Effects of spin-lock field direction on the quantitative measurement of spin-lattice relaxation time constant in the rotating frame (T 1ρ) in a clinical MRI system Seonghwan Yeea) Department of Radiation Oncology, Beaumont Health System, Royal Oak, Michigan 48073

Jia-Hong Gao Center for MRI Research, Peking University, Beijing 100871, China

(Received 29 May 2014; revised 9 October 2014; accepted for publication 13 October 2014; published 10 November 2014) Purpose: To investigate whether the direction of spin-lock field, either parallel or antiparallel to the rotating magnetization, has any effect on the spin-lock MRI signal and further on the quantitative measurement of T1ρ, in a clinical 3 T MRI system. Methods: The effects of inverted spin-lock field direction were investigated by acquiring a series of spin-lock MRI signals for an American College of Radiology MRI phantom, while the spin-lock field direction was switched between the parallel and antiparallel directions. The acquisition was performed for different spin-locking methods (i.e., for the single- and dual-field spin-locking methods) and for different levels of clinically feasible spin-lock field strength, ranging from 100 to 500 Hz, while the spin-lock duration was varied in the range from 0 to 100 ms. Results: When the spin-lock field was inverted into the antiparallel direction, the rate of MRI signal decay was altered and the T1ρ value, when compared to the value for the parallel field, was clearly different. Different degrees of such direction-dependency were observed for different spin-lock field strengths. In addition, the dependency was much smaller when the parallel and the antiparallel fields are mixed together in the dual-field method. Conclusions: The spin-lock field direction could impact the MRI signal and further the T1ρ measurement in a clinical MRI system. C 2014 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4900607] Key words: spin-lock, T1ρ, spin-lattice relaxation, rotating frame, quantitative measurement

1. INTRODUCTION In MRI utilizing the spin-locking,1 the net magnetization, initially aligned with the main magnetic field, can be excited and subsequently locked along the particular direction in the rotating frame by applying a series of specially designed radiofrequency (RF) pulses. When the magnetization is locked as such, the relaxation under the influence of the locking field is described by the time constant, T1ρ, which is analogous to the T1 relaxation time constant under the influence of the main magnetic field. This spin-lock mechanism has widely been utilized for imaging the knee,2–5 liver,6,7 and spine,8,9 and its usage has grown to neuroimaging10–12 and cancers.13,14 In spin-lock MRI, the RF pulse sequence to generate T1ρweighted images is usually implemented by adding a spin-lock preparation routine to a host imaging sequence. In general, the spin-lock preparation routine contains at least two RF components: the initial excitation component, either in the form of a block pulse or an adiabatic pulse,15 and the subsequent spinlocking component in the form of a block pulse to generate constant spin-lock field along the direction of the rotating magnetization. In some cases, the spin-locking RF component is implemented using a pair of block RF pulses, each of which could generate the locking field of the same magnitude but 122301-1

Med. Phys. 41 (12), December 2014

at opposite directions.16,17 This dual-field spin-lock method, which may sometimes include a 180◦ rotation pulse between the two spin-lock fields,18 is known for better performance to reduce artifacts, caused by inhomogeneity of the B1 field, and as reported recently, can further be extended into a four-field method,19 in which the dual fields are further paired by another dual fields placed after a 180 rotation pulse. As in many spin-lock MRI studies,11,17,20–22 when the spinlattice relaxation time constant in the rotating frame (T1ρ) is measured, a series of MRI measurements are performed at the same level of spin-lock field while the time of spin-lock (TSL, equal to the duration of applied spin-lock field) is varied, and the signal changes over the varying TSL are analyzed by a certain model function. In general, the model function is setup by a simple monoexponential function [as Eq. (1) in Sec. 2], in which no component considering the particular direction of the spin-lock field is included. The natural consequence of this modeling would be the condition that, when TSL approaches infinity, the locked magnetization would continuously relax into null (or become indistinguishable with the background noise), regardless of the direction of the applied spin-lock field. In other words, this modeling assumes that even if the antiparallel direction is used for the single spin-lock field or if two opposite field directions are used together as in the dual-field

0094-2405/2014/41(12)/122301/10/$30.00 © 2014 Am. Assoc. Phys. Med.

122301-1

122301-2

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

method, the spin-lock MRI signal would still be at the same level as long as the duration of the applied spin-lock field is the same. Therefore, this study was designed to revisit the assumption of the simple monoexponential modeling by investigating the impact of inverting spin-lock field direction in a clinical 3 T MRI system, which, unlike those nonclinical systems that can generate spin-lock fields in the range of a few kilohertz, can generate only a limited range of spin-lock fields (generally, less than 500 Hz) due to the increased RF safety concerns. Although many quantitative T1ρ measurement studies have successfully been performed utilizing the simple monoexponential signal modeling method assuming the effect is negligible, the impact of inverting spin-lock field direction on the spin-lock MRI signal (and on the quantitative T1ρ measurement) still has to be evaluated to elucidate the limitations and conditions, if any, of the simple monoexponential signal modeling and to possibly develop, when required, a better strategy of utilizing spin-lock MRI or T1ρ quantification in a clinical system.

