Probing Chemical Exchange Using Quantitative Spin-Lock R1rho Asymmetry Imaging With Adiabatic Radiofrequency Pulses

Abstract

Purpose

CEST is commonly used to probe the effects of chemical exchange. Although R1rho asymmetry quantification has also been described as a promising option for detecting the effects of chemical exchanges, the existing acquisition approaches are highly susceptible to B1 RF and B0 field inhomogeneities. To address this problem, we report a new R1rho asymmetry imaging approach, AC-iTIP, which is based on the previously reported techniques of irradiation with toggling inversion preparation (iTIP) and adiabatic continuous wave constant amplitude spin-lock RF pulses (ACCSL). We also derived the optimal spin-lock RF pulse B1 amplitude that yielded the greatest R1rho asymmetry.

Methods

Bloch-McConnell simulations were used to verify the analytical formula derived for the optimal spin-lock RF pulse B1 amplitude. The performance of the AC-iTIP approach was compared to that of the iTIP approach based on hard RF pulses and the R1rho-spectrum acquired using adiabatic RF pulses with the conventional fitting method. Comparisons were performed using Bloch-McConnell simulations, phantom, and in vivo experiments at 3.0T.

Results

The analytical prediction of the optimal B1 was validated. Compared to the other two approaches, the AC-iTIP approach was more robust under the influences of B1 RF and B0 field inhomogeneities. A linear relationship was observed between the measured R1rho asymmetry and the metabolite concentration.

Conclusion

The AC-iTIP approach could probe the chemical exchange effect more robustly than the existing R1rho asymmetry acquisition approaches. Therefore, AC-iTIP is a promising technique for metabolite imaging based on the chemical exchange effect.

Introduction

MRI is among the most widely used imaging modalities in clinical diagnosis. Conventional MRI diagnoses are often based on morphological changes in diseased tissue. In recent years, the mechanism of chemical exchange (CE) contrast has been used to probe diseases at a molecular level and has elicited increasing interest in both clinical and research settings.^1–10 Generally, CE-based contrast is studied using the chemical exchange saturation transfer.^2,10

Principally, CEST is based on the effect of saturated proton exchanges between free water and biological molecules. These molecules contain exchangeable protons that resonate at the Larmor frequency, with a chemical shift δ away from that of water. Labile protons can be saturated by applying a selective off-resonance RF pulse. The water signal is then attenuated via the exchange of saturated labile protons and water at CE rate constant, k_ex. The normalized water signal intensity can be represented as a function of the RF frequency offset (FO), which is known as the Z-spectrum. The CE signal can be extracted by analyzing asymmetry in the Z-spectrum. The CE rate can usually be divided into three regimes: slow (k_ex/δ <<1), intermediate (k_ex/δ ~1), and fast exchange (k_ex/δ >>1). CEST imaging is often performed at slow chemical exchange regime due to the spillover effect caused by direct water saturation.⁴

Spin-lock can also be used to probe the chemical exchange effect.^11–22 This technique can be performed at a range of FOs to extract the chemical exchange contrast related to specific metabolites, and the CE contrast can be calculated based on an asymmetry analysis similar to that used in CEST. These types of approaches are designated as chemical exchange spin-lock (CESL).^11,12 The preparation for CESL magnetization comprises a RF pulse that flips the longitudinal magnetization at a specific flip angle determined by the FO and the frequency of spin-lock (FSL), followed by a spin-lock pulse that locks the spin at that angle. After the spin-lock process, the spins are flipped back to the longitudinal direction by another RF pulse. Compared to CEST, CESL more sensitively detects metabolites at intermediate to fast exchange regimes.¹⁷ However, CESL is significantly hindered by the presence of B1 RF and B0 field inhomogeneities, which cause a failure of spin-lock and thus induce image artifacts and quantification errors. CESL experiments are typically performed at a relatively low FSL.¹⁷ The susceptibility of spin-lock to B0 field inhomogeneity increases as the FSL decreases. At a low FSL, even a small B0 field inhomogeneity can result in non-negligible spin-lock errors. The existing methods of artifact correction for constant amplitude spin-lock mostly address on-resonance imaging. Witschey et al. reported the compensation of B1 inhomogeneity during off-resonance spin-lock, using an approach based on the rotary echo method.²³ However, that approach ignored B0 field inhomogeneity. Other reports suggest that by replacing hard pulses with adiabatic pulses with RF amplitudes matching that of the spin-lock pulse, the spins would be locked along the effective field for both on- and off-resonance spin-lock, even in the presence of B1 RF and B0 field inhomogeneities.^{22, 24, 25} This approach should therefore provide artifact-free spin-lock images and T1rho (or $\text{T}1\text{ρ}$) quantification with simultaneous compensation of B1 RF and B0 field inhomogeneities for both on- and off-resonance spin-lock. For convenience, we describe this approach as adiabatic continuous wave constant amplitude spin-lock (ACCSL).

Recently, R1rho (or $\text{R}1\text{ρ}$, 1/T1rho) asymmetry was described as a promising option for probing metabolites.^15,16 The R1rho asymmetry signal is free from the effects of water R1 and R2 relaxation.¹⁵ The R1rho asymmetry signal is linearly proportional to the population of the chemical exchanging pool or the concentration of the metabolite of interest.¹⁶ To calculate an R1rho-spectrum, spin-lock images with various time-of-spin-lock (TSL) values can be collected using ACCSL or other spin-lock methods at each FO. Next, the R1rho can be calculated at each FO by fitting the data to an appropriate relaxation model. For convenience, we term this method the R1rho-fitting approach. The R1rho can also be obtained using a previously reported approach, irradiation with toggling inversion preparation (iTIP), where an inversion pulse is used to obtain the R1rho without reaching the steady state.¹⁵ The originally reported iTIP approach was based on a hard RF pulse spin-lock,¹⁵ which is subject to the effects of B1 RF and B0 field inhomogeneities. For convenience, we term this approach the hard pulse-based iTIP (HP-iTIP).

