Capturing Fast Relaxing Spins with SWIFT Adiabatic Rotating Frame Spin-lattice Relaxation (T_1ρ) Mapping

Abstract

Rotating frame spin-lattice relaxation, with characteristic time constant T_1ρ, provides a means to access motion-restricted (slow) spin dynamics in MRI. Due to their restricted motion, these spins are sometimes characterized by a short transverse relaxation time constant T₂ and thus can be difficult to detect directly with conventional image acquisition techniques. Here we introduce an approach for three-dimensional adiabatic T_1ρ mapping based on a magnetization prepared Sweep Imaging with Fourier Transformation (MP-SWIFT) sequence which captures signal from almost all water spin populations including the extremely fast relaxing pool. A semi-analytical procedure for T_1ρ mapping is described. Experiments on phantoms and musculoskeletal tissue specimens (tendon, articular and epiphyseal cartilages) were performed at 9.4 Tesla for both the MP-SWIFT and fast spin echo (FSE) read outs. In the phantom with liquids having fast molecular tumbling and single-valued T_1ρ time constant, the measured T_1ρ values obtained with MP-SWIFT and FSE are similar. Conversely, in normal musculoskeletal tissues, T_1ρ values measured with MP-SWIFT are much shorter relative to values obtained with FSE. Studies of biological tissue specimens demonstrated that T_1ρ-weighted SWIFT provides higher contrast between normal and diseased tissues as compared to conventional acquisitions. Adiabatic T_1ρ mapping with SWIFT readout captures contributions from the otherwise undetected fast relaxing spins allowing more informative T_1ρ measurements of normal and diseased states.

Introduction

The time constant T_1ρ characterizes spin-lattice relaxation in the rotating frame (1).T_1ρ is sensitive to the interactions between motion-restricted water molecules and the corresponding local macromolecular environment (2,3). With T_1ρ, the slow motional regime can be accessed at high magnetic field (2,3). Previous studies have shown that T_1ρ is sensitive to structural alterations in musculoskeletal tissues, often providing more information than might be obtained from analysis of conventional longitudinal or transverse relaxations (2,4-7). Specifically, T_1ρ relaxation has been shown to be sensitive to the proteoglycan (PG) loss in the early stage of articular cartilage degeneration (8-14) and in cases of vertebral disc degeneration (15), and has been found utility in the study of epiphyseal cartilage of the developing skeleton (16).

T_1ρ is traditionally measured by applying a continuous wave (CW) pulse which “locks” the magnetization to the effective field direction (17). The CW spin-lock (CW-SL) pulse creating an effective field (in the kHz range) in the ‘y’ direction (in the first rotating frame) is usually embedded between 90°_x and 90°_-x rotations that are accomplished with short hard pulses or adiabatic half passage pulses (18). Alternatively, relaxation in the rotating frame can be studied using a time-dependent spin-locking field, for example, created by a train of frequency-modulated adiabatic full-passage (AFP) pulses (19-22). This technique, entitled “adiabatic T_1ρ”, was recently shown to provide sensitive detection of structural changes in articular cartilage (13,14,23). Adiabatic T_1ρ characterizes relaxation during RF irradiation when the magnetization vector is aligned with the direction of the time-dependent effective field (B_eff(t)) (Fig.1). As compared with the conventional CW-SL method, the adiabatic T_1ρ method is less affected by inhomogeneity of B₁ and static field B₀ due to the offset independent adiabaticity property of the AFP pulses (24). The adiabatic relaxation methods are inherently sensitive to a broader range of molecular motions as compared to the CW method (19). Further, it has been recently demonstrated that adiabatic T_1ρ reduces magic angle dependence in relaxation mapping (25). All these features are critical for tissue characterization and especially during in vivo study when homogeneity of the B₁ and B₀ fields could be altered by patient motion (23).

Fig.1.

(a) Illustration of adiabatic T_1ρ relaxation in the Larmor rotating frame. During the adiabatic rotation the magnetization follows the effective field B_eff. (b) Schematic of the magnetization prepared SWIFT sequence. MP blocks are embedded after each m number of SWIFT readout periods (mTR periods). Each MP block is composed of four AFP pulses, with consecutive phases prescribed according to the MLEV4 scheme.

In real tissues, multiple spin populations which are characterized by short and long relaxation time constants have been shown to exist. Different T₂ or T_1ρ relaxation times were found in tendon or cartilage tissues by using rapid imaging sequence or spectroscopy methods (26-28). Water bound tight or closely associated to macromolecules tends to have short T₂ and T_1ρ values, thus has conventionally been undetected due to very short transverse relaxation time (26,27). Characterization of these pools and the correlation of MR properties with tissue microstructure are critically important (29). On the other hand, conventionally, T_1ρ relaxation measurements are performed by interleaving the readout of an imaging sequence with magnetization preparation (MP) blocks used for generating T_1ρ weighting. In tissues having fast relaxing components in sub-millisecond range, e.g. in highly ordered tissues or highly mineralized tissues, the measurement of T_1ρ using conventional sequences as read out is problematic due to considerable signal decay during the echo time (TE) before the detection (30).