122301-2

single-field methods of opposite spin-lock field directions for comparison, the RF2 was applied at the phase of 0◦ or 180◦ from the rotating magnetization, which would be corresponding to the “parallel” or “antiparallel” direction, respectively. 2.A.2. The 4-pulse dual-field method

In the 4-pulse dual-field spin-lock method shown in Fig. 1(b), the excitation pulse RF1 is followed by a pair of block pulses, RF2 and RF3, for spin-locking and further by the last block pulse, RF4, for flipping back. The pair of spin-lock pulses, RF2 followed by RF3, provides dual spin-lock fields, of the same magnitudes and durations but at opposite directions. To implement the dual-field methods at opposite directions for comparison, the order of the phase values (relative to the rotating magnetization) in the RF pair was either (0◦ followed by 180◦) or (180◦ followed by 0◦), which would correspond to the (parallel followed by antiparallel) or (antiparallel followed by parallel) directions, respectively. 2.A.3. The 5-pulse dual-field method and its extension

2. MATERIALS AND METHODS 2.A. Spin-lock preparation routines 2.A.1. The 3-pulse single-field method

For this study, the spin-lock preparation routines as shown in Fig. 1 were implemented using the pulse sequence developmentenvironment fromPhilipsMedicalSystems(Netherlands). In the 3-pulse single-field spin-lock method shown in Fig. 1(a), the excitation pulse, RF1, is followed by the single spin-lock pulse, RF2, and by the last block pulse, RF3, for flipping the magnetization back to the original direction. To implement the

Additionally, another dual-field spin-lock method, known for better reduction of artifact, was implemented. In the 5-pulse dual-field spin-lock method shown in Fig. 1(c), the inclusion of the 180◦ rotary pulse (RF3), applied at the 90◦ phase (relative to the initial locked magnetization), causes the locked magnetization to be positioned in the opposite direction, which would allow four possible combinations of spin-lock field directions relative to the locked magnetization. To implement the 5-pulse dual-field methods at opposite directions for comparison, the dual spin-lock fields were applied at the phase values (relative to the “initial” locked magnetization) of (0◦ followed by 180◦),

F. 1. The spin-lock preparation routines used in this study are shown in (a), (b), and (c), respectively, for the 3-pulse single-field, the 4-pulse dual-field, and the 5-pulse dual-field methods (see Sec. 2 for details). The spoiler gradient, SP, was added after the last RF component used to flip the magnetization back to the initial direction and before the RF excitation for host imaging sequence. In each method, the direction of each spin-lock field component (e.g., RF2 or RF4 in the 5-pulse method) was switched for this study between the parallel and the antiparallel directions relative to the rotating magnetization to have all possible combinations of the directions. The possible directions of the spin-lock field, relative to the rotating magnetization, are illustrated as arrows in (d), where their designations using the letters P and A (for the parallel and antiparallel directions, respectively) are also shown. Note in the 5-pulse method shown in (c) that RF3 is a 180◦ rotary pulse, which will bring the locked magnetization to the opposite direction. Medical Physics, Vol. 41, No. 12, December 2014

122301-3

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

(180◦ followed by 0◦), (0◦ followed by 0◦), or (180◦ followed by 180◦), which would correspond to the (parallel followed by parallel), (antiparallel followed by antiparallel), (parallel followed by antiparallel), or (antiparallel followed by parallel), respectively. In Fig. 1(d), the relative directions of both the locked magnetization and the spin-lock fields are illustrated, together with their designations used in this paper. As an extension of the 5-pulse dual-field method, the 7-pulse four-field method,19 in which the first dual-field was followed by a 180◦ rotary pulse and another dual-field, was also implemented. However, the 7-pulse method was used only for an additional study, as described in Sec. 4, and not used in the main study. 2.B. MRI acquisitions 2.B.1. Verification of the spin-lock pulses

All MRI acquisitions in this study were performed using an Ingenia 3 T MRI system (Philips Medical Systems). Before the main MRI acquisitions in this study, brief spin-lock MRI scans were performed to test whether the spin-locking technique implemented in the scanner would work as intended. This preliminary testing was performed by comparing the decay of the spin-lock MRI signal (T1ρ relaxation) to that of the T2

122301-3

relaxation for a small region of interest (ROI), shown in Fig. 2(a), inside a simple liquid bottle phantom provided with the MRI scanner. For this preliminary testing, the 3-pulse preparation routine, in which the parallel spin-lock field strength was set to 200 Hz, was added to a turbo spin echo (TSE) technique to perform a series of single-slice spin-lock MRI scans for the phantom, while TSL was varied from 0 to 200 ms: time to repeat (TR) = 8 s, time to echo (TE) = 15 ms, echo train length (ETL) = 16, slice thickness = 2.5 mm, field of view (FOV) = 12 × 12 cm, acquisition matrix = 128 × 172, and reconstruction matrix = 176 × 176. In addition, a multiecho TSE sequence (TR = 8 s, TE = multiples of 40 ms, ETL = 18, slice thickness = 2.5 mm, FOV = 12 × 12 cm, acquisition matrix = 140 × 172, and reconstruction matrix = 176 × 176) was also acquired for the same location to get the T2 relaxation signal decay, and the signal changes from the T1ρ and T2 relaxations were plotted together for the comparison. When acquired, the spin-lock MRI image with TSL = 200 ms was examined for any clear off-resonance artifact, and for a reference purpose, the off-resonance artifacts were also intentionally created by acquiring an image while the spin-lock RF frequency was set to 400 Hz off from the resonance.

