Errors in quantitative T1rho imaging and the correction methods

Introduction

T1rho is the time constant of spin-lattice relaxation in rotating frame, which characterizes relaxation of magnetization under influence of a radiofrequency (RF) field. Conventional spin-lattice relaxation (T₁) is particularly sensitive to processes in the lattice which occurs at high frequency near Larmor frequency (i.e., in MHz range). In contrast, T1rho is discovered to be sensitive to lattice processes occurring at much lower frequency close to the Rabi frequency of the spin-lock RF pulse, which typically is in the range of a few hundred hertz. Since slow motion in lattice is associated with macromolecular, such as proteins, T1rho is anticipated to be useful for assessment of the properties of macromolecular environment in tissue which conventional methods cannot offer.

Quantitative T1rho imaging has been investigated for many clinical applications (1-25). One of the greatest challenges of T1rho quantification in routine clinical practice is its robustness. A number of sources can cause quantification errors. A great deal of effort has been spent to develop methods to compensate these errors. It is the purpose of this article to review and discuss quantification errors in T1rho and the correction methods which are currently available.

The basics of T1rho

T1rho is often measured by the spin-lock technique described by Redfield (26). T1rho preparation (prep) typically starts with a 90-degree RF pulse (tip-down RF) to flip magnetization into transverse plane. An on-resonance continuous wave RF pulse (termed spin-lock RF pulse) is then applied in parallel to the magnetization, which causes the magnetization to process around it and appears to be “spin-locked”. During the time of spin-lock (TSL), the magnetization relaxes under the influence of the spin-lock RF pulse with time constant of T1rho instead of conventional T₂. After the spin-lock process, the magnetization is flipped back into longitudinal direction by another 90-degree RF pulse (tip-up RF). A crusher is then followed to dephase the residual signal in transverse plane. The magnetization after such T1rho prep can be expressed as:

where I₀ is a constant which is independent of TSL.

Various 2D or 3D data acquisitions methods can be used after T1rho prep to collect imaging data. To quantify T1rho value, data sets with different TSL are acquired and then fitted to Eq. [1]. Fat suppression is usually applied to avoid significant banding artifacts since spin-lock is susceptible to chemical shift of fat. Figure 1 shows a schematic diagram of conventional continues wave T1rho prep and the imaging data acquisition.

Figure 1 A schematic diagram of conventional T1rho prep using continuous wave spin-lock approach. A 90-degree RF pulse (tip-down RF) flips magnetization into transverse plane. A RF pulse is then applied in parallel to magnetization to “spin-lock” the magnetization. After time of-spin-lock (TSL), the magnetization is flipped back to longitudinal direction by another 90-degree RF pulse (tip-up RF). A crusher is then used to dephase residual signal in transverse plane. 2D or 3D data acquisition methods are used to collected data after T1rho prep. RF, radiofrequency.

Compensation of B₁ RF inhomogeneity

The conventional T1rho prep method shown in Figure 1 is susceptible to B₁ RF inhomogeneity. At the presence of B₁ RF inhomogeneity, the expected 90-degree tip-down RF pulse flips magnetization to an orientation deviated from transverse plane. Consequently, the magnetization rotates at an angle around the spin-lock RF pulse during TSL. After the tip-up RF pulse, the longitudinal magnetization becomes a complicated function of TSL shown below:

where θ is the actual flip angle of the tip-up/tip-down RF pulse, T2rho is the magnetization decay rate in the plane perpendicular to the spin-locking RF pulse, and α is the total flip angle during spin locking which is proportional to TSL. The presence of cosα term results in spatial modulation of signal which manifests as banding artifacts in acquired images.