In this paper, we introduce a three-dimensional (3D) adiabatic T_1ρ relaxation time mapping utilizing an ultrashort T₂-sensitive sequence for readout, in addition to the existing 3D T_1ρ relaxation time mapping techniques (31-34). Multiple MRI pulse sequences capable of preserving signal from fast relaxing spins have been developed in recent decades (35-40). In general all these developed techniques are applicable to use as readout for the proposed T_1ρ relaxation mapping with preserved short T₂ components. In this paper, the Sweep Imaging with Fourier Transformation (SWIFT) sequence was used as the readout sequence (39,41). SWIFT is an emerging technique that allows imaging of almost all biological tissues including tissues with ultra-short T₂ relaxation times in the microsecond time scale (39,41,42). With appropriate parameters, SWIFT provides nearly pure proton density weighted imaging, and by utilizing magnetization preparation embedded within this sequence, different types of contrasts (T₁, T₂, T_1ρ, T_2ρ etc.) can be generated (42-45). Here, we describe the experimental setup and semi-analytical procedure to generate and quantify the T_1ρ relaxation with SWIFT readout, and demonstrate application of T_1ρ for quantification of osteochondral and tendon specimens.

Methods

Pulse sequence

The pulse sequence diagram is shown in Fig.1b. MP blocks are embedded after each m number of SWIFT readout periods (m TR periods). Each MP block is composed of four AFP pulses of the hyperbolic secant HSn family (here n is the stretching factor) (46), each having a duration of t₁₈₀ with phases prescribed according to the MLEV4 phase cycling scheme (47). The minimal duration for one MP block is defined as ΔT_mp = 4t₁₈₀. The variable duration of the MP train is equal then to T_mp = ΔT_mp · N_mp, with N_mp as the number of MP blocks.

Steady state signal equation

In regular SWIFT without any magnetization preparation, the repeated excitation drives the spin system to the steady state with equilibrium magnetization:

$$A_{\mathit{\text{ss}}}=M_0(1-E_1)/(1-E_{1}cos\theta ),$$ [1]

where $E_1=e^{-\frac{\mathit{\text{TR}}}{T_1}}$ and θ is the excitation flip angle (39,48) With the preparation block, the steady-state magnetization generated during MP-SWIFT is different and depends on T_mp. Simulations based on Bloch equations show the evolutions of M_z to different steady states for different T_mp settings (Fig. 2). Of relevance, as shown in Fig. 2, two competitive processes, i.e., signal decay with time constant T_1ρ and signal recovery with T₁, cause the steady-state signal to oscillate about an average value. This oscillating steady state is used for the reconstruction of 3D images. The average steady-state signal intensity in this case is given by (see Appendix A):

Fig.2.

Bloch simulations showing evolution of the signal to the steady-state during MP-SWIFT pulse sequence with different T_mp values. The observed signal oscillation is the result of two processes: T_1ρ decay during each T_mp (black portion) and T₁ recovery during m SWIFT readouts (color-coded points). The parameters used for simulations were: T₁ = 500 ms, T_1ρ = 40 ms, TR = 2.6 ms, m = 16, t₁₈₀ = 1.5 ms and SWIFT flip angle = 2°.

$$S(T_{\mathit{\text{mp}}})=\frac{A_{\mathit{\text{ss}}}(1-B)}{2}\frac{1+E_{\rho }}{1-B{E}_{\rho }},$$ [2]

where $E_{\rho }=e^{-\frac{T_{\mathit{\text{mp}}}}{T_{1\rho }}}$ and $B=E_1^m{cos}^m\theta$. After normalization by $\frac{(1-B)}{2}S(T_{\mathit{\text{mp}}}=0)$, the Eq. 2 becomes

$$S(T_{\mathit{\text{mp}}})=\frac{1+E_{\rho }}{1-B{E}_{\rho }},$$ [3]

By separating out the exponential decay E_ρ and taking the logarithm:

$$ln{S}_e(T_{\mathit{\text{mp}}})=ln{E}_{\rho }=ln\frac{S(T_{\mathit{\text{mp}}})-1}{S(T_{\mathit{\text{mp}}})B+1}=-\frac{T_{\mathit{\text{mp}}}}{T_{1\rho }}.$$ [4]

S_e is the modified signal, which is a mono-exponential function in this case. On the logarithmic scale, S_e is represented by a straight line with slope equal to $-\frac{1}{T_{1\rho }}$. In practice, T_1ρ can be estimated from the set of data measured with different T_mp. Obviously, the signal also depends on T₁ relaxation, and thus an independent acquisition for measuring T₁ is required. Here, the variable flip angle method with SWIFT readout was used to acquire T₁ maps (49).

