MR fingerprinting for rapid simultaneous T₁, T₂, and T _{1 ρ} relaxation mapping of the human articular cartilage at 3T

Abstract

Purpose

To implement a novel technique for simultaneous, quantitative multiparametric mapping of the knee articular cartilage.

Methods

A novel MR fingerprinting pulse sequence is proposed and implemented for simultaneous measurements of proton density, T₁, T_2, and T _{1 ρ} relaxation times at 3T. The repeatability and reproducibility of the proposed technique were assessed in model phantoms. Institutional review board‐approved MR fingerprinting imaging sequence was performed on healthy volunteers and patients with mild knee osteoarthritis. The Wilcoxon test was used to compare healthy controls and patients. The intra‐ and intersubject repeatability were assessed with coefficient of variation and the RMS coefficient of variation, respectively

Results

The Bland‐Altman plots demonstrated an average difference of 4.67 ms, −0.09 ms, and 0.05 ms between 2 scans in the same scanner; and 9.68 ms, 0.29 ms, and −0.72 ms between the scans acquired on 2 different scanners for T₁, T₂, and T _{1 ρ}, respectively. The in vivo knee study showed excellent repeatability with RMS coefficient of variation less than 3%, 6%, and 5% for T₁, T₂, and T _{1 ρ}, respectively. The Wilcoxon test showed a significant difference between control and mild osteoarthritis patients for T₁ (P = .04), T₂ (P = .01), and T _{1 ρ} (P = .02) relaxation time in medial tibial cartilage, as well as for T₂ relaxation time (P = .02) in medial femoral cartilage.

Conclusion

The proposed MRF sequence is fast and can simultaneously measure the T₁, T₂, T _{1 ρ}, and ${\mathrm{B}}_1^{+}$ maps in a single scan. It is able to discriminate between mild osteoarthritis patients and healthy volunteers.

1. INTRODUCTION

Osteoarthritis (OA) of the knee, the most common joint disease, ¹ is a degenerative heterogeneous musculoskeletal disease that is mainly recognized by the progressive loss of hyaline articular cartilage. ² Although the standard MRI techniques ³ , ⁴ for imaging cartilage can quantify morphological changes such as cartilage volume and thickness as a result of OA progression, ⁵ , ⁶ they are still insensitive in detecting early‐stage OA. ⁷ On the other hand, quantitative MRI can detect early changes in cartilage biochemical components that occur before the morphological change. More specifically, early‐stage OA is associated with loss of proteoglycans, an increase in water content, and changes in the structure of collagen fibers. ² Yao et al ⁸ showed the sensitivity of T₁ and T₂ relaxation to early‐stage OA, and it has been shown that T₁ mapping can be used to calculate the water content of the cartilage. ⁹ In addition to the longitudinal T₁ ⁸ and transverse T₂ relaxation times, ⁸ the spin‐lattice relaxation in the rotating frame (T _{1 ρ}) can be used to quantify the biochemical changes in cartilage. ² , ⁷ , ¹⁰ , ¹¹ , ¹² Both T _{1 ρ} and T₂ have been consistently reported to be elevated with enzymatic cartilage degradation. ² , ⁷ , ¹⁰ , ¹¹ , ¹² T₂ is sensitive to the collagen fibril orientation and anisotropy, ¹³ , ¹⁴ whereas T _{1 ρ} is found to be sensitive to the slow motional interactions between local macromolecular environments and bulk water, ¹⁵ and as a result, to proteoglycan content in articular cartilage. ¹⁶ Moreover, quantitative evaluation of knee joint pathologies is often dependent not only on a single tissue property but also a combination of properties coregistered and evaluated together.

Conventional quantitative cartilage MRI (e.g. T₁, T₂, and T _{1 ρ}) approaches are relatively slow and sensitive to both noise and ${\mathrm{B}}_1^{+}$ variations. Moreover, they generally provide only a single parameter at a time, therefore necessitating long data acquisition times if all biochemical information is desired.

Magnetic resonance fingerprinting (MRF) is a recently developed technique ¹⁷ that can estimate multiple MR parameters simultaneously (e.g., T₁ and T₂) using dynamic signal patterns. It has improved scan efficiency and robustness for the brain, ¹⁸ , ¹⁹ prostate, ²⁰ abdomen, ²¹ , ²² hip, ²³ and cardiac ²⁴ applications. The MRF framework relies on a deliberate and continuous variation of multiple MR sequence parameters throughout the acquisition to provide unique fingerprint‐like evolutions for different combinations of tissue properties. In addition, incoherent undersampled k‐space data is acquired during this evolution, making the scan time much shorter than traditional quantitative mapping. The undersampling generates uncorrelated artifacts on the signal evolutions that are easily ignored by the dictionary‐matching task, using a dictionary constructed with predicted signal evolutions for different combinations of properties. The tissue property values associated with the best dictionary match are assigned as the measured properties for that voxel.