By reversing the amplitude or phase of the second half of the spin-locking RF pulse, the net flip angle during spin lock becomes zero. Consequently, the cosα term is canceled out in Eq. [2]. This is the rotary echo approach proposed by Charagundla et al. (27), which is commonly used to address B₁ RF inhomogeneity effect in T1rho imaging. Figure 2A shows a schematic diagram of this method. It can be shown that with rotary echo approach, the longitudinal magnetization after T1rho prep is:

Figure 2 RF pulse clusters used to compensate B₁ RF and B₀ field inhomogeneity for continues wave spin-lock. (A) Rotary echo approach for B₁ RF inhomogeneity compensation. The phase of the second half of spin-lock is reversed; (B) the composite RF approach for B₀ field inhomogeneity compensation. A 135-degree RF pulse with same phase as spin-lock RF pulse is played out before and after spin-lock. The amplitude ratio between the composite RF pulse and spin-lock RF pulse is (); (C) simultaneous compensation of B₁ RF and B₀ field inhomogeneity. A 180-degree refocusing RF pulse is inserted in the middle of rotary echo and the phase of the tip-down RF is reversed compared to conventional method; (D) combination of the composite RF pulse and a phase cycling method for simultaneous B₁ RF and B₀ field inhomogeneity compensation. Two data sets are acquired with opposite phase of the tip-up RF pulse and subtracted from each other to yield final T1rho-preped images. No particular requirement of the amplitude ratio between the composite RF pulse and the spin-lock RF pulse. RF, radiofrequency.

Note that compared to the conventional T1rho prep, cosα term is eliminated using rotary echo method. However, the T2rho term remains, which results in quantification error if mono-exponential relaxation model of Eq. [1] is used to obtain T1rho value.

It was reported that B₁ inhomogeneity effect on continuous wave T1rho prep could be fully compensated by a phase cycling method (28). In this method, two data sets are acquired with opposite phase of the tip-up RF pulse. These two data sets are then subtracted from each other. The longitudinal magnetization after subtraction is:

Note compared to the rotary echo approach, the second term in Eq. [3] is completely eliminated after phase cycling. Therefore, the mono-exponential decay model depicted by Eq. [1] can be used to fit T1rho accurately after phase cycling without being compromised by B₁ RF inhomogeneity.

The apparent downside of the phase cycling method is it doubles scan time, even though the signal-to-noise ratio (SNR) is elevated to a level similar to that of 2 NEX acquisitions. For certain T1rho imaging pulse sequences which requires phase cycling to remove T₁ relaxation effect during data acquisition, such as 3D magnetization-prepared angle-modulated partitioned k-space spoiled gradient echo snapshots (MAPSS) (29), there is no scan time penalty to use this method for B₁ inhomogeneity compensation.

Adiabatic RF pulses are commonly used to address B₁ RF inhomogeneity in MRI system. Researchers have used adiabatic half-passage (AHP) pulses to address B₁ inhomogeneity effect on continuous wave T1rho prep (6,30). In these methods, AHP pulses are used to generate uniform 90-degree excitation, followed by continuous wave spin-lock RF pulses. The magnetization is either flipped back to longitudinal direction by another AHP pulse followed with imaging data acquisition (6), or directly followed with imaging module for data collection (30).

Compensation of B₀ field inhomogeneity

The presence of B₀ field inhomogeneity can cause image artifacts to T1rho-weighted imaging and T1rho quantification error. Shimming is highly recommended for T1rho imaging. However, shimming alone usually cannot eliminate off-resonance effect.

When there is off-resonance, the effective magnetic field in the rotating frame during spin-lock is the combination of B₁ RF and B₀ field. The orientation of this effective magnetic field with respect to transverse plane is:

Note this angle diminishes when the amplitude of B₁ increases. Therefore, a simple way to overcome the adversary effect from off-resonance during spin-lock is to increase the amplitude of the spin-lock RF pulse. However, the maximum RF amplitude is limited by the power of RF amplifier. High amplitude combined with long duration of spin-lock RF also leads to elevated special absorption rate (SAR). The situation is worsened when body RF transmitter rather than local transceiver coil is used.

Dixon et al. (2) reported a method to compensate off-resonance effect during spin-lock by using composite RF pulses. In this approach, a 135-degree RF pulse with phase same as spin-lock RF pulse is inserted both before and after spin-lock, as shown in Figure 2B. The amplitude of the composite RF pulses satisfies:

where and are the amplitude of the composite RF pulse and the spin-lock RF pulse, respectively. For spin-lock RF pulse at 500 Hz, which is commonly used in practice, however, the amplitude of the composite RF pulses specified by Eq. [6] is approximately 1.2 kHz, which may not be practical to use since it is close to the power limit of RF amplifier equipped in a modern clinical scanner.