In this work, we present a new approach to R1rho asymmetry imaging for the measurement of metabolites. We use the term AC-iTIP to describe this newly proposed method based on ACCSL with iTIP acquisition. Here, we provide the theory and method by which this AC-iTIP approach can be used to achieve robust R1rho quantification in the presence of B1 RF and B0 field inhomogeneities. We also provide a theoretical derivation of the optimal B1 of the spin-lock RF pulse required to achieve maximum R1rho asymmetry for specific metabolites. We further demonstrate the AC-iTIP approach using simulations, phantom, and in vivo experiments.

Methods

Challenges to CESL

The high susceptibility of conventional CESL based on a hard RF pulse spin-lock to B1 RF and B0 field inhomogeneities presents a major challenge. However, ACCSL can be used to mitigate this problem. When performing ACCSL, the spins are locked along the effective spin-lock field after adiabatic half passage (AHP) at an angle θ from the longitudinal direction, which is determined by the nominal spin-lock B1, nominal resonance FO, and B1 RF and B0 field inhomogeneities.^{24, 25} Figure 1a) shows the θ values with and without B0 field inhomogeneity when ACCSL was used at a range of resonance FOs. Note that B0 field inhomogeneity can result in a discontinuity of θ. Consequently, the CESL Z-spectrum from the ACCSL also exhibits discontinuity, as shown in Figure 1b). In Appendix A, we determine that if the B0 field inhomogeneity is Δf, the asymmetry analysis of the CESL Z-spectrum acquired using the ACCSL is only valid at FOs outside the range of 0 to 2×Δf. This outcome causes two problems: 1. the ACCSL cannot detect metabolites with chemical shifts smaller than that of the B0 field inhomogeneity and 2. CESL Z-spectrum fitting becomes difficult because of this discontinuity.

Figure 1.

The effect of B0 field inhomogeneity on the CESL Z-spectrum and the R1rho-spectrum. Spin-lock was performed using ACCSL. a) The effective spin-lock field angle during ACCSL at different resonance FOs; b) CESL Z-spectrum using ACCSL; and c) R1rho-spectrum. Blue and red lines indicate the results in the presence and absence of B0 field inhomogeneity, respectively. Note that the ACCSL Z-spectrum exhibits discontinuity in the presence of B0 field inhomogeneity, whereas the R1rho-spectrum exhibits a shift equal to B0 field inhomogeneity.

These problems can be addressed by calculating the R1rho-spectrum. R1rho can be approximated as a superposition of three terms,²⁶ namely relaxation due to water (R_eff), relaxation due to the CE effect (R_ex), and relaxation due to the magnetization transfer (R_MT). This approximation can be represented as below:

$$R_{1rho}\left(FO\right)=R_1\cdot {\cos }^2\theta +\left(R_2+R_{ex}\right)\cdot {\sin }^2\theta +R_{MT},$$ [1]

where ${\cos }^2\theta =F{O}^2/\left(w_1{}^2+F{O}^2\right)$, ${\sin }^2\theta =w_1{}^2/\left(w_1{}^2+F{O}^2\right)$, and $w_1$ denotes the B1 RF amplitude of the spin-lock RF pulse. As shown in Appendix A, the change in θ at the discontinuity points is ±π in the presence of B0 field inhomogeneity. As ${\sin }^2\theta ={\sin }^2\left(\theta \pm \text{π}\right)$ and ${\cos }^2\theta ={\cos }^2\left(\theta \pm \text{π}\right)$, this discontinuity is removed by the squares of the sine and cosine. Therefore, the R1rho-spectrum and associated asymmetry analysis are not affected by the aforementioned problems. Figure 1c) depicts R1rho-spectra simulated using ACCSL with and without B0 field inhomogeneity. Note that B0 field inhomogeneity, Δf, only caused an equivalent shift in the R1rho-spectrum, rather than discontinuity of the spectrum.

Robust R1rho asymmetry

R1rho asymmetry can be calculated after using ACCSL to acquire the R1rho at each resonance FO. However, this approach and the corresponding relaxation model²⁵ may require a long-duration RF pulse at large FOs to accommodate the prolonged T1rho at increased FOs. Additionally, during the asymmetry analysis, any small quantification error due to noise can be amplified after the subtraction process. To improve the robustness of the R1rho quantification, we used the iTIP approach¹⁵ and replaced the hard RF pulse spin-lock in the original iTIP approach with the ACCSL RF pulse cluster. This new approach is termed AC-iTIP. Figure 2 illustrates the spin-lock RF pulse clusters used during AC-iTIP and the original HP-iTIP. Note that the spin-lock RF pulse cluster used in the ACCSL is the same as the pulse cluster used for AC-iTIP but lacked a hard pulse for inversion.²⁵

Figure 2.

The RF pulse waveforms generated using the AC-iTIP approach (a and c) and HP-iTIP approach (b and d). Crushers (not shown) were added between the inversion pulse and spin-lock pulse of both approaches. For the R1rho-fitting approach using ACCSL, the RF pulse waveform was identical to the AC-iTIP RF pulse waveform without the inversion pulse. SL represents the spin-lock pulse. The hard pulse flipped the magnetization to a corresponding effective magnetic field with a flip angle θ.