F. 2. The spin-lock MRI images, acquired for a simple Philips liquid bottle phantom using the 3-pulse P spin-lock RF routine with 200 Hz spin-lock field, are shown in (a) and (c), respectively, for TSL = 0 and 200 ms. In (a), a ROI, where the MRI signals are sampled, is also shown in the center. In (b), the spin-lock MRI signals from the ROI over the range TSL values (from 0 to 200 ms) are shown together with the T 2 relaxation signals over the same time range. Both curves were normalized to the initial value to compare them in the same scale. The estimated T 1ρ and T 2 from the curves were 84.7 and 67.4 ms, respectively. In (d), the image acquired with an intentional off-resonance setting of 400 Hz to the spin-lock RF pulses and with TSL = 200 ms shows clear artifacts, which are not seen in the image in (c). Medical Physics, Vol. 41, No. 12, December 2014

122301-4

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

122301-4

2.B.2. Main MRI acquisitions

2.D. Data analysis

The effects of inverting spin-lock field direction were investigated by acquiring a series of spin-lock MRI signals for an American College of Radiology (ACR) MRI phantom, while the spin-lock field direction was switched between the parallel and the antiparallel directions. The acquisitions were performed for different spin-locking methods (i.e., for the singleand dual-field spin-locking methods) and for different levels of clinically feasible spin-lock field: the spin-lock field was varied from 100 Hz (corresponds to 2.35 µT) to 500 Hz by the increment of 100 Hz for both the single- and the dual-field methods. The 500 Hz was close to the feasible limit in the scanner with the applied range of TSL from 0 to 100 ms. The TSL values varied to determine T1ρ were 0, 10, 20, 30, 40, 60, 80, and 100 ms. For each level of spin-lock field, a series of single-slice spin-lock MRI scans were performed at the location commonly known as the ACR slice number 1 position with a spin-lock prepared TSE sequence with the following parameters: ETL = 15, TR = 6 s, TE = 8.1 ms, slice thickness = 4 mm, acquisition matrix = 300 × 324, FOV = 25 × 25 cm, and reconstruction matrix = 400 × 400. It is worthwhile to note here that the signal with TSL = 0 was acquired, not by setting the duration of any spin-lock component to zero but by implementing the spin-lock preparation routine without the spin-locking RF component, i.e., using only the (RF1 and RF3), (RF1 and RF4), or (RF1, RF3, and RF5) in each spin-lock preparation routine, respectively, for the 3-, 4-, or 5-pulse method. The whole set of measurements in this study were repeated 8 times.

The main hypothesis of this study is that the spin-lock MRI signal would not be affected by the choice of a particular direction of the spin-lock field, and therefore, the MRI signals (and T1ρ determined by the conventional modeling) would be indistinguishable, even if obtained for different spin-lock field directions. In order to test this hypothesis, the MRI signals were sampled at two ROIs, as shown in Fig. 3(a), one in the background compartment inside the ACR phantom (ROI1) and the other inside the contrast vial of the ACR phantom (ROI2), where the relaxation value was known to be different from the background. The two ROIs were drawn to minimize the inclusion of any image artifacts, and the same ROIs were used to sample the signals over the range of TSL values and for different spin-lock directions. For a simple comparison between opposite spin-lock field directions, the signals for different spin-lock field directions, acquired from the same ROIs, were plotted together over the various values of TSL. For a quantitative comparison, each signal change curve was fitted to Eq. (1) to get the corresponding T1ρ value. At each level of spin-lock field strength, the T1ρ values for each spin-lock field direction, determined from the eight different measurements, were then compared using the paired t-test, between the “P” (parallel) and “A” (antiparallel) directions for the single-field method and between the “PA” (parallel followed by antiparallel) and “AP” (antiparallel followed by parallel) directions for the dual-field method.

2.C. Determination of T 1ρ and its reference

The spin-lock prepared MRI signal, S, is often described as follows:11,17,20–22   TSL , (1) S = S0 · exp − T1ρ where S0 is the signal when TSL = 0 ms. According to Eq. (1), the T1ρ can be obtained by measuring signals at various values of TSL and fitting the measured signals to the model equation. In this study, the measured signals at various values of TSL were fitted to the model equation using an in-house program written in  (Mathworks, Natick, MA). However, as mentioned earlier, the modeling equation as in Eq. (1) does not have any component to distinguish different directions of the spin-lock field, and therefore, does not distinguish the case when the spin-lock field is applied to the opposite direction, or, as in the dual-field spin-lock approach, the case when the spin-lock field is applied to both directions in combination. This means that the direction-dependent effect, if any, would influence the T1ρ value determined by Eq. (1). In this study, the direction-dependent effect, if any, was assumed to be effectively cancelled when a pair of signals acquired with opposite directions was combined. Therefore, the direction-independent reference T1ρ value was obtained by averaging the pair of opposite direction signals and still applying the monoexponential curve fitting to the average signal (see Sec. 4 regarding the validity of obtaining directionindependent reference T1ρ value by the average method). Medical Physics, Vol. 41, No. 12, December 2014

3. RESULTS 3.A. Verification of the spin-lock RF pulses

As shown in Fig. 2(b), the MRI signal decay due to the spinlock relaxation was clearly slower as expected than the decay from the T2 relaxation, and the MRI signal change measured by the 3-pulse spin-lock routine was showing a clear nonfluctuating exponential decay, suggesting the applied spin-lock field was on-resonance. In addition, unlike the image shown in Fig. 2(d), for which the spin-locking pulse was intentionally set to the off-resonance frequency, the image in Fig. 2(c) was not showing any clear artifacts even with the longest TSL value of 200 ms. These observations supported the validity of the spin-lock pulses used in this study. The utility of different spin-lock pulses used in this study was also verified in the images acquired in the presence of apparent artifacts. The images shown in Fig. 3 were acquired for the ACR phantom, at the 500 Hz spin-lock field strength, with TSL = 0 or 60 ms. When TSL = 0 ms, no apparent artifacts were visible, as shown in Figs. 3(a) and 3(d), which were for the cases with the 3-pulse method (or equally for the 4pulse method) and 5-pulse method, respectively. As expected, the artifacts seen in Fig. 3(b) for the 3-pulse P method were reduced in Fig. 3(c) for the 4-pulse PA method and clearly much reduced in Fig. 3(f) for the 5-pulse PA method. However, as shown in Fig. 3(e) for the 5-pulse “PP” method, the artifact reduction was not much effective even with the 5-pulse method if both of the spin-lock field directions of the dual spin-lock fields were parallel to the locked magnetization. It is

