Observation of bi-exponential T 1ρ relaxation of in-vivo rat muscles at 3T

Abstract

Background

Spin-lattice relaxation in the rotating frame, or T_1ρ relaxation, is normally described by a mono-exponential decay model. However, compartmentation of tissues and microscopic molecular exchange may lead to bi-exponential or multi-exponential T_1ρ relaxation behavior in certain tissues under the application of spin lock pulse field strength.

Purpose

To investigate the presence of bi-exponential T_1ρ relaxations in in-vivo rat head tissues of brain and muscle.

Material and Methods

Five Sprague-Dawley rats underwent T_1ρ imaging at 3T. A B₁-insensitive rotary echo spin lock pulse was used for T_1ρ preparation with a spin lock frequency of 500Hz. Twenty-five T_1ρ-weighted images with spin lock times ranging from 1 to 60 ms were acquired using a 3D spoiled gradient echo sequence. Image intensities over different spin lock times were fitted using mono-exponential as well as bi-exponential models both on region-of-interest basis and pixel-by-pixel basis. F-test with a significance level P value of 0.01 was used to evaluate whether bi-exponential model gave a better fitting than mono-exponential model.

Results

In rat brains, only mono-exponential but no apparent bi-exponential T_1ρ relaxation (∼70–71 ms) was found. In contrast, bi-exponential T_1ρ relaxation was observed in muscles of all five rats (P < 10⁻⁴). A longer and a shorter T_1ρ relaxation component were extracted to be ∼37– ∼ 41 ms (a fraction of ∼80– ∼88%) and ∼9– ∼11 ms (∼12–20%), compared to the normal single T_1ρ relaxation of ∼30– ∼ 33 ms.

Conclusion

Bi-exponential relaxation components were detected in rat muscles. The long and the short T_1ρ relaxation component are thought to correspond to the restricted intracellular water population and the hydrogen exchange between amine and hydroxyl groups, respectively.

Keywords

spin lock bi-exponential rat brain rat muscle

Spin-lattice relaxation in the rotating frame (T_1ρ relaxation), is an MR relaxation mechanism that represents the transverse magnetization decay during the application of a continuous wave (CW) radiofrequency (RF) pulse, i.e. spin lock (SL) pulse, aligned with the net magnetization vector (1). T_1ρ relaxation has high sensitivity to molecular motions and exchanges that have correlation times (τ) such that τ · FSL ∼1, where FSL is spin lock frequency, equivalent to the resonant frequency at the spin lock pulse field strength (B_1SL) according to the Larmor equation, i.e. FSL = γ · B_1SL (2). Here γ is the gyromagnetic ratio. As FSL reduces and approaches zero, the transverse magnetization relaxes without the application of any external RF pulse field. In this case, T_1ρ relaxation is identical to the normal T₂ relaxation (1) (or T₂ ^* relaxation for gradient echo sequences in the presence of field heterogeneities). Although T₂ relaxation can be traditionally well described with a mono-exponential decay model in many in-vivo tissues, there have also been many reports on the multi-exponential decay, especially bi-exponential decay, of T₂ relaxation in nature (3–7). This multi-exponential or bi-exponential decay is generally interpreted in terms of the macroscopic anatomical multi-compartments of tissue water having intrinsically different T₂ relaxation times. In a bi-exponential T2 relaxation model, the observed short and long T2 relaxation components represent anatomical compartmentation of tissue water, probably intracellular versus extracellular (4). In a multi-exponential T₂ relaxation model, at least one more relaxation component with a very small T₂ value (<10 ms) has been found and attributed to hydration shell of macromolecules (7). As T_1ρ relaxation approaches to T₂ relaxation at very low spin lock frequencies, it is rational to hypothesize that T_1ρ relaxation may behave similarly as T₂ relaxation so that multi-exponential or bi-exponential decay could also be found in T_1ρ relaxation. Actually, the mono-exponential T_1ρ relaxation could be considered as a single one-compartment model in which the relaxation rate is determined by the fluctuating local magnetic fields of dipolar interactions between protons (8). This one-compartment model becomes inadequate when used to describe more complex tissues where different proton compartments exist and interact with each other. Thus a two-compartment model may be helpful to better describe the free water proton (e.g. extracellular) and the constraint water proton (e.g. intracellular), as well as the interaction between them. Accordingly, an apparent mono-exponential T_1ρ relaxation component could be possibly split into two bi-exponential T_1ρ relaxation components. This possible bi-exponential relaxation characteristic may help us to explore the underlying biophysical mechanism for T_1ρ relaxation. For this purpose, this study aims to investigate the feasibility and capability to observe the possible bi-exponential T_1ρ relaxation in in-vivo rat tissues by using low frequency spin lock imaging. T_1ρ imaging has been used in many clinical applications, such as intervertebral disk degeneration (9–11), cartilage degeneration in osteoarthritis (12–16), neurologic diseases (17–20), muscle diseases (21), and liver fibrosis (22–24). This study may also be helpful for the better understanding of the T_1ρ contrast formation, as well as the underlying correlation of diseases with T_1ρ relaxation.