Two water pools: the fitting strategy

In the previous section the description of the single pool spin system was presented. In the case of real tissues, multiple pools of water populations should be considered (27,50). The most practical model is a two pool system, characterized by two different proton populations: free water and bound water (27), having “slow relaxation” with long $T_{1\rho }(T_{1\rho }^s)$ and “fast relaxation” with short $T_{1\rho }(T_{1\rho }^f)$, respectively. The signal having contributions from both slow and fast relaxing components can be described as:

$$S(T_{\mathit{\text{mp}}})=S_s(T_{\mathit{\text{mp}}})+S_f(T_{\mathit{\text{mp}}})=C_s\frac{1+E_{\rho s}}{1-B{E}_{\rho s}}+C_f\frac{1+E_{\rho f}}{1-B{E}_{\rho f}},$$ [5]

where $E_{\rho s}=e^{-\frac{T_{\mathit{\text{mp}}}}{T_{1\rho }^s}}$ and $E_{\rho f}=e^{-\frac{T_{\mathit{\text{mp}}}}{T_{1\rho }^f}}$, and C_s and C_f are normalized populations of the two components separately (C_s + C_f = 1). The average relaxation time constant $(T_{1\rho }^{\mathit{\text{ave}}})$ is the slope of ln(S_e) at T_mp → 0:

$$\frac{1}{T_{1\rho }^{\mathit{\text{ave}}}}=\frac{C_s}{T_{1\rho }^s}+\frac{C_f}{T_{1\rho }^f},$$ [6]

In principle, the relaxation parameters can be estimated by fitting the experimental data using Eq. 5. The quality of fitting, however, critically depends on the relative difference between intrinsic relaxation parameters of the two pools and also on the sufficiency of sampling points of the relaxation decay curves. Note that the relaxation time constants of the two components should be sufficiently different in order to be separable with a given noise level (51). Even if these two components are very different, an adequate sampling of the short component could be problematic because of the limited duration of the AFP pulses which require sufficient peak power to satisfy adiabaticity. Thus, the reliability of experimental mapping of the exact $T_{1\rho }^s$, $T_{1\rho }^f$ or even $T_{1\rho }^{\mathit{\text{ave}}}$ values is questionable. Therefore, we propose to use two values, $T_{1\rho }^a$ and $T_{1\rho }^s$, representing the asymptotic average relaxation time and the slow relaxation time, respectively. The $T_{1\rho }^a$ value can be determined from the slope of the line connecting the first two data points on the logarithmic scale (red solid line in Fig. 3a). The value of $T_{1\rho }^a$ approaches $T_{1\rho }^{\mathit{\text{ave}}}$ (empty circles in Fig. 3b) when ΔT_mp → 0, as shown in Fig. 3b. With increasing T_mp, the contribution of the fast relaxing component vanishes, which allows the long T_1ρ component to be estimated from the tail of the relaxation decay curve (see Appendix B for details). A representative example of the fitting is shown in Fig. 3a.

Fig.3.

(a) Fitting example of the simulated decay S(T_mp) (red circles). The parameters used for simulations are: $T_{1\rho }^f=10\text{ms}(50\%\text{population})$and $T_{1\rho }^s=150\text{ms}(50\%\text{population})$. T₁ was assumed to be the same for both fast and slow relaxing components, T₁ = 1000 ms. The red solid line shows the fitting using just the first two data points ( $T_{1\rho }^a$) to provide an estimation approaching $T_{1\rho }^{\mathit{\text{ave}}}$. The grey dash-dot line shows the resulting $T_{1\rho }^s$ and C_s obtained from the intermediate fitting (black dash line) (see Appendix B for details). (b) Examples of the asymptotic $T_{1\rho }^a$ approaching $T_{1\rho }^{\mathit{\text{ave}}}$ at different conditions. The empty circles are the values of $T_{1\rho }^{\mathit{\text{ave}}}$.

Experimental details

Phantoms

Test experiments were performed on three separate phantoms containing 0.1, 0.1, and 0.4 mM MnCl₂ in DI water, agar, and DI water, respectively. These solutions were poured in glass tubes immersed in a bigger tube containing saline solution. The T₂ values of these three phantoms were all above 20 ms.