122301-5

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

122301-5

F. 3. Example images acquired at the 500 Hz spin-lock field strength by different spin-lock preparation routines used in this study. The ROIs used in this study are also shown in (a). The images are, in (a), for the 3-pulse method (or equally for the 4-pulse method) when TSL = 0 ms, in (b), for the 3-pulse P method when TSL = 60 ms, in (c), for the 4-pulse PA method when TSL = 60 ms, in (d), for the 5-pulse method when TSL = 0 ms, in (e), for the 5-pulse PP method when TSL = 60 ms, and in (f), for the 5-pulse PA method when TSL = 60 ms.

worthwhile to note that the artifacts in Fig. 3(e) for the 5-pulse PP method are similar to those in Fig. 3(b) for the 3-pulse P method. This suggests the importance of “mixing” spin-lock field directions in the dual-field method in reducing the B1inhomogeneity artifacts. In addition, when the spin-lock field directions were mixed in the dual-field method, the 5-pulse method, shown in Fig. 3(f), were clearly better than the 4-pulse method, shown in Fig. 3(c). As verified by different patterns of artifacts and by the clear reduction of the artifacts especially in the 5-pulse method, shown in Fig. 3(f), the images here indirectly served to confirm that the spin-lock routines implemented in this study worked as intended.

3.B. Effects of inverted spin-lock field 3.B.1. The 3-pulse method

An example case for the 200 Hz spin-lock field strength is shown in Fig. 4, where the MRI signal curves for different spinlock methods are shown. In Fig. 4(a), the two signal curves, acquired by the 3-pulse P and A methods, are plotted together. Starting from the same level when TSL = 0 ms, both curves show a nice exponential form of decay, but they split as TSL increases, suggesting the difference of spin-lock MRI signal by the selection of spin-lock field direction. When the conventional modeling, as in Eq. (1), was separately applied to each curve, the T1ρ values for the 3-pulse P and A methods were 114.63 and 104.94 ms, respectively, for the ROI1, and 61.60 and 55.94 ms, respectively, for the ROI2 (these T1ρ values Medical Physics, Vol. 41, No. 12, December 2014

are shown in Table I together with the values for other spinlock methods); the differences between the opposite directions, in reference to either direction value, were approximately 8%–9% for the ROI1 and 9%–10% for the ROI2. 3.B.2. The 4-pulse method

The difference between the opposite spin-lock field directions gets much smaller, as shown in Fig. 4(b), when the 4pulse method are used. In Fig. 4(b), the two curves, obtained by the 4-pulse PA and the AP methods, make very little difference between them. When the conventional modeling was applied to each curve, the T1ρ values for the 4-pulse PA and the AP methods were 109.51 and 111.57 ms, respectively, for the ROI1 and 58.29 and 59.35 ms, respectively, for the ROI2 (also shown in Table I); the differences between the opposite directions, in reference to either direction value, were all less than 2%. This suggests MRI signals are less dependent on the particular order of spin-lock field directions (whether PA or AP), when the directions are mixed in the dual-field method. As previously noted, a direction-independent reference T1ρ value can be obtained when the MRI signals for the opposite spin-lock fields are combined together. The validity of combining MRI signals to minimize the direction-dependency, if any, can be verified in Fig. 4(c), where the curve for the average signal between the 3-pulse P and A methods is shown very close to the average curve between the 4-pulse PA and AP methods. For the average curves of the 3-pulse and the 4-pulse methods, respectively, the T1ρ values obtained by still applying the conventional modeling were, for the ROI1, 109.64

122301-6

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

122301-6

F. 4. Typical spin-lock MRI signal changes for both ROIs, acquired over the range of TSL values by different spin-lock methods with the 200 Hz spin-lock field strength, are shown in (a), (b), (d), and (e) (in the first two columns of the graph panels shown). In each of the panels shown, the plots for the pair of directions in each method (e.g., P and A for the 3-pulse method) were drawn together for the comparisons: in (a), between the 3-pulse P and A methods, in (b), between the 4-pulse PA and AP methods, in (d), between the 5-pulse PP and AA methods, and in (e), between the 5-pulse PA and AP methods. The T 1ρ values for different curves in (a), (b), (d), and (e) are shown in Table I. In (c) and (f) (the third column), the average signals between two opposite directions of corresponding methods are shown for both ROIs: in (c), the average signal between the 3-pulse P and A methods together with the average between the 4-pulse PA and AP methods, and in (f), the average signal between the 5-pulse PP and AA methods together with the average between the 5-pulse PA and AP methods. The T 1ρ values for different curves in (c) and (f) are shown in Table II.

and 110.53 ms, and for the ROI2, 58.70 and 58.81 ms (shown in Table II together with the values obtained for the other average curves), making only 0.2%–0.8% differences. 3.B.3. The 5-pulse method

In case of the 5-pulse spin-lock method, the signal curves are also affected by the spin-lock field directions, with varying degrees. In Fig. 4(d), where the 5-pulse PP and the “AA” methods are compared together, another clear directiondependency of the spin-lock field can be seen. One notable thing here is that the difference between the PP and the AA methods is quite similar to the case of the 3-pulse method between the P and the A directions. The T1ρ values were 115.75 and 103.83 ms for the ROI1 and 69.13 and 61.10 ms for the ROI2, respectively, for the PP and the AA methods (see Table I). However, when the spin-lock field directions are mixed,

the curves, as shown in Fig. 4(e), become close to each other, and they become similar to those for the 4-pulse PA and the AP methods; the T1ρ values were 108.79 and 111.75 ms for the ROI1 and 63.04 and 64.98 ms for the ROI2, respectively, for the PA and the AP methods (see Table I). When the signals for the PP and AA methods are averaged, the average curve, supposed to be direction-independent, was also very similar to the average of PA and AP, as shown in Fig. 4(f); the T1ρ values for the average of PP and the AA methods and the average of PA and the AP methods were 109.57 and 110.25 ms, respectively, for the ROI1, and 64.97 and 64.10 ms, respectively, for the ROI2 (see Table II). 3.B.4. The statistical comparison