Simultaneous compensation of B₁ RF and B₀ field inhomogeneity

The methods described in previous sections are aimed for compensation of either B₁ RF inhomogeneity or B₀ field inhomogeneity. The combination of both of them can compromise the effectiveness of these methods and methods which can address B₁ RF and B₀ inhomogeneity effect simultaneously are needed.

One method with aim to address this issue is proposed by Zeng et al. (31). In this method, a 180-degree refocusing RF pulse with the same phase as spin-lock RF pulse is inserted in the middle of the rotary echo RF pulse, which is used to compensate off-resonance effect accrued during spin-lock. However, it is shown that this approach can be sensitive to B₁ RF inhomogeneity (32). Incomplete compensation can arise when the flip angle of tip-down/up RF pulse is not exactly 90 degree and/or the flip angle of the refocusing pulse is not exactly 180 degree.

Witschey et al. (32) discovered that by reversing the phase of the tip-down RF pulse in the method reported by Zeng et al. (31), the same T1rho prep becomes insensitive to the flip angle of tip-down/up RF pulses. A schematic diagram of this approach is shown in Figure 2C. The effectiveness of this method for simultaneous compensation of B₁ and B₀ inhomogeneity, however, still can be compromised if the flip angle of the refocusing RF pulse is not 180 degree. This imperfection may be mitigated by increasing the amplitude of the refocusing pulse or using B₁ insensitive 180-degree refocusing pulses (32).

By combining the composite RF pulse reported by Dixon et al. (2) with phase cycling method, we can also achieve simultaneous compensation of B₁ and B₀ field inhomogeneity for continues wave T1rho prep (28). A schematic diagram of this approach is shown in Figure 2D. It is reported that this method is effective when the amplitude of the composite RF pulse deviates from that specified by Eq. [6], therefore insensitive to B₁ inhomogeneity effect (28). The downside of this method, however, is the prolonged scan time.

Spin-lock using Adiabatic RF pulse with insensitivity to B₁ RF and B₀ field inhomogeneity

Conventionally spin-lock is implemented by continuous wave RF pulses. The methods we described in previous sections are developed to improve the robustness of this type of spin-lock approach under the presence of B₁ RF and B₀ field inhomogeneity. A different way to achieve spin-lock is to use adiabatic RF pulses (33-35). The hyperbolic secant RF pulses used in these methods for spin-lock are inherently insensitive to B₁ RF and B₀ field inhomogeneity (34-40). In the studies reported in references (34-40), a train of adiabatic full-passage (AFP) hyperbolic secant RF pulses are applied to create spin-lock contrast. During the application of these pulses, both amplitude and frequency are modulated, which leads to variation of amplitude and orientation of effective field in time. When the adiabatic condition is satisfied, namely, the orientation of the effective magnetic field changes slower than the rotation of magnetization about this effective field (41), which can be achieved by sufficiently high B₁ amplitude or a slow frequency sweep, the spins are spin-locked along the effective field and decay at a time varying T1rho rate. By fitting the images collected with different levels of adiabatic T1rho contrast to a mono-exponential decay model, the average T1rho relaxation rate is measured over the pulse duration. The measured adiabatic T1rho value varies when different types of adiabatic RF pulses with different amplitude and frequency modulation is used. Recently, a type of gradient modulated adiabatic pulses is reported for adiabatic T1rho imaging which can achieve reduced artifacts from B₁ and B₀ field inhomogeneity, and the same time reduced power deposition, short scan time, and slice selectivity (42).

Compared to continuous waveform spin-lock, T1rho varies during the adiabatic spin-lock since the amplitude and frequency of the pulse is modulated during the time course. Consequently, the measured T1rho is an average value over the duration of adiabatic pulse. The clinical use of T1rho quantification using adiabatic spin-lock is not as well understood as that using continuous waveform spin-lock, and therefore further clinical study of this method is needed.

