New methods for robust continuous wave T1ρ relaxation preparation

Measurement of the longitudinal relaxation time in the rotating frame of reference (T1ρ) is sensitive to the fidelity of the main imaging magnetic field (B0) and that of the RF pulse (B1). The purpose of this study was to introduce methods for producing continuous wave (CW) T1ρ contrast with improved robustness against field inhomogeneities and to compare the sensitivities of several existing and the novel T1ρ contrast generation methods with the B0 and B1 field inhomogeneities. Four hard‐pulse and four adiabatic CW‐T1ρ magnetization preparations were investigated. Bloch simulations and experimental measurements at different spin‐lock amplitudes under ideal and non‐ideal conditions, as well as theoretical analysis of the hard‐pulse preparations, were conducted to assess the sensitivity of the methods to field inhomogeneities, at low (ω1 << ΔB0) and high (ω1 >> ΔB0) spin‐locking field strengths. In simulations, previously reported single‐refocus and new triple‐refocus hard‐pulse and double‐refocus adiabatic preparation schemes were found to be the most robust. The mean normalized absolute deviation between the experimentally measured relaxation times under ideal and non‐ideal conditions was found to be smallest for the refocused preparation schemes and broadly in agreement with the sensitivities observed in simulations. Experimentally, all refocused preparations performed better than those that were non‐refocused. The findings promote the use of the previously reported hard‐pulse single‐refocus ΔB0 and B1 insensitive T1ρ as a robust method with minimal RF energy deposition. The double‐refocus adiabatic B1 insensitive rotation‐4 CW‐T1ρ preparation offers further improved insensitivity to field variations, but because of the extra RF deposition, may be preferred for ex vivo applications.

Measurement of the longitudinal relaxation time in the rotating frame of reference (T 1ρ ) is sensitive to the fidelity of the main imaging magnetic field (B 0 ) and that of the RF pulse (B 1 ). The purpose of this study was to introduce methods for producing continuous wave (CW) T 1ρ contrast with improved robustness against field inhomogeneities and to compare the sensitivities of several existing and the novel T 1ρ contrast generation methods with the B 0 and B 1 field inhomogeneities. Four hard-pulse and four adiabatic CW-T 1ρ magnetization preparations were investigated. Bloch simulations and experimental measurements at different spin-lock amplitudes under ideal and non-ideal conditions, as well as theoretical analysis of the hard-pulse preparations, were conducted to assess the sensitivity of the methods to field inhomogeneities, at low (ω 1 << ΔB 0 ) and high (ω 1 >> ΔB 0 ) spin-locking field strengths. In simulations, previously reported single-refocus and new triple-refocus hard-pulse and double-refocus adiabatic preparation schemes were found to be the most robust.
The mean normalized absolute deviation between the experimentally measured relaxation times under ideal and non-ideal conditions was found to be smallest for the refocused preparation schemes and broadly in agreement with the sensitivities observed in simulations. Experimentally, all refocused preparations performed better than those that were non-refocused. The findings promote the use of the previously reported hard-pulse single-refocus ΔB 0 and B 1 insensitive T 1ρ as a robust method with minimal RF energy deposition. The double-refocus adiabatic B 1 insensitive rotation-4 CW-T 1ρ preparation offers further improved insensitivity to field variations, but because of the extra RF deposition, may be preferred for ex vivo applications.

| INTRODUCTION
Relaxation in the rotating frame under the presence of an external spin-locking radio frequency (RF) pulse, termed T 1ρ relaxation, 1 has been under active research for the quantitative assessment of different tissue types, such as the central nervous system, 2 liver, 3 and articular cartilage. 4,5 For instance, in articular cartilage, T 1ρ has been shown to be sensitive to the proteoglycan content, the collagen fiber network, and to degenerative changes in general. [5][6][7][8] T 1ρ relaxation depends on the amplitude of the spin-lock (SL) pulse, that is, the SL frequency, which in typical cases corresponds to the timescales of slow molecular motion. 9 In biological tissues, the processes affecting T 1ρ relaxation include dipolar interaction, chemical exchange, and the motion of spins through field gradients; broadly, any local fluctuations in the magnetic field that are on the same or lower frequency scale as the SL frequency. [8][9][10][11][12] The relative importance of each mechanism varies with the SL frequency and the strength of the main magnetic field. 13 The standard T 1ρ measurement uses on-resonance continuous-wave (CW) spin-locking (CW-T 1ρ ), and consists of tilting the magnetization 90 degrees and then locking the spins with a continuous RF pulse. 1 Several methods to produce T 1ρ contrast at constant spinlocking amplitude have been proposed, with variable sensitivity to the inhomogeneities of the main field (B 0 ) and the RF field (B 1 ).