For AC-iTIP, two datasets are acquired, one each with the toggling RF pulse turned on and turned off. According to the reference,²⁵ when the toggling RF pulse is turned off, magnetization at the end of the spin-lock RF pulse cluster can be expressed as:

$$M^{tsl}=M_{\text{ini}1}\cdot e^{-R_{1rho}\left(FO\right)\cdot tsl}+C.$$ [2]

When the toggling RF pulse is turned on, magnetization at the end of the spin-lock RF pulse cluster can be expressed as:

$$M_i^{tsl}=M_{\text{ini}2}\cdot e^{-R_{1rho}\left(FO\right)\cdot tsl}+C,$$ [3]

where M_ini1 and M_ini2 are the initial magnetizations after the AHP and at the beginning of the spin-lock, respectively; and $C$ is DC term including the contributions from the steady state magnetization and relaxation during the adiabatic pulse.²⁵ Note that the same DC term is used in Eq. [2] and [3], as the DC term is calculated using the steady state magnetization, relaxation parameters, and adiabatic waveforms²⁵ that remain constant regardless of the toggling RF pulse status. Note that M_ini1 is equal to the negative M_ini2 determined using the original HP-iTIP when the toggling RF pulse is a perfect 180º pulse. In the AC-iTIP approach, M_ini1 is not equal to the negative M_ini2 because of the following reasons: 1. Often, the flip angle of the toggling RF pulse is not exactly 180º under the influence of B1 RF inhomogeneity, particularly if a simple hard pulse is used for the inversion. 2. The relaxation effect during adiabatic pulses can cause the magnitude of M_ini1 unequal to that of M_ini2, even at a toggling RF pulse flip angle of 180º.

The subtraction of [3] from [2] yields:

$$M_t\left(FO\right)\equiv M^{tsl}-M_i^{tsl}=\left(M_{\text{ini}1}-M_{\text{ini}2}\right)\cdot e^{-R_{1rho}\left(FO\right)\cdot tsl}$$ [4]

Here, R1rho asymmetry can be calculated by determining the logarithm of $M_t\left(+FO\right)/M_t\left(-FO\right)$ if the magnitude of $\left(M_{\text{ini}1}-M_{\text{ini}2}\right)$ is equal at +FO and −FO.

As demonstrated in Figure 1, the presence of B0 field inhomogeneity causes discontinuity in the θ spectrum, which can also result in discontinuity of the M_ini1 and M_ini2 spectra. Figure 3 demonstrates this effect. In the absence of B0 field inhomogeneity, M_ini1 and M_ini2 are symmetrical with respect to the water frequency, and the magnitude of $\left(M_{\text{ini}1}-M_{\text{ini}2}\right)$ is approximately equal at +FO and −FO. In contrast, in the presence of B0 field inhomogeneity, discontinuities can be observed in the M_ini1 and M_ini2 spectra, which leads to unequal $\left(M_{\text{ini}1}-M_{\text{ini}2}\right)$ magnitudes at +FO and −FO. To address this problem, data are collected at a TSL of 0 ms to obtain the value $\left(M_{\text{ini}1}-M_{\text{ini}2}\right)$. We can combine this with Eq. [4] to calculate the R1rho-spectrum and R1rho asymmetry. If we assume a symmetrical magnetization transfer (MT) effect with respect to the water reference point, then the R1rho asymmetry can be calculated as:

$$R_{1rho,asym}=R_{1rho}\left(+FO\right)-R_{1rho}\left(-FO\right)={\sin }^2\theta \cdot (R_{ex}\left(+FO\right)-R_{ex}\left(-FO\right)).$$ [5]

Figure 3.

Bloch-McConnell simulations of the initial magnetization, M_ini1 and M_ini2, before spin-lock. M_ini1 and M_ini2 are defined in Eq. [2] and Eq. [3]. a) The blue and red solid lines respectively correspond to M_ini1 and M_ini2 without B0 inhomogeneity. The yellow and purple solid lines respectively correspond to M_ini1 and M_ini2 with B0 inhomogeneity. b) The spectrum and asymmetry of M_ini1-M_ini2 without and with B0 field inhomogeneity. The symmetrical axis used for the asymmetry calculation is indicated by the dotted lines, which correspond to 0 and −50 Hz in the absence and presence of B0 field inhomogeneity, respectively. The yellow and purple lines respectively correspond to M_ini1-M_ini2 asymmetry in the absence and presence of B0 field inhomogeneity. Note that in the presence of B0 field inhomogeneity, the M_ini1-M_ini2 values at +FO and -FO are not equal. Discontinuities are visible on the M_ini1, M_ini2, and M_ini1-M_ini2 asymmetry spectra.

According to Trott and Palmer,²⁷ $R_{ex}$ for a 2-pool model can be expressed as:

$$R_{ex}=\frac{p_b\cdot k\cdot {\delta }_b{}^2}{{\left({\delta }_b-FO\right)}^2+w_1{}^2+k^2}.$$ [6]

where $p_b$ denotes the population ratio of the labile proton to the water proton, k denotes the CE rate, and ${\delta }_b$ denotes the chemical shift of the metabolite pool.

By substituting Eq. [6] into Eq. [5], we obtain:

$$R_{1rho,asym}=p_b\cdot k\cdot {\delta }_b{}^2\cdot {\sin }^2\theta \cdot \left(\frac{1}{x_1{}^2+w_1{}^2}-\frac{1}{x_2{}^2+w_1{}^2}\right),$$ [7]

where $x_1{}^2={\left({\delta }_b+FO\right)}^2+k^2$ and $x_2{}^2={\left({\delta }_b-FO\right)}^2+k^2.R_{1rho,asym}$ can be acquired selectively for certain groups of labile protons. In contrast, the on-resonance R1rho receives signal contributions from all labile protons and therefore is not selective for specific metabolites.

Optimized B1 amplitude of the spin-lock RF pulse for R1rho asymmetry

An optimal saturation RF pulse B1 amplitude can be used to achieve maximum CEST contrast.²⁸ During R1rho asymmetry acquisition, an optimal spin-lock RF pulse B1 amplitude (or $w_1$ in Eq. [7]) also exists and yields the highest R1rho asymmetry. The optimal spin-lock RF pulse B1 amplitude can be derived analytically by equating the first derivative of Eq. [7] to zero. The optimal $w_1$ that yields the highest R1rho asymmetry, denoted as $w_{1,opt}$, can be determined using the following equation (a detailed derivation is provided in Appendix B):

$$\frac{1}{w_{1,opt}{}^2}={(\sqrt{\frac{p^3}{27}+\frac{q^2}{4}}-\frac{q}{2})}^{\frac{1}{3}}+{(-\sqrt{\frac{p^3}{27}+\frac{q^2}{4}}-\frac{q}{2})}^{\frac{1}{3}},$$ [8]

where $\text{p}=-(x_1{}^2+x_2{}^2+F{O}^2)/(x_1{}^2\cdot x_2{}^2\cdot F{O}^2)$ and $\text{q}=-2/(x_1{}^2\cdot x_2{}^2\cdot F{O}^2)$.