Tissue specimens

Two specimens were studied: a piece of mature bovine Achilles tendon (size = 1×1×1 cm³), and a juvenile femoral condyle from a 12 week-old pig (size = 3×3×3 cm³) including both articular and epiphyseal cartilage layers. The animal specimens were placed in tubes and immersed in Fluorinert (3M, Minnesota, USA) to match the magnetic susceptibility.

All images were acquired on a 9.4 T-31 cm bore horizontal animal MRI scanner (Agilent Technologies, Santa Clara, CA USA), using a volume transmit/receive coil (Agilent Technologies) or a homemade coil with three parallel loops of a 22 mm diameter. All simulations and data processing were performed using MATLAB (R2012b, The Mathworks). For T_1ρ measurement, variable numbers of MP blocks were added after every 16 SWIFT readout periods (m = 16 in Eq. 2) to obtain images with different T_mp. The experimental parameters are summarized in Table 1. Different durations of the AFP pulses (t₁₈₀) were utilized in order to test the effect of different weighting of fast and slow relaxing components. The peak RF power was matched to ensure adiabatic condition of the AFP pulses, and the time-bandwidth product of the pulse (R) was adjusted to keep excitation bandwidth of the pulse (BW_mp) the same for different pulse durations (24). Thus, the B_eff(t) functions were the same for the different t₁₈₀ values (20). The specific values of the maximal effective frequency and the averaged effective frequency are shown in Table 1. The time to acquire 128,000 radial spokes with each setting of T_mp varied from 5 to 11 minutes, depending on T_mp. The spokes in k-space were isotropically distributed on a sphere using the pseudo-random Halton approach to minimize signal oscillation effects on the steady state (52). All MP-SWIFT $T_{1\rho }^a$ and $T_{1\rho }^s$ maps were generated using linear least squares fitting on a pixel-by-pixel basis in the logarithmic coordinate of the transformed signal (S_e) according to the developed algorithm. For T₁ measurement, images with flip angles of 1, 3, 5, 7, 10 degrees were acquired, then fitted to the Ernst equation using a non-linear least square algorithm to generate the corresponding T₁ map (49). BW = 125 kHz and TR = 2.6 ms were used for all SWIFT acquisitions.

Table 1. Parameters Used In FSE and SWIFT T_1ρ Measurements.

Sample	t180 (ms)	Nmp	BWmp (kHz)	${\omega }_{1\mathit{\text{eff}}}^{\mathit{max}}$ (kHz)	${\omega }_{1\mathit{\text{eff}}}^{\mathit{\text{ave}}}$ (kHz)	θ (°)	Resolution (μm2)
Phantom 1	1.5	SWIFT: 0, 2, 4 FSE: 0, 4, 8	10	5	5	2	130 × 130
Phantom 2	3	SWIFT: 0, 1, 2 FSE: 0, 2, 4	10	5	5	2	130 × 130
Phantom 3	3	SWIFT: 0, 1, 2 FSE: 0, 2, 4	4.8	5	2.7	2	130 × 130
Tendon	0.3	SWIFT: 0, 1, 2, 3, 4, 6, 8, 12, 16	18	10	8.5	4	78 × 78
	1.2	SWIFT: 0, 1, 2, 3, 4, 5	18	10	8.5	4	78 × 78
Femoral condyle	2	SWIFT: 0, 1, 2, 3, 4 FSE: 0, 1, 2, 3, 4, 6	10	5	5	3	130 × 130

For comparison, the T_1ρ relaxation time constants were also measured with a single-slice 2D fast spin echo (FSE) sequence used as readout following a number of MP blocks. The preparation pulse parameters were matched to the MP-SWIFT (i.e., the same AFP pulses, duration and RF power). With FSE, TR = 5000 ms, effective TE = 5.5 ms, ETL = 4, thickness = 1 mm, matrix size = 256 × 256 and bandwidth = 130 kHz were used. The choice of 2D FSE which was used here for comparison with MP-SWIFT is justified because it is a commonly used as readout for T_1ρ measurements and has sufficient SNR to guarantee good accuracy. The long TR in FSE destroys the steady-state condition and therefore signal decays exponentially during the length of T_mp, and thus, T_1ρ maps were generated using linear least squares fitting on a pixel-by-pixel basis to the exponential function:

$$S=k{e}^{-T_{\mathit{\text{mp}}}/T_{1\rho }}.$$ [7]

For comparison with FSE, SWIFT images were averaged to the same thickness (= 1 mm) as the FSE images.

To assess the reproducibility of the proposed technique, a distal humeral trochlea of a 10-week old pig (size = 3×3×3 cm³) was scanned 3 times during the same day utilizing the same parameter set as was used for the porcine femoral condyle (Table 1).