Spin locking slows the relaxation process in the transverse plane by forcing the spins to rotate around the RF field. Because of the high sensitivity of the T 1ρ measurement to field inhomogeneities, the design of the SL pulse is essential for high quality T 1ρ -weighted images and accurate quantification of the T 1ρ relaxation time. 14 Typically, in the clinical setting, the amplitudes of the SL pulses (ω 1 = γB 1 /2π, where γ is the gyromagnetic ratio) are between a few hundred and a thousand Hz, most often 400-500 Hz. To allow estimation of the T 1ρ relaxation time, the same SL amplitude is maintained, while the SL durations are varied. The relaxation processes affecting T 1ρ are modulated by the molecular makeup of the tissue, and thus T 1ρ correlates with the properties of the tissues. 5 Various methods have been reported for compensating the inherent sensitivity of T 1ρ measurement to field inhomogeneities. 14-16 Witschey et al. 14 introduced a T 1ρ weighting method, which was demonstrated to be highly insensitive to variations in the B 0 and B 1 fields, in phantoms and in vivo human brains at 3 T. The sequence is a modification of the ΔB 0 insensitive SL sequence proposed by Zeng et al., 17 with a change to the phase of the final 90 pulse, effectively inverting the magnetization at the end of the preparation. While the pulse sequence was proven to be highly robust against B 0 and B 1 field inhomogeneities, the authors noted that the downside of the sequence was that it would still require a perfect 180 refocusing pulse to fully compensate against field variations. Another attempt to alleviate the sensitivity of spin locking to field inhomogeneities with a single-refocus pulse, termed paired self-compensated SL (PSC-SL), was proposed by Mitrea et al. 15 In their version, the spin-locking periods were further split into pairs of opposite phases on either side of the refocusing pulse, making the SL pairs insensitive to B 1 inhomogeneities; however, tiltin the magnetization back towards the positive z-axis. The study demonstrated the sequence with phantom and small animal imaging at 7 T with gradient echo (GRE) and fast spin echo (FSE) readout sequences. A recent double-refocusing pulse sequence, termed balanced SL (B-SL), proposed by Gram et al., 18 applies an extra 180 refocusing pulse with opposite phase compensating for both inhomogeneities. The sequence was evaluated with simulations and demonstrated with an agarose phantom at 7 T. The authors concluded that B-SL was superior in comparison with the existing single-refocus sequence in which the magnetization is returned to the +Z axis, that is, the one presented by Zeng et al. 17 However, it remains unclear how the B-SL sequence performs in comparison with the sequence presented by Witschey et al.,14 which inverts the magnetization at the end of the preparation, as this sequence was also shown to be superior in comparison with the noninverting T 1ρ preparation.
Adiabatic pulses have also been used to improve the robustness of T 1ρ imaging. Various studies used adiabatic half passage (AHP) pulses, coupled to CW spin locking to improve the B 1 robustness of the measurements 16,[19][20][21][22][23] The AHP pulses were utilized in these studies for tilting the magnetization to the transverse plane for the CW SL, followed by a reverse AHP to bring the magnetization back to the longitudinal axis. A dual acquisition method was proposed by Chen 16 to address the adverse effect from relaxation during the reverse AHP on T 1ρ quantification. The method was demonstrated with phantom and human liver imaging at 3 T. Similar methods, using pulsed, fully adiabatic T 1ρ preparation, have also been reported. [24][25][26] The purpose of this study was twofold; firstly, to perform a numerical, experimental, and partial theoretical comparison of the sensitivities of the different T 1ρ contrast generation methods to the inhomogeneities in the B 1 and B 0 fields; and secondly, to introduce additional ways of producing T 1ρ contrast with reduced sensitivity to the field inhomogeneities. We examined the different previously published and new T 1ρ preparation methods via both Bloch simulations and experimentally. In the theoretical part, we focused on the different hard-pulse implementations for T 1ρ preparation.