Simulation studies

Simulation study 1: Validation of the optimal B1

We used simulations to demonstrate the existence of the optimal B1 of the spin-lock RF pulse and validate our analytical derivation. We performed full-equation Bloch-McConnell simulations using both 2-pool and 3-pool models. Detailed pool parameters are presented in the caption to Figure 4. Hyperbolic secant (HS1) pulses were used as the AHP and reverse AHP (rAHP). The pulse parameters were as follows: AHP and rAHP duration, 35 ms; coefficient factor beta, 2; and frequency sweep amplitude, 150 Hz. The B1 amplitudes of the AHP and rAHP equal the applied FSL. We performed six simulations using a combination of two chemical shifts (1 and 3 ppm) and three CE rates (500, 1500, and 3000 s⁻¹). In each experiment, the optimal B1 determined using the numerical simulation was compared with the optimal B1 derived using Eq. [8].

Figure 4.

Comparison of the theories and Bloch-McConnell simulations used to derive the optimal B1 amplitude of the spin-lock RF pulse. The following parameters were used for the 2-pool simulation: T1/T2 of pool A and B, 1156/43 ms; chemical shift of pool B (metabolite pool), 1 ppm; and chemical exchange rate, 1500 s^-1. In the 3-pool model, a third pool representing the magnetization transfer effect was included in the simulation. The magnetization transfer parameters were as follows: T2, 8.3 $\text{μs}$ and magnetization transfer rate, 60 s^-1. For the 2-pool model, the water population (p_a) and chemical exchange population (p_b) were 99% and 1%, respectively. For the 3-pool model, the magnetization transfer population (p_c) was 18.2%, the water population (p_a) was 80.8%, and the chemical exchange population (p_b) was 1%. Both 2-pool and 3-pool Bloch-McConnell simulations were performed. The theoretical calculation was based on Eq. [8], and the chemical shifts of the exchanging protons with respect to water were a) 1 and b) 3 ppm, respectively. Note that our theoretical prediction is consistent with the results of Bloch-McConnell simulations.

Simulation study 2: Performance comparison of the AC-iTIP approach with the HP-iTIP in the presence of B1 RF and B0 field inhomogeneities

We used 3-pool Bloch-McConnell simulations to demonstrate the improved performance of the AC-iTIP approach relative to the HP-iTIP approach. We compared the R1rho-spectrum determined using AC-iTIP to the iTIP-spectrum obtained using HP-iTIP in the presence of various levels of B1 RF and B0 field inhomogeneities. The iTIP-spectrum is defined as the logarithm of Eq. [4] divided by -TSL. Note that the iTIP-spectrum is a linear function of the R1rho-spectrum according to Eq. [4]. Simulations were performed using 3 different combinations of B1 RF and B0 field inhomogeneities. The parameters of the 3-pool model were identical to those used in the simulation study 1. Unless otherwise stated, TSL 60 ms was used for the HP-iTIP approach, while 0 and 60 ms were used for the AC-iTIP approach. The following additional parameters were applied: FSL = 150, 250, and 300 Hz. FOs were selected from −300 to 300 Hz. Spectra were obtained at two different FO intervals, 2 and 25 Hz. Unless otherwise stated, an order of 15 polynomial fittings was used to fit the R1rho-spectrum and iTIP-spectrum for the asymmetry analyses. The R1rho asymmetry signal was calculated as the mean R1rho asymmetry value within the range of 1 ± 0.08 ppm.

Simulation study 3: Compare the performance of the AC-iTIP approach to the R1rho-fitting approach based on ACCSL in the presence of noise

Using 3-pool Bloch-McConnell simulations, we compared the performance of the AC-iTIP approach to that of the R1rho-fitting approach based on an ACCSL acquisition at different signal-to-noise ratios (SNRs). The pool parameters were identical to those used in simulation study 1. FOs of ±250, ±200, ±175, ±150, ±125, ±100, ±75, ±50, ±25, and 0 Hz and a FSL of 150 Hz were used. As the AC-iTIP approach requires four acquisitions to measure R1rho values, 4 TSLs (0, 20, 40, and 60 ms) were used to simulate R1rho-fitting approach data and emulate an equal scan time between the two approaches. The R1rho-spectrum determined via the R1rho-fitting approach was obtained by fitting the data to our previously reported relaxation model.²⁵ Three SNRs were used: 15, 25, and 50. The SNR was calculated as the maximum signal from the acquisition at a FO of 0 Hz and TSL of 0 ms, divided by the standard deviation of noise for both approaches. The added noise adhered to a zero-mean Gaussian distribution. Simulations without added noise were used as ground truths.

Phantom studies

Phantom Study 1: Comparison of the performance of the AC-iTIP approach with the R1rho-fitting approach based on ACCSL in the presence of noise

Imaging datasets were acquired using a Philips Achieva TX 3.0T scanner equipped with dual transmission (Philips Healthcare, Best, the Netherlands). An 8-channel head coil (Invivo, Gainesville, FL, USA) was used as the receiver. Phantoms containing 3% agarose gel were used in this study. Two-dimensional (2D) fast spin echo (FSE) was used to acquire the imaging data. The FSL, FOs, and TSLs used in the AC-iTIP and R1rho-fitting approaches were identical to those used in simulation study 3. Data were acquired at different levels of SNR and varying echo times (TE) of 11, 30, and 40 ms. R1rho-spectra obtained using both approaches were compared.