Results

The signal-to-noise ratio (SNR) of the SWIFT image in all experiments with N_mp = 0 was higher than 60. The SNR decreases as T_mp increases, but was greater than 20 for all T_mp. SNR was calculated by taking the ratio of the mean of the signal intensities in a given ROI and the standard deviation of the signal of a ROI from the background.

In Fig.4 the T_1ρ relaxation time constants of the MnCl₂ phantoms (with T₂>20ms) measured by FSE and SWIFT sequences are shown. The T_1ρ of the 0.1 mM of MnCl₂ solution was approximately 320 ms. The addition of agar to the 0.1 mM MnCl₂ solution changed the T_1ρ time constant to approximately 200 ms as measured by either sequence. The T_1ρ values of the phantom with higher concentration of MnCl₂ at 0.4 mM were around 85 ms in both FSE and SWIFT measurements (Fig. 4). The T_1ρ of saline was around 2.6 s with both SWIFT and FSE measurements, as expected for the fast tumbling spins. This also further verified that the signal equation for the single component is accurately described by Eq. 2.

Fig.4.

(a) Representative T_1ρ time constant maps of MnCl₂ doped agar (smaller tube) merged in the bigger tube containing saline. (b) Example plots of the signal evolution for both saline and MnCl₂ doped agar. Both FSE and SWIFT plots are indicating single component decay. (c) Comparison of the adiabatic T_1ρ values of three different phantoms measured with FSE and SWIFT sequences. 400 data points were plotted for each phantom. The solid line is the line of identity, representing perfect correspondence. The dash line is the linear fit of the averaged T_1ρ values from the three data sets, with r = 0.999 and p < 0.01. Each data point corresponds to one voxel in the T_1ρ maps.

The T_1ρ decay curves of a bovine tendon specimen obtained with the MP-SWIFT sequence at different t₁₈₀ values are shown in Fig. 5. Because tendon is a highly ordered tissue and characterized by short T₂, it is practically undetectable with conventional MRI sequences. Therefore, only measurements with SWIFT are presented. From the data points shown in Fig. 5, it is apparent that the S_e decay has multiple components with different decay rates. Since the effective fields produced with t₁₈₀ = 0.3 and 1.2 ms were kept the same, some data points are overlapped as expected. In the case of t₁₈₀ = 2.0 ms, the fitted $T_{1\rho }^a$ is equal to 16.8 ms, whereas for t₁₈₀ equal to 0.3 ms, $T_{1\rho }^a$ decreases to 6.0 ms. These results suggest that reducing t₁₈₀ increases weights of fast relaxing spins. Fittings of $T_{1\rho }^s$ with T_mp > 5 ms demonstrate the method of extraction of information about slowly relaxing spins. In both t₁₈₀ = 0.3 and 1. 2 ms cases, the fitted $T_{1\rho }^s$ value and the population are similar.

Fig.5.

MP-SWIFT images of the bovine tendon specimen acquired with different T_mp (a) and graphs (b,c) representing S_e signal measured in ROI (shown in the image by yellow square) with two different t₁₈₀ durations. The data points did not fall on the same line indicate multiple decay rates. Since the effective field for pulses with durations of t₁₈₀ = 0.3 and 1.2 ms were kept the same, some data points were overlapped as expected. (b,c) The solid lines are drawn by connecting first two data points, the slopes of which determines ${\mathit{T}}_{\mathbf{1}\mathit{\rho }}^{\mathit{a}}$ in experiments with different t₁₈₀. The asymptotic ${\mathit{T}}_{\mathbf{1}\mathit{\rho }}^{\mathit{a}}$ decreases with decreasing t₁₈₀ demonstrating increased weighting from the fast relaxing spins. The dash lines are the fittings of data points with T_mp > 5 ms from which the contribution from slowly relaxing spins can be retrieved.