| CW-T 1ρ preparation schemes
Here, we focus on the conventional non-refocused hard-pulse, single-refocused ΔB 0 and B 1 insensitive preparation scheme presented by Witschey et al., 14 the double-refocused B-SL preparation scheme presented by Gram et al., 18 and on a novel triple-refocused hard-pulse CW-T 1ρ preparation scheme. Triple refocused hard-pulse CW-T 1ρ attempts to account for the reported inability of the single-refocus sequence presented by Witschey et al., 14 to fully compensate for the field variations if the single refocus is not a perfect 180 pulse (Figures 1, S1, and S2). Theoretical derivations on the sensitivities of the preparation are provided in the supporting information and in Witschey et al. 14 In addition, the ΔB 0 and B 1 insensitive T 1ρ preparation presented by Mitrea et al. 15 was considered in simulations.
Adiabatic pulses are amplitude-and frequency-modulated RF pulses that are highly insensitive to B 1 inhomogeneity and off-resonance effects. 27 In adiabatic pulses, the amplitude of the effective field (ω eff [t]) of the pulse is the vectorial sum of the time-dependent B 1 and the offresonance component. The flip angle (φ) is largely independent of the applied B 1 field, given that the adiabatic condition jω eff (t)j>> jdφ / dtj is satisfied, that is, the sweep of the direction of the effective field (dφ/dt) is slow compared with its amplitude (ω eff ). During an adiabatic sweep, spins at different resonances are primarily affected at different times of the pulse, in contrast to the CW-pulse, which simultaneously affects the spins within its frequency bandwidth. Adiabatic pulses can be categorized as excitation, refocusing, and inversion pulses. 28 AHP pulses (Figure 2A) are employed to generate uniform excitation with a 90 flip on a defined frequency band, leaving the magnetization in the transverse plane, while reverse AHP pulses brings the magnetization back to the z axis from the transverse plane. 19 With the adiabatic excitation and CW-SL, the SL continues from the same phase where the adiabatic excitation pulse ends, but the amplitude of the RF pulse is reduced to the desired spin-lock amplitude (i.e., unlike in the adiabatic CW T 1ρ reported by Chen, 16 where the amplitude of the SL equals the maximum amplitude of the AHP). Similarly, the reverse AHP starts from the phase where the SL ends, with amplitude ramped up to the maximum of the AHP. 16,19,22,24 Besides AHP excitation pulses, either B 1 insensitive rotation (BIR)-4 plane rotation pulses or adiabatic full passage (AFP) inversion pulses, such as hyperbolic secant (HS)n pulses, can be used for adiabatic refocusing/inversion during the spin-locking train, both providing largely B 1insensitive means for the refocusing/inversion. 28,29 As long as the adiabaticity can be sufficiently maintained during the pulses, inhomogeneities in the B 1 field will not have an effect on the resulting flip angles using the adiabatic pulses. Here, we investigated four different CW-T 1ρ preparations utilizing AFP, AHP, BIR-4, and HS1 adiabatic pulses, without refocusing 22 or using single or double BIR-4 refocusing, or double AFP inversion, in between the SL ( Figure 2).

| Numerical simulations
Numerical Bloch simulations of the pulse trains were performed for ΔB 0 and B 1 field inhomogeneities of up to ±1 kHz and ±40%, respectively, to analyze the sensitivities of the sequences. The simulations for all the spin locking schemes were performed using SL durations of 8, 32, and 128 ms and SL amplitudes of 100 and 400 Hz. The duration of each of the hard 90 and 180 pulses was 200 μs. Maximum amplitudes of the adiabatic pulses were set to 2.5 kHz and the durations were 4, 3.03, and 5.17 ms for AHP, AFP, and BIR-4, respectively. Additionally, conventional adiabatic CW T 1ρ was simulated with a longer and lower maximum RF amplitude of 600-Hz of the AHP pulses. 16 The following modulation functions were used for adiabatic pulses: the AHP and BIR-4 pulses utilized tanh/tan modulations 30 and the AFP pulse was an HS1 pulse with a timebandwidth product value (R = 20). Relaxation effects were neglected in the simulations to focus on the effects of field inhomogeneity.

| Sample preparation
Cylindrical osteochondral plugs (n = 4, diameter = 6 mm) were prepared from the patella of bovine knee joints obtained from a local grocery store. The samples were immersed in phosphate buffered saline containing enzyme inhibitors and frozen at À20 C. Prior to imaging, the samples were thawed and transferred into a custom-built sample holder and test tube filled with perfluoropolyether (Galden HS-240, Solvay Solexis, Italy).