Phantom Study 2: Comparison of the performances of the AC-iTIP approach, HP-iTIP approach, and R1rho-fitting approach in the presence of B1 RF and B0 field inhomogeneities

In this phantom study, we applied all three approaches to three phantoms with agarose concentrations of 3% (ROI 1), 4% (ROI 2), and 5% (ROI 3). Phantom datasets were acquired using a 32-channel cardiac coil (Invivo, Gainesville, FL, USA) as the receiver. Scans were performed at FO values of ±125, ±100, ±75, ±50, and 0 Hz. Datasets were acquired at a FSL of 150 and 300 Hz. In addition to datasets acquired using default shimming, we also acquired datasets using the pencil-beam (PB) shimming over ROI 2 to minimize B0 field inhomogeneity within the ROI 2. We then compared the R1rho-spectra and iTIP-spectra obtained using the respective approaches.

Phantom study 3: Use of the AC-iTIP approach to measure metabolite concentrations

In this phantom study, we applied the AC-iTIP approach to phantoms containing various concentrations of myo-inositol (0, 20, 30, 50, 100, 150, and 200 mM) dissolved in phosphate-buffered saline (pH = 7.4). The phantoms also included 0.2 mM MnCl₂ to modulate both the R1 and R2 to approximately 1.6 and 20 Hz, respectively. The same 8-channel head coil was used as the receiver. Scans were performed over a FO range of −300 to 300 Hz in 25-Hz increments. Datasets were collected at a FSL of 150 and 250 Hz. The experiments were conducted at room temperature.

In vivo study

Healthy volunteers underwent in vivo imaging under approval of the institutional review board. The imaging parameters of the in vivo scan included: FOV 16×16 cm², single-slice 2D FSE acquisition with a slice thickness of 5 mm, echo train length 27, TR/TE 2000/7.4ms, and spectral attenuated inversion recovery (SPAIR) for fat suppression. Volunteer imaging experiments were completed using SAR within the FDA limit. Datasets were collected at a FSL of 150 and 250 Hz. For the HP-iTIP and the AC-iTIP approaches, scans were performed over a FO range of −300 to 300 Hz in 25-Hz increments. For the R1rho-fitting approach, scans were performed at FOs of ±250, ±200, ±175, ±150, ±125, ±100, ±75, ±50, ±25, and 0 Hz. For all phantom and in vivo scans, a B0 field map was collected using a standard dual echo gradient echo acquisition approach with a delta TE of 2 ms. This B0 map was used to identify the center of the R1rho-spectrum.

Results

Figure 4 compares the analytical optimal B1 of the spin-lock RF pulse to the optimal B1 obtained from Bloch-McConnell simulations. Note the consistency between the results. For a fast CE process with a chemical shift of 1 ppm and CE rate of 1500 s⁻¹, the optimal B1 of the spin-lock RF pulse would be approximately 150 Hz. This parameter was used in our simulation, phantom, and in vivo experiments.

Figure 5 a-l compares the simulated performances of the HP-iTIP and AC-iTIP approaches under B1 RF and B0 field inhomogeneities. Both approaches yielded comparable results in the absence of B1 RF and B0 field inhomogeneity. However, the R1rho asymmetry signal decreased with increasing FSL, consistent with our theory. In the presence of field inhomogeneities, the iTIP-spectrum acquired via HP-iTIP exhibits oscillations that can lead to incorrect R1rho asymmetry. In contrast, when using the AC-iTIP approach, B0 field inhomogeneity only results in an equal shift of the R1rho-spectrum. More information regarding the performance of both approaches under B1 RF field inhomogeneity is included in Supporting Information Figure S1.

Figure 5.

The 3-pool Bloch-McConnell simulations of the HP-iTIP and AC-iTIP approaches under three levels of field inhomogeneity, including control (no B1 RF or B0 field inhomogeneities), moderate (actual B1 = 90% of the expected B1 RF amplitude, B0 field inhomogeneity = 50 Hz), and severe (actual B1 = 80% of the expected B1 RF amplitude, B0 field inhomogeneity = −100 Hz). The top and second rows correspond to FO increments of 2 (a, b, and c) and 25 Hz (d, e, and f), respectively. Blue and red lines represent the spectra generated using the HP-iTIP and AC-iTIP approaches, respectively. The spectra shown in (a–f) were simulated using the chemical exchange population, $p_b$ 0.01. The third and fourth rows correspond to R1rho asymmetry determined using the AC-iTIP (g, h, and i) and HP-iTIP approaches (j, k, and l), respectively. Blue, red, and yellow lines correspond to results derived at a FSL of 150, 200, and 300 Hz, respectively. The results shown in (g–l) were simulated using 5 equally spaced $p_b$ concentrations ranging from 0 to 0.01. The left, middle, and right columns correspond to control (a, d, g, and j), moderate inhomogeneity (b, e, h, and k), and severe inhomogeneity (c, f, i, and l), respectively. Note the oscillations in the iTIP-spectra due to a failure of spin-lock, which also caused errors in R1rho asymmetry. In contrast, B0 field inhomogeneity induced a shift equal to field inhomogeneity in the R1rho-spectrum, rather than the oscillation observed when using the AC-iTIP approach. Note that under severe B1 inhomogeneity, the FSL of 150 Hz is no longer the optimal B1, and the R1rho asymmetry signal decreases.

Figure 6 compares the AC-iTIP and R1rho-fitting approaches under different SNR levels using both simulations and phantom scans. Both approaches yielded similar R1rho-spectra when the SNR was large. However, the R1rho-fitting approach exhibited increasing error as the SNR decreased. In contrast, the AC-iTIP approach could still obtain a reasonable R1rho-spectrum at the same SNR level. In the phantom experiments, noticeable oscillations appeared on the R1rho-spectra at increased TE values when the R1rho-fitting approach was used, and these were attributed to the decreased SNR. In contrast, such oscillations did not occur in the R1rho-spectra obtained using the AC-iTIP approach.

