acquisition eliminates potential misregistration due to motion between separate measurements, which can plague traditional standalone methods that may require approximately 45 minutes to separately acquire T₁, T₂, and T_1ρ maps (41). In comparison, we used TB-SL MRF to measure T₁, T₂, and T_1ρ in four slices in the lower extremity with 0.6×0.6×4.0 mm³ resolution in 4:45 min (1:11 min per slice).

Recently, Wyatt et al. (49) proposed a spiral MRF technique with variable flip angles and TRs for simultaneous mapping of T₁, T_2, and T_1ρ. They used the Dixon module with a rotary spin-lock pulse, which is not robust to B₀ inhomogeneities. Similar to our work, B₁ variation was not considered in the T_1ρ preparation module Bloch simulation. However, their use of rotary spin-lock and phase cycling made their sequence robust to B₁ variations up to ±30% (49). We proposed using a balanced module with a rotary spin-lock pulse for B₁⁺ compensation and 180° refocusing pulses to compensate for B₀ inhomogeneities. Our in-vivo results showed the robustness of this technique. We were able to obtain good results, even in the sample periphery, where inhomogeneities of up to ±50% were observed. Several works proposed using adiabatic pulses for spin-locking due to their insensitivity to field inhomogeneities (50–52). In contrast to conventional continuous pulses, the measured T_1ρ value depends on the type of adiabatic pulse and its frequency modulation and amplitude. Moreover, T_1ρ alters during the application of adiabatic spin-locking due to the frequency and amplitude modulation. Hence, the measured T_1ρ is an average of its value over the adiabatic pulse duration (36). The SAR constraint also limited the use of adiabatic pulses. Recently, Ma et al. (53) proposed a 3D adiabatic T_1ρ prepared ultrashort echo time technique for knee imaging. The proposed technique has lower power than continuous spin-lock pulses; however, the sequence was ~18 minutes long, limiting its use in clinical applications (53). Other studies (54,55) proposed using a constant amplitude adiabatic tip-down and tip-up pulses that simultaneously compensated for B₁ and B₀ inhomogeneities. In comparison with the hard pulse, the adiabatic pulse is more robust to the field inhomogeneities. However, since the spins are locked in a tilted angle instead of the transverse plane, the measured T_1ρ value is different from the value measure on resonance, and the on resonance T_1ρ must calculated retrospectively from the tilted angle value (54).

We used a radial readout. Compared to spiral readouts, radial trajectories are less sensitive to systematic imperfections, such as eddy current and B₀ inhomogeneities (56). On the other hand, the radial pattern is less efficient in sampling the k-space and requires temporal averaging or multiple MRF train repetition (56). Block et al. (57) proposed an adaptive compensation of gradient delay where the shift in the k-space caused by the delay is estimated from a set of calibration spokes with opposite orientation. The shift is then adjusted in the k-space according to echo-pixel shifts in the gridding step (57,58). We have developed routines to calibrate out these delays in the past. However, the latest generation of scanners such as the one used here demonstrated negligible shifts for the dwell times used in this work.

Several limitations potentially affect our study. The acquisition was highly undersampled, and as a result, streaking artifacts are visible in some maps, such as T₂ maps. Although the 2D TB-SL MRF total scan time is short (~5 minutes) in comparison to separate acquisition of T₁, T₂, and T_1ρ maps, its lack of coverage (4 slices) makes volumetric measurement infeasible. One promising possibility to shorten scan time and improve coverage is to utilize a 3D-sequence with stack-of stars readout (59–62). Moreover, online reconstruction is not possible due to the computationally expensive and memory inefficient dictionary matching method used in this work. We are currently optimizing the MRF sequence (e.g., flip angle train and optimal T_sl’s, etc.) based on Crammer-Rao Lower Bound (CRLB) (63) and deep learning-based reconstruction (64) instead of template matching to alleviate the problem.

Conclusion

In this work, we implemented an MRF-sequence and showed the feasibility of rapid simultaneous acquisition of accurate PD image and T₁, T₂, and T_1ρ maps of the lower leg muscle, yielding valuable information about musculoskeletal complications. The proposed MRF method is fast, robust to B₀ and B₁ inhomogeneity, and repeatable, making it a candidate to assess muscle composition in pathology.

Supplementary Material

FIG S1

Supplementary Figure 1. The error of estimating T_1ρ from Bloch simulation for SC-SL (a,c) and (b,d) TB-SL module in the presence of high and low field inhomogeneities. The estimation error is smaller using the TB-SL module.