Material and Methods

MRI experiments

Five male Sprague-Dawley rats weighting 200–250 g were scanned under the ethical approval by the local Animal Experimentation Ethics Committee. Spin lock imaging was performed on a Philips Achieva 3T clinical scanner (Philips Medical Systems, Best, The Netherlands) using a T_1ρ prepared 3D spoiled gradient echo sequence. A custom-designed 6-channel receive-only rat head coil with an inner diameter of 5 cm was used for signal acquisition. Rats were anesthetized with a combination of xylazine (10 mg/kg) and Ketamine (90 mg/kg). After anesthesia, animals were positioned prone for scanning. A B₁-insensitive rotary echo spin lock pulse was used for T_1ρ preparation (25), subsequent to a spectrally selective RF pulse for fat suppression. Spin lock time series of 1 ms, 2.5 ms to 60 ms with an increment of 2.5 ms were applied (i.e. 25 TSLs in total) and the spin lock field strength was 11.74 µT, equivalent to a spin lock frequency of 500 Hz. Primary imaging parameters included: TR/TE, 7.2/3.5 ms; flip angle, 30°; shot length, 40; isotropic pixel size, 0.3 mm; matrix size, 160 × 160; slices, 6; and slice thickness, 2 mm. Number of excitation (NEX) of four was used to achieve sufficiently high signal-to-noise ratio (SNR) for accurate T_1ρ fitting. A centric phase-encoding order was applied to minimize the influence of spin lock signal variation over the echo train on the T_1ρ-weighting contrast. A sensitivity encoding factor of two was used to reduce phase encoding numbers to shorten the scan time. A dummy delay time of 5000 ms for equilibrium magnetization restoration was inserted after each segmented shot acquisition prior to the next T_1ρ magnetization preparation. The total acquisition time was around 30 min. The diagram for the rotary echo spin lock pulse and the T_1ρ prepared FFE sequence is shown in Fig. 1.

Fig. 1
The rotary echo spin lock pulse and the pulse sequence schematic for T_1ρ imaging

Data analysis

Acquired images were processed off-line using Matlab version 7.9.0 (The MathWorks, Inc. Natick, MA, USA,) numerical programs.

First, SNR was measured on the T_1ρ-weighted images acquired at different TSLs. A signal region-of-interest (ROI) was drawn as an 8 × 8 (pixel) square in a representative brain region and in a muscle region that both had relatively homogenous image intensities, respectively. The noise ROI was drawn as an identical size square in the image background that was sufficiently far away from brain and muscle tissues. SNR was calculated by the mean intensity of the signal ROI divided by the standard deviation of the intensity in the noise ROI.

Mean image intensities with different N TSLs were fit by the mono-exponential model (Equation 1) and the bi-exponential model (Equation 2) using the non-linear least square fitting method based on Levenberg-Marquardt algorithm in the selected regions-of-interest (ROIs) in the rat brain and muscle, respectively.

where S₀ is the baseline image intensity without the application of spin lock pulse and T_1ρn is the nominal mono T_1ρ relaxation time; T_1ρl and T_1ρs denote the long and the short bi-exponential T_1ρ relaxation times, respectively. α is the fraction of long relaxation component and (1-α) is the fraction of short relaxation component.

To justify the validity of the bi-exponential fitting results, the following criteria were set to exclude the bi-exponential fit results if: (a) T_1ρl > 500 ms; (b) T_1ρs < 1 ms; (c) either T_1ρl or T_1ρs is negative; or (d) | T_1ρl – T_1ρs| < 0.02T_1ρl. In the cases of (a–c), the fitting results might not be reasonable physiologically. In the case of (d), it would be a false bi-exponential fitting as both T_1ρl and T_1ρs were almost identical to the single T_1ρn without improvement in goodness-of-fit.