In addition to osteochondral plugs, cherry tomatoes (n = 2) and an agarose phantom (n = 1) were used as test samples. The cherry tomatoes were chosen such that they neatly fit within the RF coil. The cherry tomatoes were placed into the coil without immersion solution. The agarose phantom was prepared with 3% w/v agarose and water by heating the solution at 90 C. The agar solution was then transferred to a test tube and placed into a refrigerator (at $ 5 C) for cooling and gel formation. The test tube was taken out of the refrigerator then allowed to settle to room temperature for 2 h prior to imaging.

| MR imaging
MRI studies were performed using a 9.4-T preclinical Varian/Agilent scanner (Vnmrj DirectDrive console v. 3.1) and a 19-mm quadrature RF volume transceiver (Rapid Biomedical GmbH, Rimpar, Germany). A set of RF shapes for all the methods shown in Figures 1 and 2 for generating T 1ρ contrast was created for the experiments. All the CW-T 1ρ measurements were conducted using a magnetization preparation block consisting of the RF train and a crusher gradient coupled to an FSE readout sequence. For each of the CW-T 1ρ methods, five SL amplitudes (γB 1 /2π = 0, 50, 100, 200, and 400 Hz) were used. Hard 90 and 180 pulses were both set to have a duration of 200 μs and the adiabatic refocusing/ inversion pulses used were BIR-4 and HS1, with durations of 5.17 and 3.03 ms, respectively. The AHP pulse duration was 4 ms. All the adiabatic pulses ( Figure 2) were set to have a maximum B 1 amplitude of 2.5 kHz. All the T 1ρ measurements were performed using SL (CW) durations of 0, 4, 8, 16, 32, 64, 128, and 192 ms. In addition to T 1ρ measurements, a B 0 map was acquired using the same FSE readout sequence, coupled to a water saturation shift referencing (WASSR) 31 preparation module utilizing a saturation range of À300 to +300 Hz with a 50-Hz step and saturation power of 30 Hz. Furthermore, the B 1 field was estimated using a set of hard-pulse saturation preparations around the expected 90 power F I G U R E 2 Adiabatic and CW SL preparations. (A) Conventional adiabatic CW-T 1ρ preparation, consisting of an AHP excitation, a SL of duration τ, and a reverse AHP. 19 Adiabatic CW-T 1ρ with (B) A single adiabatic BIR-4 refocusing pulse, (C) With two BIR-4 refocusing pulses, or (D) Using double refocusing with HS1 pulses. The negative sign in front of τ indicates a phase shift of 180 . AHP, adiabatic full passage; BIR, B 1 insensitive rotation; CW, continuous wave; CW-T 1ρ , continuous wave T 1ρ ; HS, hyperbolic secant; SL, spin lock (±40% from the expected power), coupled to a low-resolution scan with the same FSE readout. The scan time for each of the aforementioned T 1ρ setups was $ 48 min, for WASSR $ 8 min, and for the B 1 scan $ 13 min. The parameters of the readout FSE sequence varied slightly depending on the sample and its size ( Table 1).
The samples were scanned under two nominal conditions: (i) as homogenous B 0 and B 1 as possible; and (ii) altered B 0 and B 1 settings to introduce inhomogeneities. At the beginning of every session, manual shimming of B 0 and a calibration of the B 1 transmit power was performed.
The measurements were first conducted for case (i) with as good conditions and homogenous fields as possible, and subsequently for case (ii) with the shims deliberately set to an incorrect value along a specific axis to induce B 0 variation of approximately ±250 Hz along the chosen direction (in-plane, across the cartilage surface for osteochondral samples, and along the same axis for the other samples). Additionally, the B 1 amplitude was either set to 20% lower or higher than the nominal calibrated value, or the specimen was pulled approximately 15 mm away from the RF center (approximately 50% of the RF visibility range) so that the B 1 field along the sample became inhomogeneous. For those specimens that exceeded the homogenous region of the B 1 field, no additional B 1 inhomogeneities were introduced (Table 1).