T_1ρ maps and decay plots of a juvenile porcine femoral condyle are shown in Fig.6. The juvenile femoral condyle reveals the homogenous appearing epiphyseal cartilage (z2 in Fig.6a), in addition to the articular cartilage in the most superficial layer of the tissue (z1 in Fig.6a). Longer T_1ρ in the articular cartilage compared to the epiphyseal cartilage is observed. The zonal organization is similar in both SWIFT $T_{1\rho }^a$ (Fig.6a) and FSE T_1ρ maps (Fig.6b), however with different absolute values. A focal lesion due to vascular failure within the epiphyseal cartilage is easily identifiable (black arrows, Fig.6a). The focal lesion near the interface of cartilage and bone reveals higher T_1ρ values in all T_1ρ maps. The corresponding hematoxylin and eosin (H&E) stain histology shows the necrotic cartilage matching the focal lesion (Fig.6c). The T_1ρdecays on the logarithmic scale of the 2D FSE and 3D SWIFT T_1ρ measurements are shown in Fig.6d and Fig.6e, respectively. For normal tissues, the signal obtained with FSE readout (blue line in Fig.6d) is apparently single component decay, while the signal from SWIFT readout (blue line in Fig.6e) reveals multiple decay rates. Interestingly, the lesion shows multiple components even in the FSE measurement (red data points in Fig.6d). The fitted $T_{1\rho }^a$ and $T_{1\rho }^s$ values from the ROI in the lesion are very similar in both SWIFT (Fig.6e) and FSE (Fig.6d) measurements (red points and lines). This implies the absence of fast relaxing components within the lesion. SWIFT $T_{1\rho }^s$ maps obtained using the strategy described above are shown in Fig.6f. Notably, the SWIFT $T_{1\rho }^s$ map is very similar to the FSE T_1ρ map in Fig.6b. The apparent population map of the fast relaxing spins, which was generated from C_s in the SWIFT measurement, is shown in Fig.6g. The overall fraction of the fast relaxing component is around 50% in epiphyseal cartilage and 30% in articular cartilage. The fraction of the fast relaxing component in the area of the lesion is close to 2%. The T₁ value measured in the lesion area was ∼1600 ms, which is longer than the T₁ of normal surrounding tissues (1100 ms). The contrast between normal tissue and the lesion is shown in Fig.6h. The maximal relative relaxation time's difference (RRTD) between normal and lesion tissues RRTD = [T_1ρ(lesion) - T_1ρ (normal)]/ T_1ρ (normal) from SWIFT $T_{1\rho }^a$ map is about 6 times higher than that obtained with FSE readout.

Fig.6.

T_1ρ maps and example of the fitting strategies of the juvenile porcine femoral condyle specimen. The maps in (a) are the same map presented with different color scale. A gradient of the T_1ρ values along the direction of the cartilage depth is observed in all maps. Below the articular cartilage (labeled as z1 in (a) is the epiphyseal cartilage (labeled as z2 in a). SWIFT $T_{1\rho }^a$ values of the normal epiphyseal growth and articular cartilage are much shorter than T_1ρ measured by FSE (b), while the SWIFT $T_{1\rho }^s$ (f) values are close to FSE T_1ρ (b). (c) H&E stain of the same specimen revealing the focal area of chondronecrosis matching the lesion detected in MR images. The signal from a ROI in normal tissues (blue line in d) from FSE experiment is apparently single component decay, while the signal from SWIFT experiment (blue line in e) exhibits multi-component decay. The signal from the ROI in the lesion region shows multi-exponential decay even in the FSE measurement (red data points in d). Of note, the T_1ρ values within the lesion region is comparatively similar for SWIFT and FSE measurements, which implies the absence of fast relaxing components within the lesion. This conclusion is also supported by population map of the short component shown in (g). (h) The average values of T_1ρ from ROI over the normal epiphyseal cartilage and the focal lesion areas. The relative contrast between normal and lesion tissues in the SWIFT $T_{1\rho }^a$ map is much higher than in the FSE T_1ρ map.

Since an independent acquisition aiming at measuring T₁ is needed for determination of T_1ρ values, the dependence of the deviation in T_1ρ estimation (defined a $D_{T_{1\rho }}=\frac{(T_{1\rho \mathit{\text{fitted}}}-T_{1\rho \mathit{\text{real}}})}{T_{1\rho \mathit{\text{real}}}}$) on the deviation of T₁ ( $D_{T_1}=\frac{(T_{1\mathit{\text{fitted}}}-T_{1\mathit{\text{real}}})}{T_{1\mathit{\text{real}}}}$) is analyzed and shown in Fig.7a. As can be seen, D_T1ρ does not have an apparent dependency on the T_1ρ values, and is roughly linear with the D_T1. From the theory section and Appendix B, the obtained $T_{1\rho }^s$ and C_f will deviate from the true values if the approximation $T_{1\rho }^s\gg T_{1\rho }^f$ is not fully satisfied. Figure 7b-d shows examples of the estimated deviation of $T_{1\rho }^s$, C_s and C_f originating from the fitting procedure. Within the range of $\frac{T_{1\rho }^s}{T_{1\rho }^f}$ ratio from 10 to 30, the error from the fitting model is less than 15% in most cases. The fitting error source from SNR were also analyzed by Monte-Carlo simulation and showed in Fig. 7e & f.

Fig.7.