The main aim of this study is to implement a novel MR fingerprinting sequence for simultaneous T₁, T₂, and T _{1 ρ} relaxation mapping of the human knee joint at 3T. We evaluated the feasibility and performance of our MRF‐sequence on model systems, healthy and early knee OA patients.

2. METHODS

2.1. MRF‐sequence design

We developed an MRF‐sequence based on the method described in Ref. 23 by adding T _{1 ρ} preparation modules to estimate proton density, T₁ and T₂, T _{1 ρ}, and ${\mathrm{B}}_1^{+}$ on 6 slices with 0.6 mm × 0.6 mm × 4 mm voxel resolution in less than 8 min. The proposed MRF‐sequence started with an adiabatic inversion pulse followed by 2 fast imaging with steady‐state precession segments, which predominantly encode T₁/T₂; and 2 fast FLASH segments, which encode T₁ and ${\mathrm{B}}_1^{+}$ (Figure 1). Each segment contains 250 RF excitations with a time‐bandwidth product of 3 followed by a single radial readout. The flip angle (Figure 1) varies in a sinusoidal fashion to smoothly vary the transient state of the magnetization, ranging from 0° to 60° in the first segment and from 0° to 20° in the second segment of both fast imaging with steady‐state precession and FLASH readouts. ²³ The radial rotation was incremented between excitation by the golden angle. ²⁵ There was a delay equal to 50 repetition times between segments for partial recovery of the magnetization and enhancing T₁ encoding. To encode the T _{1 ρ}, N = 6 paired self‐compensated spin‐lock preparation modules ²⁶ with different spin‐lock duration (T_sl = 2.0, 3.7, 6.9, 12.9, 24.1, 45 ms) were added at the end of the train. The most basic T _{1 ρ} 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 magnetization in the transverse plane. The magnetization will decay during the lock time (T_sl) according to T _{1 ρ} relaxation time. Applying a 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 the field inhomogeneities. ²⁷ The paired self‐compensated spin‐lock, ²⁶ which was used in this study, tries to compensate for the ${\mathrm{B}}_1^{+}$ inhomogeneities by altering the phase of the spin‐lock pulse. In this method, the spin‐lock pulse was divided into 4 segments with an alternative phase, and a refocusing pulse is applied in the middle between 2 pairs to compensate for the B₀ inhomogeneities. ²⁷ Each of the preparation modules was followed by a FLASH readout segment consisting of 125 RF excitations, with variable flip angle ranging from 0° to 20° (Figure 1). The complete train of 1750 excitations constitutes 1 shot. We acquired 4 shots per slice, uniformly distributed within k‐space. ²³

FIGURE 1.

MRF sequence timing diagram for multiparametric mapping. The adiabatic inversion pulse is followed by 2 FISP and 2 FLASH segments to encode T₁/T₂ and T₁/ ${\mathrm{B}}_1^{+}$, respectively. Each segment contains 250 RF excitations followed by a single radial readout. There was a delay equal to 50 TR between segments for partial recovery of the magnetization and enhancing T₁ encoding. The train is followed by T _{1 ρ} preparation modules with different spin‐lock durations. The spin‐lock pulse (α_y) was divided into 4 segments with an alternative phase, and a refocusing pulse was applied in the middle between 2 pairs to compensate for the B₀ inhomogeneities. The crusher gradients were applied after the T _{1 ρ} module to destroy any remnant of transverse magnetization. Each of the preparation modules was followed by a FLASH readout segment with radial readout consisting of 125 RF excitations with variable FA ranging from 0° to 20°. FA, flip angele; FISP, fast imaging with steady‐state precession; RF, radiofrequency

2.2. Model phantoms study

A model phantom consisting of 3%, 4%, and 8% agarose gels and cross‐linked bovine serum albumin was scanned on a 3T MRI scanner (Magnetom Prisma, Siemens Healthcare GmbH, Germany) with our proposed MRF sequence as well as the conventional T₁ (MPRAGE), T₂ (spin‐echo), and T _{1 ρ} (customized turbo‐flash ²⁸ ) mapping sequences. The imaging parameters are shown in Table 1. The conventional T₁ map was calculated using the inline MapIt feature on the Siemens scanner. Scans acquired with different TEs, including 25, 24, 36, 48, 60, 72, 84, 144, 278 ms, were fitted voxel by voxel to the monoexponential model to estimate the T₂ relaxation time. The same method was used to estimate the T _{1 ρ} relaxation time from scans with different T_sl, including 2.0, 3.7, 6.9, 12.9, 24.1, 45, and 85 ms.