For all spin-lock fields ranging from 100 to 500 Hz, the three T1ρ values, the two obtained by separately fitting each

T I. T 1ρ values (in ms) for both ROIs determined by the conventional modeling in Eq. (1) for the example curves shown in (a), (b), (d), and (e) of Fig. 4. Different columns show the values for different spin-lock methods.

ROI ID

3-pulse P

3-pulse A

4-pulse PA

4-pulse AP

5-pulse PP

5-pulse AA

5-pulse PA

5-pulse AP

ROI1 ROI2

114.63 61.6

104.94 55.94

109.51 58.29

111.57 59.35

115.75 69.13

103.83 61.1

108.79 63.04

111.75 64.98

Medical Physics, Vol. 41, No. 12, December 2014

122301-7

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

T II. T 1ρ values (in ms) for both ROIs determined by the conventional modeling in Eq. (1) for the average curves shown in (c) and (f) of Fig. 4. Different columns show the values for different spin-lock methods.

ROI ID ROI1 ROI2

3-pulse P and A

4-pulse PA and AP

5-pulse PP and AA

5-pulse PA and AP

109.64 58.7

110.53 58.81

109.57 64.97

110.25 64.1

spin-lock field direction to the conventional modeling function as Eq. (1) and the third obtained by the direction-independent averaging method, were grouped together for the eight repeated measurements and are plotted in Figs. 5(a) and 5(b) for the single- and the dual-field (4-pulse) methods, respectively. For the single-field method, the T1ρ values for the antiparallel spin-lock field (the A method) were clearly smaller than those for the parallel spin-lock field (the P method) for both ROIs (p < 0.00001, paired 1-tail t-test). The differences between the parallel and the antiparallel fields, when compared to the reference value obtained by the direction-independent averaging method, reached maximum of 15% and 22% for ROI1 and ROI2, respectively, and were statistically significant (p < 0.00001) for all levels of spin-lock field strength. For the dual-field method, the T1ρ values for the AP method were larger than those for the PA method (p < 0.016 for ROI1, p < 0.00001 for ROI2, paired 1-tail t-test) for all levels of spinlock field. However, the differences of maximum 1.5% and 6.3% for ROI1 and ROI2, respectively, when compared to the direction-independent reference value, were not statistically significant (p < 0.66 for ROI1, p < 0.09 for ROI2).

122301-7

4. DISCUSSIONS As shown in the results, the spin-lock MRI signals over the range of TSL values could be affected by the selection of the spin-lock field direction. In the single-field spin-lock method, the signal curves were noticeably different between the P and A methods (equivalent to the PP and AA methods for the case of 5-pulse method) and the difference in the resulting T1ρ values obtained by the conventional modeling was statistically significant. The results demonstrate the direction-dependency of the spin-lock MRI signal and the limitation of simply applying the conventional modeling of the spin-lock MRI, which does not take the particular spin-lock field direction into account. In order to explain the observed direction-dependency of spin-lock MRI signals, a simple modification to the conventional modeling (although not compelling as described later) was first considered. The modification was, as previously used,23 to assume a nonzero equilibrium value of the locked magnetization undergoing the T1ρ relaxation process. Then, the relaxing magnetization starting from the initial value MSL (0) to the limiting value MSL (∞) can be written as follows from the Bloch equation:   t MSL (t) = MSL (0) · exp − T1ρ    t . (2) + MSL(∞) · 1 − exp − T1ρ It is straightforward to note here that when MSL (∞) is zero, Eq. (2) would simply be the conventional monoexponential spin-lock modeling as Eq. (1).

F. 5. The different T 1ρ values from both ROIs, shown in Fig. 3, obtained by the conventional modeling (simple monoexponential modeling separately for each spin-lock field direction) and by the reference method (simple monoexponential modeling after averaging the signals of the opposite spin-lock field directions) are shown for both of the 3-pulse single-field method and the 4-pulse dual-field method, in (a) and in (b), respectively. The plots are for mean values of the total eight measurements made at each level of spin-lock field strength, and the error bars represent standard deviations. For the comparison between the single- and the dual-field methods, the plots in (a) and (b) were drawn in the same scale. Medical Physics, Vol. 41, No. 12, December 2014

122301-8

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

Based on this equation, more equations to describe the spinlock MRI signals used in this study can be derived, as shown in the Appendix, and the derived equations can be used to explain the observations made in this study. When Eqs. (A1) and (A2) are compared together, Eq. (A1) would always be greater than Eq. (A2) at the same TSL value. This expectation seems to be well supported by the results of this study showing the rate of signal reduction for the 3-pulse A method is greater than for the P method, resulting in a smaller value of T1ρ for the A method. When mixed directions are used in the dual-field method, as in the PA and the AP methods, the comparison of Eqs. (A3) and (A4) suggests that the rate of signal reduction for the PA method would be greater than for the AP method (and, therefore, the T1ρ for the PA method would be smaller), which is also supported by the study results. More importantly, the second terms in Eqs. (A1)–(A4), when compared amongst them, suggest that the difference between Eqs. (A3) and (A4) would always be much smaller than the difference between Eqs. (A1) and (A2) due to the existence of the 1/2 factor in the exponent and the square of the fraction in the second term of the dual-field modeling equations. This expectation also seems to be well supported by the study results showing the difference between PA and AP methods are much smaller than the difference between P and A methods. However, there is one important observation that is hard to explain from the modeling based on the Eq. (2). That is, as shown in the plots of Fig. 5, the difference of spin-lock MRI signals between the opposite directions seems to get bigger as the spin-lock field gets weaker, while Eq. (2) suggests that, if the stronger spin-lock field would generate the higher m0 (the equilibrium magnetization by the spin-lock field), the difference caused by the second term should get bigger as well for the stronger field. This observation, i.e., the bigger directiondependency for the weaker spin-lock field, is also confirmed in Fig. 6, where the fitted m0 values (relative to S0) from one