The residual sum of squares (RSS) by using mono-exponential and bi-exponential fitting was also calculated and compared. In order to evaluate whether the bi-exponential model gave a significantly better fit than the mono-exponential model, an F-test was performed and a significance level (P value) of 0.01 was applied (26). With N data points to estimate parameters for two models, then the F-ratio is given by

Where RSS _i is the residual sum of squares of model i. x _i is the total number of independent coefficients of model i. With F-ratio, the P value could be found from the F-distribution with (x ₂ − x ₁, N − x ₂) degrees of freedom.

Pixel-wise mono-exponential and bi-exponential fitting were also performed. Specifically, pixel-by-pixel maps of T_1ρn and residual sum of squares RSS _mono were generated through mono-exponential fitting. Maps of T_1ρl, T_1ρs, fraction of long relaxation (α), fraction of short relaxation (1-α), and RSS _bi were generated through bi-exponential fitting. Pixels with F-test P values larger than 0.01 were excluded from bi-exponential mapping. Other exclusion criteria as described above were also applied. For RSS mapping, the pixels associated with the RSS value larger than 640 (a threshold value selected to remove the poor fitting pixels) were excluded. The absolute RSS difference map between RSS _mono and RSS _bi was also calculated to compare the goodness-of-fit of mono- and bi-exponential fitting. Spearman rank-order correlation was performed to assess the relationship between the bi-exponential relaxation times T_1ρl, T_1ρs, and the mono-exponential relaxation time T_1ρn. The correlation was considered weak if the absolute value of Spearman rank-order correlation coefficient was smaller than 0.5.

Results

Fig. 2 shows T_1ρ-weighted in-vivo brain images of rat one acquired at all TSLs from 1 to 60 ms. S_b, S_m, and N in Fig. 3a denote the ROI in brain, muscle, and noise background, respectively. The average SNRs for five rats were 318.2 ± 21.3 and 138.5 ± 12.5 in the brain, and 382.4 ± 17.2 and 71.1 ± 7.4 in the muscle for TSLs at 1 ms and 60 ms, respectively.

Fig. 2
T_1ρ-weighted images of in vivo rat brain acquired at all TSLs from 1 to 60 ms

Fig. 3
(a) Rat head T_1ρ-weighted image acquired at the TSL of 1 ms. S_b and S_m are the region-of-interests (ROIs) in the brain and muscle with a size of 8 × 8 (pixel), respectively. The noise ROI N was drawn as an identical size square in the image background sufficiently far away from brain and muscle tissues. (b) The fitting results in the brain ROI. No evident bi-exponential relaxation component was found; (c) the fitting results in the muscle ROI. A longer (39.45 ms) and a shorter (9.15 ms) bi-exponential relaxation component than the normal T_1ρ of 33.50 ms were found with different fractions

The fitting results of the brain ROI and the muscle ROI by using the mono-exponential model and bi-exponential model are illustrated in Fig. 3b and c, respectively. The fitting statistics for the muscle ROI are also listed in Table 1. As shown in Fig. 3b, results of bi-exponential fitting were almost identical to mono-exponential fitting in the brain ROI, i.e. T_1ρn ≈ T_1ρl ≈ T_1ρs and α ≈ 1–α ≈ 50%. The RSS values for both mono- and bi-exponential fitting were 48.14. An F-ratio of 1.52 × 10⁻⁷ and a P value of 1 (≫0.05) were obtained, indicating no significantly better fitting by the bi-exponential model. In contrast, the bi-exponential fitting in the muscle ROI (Fig. 3c) produced two apparently different components of T_1ρl (39.45 ms) and T_1ρs (9.15 ms) from the T_1ρn (33.50 ms) obtained by the mono-exponential fitting. The fractions of T_1ρl and T_1ρs were 80.38% and 19.62%, respectively. The RSS value for bi-exponential fitting was 22.91, much smaller than the corresponding RSS value of 132.52 for mono-exponential fitting. F-test produced an F-ratio of 35.01 in the muscle ROI that corresponded to a P value smaller than 1 × 10⁻⁴, indicating a significantly better fitting by the bi-exponential model.