| Data analysis
The results of the simulations were evaluated visually and semiquantitatively. For ΔB 0 response with a correct B 1 value and for ΔB 1 response with correct B 0 , a semiquantitative metric was estimated: the width of the flat region of the response, that is, the width of the relatively smooth and flat response around the on-resonance condition after applying a moving average window of 50 Hz width and a threshold of 90% of the onresonance amplitude. The averaging window width was changed to 10 Hz for the nonrefocused schemes and simulations of ΔB 0 response at 100-Hz SL amplitude to obtain reliable estimates. The results were calculated and visualized using the absolute values of the simulated z magnetization to facilitate comparison between the preparation schemes, because some of them deliberately take the magnetization to the -z axis.
Relaxation time maps were fitted in a pixel-wise manner using the three-parameter monoexponential fit, using in-house developed plugins for Aedes (http://aedes.uef.fi) in Matlab (Matlab R2019b; MathWorks, Natick, MA, USA). B 0 maps were calculated using Lorenzian fits to the acquired WASSR saturation datasets 31 and the B 1 maps were estimated via linear fitting to the acquired saturation datasets.
To compare the reliability and robustness of the different T 1ρ preparation schemes, mean normalized absolute deviation (MNAD) values in large regions of interest (ROIs) were calculated for each of the preparation schemes between the relaxation times measured under ideal and nonideal conditions. The large ROIs for each specimen were defined on an average T 1ρ map calculated over all the preparation schemes for the SL amplitude of 400 Hz. These ROIs, comprising areas with high SNR, were then used to extract the T 1ρ values from all the measurements under both conditions for further computations. The MNADs of the relaxation times were calculated by where i refers to an individual voxel within the ROIs under ideal and non-ideal conditions. The MNAD value of 0.5 corresponds to a mean deviation of 50% of the T 1ρ relaxation times under the nonideal conditions. For the comparison of the different T 1ρ preparation schemes, MNAD values from all the samples available for a given preparation were averaged.
In addition to the primary spin-locking pulse, each of the T 1ρ preparation schemes requires other RF pulses to tilt and refocus the magnetization. Depending on the configuration, the RF power deposited by these additional pulses varies significantly. To assess the relative differences in RF energy deposition between the preparations, root mean square (RMS) integrals of the pulse trains with zero SL duration were calculated. To facilitate the comparison, the RMS values were normalized with that of the conventional CW-T 1ρ preparation.

| RESULTS
Numerical simulations demonstrated variable sensitivity of the sequences to a range of offsets in the B 0 and B 1 fields (Figures 3, 4, and S3). 2D plots of the simulated responses on both ΔB 0 and B 1 offset axes demonstrate the differences in the sensitivities of the T 1ρ preparations: adiabatic refocused schemes demonstrated the least B 1 -dependent variation and especially the double-refocused versions also minimal ΔB 0 -dependent variation at all simulated SL amplitudes (100 and 400 Hz) and SL times (8,32, and 128 ms) ( Figures 3F-H and 4F-H).
Quantification of the flatness of the simulated ΔB 0 and ΔB 1 responses at the nominally correct B 1 and B 0 indicated that the non-refocused schemes had a very poor B 0 off-resonance response with almost no flat region even at the correct B 1 , while the refocused versions showed significantly improved responses ( Figures 3C-H, 4C-H, S7 and S8). However, the adiabatic CW pulse simulated at 600-Hz maximum amplitude ( Figure S3B) had a broader flat response for both B 0 and B 1 inhomogeneities at the higher SL amplitude (400 Hz) (Figures S3B and S9) when compared with the 2.5-kHz maximum amplitude simulations of the pulse (Figures 3, 4, and S7-S9).
The adiabatic double-refocused schemes had the broadest ΔB 0 robustness, with the flat range essentially covering the entire simulated range from À1 to +1 kHz (and beyond), while the single-and triple-refocused preparations had the broadest flat responses among the hard-pulse preparation schemes ( Figures 3C,E and 4C,E), but with a slight drop at B1 amplitudes beyond ±31% of the nominally correct amplitude. The doublerefocused hard pulse was highly insensitive to a wide range of B 1 offsets, but was more sensitive to B 0 inhomogeneities, being the least robust among the refocused schemes ( Figures 3D, 4D, S7 and S8).