F. 6. The plots of m 0 values, relative to S0, obtained by fitting the 3-pulse P spin-lock MRI signals to the modeling based on Eqs. (2) and (A1) for one series of measurements in this study. For both ROIs, the m 0 to S0 ratio decreases as the spin-lock field strength increases. Medical Physics, Vol. 41, No. 12, December 2014

122301-8

series of measurements are plotted over the range of spinlock fields. Therefore, unless a stronger spin-lock field can somehow generate a much lower equilibrium value (or something else is playing a role), this explanation based on the “nonzero” equilibrium magnetization is less compelling and hard to be supported, let alone the presumption that, since B1 field strength is negligible compared to B0 strength, the equilibrium magnetization under the spin-lock field would also be negligible. Although a theoretical explanation may still be needed, a plausible explanation of the observed direction-dependency may be developed focusing on the limitations of spin-lock MRI scans performed in a clinical scanner; the spin-lock field strength is limited to the range below the maximum of 500 Hz, and the imaging object is often large and naturally nonhomogeneous, and therefore, all of these limitations would make the applied spin-lock RF field inevitably suffer from varying degrees of off-resonances throughout the imaging plane. In order to further confirm the observed direction-dependency and its possible link to the inevitable off-resonances experienced by the spin-lock pulses, an additional experiment was performed for a few different types of spin-lock routines. In the experiment, a series spin-lock MRI signals were acquired for the same spin-lock method while the frequency of the spin-lock RF pulse routine was intentionally varied in the range from −180 to 180 Hz (in terms of the offset frequency from the resonance frequency) in the steps of 20 Hz. Since the long TSL would induce the large difference, the test was performed using a long TSL value of 100 ms to see a clear difference between the opposite directions, and other scan parameters were the same as the main study described before. In order to see how the sensitivity of direction-dependency over the range of off-resonances would change to the spin-lock field strength change, the spin-lock field was first set to 200 Hz for the 3-pulse P and A methods and later doubled to 400 Hz. Furthermore, to test the sensitivity to the number of spin-lock fields used, the number of spin-lock fields was later increased to make the dual- or four-field method (5-pulse PA and AP, and 7-pulse “PAPA” and “APAP”) for the 200 Hz spin-lock field strength. For this experiment, extra efforts in shimming and positioning the ACR phantom were made to ensure a high-degree of homogeneity. As shown in the homogeneity map in Fig. 7, the homogeneity in terms of the off-resonance frequency range in the phantom was maintained in the range less than approximately 80 Hz (0.6 ppm) during the experiment. In the similar areas of ROI1 and ROI2 of the main study, the mean off-resonance frequencies were approximately 34 Hz (0.3 ppm) and 78 Hz (0.6 ppm) with the standard deviation of 6.2 and 5.2 Hz, respectively. The results of the aforementioned additional experiment are well illustrated in Fig. 8, where the same colors but different markers were used to represent each pair of the plots acquired by the same spin-lock method with opposite spin-lock field directions. In Fig. 8, the plots were obtained from an area similar to the ROI1 used in the main study (the plots from ROI2 area, not shown here, showed very similar behaviors). It is worthwhile to note that the pair of plots for the same

122301-9

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

F. 7. The homogeneity map for the acquired imaging plane in the additional experiment described in Sec. 4. The field homogeneity map, depicted in terms of the off-resonance frequency, was obtained by linear-fitting the phase changes of MRI signals acquired by a gradient echo sequence at the increasing TE values from 4.5 to 5.1 ms by the steps of 0.2 ms (TR = 200 ms, flip angle = 65◦, slice thickness = 5 mm, FOV = 25 × 25 cm, pixel bandwidth = 288 Hz, acquisition matrix = 250 × 252, and reconstruction matrix = 672 × 672). The overall homogeneity was less than approximately 80 Hz (0.6 ppm).

method with opposite spin-lock field directions, similar to the “X”-shape, are roughly symmetric around the offset = 0. As seen in the plots, the gaps between the MRI signals acquired with opposite spin-lock field directions exist for all spin-lock methods over the range of off-resonance frequencies with different degrees. For some spin-lock methods, the direction-dependency could be very sensitive to even small degree of inhomogeneity (which would cause the off-resonance), as verified by the curves for the 3-pulse P and A method with 200 Hz spin-lock field strength. Consistent with the observations in the main study, the gaps between opposite directions, when compared among the 3-pulse 200 Hz, 3-pulse 400 Hz, 5-pulse 200 Hz, and 7-pulse 200 Hz methods, generally tend to be smaller for the later (in the aforementioned order) method in most of the off-resonance frequency range: the biggest for the 3-pulse 200 Hz and the smallest for the 7-pulse 200 Hz method. The existence of such gaps confirms that the directiondependency could be more problematic for the weaker spinlock field and for the 3-pulse methods than for the multiple field methods. Another important thing to note from the plots in Fig. 8 is that the average of both direction signals, even in the presence of off-resonance, could be a reasonable approximation to the direction-independent MRI signal, although as the degree of off-resonance increases, the average signal may still suffer from the direction-dependency, particularly in the case of 3-pulse method. In this study, the dependency of the spin-lock MRI signals on the spin-lock field direction and the limitation of simply applying the conventional modeling based on the simple monoexponential function were demonstrated. The study results suggest that, when the quantitative measurement of T1ρ is performed without considering the direction of the spin-lock Medical Physics, Vol. 41, No. 12, December 2014