Table 1
Statistics of the data fitting in the muscle ROI of rat 1

Mono-exponential Bi-exponential

Parameters T_1ρn T_1ρl T_1ρs α

Fit value (ms) 33.50 39.45 9.15 80.38%

95% confidence interval (ms) (32.35, 34.49) (38.67, 40.48) (7.46, 10.32) (78.68%, 82.14%)

Fig. 4 shows the parameter maps generated by the pixel-by-pixel mono-exponential and bi-exponential fitting. The first row in Fig. 4 shows the T_1ρ-weighted image acquired at TSL of 1 ms, T_1ρn map, and RSS _mono map from left to right. The second row shows T_1ρl map, T_1ρs map (both overlaid on the gray T_1ρn map) and RSS _bi map generated by the bi-exponential mapping. The third row shows the maps of the percentage of the long relaxation (100 × α) and the short relaxation (100 × (1–α)), also overlaid on the gray T_1ρn map, as well as the absolute RSS difference map of |RSS _mono– RSS _bi|. More than 80% of muscle pixels showed significantly better fit by the bi-exponential model. The fraction of the long relaxation component was generally larger than the short relaxation component in the muscle. As comparison, only less than 10% of brain pixels showed bi-exponential relaxation. The absolute RSS difference map also showed that the RSS values by using mono- and bi-exponential mapping within the brain were very close, whereas bi-exponential model gave much better fitting within the muscle with much smaller RSS values than the mono-exponential model. The Spearman rank-order correlation coefficients for T_1ρn and T_1ρl, as well as for T_1ρn and T_1ρs, were 0.37 and 0.08, respectively, indicating a relatively weak positive correlation between the mono- and bi-exponential relaxation times.

Fig. 4
Pixel-by-pixel maps generated by the mono-exponential and bi-exponential fitting, respectively. More than 80% of muscle pixels show bi-exponential relaxation. The fraction of the long relaxation component is generally larger than the short relaxation component. The residual sum of squares (RSS) in muscle is much smaller by using bi-exponential fitting than mono-exponential fitting in muscle while the RSS is comparable in brain

For the other four rats, apparent bi-exponential relaxations were found in over 80% of the muscle pixels with significantly better fitting (P < 1 × 10⁻⁴). On the other hand, less than 10% of the brain pixels showed better bi-exponential fitting. The fitting statistics of all five rats are summarized in Table 2.

Table 2
Statistics of the fitting for all five rats

Brain Muscle

Parameters (ms) T_1ρn T_1ρn T_1ρl T_1ρs α

Rat1 70.99 ± 2.43 33.50 ± 1.74 39.45 ± 2.81 9.15 ± 2.24 80.38% ± 3.63%

Rat2 70.32 ± 2.38 31.92 ± 2.46 41.16 ± 2.29 11.44 ± 2.68 87.69% ± 4.48%

Rat3 71.36 ± 2.21 30.28 ± 1.80 38.85 ± 2.74 9.63 ± 2.17 82.56% ± 4.81%

Rat4 70.04 ± 2.18 31.75 ± 1.98 37.38 ± 3.41 10.48 ± 1.96 85.60% ± 5.28%

Rat5 71.82 ± 3.25 31.38 ± 2.19 37.92 ± 3.13 9.68 ± 2.24 84.19% ± 4.12%

Data are reported as mean ± SD

Discussion

In this study, feasibility and capability of finding bi-exponential T_1ρ relaxation components from in-vivo rat brain and muscles by using low frequency spin lock imaging at 3T were investigated. A longer relaxation component T_1ρl and a shorter relaxation component T_1ρs than the normal mono-exponential relaxation time T_1ρn were observed in the rat muscle but not in the rat brain.

A large number of data points, high spatial resolution, and high SNRs are generally desirable for bi- and multi-exponential model fitting and analysis (6). However, as T_1ρ imaging is quite time-consuming, these factors had to be compromised within the allowable scan time in practice. A dedicated rat brain coil and a NEX of four were used to maximize SNR. As many as 25 TSLs were used in this pilot study in order to ensure the accurate and reliable mono- and bi-exponential fitting, although 5–6 TSLs would be sufficient for normal mono-exponential T_1ρ imaging and mapping. In the future, the number of TSLs could be reduced to shorten the acquisition time for bi-exponential mapping in practical use.