TABLE 1.

Imaging parameters of the proposed MRF and the conventional T₁, T₂, and T _{1 ρ} sequences

	MRF	IR‐MP2RAGE (T1‐Conv)	SE (T2‐Conv)	T1rTFL (T 1 ρ‐Conv)
FOV (mm2)	160	220	160	160
TR (ms)	7.5	5000	6000	1500
TE (ms)	3.4	3.4	25, 24, 36, 48, 60, 72, 84, 144, 278	3.4
Tsl (ms)	2.0, 3.7, 6.9, 12.9, 24.1, 45	–	–	2.0, 3.7, 6.9, 12.9, 24.1, 45, 85
FA (°)	0‐60	4,5	90	8
Slice thickness (mm)	4	4	4	4
Matrix size	192 × 192	256 × 256	128 × 128	128 × 128
Receiver bandwidth (Hz/px)	390	240	150	390
TA (min)	7:06	4:00	25:44/TE	3:00/Tsl

Conv, conventional; FA, flip angle; IR, inversion recovery; MRF, MR fingerprinting; T_sl, spin‐lock duration, TA, total acqusition time; TFL, turbo‐FLASH.

In addition,  the MRF sequence was repeated on the same scanner to evaluate the repeatability and tested on another 3T MRI scanner (Magnetom Skyra, Siemens Healthcare GmbH, Germany) to assess the reproducibility.

2.3. In vivo study

Institution review board‐approved MRF imaging was performed on healthy volunteers (n = 5, mean age: 38 ± 12 years) and patients (n = 3) with mild knee OA (MOA) (KL score 1‐2, mean age: 63 ± 5 years) using a 15 channel Rx/Tx knee coil (Quality Electrodynamics, Mayville, OH). Six sagittal images were acquired with 0.6 × 0.6 mm² in‐plane resolution, 4.0 mm slice thickness, 224 × 224 matrix size, TE/TR = 3.5/7.5 ms, bandwidth = 420 Hz/pixel, number of shots = 4, spin‐power f_sl = 500 Hz. The acquisition time was 7:06 min. Three control subjects were scanned twice in the same session to assess in vivo repeatability.

2.4. MRF‐dictionary construction for multiparametric mapping

All the algorithms were implemented in MatLab (R2018a, MathWorks, Natick, MA). A dictionary of simulated MR fingerprints for possible T₁, T₂, T _{1 ρ}, and ${\mathrm{B}}_1^{+}$ values was computed based on the extended phase graphs. ²⁹ The T _{1 ρ} preparation module was simulated as a mono‐exponential decay of longitudinal magnetization because the application of the crusher gradients after the tip‐up 90° pulse destroyed any remnant transverse magnetizations. Assuming the initial magnetization of M_{z 1} at the beginning of the T _{1 ρ}, the final magnetization, M_{z 2} was estimated as:

$$M_{z2}=M_{z1}\exp \left(\frac{T_{\mathit{sl}}}{T_{1\rho }}\right).$$ (1)

The slice profile was incorporated into the simulation based on the Fourier transform of the RF waveform. ²¹ The T₁, T₂ (same range for T _{1 ρ}), and ${\mathrm{B}}_1^{+}$ were ranged from 50 to 3000 ms, 2 to 200 ms, and 30° to 90° with the 5% increments, respectively. The dictionary and the measured fingerprints were then compressed using the singular value decomposition approach ²¹ , ³⁰ and matched with each other using an iterative approach ³¹ , ³² , ³³ , ³⁴ to generate 5 multiparametric maps (proton density, T₁, T₂, T _{1 ρ}, and ${\mathrm{B}}_1^{+}$) simultaneously.

2.5. Statistical analysis

The average of each parameter over all slices was calculated in phantom for each agarose gel and for bovine serum albumin, and for each volunteer over 5 regions of interest (medial and lateral femoral cartilage, medial and lateral tibial cartilage, and patellar cartilages).

The Bland‐Altman analysis was performed to assess the reproducibility and repeatability in the model phantoms. The Wilcoxon test was used to compare healthy control and MOA patients. The mean and SD of each parameter was calculated for each subject across the test–retest scan, and the coefficient of variation (CV) is calculated as CV = SD/Mean to assess intrasubject repeatability.