122301-9

F. 8. The spin-lock MRI signals acquired while the frequency setting of spin-lock routine was intentionally varied in the range from −180 to 180 Hz off from the resonance frequency in the region similar to the ROI1 used in the main study. The same colors were used for the plots acquired by the same spin-lock method, but different markers were used to distinguish opposite spin-lock field directions. The vertical arrow, inserted arbitrary at 40 Hz for an explanatory purpose, represents the signal difference between opposite spin-lock field directions when the 3-pulse spin-lock routine with 200 Hz spin-lock field strength is at approximately 40 Hz off from the resonance. Such difference between opposite spin-lock field directions generally tends to be smaller for the stronger spin-lock field and for the multifield spin-lock methods.

field(s), systemic errors could be introduced in the measurement, especially in the clinical spin-lock MRI environment, where a certain degree of inhomogeneity in the imaging plane is inevitable. Although, a better signal modeling could be developed in the future to quantitatively address this directiondependency in terms of the degree of off-resonance, a possible strategy to minimize the direction-dependency would be, as performed in this study, to perform spin-lock MRI acquisitions twice with opposite spin-lock fields, average them to approximate the direction-independent signal curve for various TSL values. However, this method, unless other strategy to shorten the total scan time is developed, would not be so practical for clinical scans because it would require doubling the time of the already long scan procedure. When the total scan time is a main concern, another feasible approach would be, as verified in this study, to utilize the multifield (dual- or four-field) spin-lock method in the manner of using “mixed” directions of the spin-lock fields (as in the 5-pulse dual-field PA or AP method). 5. CONCLUSIONS When acquired in a clinical system, the spin-lock MRI signal can be affected by the direction of the spin-lock field. The effects of spin-lock field direction are less prominent for the stronger spin-lock fields or for the multifield methods. When necessary, the direction-dependency can effectively be minimized either by combining the spin-lock MRI signals obtained with opposite spin-lock field directions or by utilizing the multifield spin-lock method.

122301-10

S. Yee and J.-H. Gao: Effects of spin-lock field direction on T 1ρ measurement

APPENDIX If the equilibrium magnetization, MSL (∞), under the spinlock field is assumed to be m0 (not necessarily zero) when the locking field is parallel with the locked magnetization, Eq. (2) can be written as follows for the MRI signal with the TSL:      TSL TSL + m0 · 1 − exp − , (A1) SP = S0 · exp − T1ρ T1ρ where SP is the MRI signal when the locking field is applied to parallel direction and S0 is the signal when TSL = 0 ms. If the locking field is applied to the antiparallel direction, the nonzero equilibrium magnetization would now be in the opposite direction, and the MRI signal can be expressed as follows:      TSL TSL − m0 · 1 − exp − , (A2) S A = S0 · exp − T1ρ T1ρ where S A is the MRI signal when the locking field is applied to the antiparallel direction. If a pair of spin-lock pulses is sequentially applied, at first, to the parallel direction for TSL/2 duration and then, to the antiparallel direction for another TSL/2 duration, the signal expression can be derived from Eq. (A2) with S0 being replaced with the signal value obtained from Eq. (A1) and is written as follows:      2 TSL TSL SPA = S0 · exp − − m0 · 1 − exp − , (A3) T1ρ 2 ·T1ρ where SPA is the signal when the locking field is applied first to the parallel and then to the antiparallel directions, each time in the equal duration of TSL/2. Likewise, if the order of spin-lock field directions is switched, the signal is expressed as follows:      2 TSL TSL SAP = S0 · exp − + m0 · 1 − exp − , (A4) T1ρ 2 ·T1ρ where SAP is the signal when the locking field is applied first to the antiparallel and then to the parallel directions, again in the equal durations of TSL/2. In addition, it would be straightforward that when the pair of spin-lock fields are applied to the (parallel followed by parallel) or (antiparallel followed by antiparallel) directions in the 5-pulse methods, the signal expressions for SPP and SAA would be the same as SP and S A, respectively, as in Eqs. (A1) and (A2). a)Author

to whom correspondence should be addressed. Electronic mail: [email protected]; Telephone: 248-551-7024; Fax: 248551-3784. 1R. E. Sepponen, J. A. Pohjonen, J. T. Sipponen, and J. I. Tanttu, “A method for T1 rho imaging,” J. Comput. Assist. Tomo. 9, 1007–1011 (1985). 2U. Duvvuri, R. Reddy, S. D. Patel, J. H. Kaufman, J. B. Kneeland, and J. S. Leigh, “T1rho-relaxation in articular cartilage: Effects of enzymatic degradation,” Magn. Reson. Med. 38, 863–867 (1997). 3S. K. Pakin, M. E. Schweitzer, and R. R. Regatte, “3D-T1rho quantitation of patellar cartilage at 3.0 T,” J. Magn. Reson. Imaging 24, 1357–1363 (2006).

Medical Physics, Vol. 41, No. 12, December 2014

4S.