(a) The dependence of the deviation of T_1ρ, $D_{T_{1\rho }}(=\frac{(T_{1\rho \mathit{\text{fitted}}}-T_{1\rho \mathit{\text{real}}})}{T_{1\rho \mathit{\text{real}}}})$, on the deviation of T_1, $D_{T_1}(=\frac{(T_{1\mathit{\text{fitted}}}-T_{1\mathit{\text{real}}})}{T_{1\mathit{\text{real}}}})$. (b), (c) & (d) show the relative deviations $D_v=\frac{|V_{\mathit{\text{fitted}}}-V_{\mathit{\text{real}}}|}{V_{\mathit{\text{real}}}}$, with v representing, $T_{1\rho }^s$, C_s or C_f respectively. The deviations originated from the approximations used in the fitting procedure. $T_{1\rho }^f$ was fixed to 10 ms. For the $\frac{T_{1\rho }^s}{T_{1\rho }^f}$ ratio in the range from 10 to 30, the intrinsic error from the fitting model was less than 15%. (e) & (f) Dependence of the fitting error on SNR by using Monte-Carlo simulation. $T_{1\rho }^f=10\text{ms}$ and $T_{1\rho }^s=250\text{ms}$ was used with equal population. For each data point in (e) & (f), the fitting process was repeated 1000 times with noise chosen from the corresponding normal distribution randomly.

For the reproducibility experiment, the measured relaxation time constants and population from the three separate scans with SWIFT readout on the same specimen in the epiphyseal cartilage layer from the same ROI were [average ± standard deviation (coefficient of variation) over the three scans]: $T_{1\rho }^a=65.1\pm 2.7\text{ms}(4.14\%)$, $T_{1\rho }^l=271\pm 8.0\text{ms}(2.95\%)$, C_f = 0.59 ± 0.03 (5.08%).

Discussion

In this work measurement of adiabatic T_1ρ in 3D using the SWIFT sequence was proposed and analyzed. Sensitivity of the sequence to different spin populations, including both fast and slow relaxing spins, was shown and the application to the musculoskeletal system was exemplified.

In biological tissues, several types of motional processes contribute to the relaxation mechanisms. Depending on the tissue, more than one relaxation mechanism may be operative simultaneously, but with different relative contributions. Generally, the more rapidly relaxing component is assigned to water that is more tightly bound to macromolecules (such as proteoglycans and collagens in cartilage), and the slow relaxing component is assigned to bulk water.

In the phantom study of single component relaxation with comparatively long T₂, FSE-T_1ρ matches well with the SWIFT-T_1ρ in phantoms with different T_1ρ values (Fig.4). For the juvenile porcine femoral condyle (Fig. 6), the measured FSE-T_1ρ in the articular and epiphyseal cartilage is around 300 and 200 ms, respectively. This is similar to the values previously reported by Toth etc. on juvenile goat specimens using FSE readout (16), but higher than the adiabatic T_1ρ values measured in mature specimens with FSE readout, which fall in 100-200 ms range (13,14,23). Note besides specimens, the specific parameters used in these studies were also not the same. While only one relaxing component was found in these previous studies with FSE readout, here by using SWIFT, apparent multi-component decay rates are observed in biological specimens (Fig.5 & 6). The measured $T_{1\rho }^a$ values using SWIFT were all much shorter than the T_1ρ measured with FSE (Fig.6). In Fig.6, the T_1ρ values of a focal lesion in a juvenile porcine femoral condyle specimen are much longer than those in the normal surrounding tissues in both FSE and SWIFT measurements. T_1ρ within the lesion is much closer in SWIFT and FSE mapping comparing to normal tissues, which implies the lack of fast relaxing spins within the area of concern. It is consistent with the histological finding of chondronecrosis, a disease process characterized by the degradation of the normal, tightly bound collagen and proteoglycan structures. This is also in agreement with the population map of the short component shown in Fig.6g, where in the lesion region, the lowest population of fast relaxing component is close to 2%.

From the apparent population map of the fast relaxing spins shown in Fig.6g, the overall fraction of the fast relaxing component was around 30% in the articular cartilage. The fast relaxing component originated from water with highly restricted motion, which is more tightly bound to proteoglycan and collagen in cartilage. Prior reports estimated the population of water pool bound to proteoglycan in cartilage at about 15-30% (26,27,50,53), and at 3-6% for the pool of water bound to collagen (50). Thus the total population of fast relaxing spins is measured in same range as our result. In contrast, the populations of the fast relaxing component in epiphyseal cartilage in the developing skeleton from our experiments are around 50% which is a considerably higher value relative to that obtained in articular cartilage. This is expected due to difference in matrix composition between epiphyseal and articular cartilage, for example, the greater concentration of glycosaminoglycan in epiphyseal cartilage (54). A full explanation will require a separate analysis which is beyond the scope of the present work.