Figure 6.

Comparison of simulation and phantom results to determine the performances of the AC-iTIP and R1rho-fitting approaches under noise. First row: simulated R1rho-spectrum under SNRs of a) 50, b) 25, and c) 15. Blue and red lines indicate the R1rho-spectra determined using the R1rho-fitting approach and AC-iTIP approach, respectively, in the absence of noise (ground truth). Yellow and purple lines indicate the R1rho-spectra determined using the R1rho-fitting and AC-iTIP approaches, respectively, in the presence of noise. Second row: histograms of simulated on-resonance R1rho values at SNRs of d) 50, e) 25, and f) 15. Red and green histograms correspond to the results derived using the R1rho-fitting and the AC-iTIP approaches, respectively. Third row: R1rho-spectra obtained from phantom experiments at TE values of g) 11, h) 30, and i) 40 ms, respectively. Blue and red lines indicate the R1rho-spectra derived using the R1rho-fitting and AC-iTIP approaches, respectively. Note that the AC-iTIP approach was more robust under noise, compared to the R1rho-fitting approach. Noticeable oscillation is visible in the R1rho-spectrum obtained using the R1rho-fitting approach, which could lead to errors of R1rho asymmetry.

Figure 7 presents the agarose phantom results acquired using the three approaches. When PB shimming was not applied, the iTIP-spectra acquired using the HP-iTIP approach contained oscillations. When PB shimming was applied within ROI 2, these distortions became more significant at regions in ROI 1 and ROI 3 because of exacerbated B0 field inhomogeneity in these regions. The R1rho-fitting approach led to observable oscillations on the R1rho-spectra, which were likely due to noise. In contrast, the AC-iTIP approach yielded reasonable R1rho-spectra under all scenarios, even at ROIs outside the PB shimming region.

Figure 7.

Comparison of the performances of the R1rho-fitting, HP-iTIP approach, and AC-iTIP approaches using phantoms containing 3% (ROI 1), 4% (ROI 2), and 5% (ROI 3) agarose. (a–c) and (g–i) R1rho-spectra obtained at a FSL of 150 and 300 Hz, respectively. (d–f) R1rho-spectra obtained using the parameters described in (a–c) as well as pencil-beam (PB) shimming applied to ROI 2. (j–l) R1rho-spectra obtained using the same parameters described in (g–i), as well as PB shimming applied to ROI 2. PB shimming reduces B0 field inhomogeneity at ROI 2 but can exacerbate this inhomogeneity at ROI 1 and ROI 3, resulting in oscillations of the iTIP-spectra in those regions. The R1rho-spectra obtained using the R1rho-fitting approach exhibited oscillations that were likely due to increased sensitivity to noise. Compared to the other two approaches, the AC-iTIP approach yielded a more robust R1rho-spectrum in the presence of B0 field inhomogeneity.

Figure 8 presents the metabolite concentrations measured in phantoms using the AC-iTIP approach. Note that the measured R1rho asymmetry signal exhibits a linear relationship with the metabolite concentration and that the signal decreases as the FSL increases. These findings are consistent with our theoretical prediction of the optimal B1.

Figure 8.

AC-iTIP analysis of phantoms containing various concentrations of myo-inositol. a) Quantitative R1rho asymmetry map acquired at a FSL of 150Hz. b) Quantitative R1rho asymmetry map acquired at a FSL of 250Hz. c) Line plots of the averaged R1rho asymmetry within each ROI vs. the myo-inositol concentration at different FSLs. The error bars represent the standard deviations, while blue and red lines correspond to a FSL of 150 and 250 Hz, respectively. Note the presence of a linear relationship between R1rho asymmetry and the metabolite concentration. Moreover, R1rho asymmetry decreases with increasing FSL, consistent with our theory.

Figure 9 and 10 show the results from in vivo knee scans. Cartilage forms a fairly thin layer, and therefore the SNR is not sufficient for the R1rho-fitting approach. Accordingly a map of cartilage R1rho asymmetry using the R1rho-fiting approach is not shown. To accommodate the residual fat signal, ROIs were selected on areas of cartilage with minimal fat chemical shift artifacts and minimal fluid, as this would enable a better comparison of the R1rho asymmetry signals obtained using both approaches. In the muscle regions, the signal averaging within the ROI yielded a sufficient SNR for the R1rho-fitting approach. Therefore, the signal spectra determined using all three approaches were compared in the muscle regions. In the cartilage regions, where B0 field inhomogeneity was large, the AC-iTIP approach was more robust than the HP-iTIP approach. AC-iTIP and HP-iTIP yielded comparable R1rho asymmetry signals in the other cartilage regions. In the muscle regions, the three approaches yielded similar results in areas with low B0 field inhomogeneity. However, the AC-iTIP approach was significantly more robust than the other 2 approaches in the muscle region characterized by high B0 field inhomogeneity.

Figure 9.

Maps of R1rho asymmetry from in vivo knee images, obtained using the HP-iTIP and AC-iTIP approaches. a) B0 field map (in Hz). b) B1 field map (in unit percentages; 100% = no B1 inhomogeneity). c) and d) R1rho asymmetry maps obtained using the HP-iTIP approach at FSL values of 150 and 250 Hz, respectively. e) and f) R1rho asymmetry maps obtained using the AC-iTIP approach at FSL values of 150 and 250 Hz, respectively. R1rho asymmetry maps are overlaid on anatomical maps.

Figure 10.