For the experimental measurements under as ideal as possible conditions, the T 1ρ relaxation time maps of the cartilage bone samples, cherry tomatoes, and phantom were visually artifact-free for all the preparation schemes for SL amplitudes above 100 Hz (Figures 5-7). Under the nonideal conditions, however, at SL amplitudes equal to and below ΔB 0 , the conventional and adiabatic non-refocused T 1ρ relaxation time maps The conventional hard-pulse CW-T 1ρ preparation with only two 90 pulses imposes the least additional RF energy deposition and thus produces the least specific absorption rate (SAR) (Figure 9). The preparations including adiabatic pulses add a constant adiabatic T 1ρ weighting in addition to the T2 weighting from finite TE of the readout, and these pulses induce significantly higher RF energy deposition (the RMS integral of the 0-ms SL pulse for the double-refocus BIR-4 is approximately 86 times that of the conventional T 1ρ preparation) ( Figure 9, Table S1). However, for a plain SL pulse (i.e., without the 90 or 180 pulses) of 50-ms duration and 400-Hz amplitude, the RMS integral is $40 times that of the 0-ms SL pulse of the conventional T 1ρ preparation with the least extra RF. For increasing SL durations and amplitudes, relative differences in the energy deposition between the preparation schemes are reduced (an RMS integral ratio of a SL pulse of 64-ms duration and 400-Hz amplitude using double-refocus BIR-4 with respect to conventional is reduced from $86 times to just under three times) ( Figure 9, Table S1). The 0-ms SL adiabatic CW T1ρ pulse, with a longer duration and a reduced maximum RF amplitude of 600 Hz of the AHP, was observed to have approximately one-quarter of the RMS integral of the original pulse with a maximum amplitude of 2.5 kHz. With the same lower-power AHP pulses, the RMS integral of a SL pulse of 64-ms duration and 400-Hz amplitude was reduced by a factor of approximately 1.5 compared with the original using 2.5-kHz AHP pulses (Table S1, Figure S6).

| DISCUSSION
T 1ρ contrast remains interesting for various applications in the human body because of its sensitivity to low frequency molecular interactions that are often biologically important. 5,9 The different T 1ρ contrast preparation methods, particularly at very low SL amplitude, are however sensitive to imperfections of the imaging field and the RF field. In this study, we proposed four new methods for generating T 1ρ contrast and compared them experimentally and numerically with four existing methods for their sensitivity to the field inhomogeneities. The study builds on earlier reports introducing ΔB 0 and B 1 insensitive T 1ρ preparation schemes, 15,18,19,22 particularly the one by Witschey et al., 14 and utilizes the same theoretical examination of the proposed hard-pulse schemes (see the supporting information). The results of the study indicate that those methods employing a refocusing pulse are significantly more robust against field inhomogeneities than those methods which do not, and also that combining CW spin locking with fully adiabatic excitation and refocusing is the most robust method against field inhomogeneities. However, the fully adiabatic schemes have the additional cost of significantly increased RF energy deposition. Among the non-adiabatic hard-pulse refocusing Recently, there has been an increase in interest towards T 1ρ dispersion in cartilage, 13,32-36 because the measurement could provide information beyond a single amplitude T 1ρ scan. However, especially lowering the SL amplitudes requires methods that are robust against field inhomogeneities. If the B 0 variations exceed the spin-locking amplitude, the locking becomes inefficient, resulting in spurious signal loss, which is further amplified with methods that do not compensate for field variations. 1,12 The theoretical considerations regarding the triple-refocused hard-pulse CW-T 1ρ preparation lead to the same conclusions that were found for the single-refocused preparation scheme earlier by Witschey et al., 14 suggesting the methods should be approximately equal. The simulations showed a slightly broader flat response with respect to variations in B 0 for the single-refocus method, while the response of the triple-refocused method was slightly smoother. The double-refocused pulse scheme brings the magnetization back to the positive z axis; however, it appears to require nearly perfect 90 and 180 pulses, while the single-and triple-refocused methods only require that the 180 pulses should be nearly perfect. Because of this difference, the single-or triple-refocused schemes appeared more robust against field inhomogeneities, as confirmed by the simulations. In practice, however, all the refocused hard-pulse options were observed to be very similar in soft tissues.