The fact that the abnormal tissue within the lesion is dominated by slowly relaxing spins, while the surrounding tissue remains normal with multiple pools of water, reveals the different range of sensitivity of T_1ρ values obtained with SWIFT and FSE readouts. The fitting for $T_{1\rho }^s$ of the slow relaxing components showed in Appendix B was mainly for the purpose of providing proof of principle. In practice, the map of $T_{1\rho }^a$ would be more informative and useful. As illustrated in the theory section, $T_{1\rho }^a$ is a parameter approaching to $T_{1\rho }^{\mathit{\text{ave}}}$ which is the weighted harmonic mean of the long and short T_1ρ values. The slope for first two data points was calculated as the asymptotic value. $T_{1\rho }^a$ contains weighting from $T_{1\rho }^s$, $T_{1\rho }^l$, C_s, C_l and. From Fig.6, the SWIFT $T_{1\rho }^a$ map not only showed the similar multilayer features as the FSE T_1ρ map, but also provided much higher relative contrast between normal and lesion tissues as compared to the T_1ρ maps obtained with FSE readout. Therefore, with the capability of measuring the full dynamic range of the entire spin population in biological tissues, SWIFT $T_{1\rho }^a$ map can maximize contrast for detecting pathology.

The fitting of $T_{1\rho }^a$ only uses the first two data points. The first points are crucial since they include contribution from fast relaxing spins. In the adiabatic T_1ρ, the first point is obtained without any preparation pulse which can preserve maximal fast relaxing signal. In the case of the CW-SL T_1ρ mapping, the first point is measured in presence of two 90° pulses with zero spin-lock time to keep the condition the same for measurements of all points in the relaxation decay. During these pulses the signal from spins having relaxing times comparable to the pulse durations could decay significantly. The latter is why the adiabatic version of T_1ρ was preferred for the present study.

There are several limitations of the developed method and analytical formalism, which need to be elaborated further. Firstly, since the approximation $T_{1\rho }^s\gg T_{1\rho }^f$ was used during the fitting, the fitted $T_{1\rho }^s$, C_s and C_f have intrinsic deviation from the fitting model in addition to experimental errors. Therefore, if separation of the multiple components is desirable, a more extended fitting strategy will be needed to better separate different relaxing components. Secondly, four AFP pulses were used in one MP block which may lead to SAR limitation for in vivo applications, particularly at high field. To reduce SAR and increase efficiency, the AFP preparation was applied every m TR (m = 16 in this paper) instead of every single TR. The SAR of adiabatic pulses could be compared with that of CW-T_1ρ by calculating the root-mean-square RF power; however, due to the differences in pulse modulations, the relaxation phenomena probed by the two methods would be different (20). The benefit of adiabatic pulses is that they offer additional flexibility for alleviating SAR issues (24). Finally, an independent T₁ measurement is required for the quantification of T_1ρ, which leads to a longer total acquisition time. In future work, a view-sharing method might be utilized to reduce the total measurement time (55). Furthermore, the assumption of a single T₁ component, which was applied in both the T₁ and T_1ρ measurements, was based on our earlier work in which multiple T₁ components were not observed in the cartilage system (49). To be more precise, for the systems with multiple T₁ components, further extension of the analytical procedure will be needed. Despite these limitations, many MRI applications may benefit from the improved contrast provided by approaches similar to those introduced here.

Conclusion

In conclusion, a method called MP-SWIFT has been described for measuring T_1ρ in tissues containing fast relaxing spins. The signal equation of the proposed method and a semi-analytical procedure for the T_1ρ mapping were derived. SWIFT-T_1ρ and FSE-T_1ρ values matched well with each other in the case of spins having long T₂ values. However, in normal biological tissues, multiple T_1ρ relaxing components were observed in SWIFT measurements. Besides information about slowly relaxing spins, both simulations and experimental results suggest that SWIFT $T_{1\rho }^a$, a parameter approaching the weighted harmonic mean of the T_1ρ of all decaying components, contains extra contributions from fast relaxing spins which are undetected with FSE readout. The relative contrast ratio between normal and lesion tissues in SWIFT $T_{1\rho }^a$ map was also much higher than in the FSE T_1ρ map. The potential application for detecting degeneration in the musculoskeletal system has been demonstrated, but the extent to which this method can be used remains to be shown. Furthermore, T_1ρ is not only applicable in musculoskeletal tissues, but has also been associated with neurological disorders such as Parkinson's and Alzheimer's diseases (56,57), and has been proposed recently for applications in cardiac (58) and abdominal (59) MRI. The developed 3D SWIFT T_1ρ relaxation mapping technique in this paper also has high potential for studying these diseases.

Abbreviations

T_1ρ

spin-lattice relaxation time in rotating frame

SWIFT

sweep imaging with Fourier transformation

MP-SWIFT

magnetization prepared-SWIFT

FSE

fast spin echo