Comparison of the HP-iTIP and AC-iTIP approaches when applied to in vivo knee scan data. When using the AC-iTIP approach, a clear residual fat signal was observed when the toggling RF was switched on, with a fat shift direction toward the feet. The readout bandwidth was selected as the maximum water-fat shift for the purpose of the SNR. Seven ROIs that excluded chemical shift artifacts and obvious fluid signals were selected, as indicated in a). b) and c) Regional average R1rho asymmetry values within the ROIs at FSL values of 150 (blue bars) and 250 Hz (yellow bars) determined using the HP-iTIP and AC-iTIP approaches, respectively. Note that for the HP-iTIP approach, R1rho asymmetry in ROI 1 did not decrease as the FSL increased, likely due to the presence of larger B0 field inhomogeneity (blue circle in Figure 9a). d) and e) Spectra at ROI 1 obtained using the HP-iTIP and AC-iTIP approaches, respectively. Note that the iTIP-spectrum at FSL values of 150 and 250 Hz is clearly distorted at a FO of ~50 Hz. In contrast, the AC-iTIP approach was not affected by B0 field inhomogeneity. f) and g) Respective spectra obtained at two muscle ROIs (the two white circles in Figure 9a) using the R1rho-fitting, HP-iTIP, and AC-iTIP approaches at a FSL of 150 Hz. All three approaches yielded similar spectra at the muscle region with minor B0 field inhomogeneity. However, visible distortions appeared on the iTIP-spectrum at the region with large B0 field inhomogeneity. Moreover, the R1rho-spectrum derived using the R1rho-fitting approach exhibits oscillations that are likely due to noise. The AC-iTIP approach was more robust than the other 2 approaches.

Discussion

Imaging methods based on spin-lock techniques are considered promising approaches for the detection of CE effects. However, these methods are considerably impeded by the strong susceptibility of spin-lock to B1 RF and B0 field inhomogeneities. The issue becomes more pronounced when the B1 amplitudes of spin-lock RF pulses are reduced. B1 RF and B0 field inhomogeneities are common occurrences in modern MRI systems. Therefore, the clinical application of spin-lock MRI will require techniques that can address this problem. In this work, we proposed the AC-iTIP approach as a method for obtaining the R1rho-spectrum and asymmetry in the presence of B1 RF and B0 field inhomogeneities. Both our theoretical and experimental analyses demonstrated that this AC-iTIP approach could improve robustness in the presence of system imperfections when compared to existing spin-lock approaches.

The T1rho dispersion (i.e. dependency of T1rho on the spin-lock RF amplitude) at the on-resonance spin-lock is sensitive to the CE effect. As the T1rho dispersion is performed in an on-resonant manner, it is not affected by the direct water saturation effect and could potentially be used to probe intermediate to fast exchange protons. However, T1rho dispersion is not specific for a certain metabolite. Therefore, R1rho asymmetry analysis is advantageous because it improves the specificity for target metabolites.

We further performed 5-pool Bloch-McConnell simulations using multiple CE pools and have provided the simulation parameters and results in Supporting Information Figure S2. Notably, the HP-iTIP and AC-iTIP approaches yielded nearly identical R1rho asymmetries. The inclusion of additional chemical shift pools in the 5-pool model and the consequent broadening of R1rho asymmetry led to a shift of the R1rho asymmetry signal when compared to that of the 3-pool model. However, the additional pools did not affect the linear relationship between R1rho asymmetry and the concentration of the specified metabolite. These simulation studies indicate that the HP-iTIP and AC-iTIP exhibit comparable specificity for metabolites.

We additionally derived an analytical expression of the optimal B1, the calculation of which requires prior knowledge of the exchange rate. For a chemical shift of 1 ppm at 3.0T, the optimal B1 would range from approximately 120 to 170 Hz at exchange rates of 1000 to 2000 s^™1. As we do not know the exact exchange rate, the calculated optimal B1 may only estimate the actual optimal B1. Nevertheless, the theory of an optimal B1 can be used to guide the selection of the spin-lock RF amplitude during R1rho asymmetry imaging. Moreover, the formula derived for the optimal B1 may be used to derive the exchange rate from the observed maximum R1rho asymmetry.

The AC-iTIP approach requires the additional acquisition of data at a TSL of 0 ms, which provides information to generate a full R1rho-spectrum. However, this additional acquisition increases the scan time. When using the HP-iTIP approach, a signal average may be needed for data acquired at a non-zero TSL. Images acquired with a TSL of 0 ms typically have a much higher SNR than images with non-zero TSLs, which may not require signal averaging. Data acquired using the AC-iTIP provided redundant information along both the TSL and frequency dimension. Advanced image reconstruction methods could potentially utilize this data redundancy and thus reduce the AC-iTIP scan times.

Note that the AC-iTIP approach requires an adiabatic condition. In our experiments, we used hyperbolic secant (HS1) pulses for the AHP and reverse AHP, with a relatively long duration of 35 ms at a FSL 150 Hz. Other adiabatic RF pulse designs have been reported for the spin-lock.²² It becomes increasingly difficult to satisfy the adiabatic condition at lower FSL values. The AC-iTIP approach would benefit from the development of adiabatic RF pulses that could satisfy the adiabatic condition together with an optimized RF pulse duration at a low FSL.

In our R1rho asymmetry derivation, we assumed a symmetrical MT effect with respect to the water reference point. However, other reports indicate that MT exhibits a chemical shift away from the water reference point in vivo.^29–30 This effect on R1rho asymmetry should be investigated in future studies.

In our in vivo studies, we noticed that the SPAIR fat suppression method used in our pulse sequence did not provide sufficient fat suppression for the proposed AC-iTIP approach when the toggling RF pulse was turned on, leading to noticeable chemical shift artifacts. This chemical shift effect decreased the reliability of R1rho asymmetry at the bone-cartilage interfaces. This problem may be addressed using alternative pulse sequence design, which will be discussed in our future work.

The repeatability and reproducibility of an imaging technique must be determined before its application in clinical practice. Accordingly, the AC-iTIP approach relies on the determination of the correct field map, which is then used to calculate R1rho asymmetry accurately. In our studies, we acquired a field map using the standard dual echo gradient echo acquisition method, although the map could also be obtained using the R1rho-spectrum itself or the WASSR³¹ approach. Further studies are needed to evaluate the method used to obtain the field map and the repeatability and reproducibility of the AC-iTIP approach. The preliminary repeatability and reproducibility are shown in Supporting Information Figures S3 and S4.