The analysis based on both ROI fitting and pixel-by-pixel mapping justified the reliability of the presence of bi-exponential relaxation in the muscle. In previous studies, bi-exponential fitting was usually performed based on ROI or non-spatial-selective volume. However, the averaging in the ROI or volume may cancel out the heterogeneity in pixels. F-test and a small critical P value of 0.01 were adopted in this study to evaluate the statistically significant improvement of the goodness-of-fit by using the bi-exponential model. Careful exclusion criteria were also set to eliminate false and unreasonable bi-exponential fitting results effectively. The narrow 95% confidence intervals and no overlap of T_1ρl and T_1ρn ensured the validity and reliability of the bi-exponential T_1ρ relaxation. The small Spearman rank-order correlation coefficient values indicated that T_1ρl and T_1ρs should be quite independent of T_1ρn, and may reveal information of the tissue intrinsic features beyond T_1ρn.

According to Zimmerman-Brittin relaxation model (27), if a sample placed in a magnetic field is comprised of a finite number of compartments, each of them can be characterized by a single relaxation component. If the exchange of molecules between the compartments is slow compared to the relaxation times, the overall relaxation curve could be expressed by a multi-exponential model and individual relaxation time could be extracted. As T_1ρ relaxation approximates the normal T₂ relaxation at low FSLs, the interpretation of bi-exponential T_1ρ relaxation may refer to the macroscopic anatomical multi-compartments of tissue water and the slow exchange between them. Previous delicate high-SNR T₂-spectra acquired by Carr-Purcell-Meiboom-Gill sequences have shown at least three T₂ relaxation components with values approximately <10 ms, 25–45 ms and >100 ms, and the corresponding fractions of ∼10%, around 80%, and ∼10%, respectively (4, 7). These three components have been attributed to the hydration shell of macromolecules, intracellular water, and extracellular water, respectively (4, 7, 28). Our observation of T_1ρl (∼37–41 ms) with the fraction around 80% in muscle was analogous with the intracellular water T₂ and its corresponding fraction in the study of multi-exponential T₂ relaxation. On the other hand, T_1ρ relaxation is different from T₂ relaxation due to the presence of the spin lock pulse with a μT-level B₁ field strength, which makes it sensitive to molecular motions that have correlation times (τ) such that τ · FSL ∼ 1. Spin lock pulses refocus relaxation effects of slow exchange processes, so that T_1ρ contrast is more sensitive to intermediate and fast processes than T₂. Despite the refocusing effect of spin lock pulses on slow relaxation components, even longer T_1ρ relaxation component (like the T₂ component over 100 ms), might also be observed by using longer TSLs. However, this leads to the T_1ρ-weighted images with very low SNRs and the allowable specific absorption rate (SAR) could be exceeded, making it impractical for clinical use. On the other hand, the high sensitivity of T_1ρ to fast exchange processes leads to the observation of a very short bi-exponential relaxation component T_1ρs (∼10 ms) with the fraction of around 10 ∼ 20%. Although the short T₂ component (<10 ms) found in the previous studies was attributed to the hydration shell of macromolecules (4, 7, 28), it could not be straightforwardly used for the attribution of the short bi-exponential T_1ρ component because the residence time of water molecules in the hydration layer may be too short (in the micro-to-picosecond range) (8) to be detected by a spin lock pulse at 500 Hz. Alternatively, it has been known that hydrogen exchange from amine (NH⁺) and hydroxyl (OH⁻) groups to water is of importance in low frequency water T_1ρ relaxation or dispersion (2). We thus speculate this short bi-exponential relaxation component T_1ρs may associate with the fast hydrogen exchange between amine and hydroxyl groups at low frequencies. This speculation remains to be explored by the investigation of bi-exponential T_1ρ dispersion with spin lock frequency in the future. It is worth noting that the observed bi-exponential T_1ρ relaxation in this study could not be caused by fat and water compartments in that fat signal was suppressed in this study. As indicated in the literature (25), partial volume effects seem to be of minor significance in the observation of bi-exponential relaxations. The argument that the bi-exponential relaxation may be induced by the noise can also be rejected for the following reasons. First, the SNRs for T_1ρ-weighted images should be sufficiently high for accurate extraction of bi-exponential components (6, 7). Second, pixel-by-pixel bi-exponential T_1ρ maps showed relatively homogeneous and consistent T_1ρl and T_1ρs values rather than the random distribution of bi-exponential relaxations. Finally, rat brains showed comparable SNRs while no bi-exponential T_1ρ relaxation was found.