Errors from data acquisition and the correction methods

There is a multitude of imaging sequences which can be used to collect data after T1rho contrast is imparted to the magnetization. The imaging sequence usually is put after T1rho prep, as shown in Figure 1. With inclusion of particular imaging sequence, the whole pulse sequence of T1rho imaging inherits its sensitivity to system imperfection, i.e., Fast (Turbo) Spin Echo is sensitive to factors causing the violation of CPMG condition. In addition, the signal evolution during imaging sequence may complicate the quantification of T1rho and care is needed to address these issues.

Borthakur et al. (43) reported a 3D T1rho imaging approach based on steady state spoiled gradient echo acquisition. Only one phase encoding line is acquired for every T1rho prep in this approach. The signal at steady state is expressed by the following equation which is used to fit the T1rho value:

where α is the flip angle, and TR is the repetition time. Eq. [7] indicates that erroneous value of α due to B₁ inhomogeneity and inaccurate prior knowledge of T₁ can lead to T1rho quantification error in this method.

Li et al. (29) reported a 3D quantitative T1rho imaging method termed MAPSS which is based on segmented SPGR acquisition. The data is acquired during the transient signal evolution toward steady state. A primary concern of direct use of segmented SPGR acquisition for T1rho quantification is that T₁ relaxation during imaging data acquisition can degrade T1rho contrast. As shown by Li et al. (29), the transverse magnetization after the nth RF pulse during SPGR readout can be expressed as:

where A(n) and B(n) are complicated functions of relaxation parameters and pulse sequence parameters. The expression of these two terms can be found in reference (29). Note the term B(n) in Eq. [8] is an additive term and impacts quantification accuracy if not corrected. To address this issue, Li et al. (29) proposed to acquire two data sets with opposite phase of the tip-up RF pulse, and then subtract them from each other, which yield:

Note the magnitude image after subtraction can be fitted to a mono-exponential decay model to calculate T1rho without error.

For multi-slice 2D imaging, if multiple slices are acquired after one T1rho prep, T₁ relaxation during the time course after T1rho prep can lead to quantification error when Eq. [1] is used as the relaxation model (44), in a similar manner as in MAPSS. The same phase cycling method has been used to address this issue in multi-slice quantitative T1rho imaging (44).

Fast (or Turbo) Spin Echo (FSE or TSE) with long echo train has also been reported for quantitative T1rho imaging (45,46). In FSE (TSE) acquisition, when the CPMG condition is met and the crusher gradient is sufficient so that FID is eliminated, T₁ recovery during the readout is eliminated. The point spread functions for all TSL values are identical and relative image intensity between images acquired with different TSL values depends only on T1rho exponential decay during spin lock. Therefore, no phase cycling is needed to address T₁ relaxation effect during long readout of FSE, which makes FSE based T1rho imaging highly SNR efficient. Compared to 3D gradient echo acquisition, the downside of 3D FSE acquisition, however, is increased echo time which is unfavorable when imaging tissue with relative short T₂, increased sensitivity to eddy current, and potential blurring when long echo train is used (46).

Balanced gradient echo sequence (47) can also be used for fast quantitative imaging. Instead of acquiring imaging data in steady state after a number of dummy pulses, signal has to be acquired during transient stage in this approach. Otherwise, contrast loss during the transient decay can result in elevated T1rho estimation (47). Collecting date during transient stage in balanced gradient echo sequence can cause image blurring. The authors proposed to design a filter applied in k-space to address this issue (47).

Errors from insufficient SNR and the correction methods

SNR plays a critical role in quantitative imaging. There is increasing interest in acquiring parametric map with high resolution and/or fast scan, which inevitably costs SNR. Care must be used to avoid quantification error from insufficient SNR.

In MRI system, noise follows Gaussian distribution with zero mean in frequency domain. The commonly used linear regression approach, which is based on weighted least square fit of the logarithm of the magnitude image, has advantage of simplicity and fast computation time. However, the logarithm transform of the image causes the noise distribution no longer to be normal, which violates the assumption underneath the least square fit. The quantification using this approach is still approximately accurate when SNR is high, but large bias appears when SNR is low (48). Non-linear fit of Eq. [1] without applying logarithm transform (49,50) may improve quantification accuracy. However, large bias remains since the noise in magnitude image can deviate from Gaussian distribution significantly with a non-zero mean when SNR is low (49,50).