Conclusion

Herein, we proposed the AC-iTIP approach to improve the robustness of R1rho-spectrum and asymmetry measurements. Using simulation, phantom, and in vivo studies, we demonstrated that this approach achieved better performance than that of other spin-lock approaches in terms of calculating R1rho-spectrum and asymmetry, which can be used to probe the CE effect.

ABBREVIATIONS USED:

AHP

adiabatic half passage

FSL

frequency of spin-lock

TSL

time of spin-lock

FO

frequency offset

ROI

region of interests

SPAIR

spectral attenuated inversion recovery

CESL

chemical exchange spin-lock

AM

amplitude modulation

FM

frequency modulation

SAR

specific absorption rate

FSE

Fast Spin Echo

Appendix A

As shown in our previous work,²⁵ the ACCSL can ensure the spins are effectively locked throughout the spin-lock process at an angle:

$$\text{θ}\left(\text{r}\right)=\{\begin{array}{c}{\tan }^{-1}\left(\frac{{\widetilde{\text{ω}}}_{\text{sl}}\left(\text{r}\right)}{\Delta {\omega }_{\text{c}}+{\text{Δω}}_0\left(r\right)}\right)+\pi ,if\Delta {\omega }_{\text{c}}>0and\Delta {\omega }_{\text{c}}+\Delta {\omega }_0\left(r\right)\le 0\\ {\tan }^{-1}\left(\frac{{\tilde{\omega }}_{\text{sl}}\left(\text{r}\right)}{\Delta {\omega }_{\text{c}}+{\text{Δω}}_0\left(r\right)}\right)-\pi ,if\Delta {\omega }_{\text{c}}<0and\Delta {\omega }_{\text{c}}+{\text{Δω}}_0\left(r\right)\ge 0\\ {\tan }^{-1}\left(\frac{{\widetilde{\text{ω}}}_{\text{sl}}\left(\text{r}\right)}{\Delta {\omega }_{\text{c}}+\Delta {\omega }_0\left(r\right)}\right),\text{otherwise}\end{array},$$ [A1]

where $\text{θ}\left(\text{r}\right)$ represents the angle between the magnetization and the z-axis, $\text{r}$ is the spatial location, ${\text{Δω}}_{\text{c}}$ is the resonant FO of the spin-lock RF pulse, ${\text{Δω}}_0\left(r\right)$ is the B0 field inhomogeneity, and ${\tilde{\omega }}_{\text{sl}}\left(\text{r}\right)$ is the actual spin-lock B1 amplitude, which is the expected spin-lock amplitude under the influence of B1 RF inhomogeneity. The discontinuity of $\text{θ}$ occurs at ${\text{Δω}}_{\text{c}}=0$, and ${\text{Δω}}_{\text{c}}+{\text{Δω}}_0\left(r\right)=0$. This is due to the fact that the magnetization and the effective spin-lock field can be either parallel or anti-parallel with each other, depending on the FO of spin-lock and the B0 field inhomogeneity. Consequently, the asymmetry analysis of the CESL Z-spectrum acquired using the ACCSL is only valid at FO outsides the range of 0 to $\text{2}\cdot {\text{Δω}}_0\left(r\right)$, and the ACCSL is unable to detect metabolites with chemical shift smaller than that of the B0 field inhomogeneity.

Appendix B

Starting from Eq. [6], if we define $w_1{}^2$ as x, and f(x) as the R1rho asymmetry, it can be written as:

$$\text{f}\left(\text{x}\right)=A\cdot \frac{x}{x+F{O}^2}\cdot \left(\frac{1}{x+x_1{}^2}-\frac{1}{x+x_2{}^2}\right),$$ [B1]

where $\text{A}=pb\cdot k\cdot {\delta }_b{}^2,x_1{}^2={\left({\delta }_b+FO\right)}^2+k^2$, and $x_2{}^2={\left({\delta }_b-FO\right)}^2+k^2$. Rearranging terms, we get:

$$\text{f}\left(\text{x}\right)=a1\cdot \frac{x}{\left(x+F{O}^2\right)\cdot \left(x+x_1{}^2\right)\cdot \left(x+x_2{}^2\right)},$$ [B2]

where $a1=A\cdot \left(x_2{}^2-x_1{}^2\right)$. The first derivative of f(x) equals to zero can be written as:

$$f^{\prime }\left(x\right)=\frac{1}{x}-\frac{1}{\left(x+F{O}^2\right)}-\frac{1}{\left(x+x_1{}^2\right)}-\frac{1}{\left(x+x_2{}^2\right)}=0,$$ [B3]

Eq. [B3] can be reduced to a cubic equation:

$$2\cdot x^3+x^2\cdot \left(x_1{}^2+x_2{}^2+F{O}^2\right)-x_1{}^2\cdot x_2{}^2\cdot F{O}^2=0,$$ [B4]

by multiplying with ${\text{y}}^3$, where y $=1/x$, Eq. [B4] can be rewritten as:

$$-x_1{}^2\cdot x_2{}^2\cdot F{O}^2\cdot y^3+\left(x_1{}^2+x_2{}^2+F{O}^2\right)\cdot y+2=0,$$ [B5]

Eq. [B5] has roots defined as:

$$\frac{1}{w_{1opt}{}^2}={(\sqrt{\frac{p^3}{27}+\frac{q^2}{4}}-\frac{q}{2})}^{\frac{1}{3}}+{(-\sqrt{\frac{p^3}{27}+\frac{q^2}{4}}-\frac{q}{2})}^{\frac{1}{3}},$$ [B6]

where $\text{p}=-(x_1{}^2+x_2{}^2+F{O}^2)/(x_1{}^2\cdot x_2{}^2\cdot F{O}^2)$, and $\text{q}=-2/(x_1{}^2\cdot x_2{}^2\cdot F{O}^2)$. The Eq. [B6] is known as the Cardano-Tartaglia formula.