Adiabatic pulses are known for their excellent tolerance to RF inhomogeneity 28 and thus stand out as an interesting possibility to improve the robustness of CW T 1ρ preparation. Furthermore, adiabatic T 1ρ could be measured in fully adiabatic mode, using a train of AFP HS RF pulses, instead of a constant amplitude CW SL pulse in between AHP pulses. 22,24,29,37,38 In comparison with a CW SL with fixed B1 amplitude and F I G U R E 6 T 1ρ relaxation time maps of a cherry tomato sample, under as ideal as possible conditions and under non-ideal conditions, with inhomogeneous B 0 field, for SL amplitudes of 0-400 Hz acquired with the different methods. Anatomical reference (showing the MNAD analysis ROI with red shading) and the corresponding B 1 and B 0 maps are shown at the top. Under the ideal conditions, all the refocused methods provided largely artifact-free T 1ρ relaxation time maps at all SL amplitudes, while the nonrefocused methods showed artifacts at the edges of the FOV at low SL amplitudes. Under the non-ideal conditions, the nonrefocused T 1ρ methods in particular performed poorly at lower SL amplitudes, while the refocused methods provided mostly artifact-free relaxation time maps at all SL amplitudes. The differences between the ideal and nonideal conditions can particularly be seen at the top and bottom edges with more significant field inhomogeneities. FOV, field of view; MNAD, mean normalized absolute deviation; ROI, region of interest; SL, spin lock orientation, the adiabatic T 1ρ SL varies between off-resonance and on-resonance T1ρ during the adiabatic sweep, where the amplitude and frequency of the pulse are modulated during the time course of the pulse. 39 From the simulations, it was evident that the refocused adiabatic methods presented here are highly insensitive to ΔB 0 and B 1 field inhomogeneities. The robustness of the refocused adiabatic methods exceeded the simulated range of variation for the RF power, while the robustness against B 0 variations depended on the specific scheme. The doublerefocused adiabatic BIR-4 and HS1 versions were found to be the most robust in the simulations, while experimentally, the double-refocused BIR-4 scheme was found to be the most robust. The low-powered (600-Hz) adiabatic CW-T 1ρ , which had an AHP pulse approximately four times longer than the high-powered (2.5-kHz) AHP pulse, was highly insensitive to field inhomogeneities at the higher SL amplitude of 400 Hz in the simulations ( Figure S3B). This simulation demonstrates that when the maximum B 1 amplitude of the AHP pulses is brought closer to the spinlocking amplitude, then adiabatic CW-T 1ρ becomes highly insensitive to B 0 inhomogeneities that are of the order of or smaller than the spin- Under the ideal conditions, all the refocused methods provided largely artifact-free T 1ρ relaxation time maps at all SL amplitudes, while the nonrefocused methods showed artifacts at the edges of the FOV at low spin-lock amplitudes. Under the non-ideal conditions, the non-refocused T 1ρ methods performed poorly at lower SL amplitudes, while the refocused methods were able to mitigate the most severe artifacts, especially at the higher SL amplitudes. The arrows indicate locations where differences (artifacts) can be noted between the conditions. FOV, field of view; MNAD, mean normalized absolute deviation; RF, radio frequency; ROI, region of interest; SL, spin lock severe banding artifacts in the T 1ρ relaxation time maps under the non-ideal conditions, at SL amplitudes equal to and below ΔB 0 . At higher SL amplitudes (ω 1 > ΔB 0 , or ω 1 >> ΔB 0 ), the banding artifacts were minimal for all the schemes, unless B 1 variation was also present.
The differences in the sensitivities to field inhomogeneities between the preparation schemes were assessed by calculating the MNAD values between the measurements conducted at ideal versus non-ideal conditions. This approach, while potentially dependent on the changes in the experimental conditions, provides a handle on the sensitivities of the methods, summarizing the results over all the measured samples. Among the hard-pulse schemes, the non-refocused preparations stood out with the largest deviations between the ideal and non-ideal cases, while the refocused methods showed significantly smaller deviation between the cases at all SL amplitudes. The adiabatic refocused schemes were aligned with the hard-pulse alternatives with similar small deviations. However, these analyses were conducted only in the tissues that had high SNR and were not clearly at off-resonance (such as the fatty bone marrow tissue). Further experimental differences were seen at the extreme areas, such as the fat, or the edges of the coil-visible region for the tomato specimen in Figures 5 and 6, and particularly in the phantom (Figure 7), where the non-refocused methods, the B-SL method, 18 and the double-refocus adiabatic HS1 preparations showed signal loss and banding artifacts. The experimental performance of the adiabatic double-refocus scheme incorporating HS1 inversion pulses was not as good as that of the BIR-4 approach, despite providing the most promising simulation results. This could be because of the flip angle dispersion effects of the HS1-AFP pulse on the magnetization components not being collinear with it, 28 as is the case here. Two HS1-pulses were utilized to compensate for this effect, but the result remained inferior to that achieved by using an adiabatic plane rotation BIR-4 pulse.