Truncation method is used in some studies to address the SNR issue. In this method, data sets acquired with long TSL are discarded if they are regarded with insufficient SNR. However, such practice is not preferred since quantification accuracy requires the entire decay curve, including long TSL, is sampled (51).

A common practice of quantitative imaging is to measure parameter within a ROI instead of on one single pixel. SNR can be greatly increased by averaging signal within ROI. For such practice, it is preferred to take average of ROI within a complex image instead of magnitude image to avoid significant error due to non-zero mean of noise in magnitude image at low SNR. The downside of the ROI approach is reduced resolution of acquired parametric map.

A modification of the relaxation model has been investigated to address noise issue in tissue parameter quantification. Instead of fitting using Eq. [1], it is proposed by Mosher (52) to fit the magnitude image using the following equation:

where C is an unknown constant. However, it is reported that, even though this model improves the accuracy of relaxation parameter estimation at low range, it prone to underestimate relaxation parameter, especially for long relaxation (49).

Compared to Eq. [10], a more accurate model to include noise in magnitude image for tissue parameter quantification is reported by Miller and Joseph (53). For a single receiver system, without partial Fourier, parallel imaging, and other advanced reconstruction, Miller and Joseph discovered that the mean of the square of magnitude image can be expressed as (53):

where I_true is the image in absence of noise, and σ is the standard deviation of noise in either real or imagery channel. Therefore, we can subtract noise 2σ² from the mean of square of image intensity before fitting the data to a mono-exponential decay model (53). This approach was shown to be more accurate than linear or non-linear fit using Eq. [1] (49).

For single receiver system, the magnitude image follows Rician distribution (54-56). Raya et al. (49) calculated the analytical solution of the mean of image intensity (termed noise corrected exponential function), and then estimate relaxation parameter by non-linear fitting of magnitude image to this noise corrected exponential function. They demonstrated that such fit method results in precisions comparable to the best achievable precisions determined by Cramer-Rao lower bound.

One limitation of these noise-corrected approaches is that they are only applicable for single receiver system. Hardy and Andersen (50) established a noise-corrected approach for phased array system. Ignore noise correlation between receivers in phased array and assume they are statistically independent; the magnitude image of standard square-root-of-sum-of-square reconstruction follows non-central chi distribution (57). Hardy and Andersen proposed a lookup table approach where the difference between the magnitude image and the true image caused by noise is pre-calculated offline based on the analytical expression of non-central chi distribution. These values are stored in a lookup table and the corresponding amount of correction for particular imaging case is read from the table and applied to the magnitude image for correction. A mono-exponential decay model based on non-linear least square fit is then applied to the corrected image to estimate relaxation parameter.

Another approach which is applicable for parameter quantification using phased array is maximum likelihood method (48). This method derives the best estimate of relaxation parameter by maximizing the joint distribution of magnitude image at different TSL (48,50). Hardy and Andersen show that the maximum likelihood approach and the noise-corrected lookup table approach provide very close estimation, but the great difference in computational complexity and computational time makes the lookup table approach a favorable choice (50).

Summary

The spin-lock technique used to generate T1rho contrast provides a mechanism to probe into macromolecular environment which conventional imaging methods cannot offer. Consequently, T1rho quantification has potential in many clinical applications. However, despite the promising outcomes of the published studies, it remains challenging to achieve robust and accurate T1rho quantification in routine clinical practice. In this article, the major sources which can cause errors to T1rho quantification and the correction methods are reviewed. The review is focused on error sources including system imperfections, inappropriate pulse sequence design, and insufficient SNR. For certain tissue types, additional factors which may confound T1rho quantification can arise due to inherent tissue properties. For example, magic angle effect (58,59) and multiple relaxation components (60-62) are commonly observed when imaging cartilage and fibrocartilage. Review of these confounding factors for relaxometry due to inherent tissue properties is not included in this article.

Acknowledgements

The author would like to thank Dr. Yì-Xiáng J. Wáng for proofreading the article and reviewers for reviewing the article.

Footnote

Conflicts of Interest: The author has no conflicts of interest to declare.

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