Absence of observable of bi-exponential T_1ρ relaxation in rat brain, including both gray matter and white matter, is consistent with the similar mono-exponential findings in a study of human brain T₂ relaxation (25). However, no observation of bi-exponential T_1ρ relaxation in rat brain in this study cannot completely exclude the possible presence of such bi-exponentiality due to some limiting factors in the experiments. Although dipolar interaction of water could be more efficient in ordered tissues like muscles and contributes to bi-exponential relaxation, it may not be sufficient to explain the no observation of bi-exponentiality in the white matter that is also highly anisotropic. In this case, the specimen orientation must be considered with respect to the spin lock field as well as B0 direction. The smaller sizes of fiber tracts and their more complicated orientations in rat brain may be canceled out within the macroscopic voxel size and hence lead to the mono-exponentiality of T_1p as observed. In addition, as T_1p is about 100% longer in brain than in muscle, a much smaller part of the total relaxation curve sampled in brain obtained with the longest spin lock time of 60 ms may also hinder the detection of the longer bi-exponential relaxation component in the brain. Unfortunately, the use of longer spin lock times was not allowed in our experiments performed on clinical MRI scanners due to the RF amplifier and SAR restriction. On the other hand, the lack of shorter T_1ρ relaxation in brain may indicate the faster hydrogen exchange rate in brain than in muscle, which may require the use of even higher spin lock frequencies, but associated with higher SAR. Therefore, the detection of T_1ρ bi-exponentiality in brain is yet to be further explored in future studies, preferably on a dedicated animal scanner.

In conclusion, bi-exponential T_1ρ relaxation components were observed in in-vivo rat muscles at 3T using low frequency spin lock imaging at 500 Hz. The long and the short T_1ρ relaxation component are speculated to correspond to a restricted intracellular water population and the hydrogen exchange between amine and hydroxyl groups, respectively. No apparent T_1ρ bi-exponentiality was observed in rat brains. It is still unclear whether this finding reflects the true absence of bi-exponential T_1ρ in rat brains, or is restricted by the experiment limitations. Therefore, further investigations are warranted. This study of bi-exponential T_1ρ relaxation should be helpful for better understanding of T_1ρ contrast formation and tissue characterization.

	Mono-exponential	Bi-exponential
Parameters	T_1ρn	T_1ρl	T_1ρs	α
Fit value (ms)	33.50	39.45	9.15	80.38%
95% confidence interval (ms)	(32.35, 34.49)	(38.67, 40.48)	(7.46, 10.32)	(78.68%, 82.14%)

	Brain	Muscle
Parameters (ms)	T_1ρn	T_1ρn	T_1ρl	T_1ρs	α
Rat1	70.99 ± 2.43	33.50 ± 1.74	39.45 ± 2.81	9.15 ± 2.24	80.38% ± 3.63%
Rat2	70.32 ± 2.38	31.92 ± 2.46	41.16 ± 2.29	11.44 ± 2.68	87.69% ± 4.48%
Rat3	71.36 ± 2.21	30.28 ± 1.80	38.85 ± 2.74	9.63 ± 2.17	82.56% ± 4.81%
Rat4	70.04 ± 2.18	31.75 ± 1.98	37.38 ± 3.41	10.48 ± 1.96	85.60% ± 5.28%
Rat5	71.82 ± 3.25	31.38 ± 2.19	37.92 ± 3.13	9.68 ± 2.24	84.19% ± 4.12%

Footnotes

ACKNOWLEDGEMENTS

This work is supported by Hong Kong ITF grant ITS-021-10 and partially supported by grants CUHK475911 and SEG_CUHK02 from the Research Grants Council of the Hong Kong Special Administrative Region, China.

Conflict of interest: None.

References

Santyr

, Henkelman

, Bronskill

. Spin locking for magnetic resonance imaging with application to human breast. Magn Reson Med 1989;12:25–37

Duvvuri

, Goldberg

, Kranz

, Water magnetic relaxation dispersion in biological systems: the contribution of proton exchange and implications for the noninvasive detection of cartilage degradation. Proc Natl Acad Sci U S A 2001;98:12479–84

Menon

, Rusinko

, Allen

. Multiexponential proton relaxation in model cellular systems. Magn Reson Med 1991;20:196–213

Cole

, LeBlanc

, Jhingran

. The origin of biexponential T2 relaxation in muscle water. Magn Reson Med 1993;29:19–24

Ababneh

, Beloeil

, Berde

, Biexponential parameterization of diffusion and T2 relaxation decay curves in a rat muscle edema model: decay curve components and water compartments. Magn Reson Med 2005;54:524–31