122301-10

K. Pakin, J. Xu, M. E. Schweitzer, and R. R. Regatte, “Rapid 3D-T1rho mapping of the knee joint at 3.0 T with parallel imaging,” Magn. Reson. Med. 56, 563–571 (2006). 5C. S. Wong, C. H. Yan, N. J. Gong, T. Li, Q. Chan, and Y. C. Chu, “Imaging biomarker with T1rho and T2 mappings in osteoarthritis—In vivo human articular cartilage study,” Eur. J. Radiol. 82, 647–650 (2013). 6J. T. Halavaara, R. E. Sepponen, A. E. Lamminen, T. Vehmas, and S. Bondestam, “Spin lock and magnetization transfer MR imaging of local liver lesions,” Magn. Reson. Imaging 16, 359–364 (1998). 7M. Deng, F. Zhao, J. Yuan, A. T. Ahuja, and Y. X. Wang, “Liver T1rho MRI measurement in healthy human subjects at 3 T: A preliminary study with a two-dimensional fast-field echo sequence,” Br. J. Radiol. 85, e590–e595 (2012). 8W. Johannessen, J. D. Auerbach, A. J. Wheaton, A. Kurji, A. Borthakur, R. Reddy, and D. M. Elliott, “Assessment of human disc degeneration and proteoglycan content using T1rho-weighted magnetic resonance imaging,” Spine 31, 1253–1257 (2006). 9Z. Zhou, B. Jiang, Z. Zhou, X. Pan, H. Sun, B. Huang, T. Liang, S. Ringgaard, and X. Zou, “Intervertebral disk degeneration: T1rho MR imaging of human and animal models,” Radiology 268, 492–500 (2013). 10M. Haris, A. Singh, K. Cai, C. Davatzikos, J. Q. Trojanowski, E. R. Melhem, C. M. Clark, and A. Borthakur, “T1rho (T1rho) MR imaging in Alzheimer’s disease and Parkinson’s disease with and without dementia,” J. Neurol. 258, 380–385 (2011). 11A. Borthakur, M. Sochor, C. Davatzikos, J. Q. Trojanowski, and C. M. Clark, “T1rho MRI of Alzheimer’s disease,” NeuroImage 41, 1199–1205 (2008). 12U. A. Ramadan, A. T. Markkola, J. Halavaara, J. Tanttu, A. M. Hakkinen, and H. J. Aronen, “On- and off-resonance spin-lock MR imaging of normal human brain at 0.1 T: Possibilities to modify image contrast,” Magn. Reson. Imaging 16, 1191–1199 (1998). 13H. J. Aronen, U. A. Ramadan, T. K. Peltonen, A. T. Markkola, J. I. Tanttu, J. Jaaskelainen, A. M. Hakkinen, and R. Sepponen, “3D spin-lock imaging of human gliomas,” Magn. Reson. Imaging 17, 1001–1010 (1999). 14M. I. Kettunen, A. Sierra, M. J. Narvainen, P. K. Valonen, S. Yla-Herttuala, R. A. Kauppinen, and O. H. Grohn, “Low spin-lock field T1 relaxation in the rotating frame as a sensitive MR imaging marker for gene therapy treatment response in rat glioma,” Radiology 243, 796–803 (2007). 15H. I. Grohn, S. Michaeli, M. Garwood, R. A. Kauppinen, and O. H. Grohn, “Quantitative T(1rho) and adiabatic Carr-Purcell T2 magnetic resonance imaging of human occipital lobe at 4 T,” Magn. Reson. Med. 54, 14–19 (2005). 16W. R. Witschey, A. Borthakur, M. A. Elliott, E. Mellon, S. Niyogi, C. Wang, and R. Reddy, “Compensation for spin-lock artifacts using an off-resonance rotary echo in T1rhooff-weighted imaging,” Magn. Reson. Med. 57, 2–7 (2007). 17A. J. Wheaton, A. Borthakur, J. B. Kneeland, R. R. Regatte, S. V. Akella, and R. Reddy, “In vivo quantification of T1rho using a multislice spin-lock pulse sequence,” Magn. Reson. Med. 52, 1453–1458 (2004). 18W. R. Witschey II, A. Borthakur, M. A. Elliott, E. Mellon, S. Niyogi, D. J. Wallman, C. Wang, and R. Reddy, “Artifacts in T1 rho-weighted imaging: Compensation for B(1) and B(0) field imperfections,” J. Magn. Reson. 186, 75–85 (2007). 19K. Liu and T. Zhao, “System for reducing artifacts in imaging in the presence of a spin-lock radio-frequency field,” U.S. patent application publication 2014/0021951A1, 13/870,063 (January 23, 2014). 20M. Haris, E. McArdle, M. Fenty, A. Singh, C. Davatzikos, J. Q. Trojanowski, E. R. Melhem, C. M. Clark, and A. Borthakur, “Early marker for Alzheimer’s disease: Hippocampus T1rho (T(1rho)) estimation,” J. Magn. Reson. Imaging 29, 1008–1012 (2009). 21C. Taylor, J. Carballido-Gamio, S. Majumdar, and X. Li, “Comparison of quantitative imaging of cartilage for osteoarthritis: T2, T1rho, dGEMRIC and contrast-enhanced computed tomography,” Magn. Reson. Imaging 27, 779–784 (2009). 22X. Li, C. Benjamin Ma, T. M. Link, D. D. Castillo, G. Blumenkrantz, J. Lozano, J. Carballido-Gamio, M. Ries, and S. Majumdar, “In vivo T(1rho) and T(2) mapping of articular cartilage in osteoarthritis of the knee using 3 T MRI,” Osteoarthr. Cartil. 15, 789–797 (2007). 23K. Murase, “Behavior of the magnetization in spin-locking magnetic resonance imaging using numerical solutions to the time-dependent bloch equations,” Phys. Med. Biol. 57, N481–N492 (2012).