The intersubject repeatability was evaluated using the RMS CV:

$$\text{RMS CV}=\sqrt{\frac{{\sum }_{i=1}^N{\text{CV}}_i^2}{N}},$$ (2)

where CV_i is the CV of an individual subject and N (=5) is the total number of subjects.

3. RESULTS

Figure 2A shows the representative T₁, T₂, T _{1 ρ} relaxation and ${\mathrm{B}}_1^{+}$ maps of the model agar gel phantoms. Analysis of the Bland‐Altman plot demonstrated an average difference of 4.67 ms, −0.09 ms, and 0.05 ms between 2 scans from the same scanner (Figure 2B); and 9.68 ms, 0.29 ms, and −0.72 ms between the scans acquired on 2 scanners for T₁, T₂, and T _{1 ρ} (Figure 2C), respectively.

FIGURE 2.

Representative PD, T₁, T₂, and T _{1 ρ} and ${\mathrm{B}}_1^{+}$ maps of the agar gel model phantoms. The gels with higher agar concentrations have lower relaxation times (A). Regression and Bland‐Altman plots show excellent repeatability (B) and reproducibility (C) in estimating PD, T₁, T₂, and T _{1 ρ} in the agar gel model phantoms. PD, proton density

Comparisons between the proposed MRF relaxation times and the conventional techniques are shown in Figure 3. We observed average absolute difference of 328.0 ± 123.8 ms with a correlation coefficient of r = 0.96, 2.4 ± 2.1 ms with r = 0.99, and 2.3 ± 2.0 ms with r = 0.99 between the conventional and our proposed MRF technique for T₁, T₂, and T _{1 ρ}, respectively. The high correlation coefficient between our proposed method and the conventional techniques confirmed the agreement between MRF and conventional relaxation mappings.

FIGURE 3.

Regression and Bland‐Altman plots indicate good agreement between our proposed MRF method and the conventional mapping techniques. The average absolute difference of 328.0 ± 123.8 ms with a correlation coefficient of r = 0.96, 2.4 ± 2.1 ms with r = 0.99, and 2.3 ± 2.0 ms with r = 0.99 was observed between the conventional and our proposed MRF technique for T₁, T₂, and T _{1 ρ}, respectively. MRF, MR fingerprinting

The representative maps of the knee joint (medial and lateral cartilages) for control and MOA patient are shown in Figure 4A. The in vivo study showed excellent interscanner repeatability with CV smaller than 5%, 10%, and 7% for all individuals; and RMS CV less than 3%, 6%, and 5% across all ROIs for T₁, T₂, and T _{1 ρ}, respectively. The global average of T₁ = 778.33 ± 48.46 ms, T₂ = 23.25 ± 4.39 ms, and T _{1 ρ} = 32.42 ± 5.52 ms was observed in the control group, whereas the numbers were increased to T₁ = 834.31 ± 37.79 ms, T₂ = 26.05 ± 2.53 ms, and T _{1 ρ} = 33.88 ± 4.41 ms in the MOA patients. The boxplot comparisons of 3 relaxation parameters between control and MOA patients are shown in Figure 4B. An overall increase was observed in the patients. The Wilcoxon test showed a significant difference between control and MOA patients for T₁ (P = .04), T₂ (P = .01), and T _{1 ρ} (P = .02) relaxation parameters in medial tibial cartilage, as well as for T₂ relaxation time (P = .02) in medial femoral cartilage.

FIGURE 4.

(A) Representative PD, T₁, T₂, and T _{1 ρ} relaxation maps of the knee joint (medial, lateral, and patellar cartilages) for healthy control and MOA of knee patient. (B) Boxplot comparison of T₁, T₂, and T _{1 ρ} relaxation times in different cartilage compartments (LFC, LTC, MFC, MTC, and PC) between healthy controls and MOA patients. A significant increase was observed in T₂ and T _{1 ρ} values in MOA patients. LFC, lateral femoral cartilage; LTC, lateral tibial cartilage; MFC, medial femoral cartilage; MTC, medial tibial cartilage; MOA, mild osteoarthritis; PC, patellar cartilage

4. DISCUSSION

In this work, we implemented an MRF sequence and showed the feasibility of rapid simultaneous acquisition of accurate proton density, T₁, T₂, ${\mathrm{B}}_1^{+}$, and T _{1 ρ} maps of the human knee joint. The proposed MRF method is fast, reproducible, and robust to ${\mathrm{B}}_1^{+}$ inhomogeneity. Integrating the T _{1 ρ} module allowed us to perform voxel‐wise comparisons between different relaxation times. Moreover, when measured separately, each of these quantities can easily be biased by residual effects from the others. Measuring all of them at once and reconstructing multiparametric maps in 1 single step provides an elegant way to disentangle the individual contrast mechanisms and eliminate experimental imperfections such as ${\mathrm{B}}_1^{+}$ inhomogeneities.