Graham

, Stanchev

, Bronskill

. Criteria for analysis of multicomponent tissue T2 relaxation data. Magn Reson Med 1996;35:370–8

Saab

, Thompson

, Marsh

. Multicomponent T2 relaxation of in vivo skeletal muscle. Magn Reson Med 1999;42:150–7

Hills

. Magnetic resonance imaging in food science. New York, NY: Wiley; 1998

Johannessen

, Auerbach

, Wheaton

, Assessment of human disc degeneration and proteoglycan content using T1rho-weighted magnetic resonance imaging. Spine (Phila Pa 1976) 2006;31:1253–7

10.

Nguyen

, Johannessen

, Yoder

, Noninvasive quantification of human nucleus pulposus pressure with use of T1rho-weighted magnetic resonance imaging. J Bone Joint Surg Am 2008;90:796–802

11.

Auerbach

, Johannessen

, Borthakur

, In vivo quantification of human lumbar disc degeneration using T(1rho)-weighted magnetic resonance imaging. Eur Spine J 2006;15 (Suppl. 3):S338–44

12.

Regatte

, Akella

, Borthakur

, Proton spin-lock ratio imaging for quantitation of glycosaminoglycans in articular cartilage. J Magn Reson Imaging 2003;17:114–21

13.

Keenan

, Besier

, Pauly

, Prediction of glycosaminoglycan content in human cartilage by age, T1rho and T2 MRI. Osteoarthritis Cartilage 2011;19:171–9

14.

, Pai

, Blumenkrantz

, Spatial distribution and relationship of T1rho and T2 relaxation times in knee cartilage with osteoarthritis. Magn Reson Med 2009;61:1310–8

15.

Regatte

, Akella

, Lonner

, T1rho relaxation mapping in human osteoarthritis (OA) cartilage: comparison of T1rho with T2. J Magn Reson Imaging 2006;23:547–53

16.

Regatte

, Akella

, Borthakur

, In vivo proton MR three-dimensional T1rho mapping of human articular cartilage: initial experience. Radiology 2003;229:269–74

17.

Haris

, Singh

, Cai

, T1rho (T_1ρ) MR imaging in Alzheimer's disease and Parkinson's disease with and without dementia. J Neurol 2011;258:380–5

18.

Michaeli

, Oz

, Sorce

, Assessment of brain iron and neuronal integrity in patients with Parkinson's disease using novel MRI contrasts. Mov Disord 2007;22:334–40

19.

Borthakur

, Sochor

, Davatzikos

, T1rho MRI of Alzheimer's disease. Neuroimage 2008;41:1199–205

20.

Borthakur

, Gur

, Wheaton

, In vivo measurement of plaque burden in a mouse model of Alzheimer's disease. J Magn Reson Imaging 2006;24:1011–7

21.

Lamminen

, Tanttu

, Sepponen

, T1rho dispersion imaging of diseased muscle tissue. Br J Radiol 1993;66:783–7

22.

Wang

, Yuan

, Chu

, T1rho MR imaging is sensitive to evaluate liver fibrosis: an experimental study in a rat biliary duct ligation model. Radiology 2011;259:712–9

23.

Yuan

, Zhao

, Griffith

, Optimized efficient liver T1rho mapping using limited spin lock times. Phys Med Biol 2012;57:1631–40

24.

Deng

, Zhao

, Yuan

, Liver MR T1rho measurement in healthy human subjects at 3 T: a preliminary study with a two-dimensional fast-field echo sequence. Br J Radiol 2012. Epub 2012 Mar 14, doi: 10.1259/bjr/98745548

25.

Charagundla

, Borthakur

, Leigh

, Artifacts in T1rho-weighted imaging: correction with a self-compensating spin-locking pulse. J Magn Reson 2003;162:113–21

26.

Kjaer

, Thomsen

, Henriksen

. Evaluation of biexponential relaxation behaviour in the human brain by magnetic resonance imaging. Acta Radiol 1989;30:433–7

27.

Zimmerman

, Brittin

. Nuclear magnetic resonance studies in multiple phase systems. Lifetime of a water molecule in an adsorbing phase on silica gel. J Phys Chem 1957;61:1328–33

28.

Gambarota

, Cairns

, Berde

, Osmotic effects on the T2 relaxation decay of in vivo muscle. Magn Reson Med 2001;46:592–9