In the clinical setting, T 1ρ relaxation measurements could provide important insights into disease diagnosis and progression. 33 was found to be the most robust against field inhomogeneities for improving the T 1ρ quantification. However, the most significant problem with this method is its significantly increased RF energy deposition: as realized here, the baseline zero SL pulse has a duration of approximately 18 ms at an RMS amplitude of 2.3 kHz, which is already well beyond what is typically even achievable on a clinical scanner (often the maximum transmit power is below 1 kHz, even for local transmit coils). 43 Besides the increased power requirements, such pulses are also likely to exceed SAR safety limits, 14 further limiting the use of such T 1ρ preparations. Among the less RF-intensive, yet ΔB 0 and B 1 insensitive T 1ρ preparation schemes, the single-refocus scheme 14 with minimal RF energy deposition appears to be the most feasible for in vivo imaging. However, because the magnetization after this preparation will be at the negative z axis, a spin-echo type of readout sequence would be preferable over a gradient-echo sequence with relatively small tip angles, which will drive the magnetization through zero if longer echo trains are collected. Alternatively, for a gradientecho readout sequence, an additional (adiabatic) inversion pulse could potentially be utilized at the end of the preparation to avoid this effect.
Considering the overall scan duration, gradient-echo sequences with short TR and RF cycling 44 or tailored flip angles 45 could be utilized to enable faster scans.
Other possibilities for improved T 1ρ have been presented previously, such as the one by Mitrea et al. 15 Initial tests ( Figure S5), however, suggested it to be more sensitive to field variations than the single-refocus method reported by Witschey et al., 14 further supported by the simulations (see the supporting information). Another very promising approach utilizes adiabatic excitation and rewinder pulses at the same amplitude as the target SL amplitude. 16,46,47 Simulations with a nearly matched amplitude SL pulse 16,47 suggested that this non-refocused adiabatic scheme performs very well against the field inhomogeneities (see the supporting information). However, this sequence is more akin to the adiabatic T 1ρ method, 7,24,25,43 and is a combination of on-resonance and off-resonance T 1ρ relaxation. Another potential challenge with this method is maintaining the adiabatic condition at very low SL amplitudes. Utilizing fully adiabatic spin locking 22,24,29,37,38 can further mitigate the effects of field inhomogeneities and even provide slice selectivity 37 as well as reduced orientation/magic angle dependence. 7 A variation of the doublerefocused hard-pulse preparation scheme investigated here 18 was presented recently with promising results, but without direct comparison with other preparation methods. 48 Besides presenting a method for faster T 1ρ acquisition by using tailored variable flip angle scheduling, Johnson et al. 45 also utilized a partially adiabatic variation of the single-refocus method by Witschey et al., 14 replacing the hard 90 pulses with adiabatic pulses. This variation presents another interesting option for T 1ρ preparation; however, no direct comparison with other T 1ρ preparations with respect to sensitivity to inhomogeneities was provided.
The present study has certain limitations, including a limited selection of previously presented methods for the experimental generation of T 1ρ contrast. The number of samples is limited, and all the experiments were carried out at 9.4 T and using a relatively high maximum B 1 amplitude. However, the differences between the methods were generally confirmed with the simulations; similar practical differences may be expected with B 0 and B 1 variations regardless of the main field strength, although the practical in vivo importance is ultimately revealed with real measurements.
In conclusion, artifacts arising from the field inhomogeneities in CW-T 1ρ -weighted imaging can be efficiently suppressed by different refocused spin-locking pulse schemes. In this numerical, experimental, and theoretical comparison of different T 1ρ contrast preparation methods, the double-refocus adiabatic BIR-4 preparation was found to be the most robust. However, because of the excessive RF energy deposition of the adiabatic method, its use is likely restricted to the preclinical setting. Of the less RF-intensive methods, the ΔB 0 and B 1 compensated singlerefocus hard-pulse CW-T 1ρ method reported by Witschey et al. 14 and the proposed triple-refocused method proved to be very robust against field inhomogeneities. The simulations confirm the increased robustness of the low-power AHP CW spin locking, and both the experimental and the simulation findings promote the use of the previously reported hard-pulse single-refocus ΔB 0 and B 1 insensitive method for clinical use, while the adiabatic double-refocused BIR-4 method could be preferred for ex vivo experiments.