The estimated T _{1 ρ} was higher than T₂, which is in agreement with the findings of previous literature. ⁷ , ³⁵ , ³⁶ The range was also comparable to the other studies. ³⁵ , ³⁶ , ³⁷ , ³⁸ Li et al ³⁷ reported RMS CV of 6.0% and 6.3% for the knee T₂ and T _{1 ρ} estimation, which is in agreement with our repeatability studies. Our relaxation times estimation in phantoms showed a good agreement with conventional techniques. The difference in T₁ values could be due to the magnetization transfer effect, ³⁹ which we did not include in our dictionary. We plan to use a more accurate simulation for our dictionary in the future.

Our proposed technique yields T₁, T₂, and T _{1 ρ} maps of the 6 sections of the knee cartilage with 0.6 × 0.6 × 4.0 mm³ resolution in 7:06 min (1:12 min per slice). Previous work reported 9:30 min to acquire T₂ and T _{1 ρ} maps of 26 slices with 0.54 × 1.1 × 4.0 mm³ resolution, ³⁷ and ~15 min to acquire a 3D biexponential T₂ ⁴⁰ or T _{1 ρ} ²⁸ map of the cartilage with 0.54 × 1.1 × 2.0 mm³ resolution. The T₁ map was not provided in other studies. We note that to acquire T₁, T₂, and T _{1 ρ} data separately via traditional methods would require ~45 min of scan time.

The MRF sequence can be sensitive to motion. Whereas Ma et al ¹⁷ suggested the MRF is relatively robust to in‐plane motion at the end of the scan, Yu et al ⁴¹ showed a substantial decrease in T₂ values when a through‐plane motion happened in the middle of the scan. They suggested that the difference in sensitivity to 2 different motions is due to the difference in the gradient used in in‐plane (balanced) and thorough‐plane (gradient spoiled), which leads to different phase accumulation for each coherence pathways when a through‐plane motion occurs. ⁴¹ Moreover, when using a 2D‐MRF implementation, the spin history is biased by fresh magnetization entering the excitation plane due to motion. Compared to T₂ values, T₁ values are shown to be less affected by motion, although some blurring in the fine details was observed. ⁴¹ We used extensive padding to avoid motion during scan time. Further studies are warranted to investigate motion sensitivity during the T _{1 ρ} acquisition.

Our study has some limitations. First, there were a small number of volunteers in each group, which is not enough to run reliable statistics. Moreover, the dictionary matching used in the proposed method is computationally costly and memory consuming, preventing online reconstruction. However, fast reconstruction and matching methods that can alleviate this problem are under investigation. Second, although the total scan time (~7 min) is shorter compared to acquiring T₂, T₁, and T _{1 ρ} data separately, the per slice scan time of our 2D‐multislice MRF is relatively long (~7 min for the 6 slices with 4 shots). To reduce scan time and improve the SNR, a 3D‐sequence with stack of stars ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ could be used. Future work could also explore the optimal design of experiments (e.g., flip angle train and optimal T_sls) based on Crammer‐Rao lower bound ⁴⁷ and deep learning‐based reconstruction ⁴⁸ instead of template matching. Finally, we simulated the slice profile based on the Fourier transform of the RF waveform. This method is valid for small tip angle approximation and hence may not be accurate for large flip angle. A general approach proposed by Ma et al ⁴² can be used to increase accuracy. This problem could also be addressed by using a 3D image‐encoding strategy. ⁴³ , ⁴⁴

5. CONCLUSION

In summary, we implemented and demonstrated the feasibility of an MRF sequence that can simultaneously measure the T₁, T₂, T _{1 ρ}, and ${\mathrm{B}}_1^{+}$ maps in a single scan. Nevertheless, the in vivo results showed that it could distinguish the mild OA patients from the healthy controls and hence has the potential to be used for the quantitative assessment of the cartilage for the early detection of OA.

Sharafi A, Zibetti MVW, Chang G, Cloos M, Regatte RR. MR fingerprinting for rapid simultaneous T₁, T₂, and T ₁ ρ relaxation mapping of the human articular cartilage at 3T. Magn Reson Med. 2020;84:2636–2644. 10.1002/mrm.28308