In-phase simultaneous spectral editing of lactate and alanine with suppression of J-coupled lipids by the modified selective multiple quantum coherence sequences

Abstract

¹H magnetic resonance spectroscopy (MRS) with the multiple quantum coherence (MQC) technique allows for the detection of lactate, an end product of glycolysis, in the environment of lipids. The method can also be used to detect alanine, a byproduct of glutaminolysis. An issue is that when both lactate and alanine are detected together by the MQC technique, a phase mismatch arises between lactate and alanine signals due to off-resonance rotations and the difference in double quantum coherence frequencies between the two molecules. Such phase mismatch can cause errors in spectral fitting and metabolite quantification. In this study, we designed two pulse sequences that eliminate such phase differences of lactate and alanine while suppressing lipid signals by modifications of the Selective Multiple Quantum Coherence (Sel-MQC) sequence, a well-known MQC technique. Using the product operator formalism and the off-resonance rotation matrices, the phase evolutions of lactate and alanine during the spectrally selective pulses and the free precession times of the sequence at the single quantum, double quantum and zero quantum coherence states of these molecules were calculated. The multiple quantum (MQ) evolution time t₁ that can remove the phase difference of lactate and alanine at the echo was calculated and fine-tuned with experiments. The lactate and alanine signal intensities and the editing efficiencies from the two modified Sel-MQC sequences were theoretically predicted by using the product operator evolutions and compared with the experimental data. The J-coupled lipid signals were successfully suppressed by both sequences. One of the two developed sequences was applied to a human body with a phantom of lactate and alanine, which resulted in successful in-phase editing of lactate and alanine and suppression of the lipid signals from the body. The study sets an important foundation for the noninvasive detection of lactate and alanine from tumors of cancer patients.

1. INTRODUCTION

Spectral editing techniques in magnetic resonance spectroscopy (MRS) enable the detection of the desired signals from overlapping resonances [1]. While two-dimensional nuclear magnetic resonance (2D NMR) techniques are commonly used in chemistry, one-dimensional (1D) NMR techniques are preferred for in vivo ¹H MRS due to the lengthy acquisition time of 2D NMR [2]. The J-difference method and the multiple quantum coherence (MQC) method are representative 1D spectral editing techniques [1, 2]. While the J-difference method [2–4] is more commonly utilized than the MQC method [1, 2], as the former relies on the subtraction of signals from two different scans, the method is inherently sensitive to subtraction errors and is thus ineffective when the overlapping signals are very large compared to the desired signal or when motion prevents complete cancellation of unwanted signals. On the other hand, the MQC method achieves spectral editing by the coherence pathway selection using pulsed-field gradients and does not need the subtraction procedure. Despite an inherent 50% signal loss during the coherence pathway selection [5], the MQC method is required when the J-difference method is not suitable for the aforementioned reasons. Spectral editing of lactate from tumors or oxygen-limited tissues in the body parts outside the brain is such an example [6–9].

The selective multiple quantum coherence (Sel-MQC) sequence [10] is a well-known MQC technique. The Sel-MQC sequence and its variants have been utilized in numerous tumor xenograft studies [11–19] as well as being applied to human subjects in clinical scanners [7–9, 20, 21]. While the conventional MQC sequence for lactate detection [5, 6, 22, 23] exploits the coherence pathway, SQC→DQC→SQC, where SQC is the single quantum coherence and DQC is the double quantum coherence, the Sel-MQC sequence exploits the coherence pathway, SQC→DQC→ZQC→SQC or SQC→ZQC→DQC→SQC depending on the applied gradients, where ZQC is the zero quantum coherence [10]. The sequence allows for improved lipid suppression compared to the conventional MQC sequence by better suppressing the MQC-derived signals of J-coupled lipids with multiple spectrally selective pulses [10]. However, the detailed MQC pathways of J-coupled lipids developed with the Sel-MQC sequence had been unknown, which limited access to the most intelligent use of the sequence to suppress J-coupled lipid signals. To solve this problem, we recently performed a thorough analysis of the coherence pathways of J-coupled lipids upon the Sel-MQC sequence implemented at a 3T scanner by using the product operator formalism [24] and off-resonance rotation matrices [25]. The study revealed the various coherence pathways of J-coupled lipids upon the Sel-MQC sequence and showed the strategy to effectively suppress the coherence pathways of lipids while maintaining the lactate signal by the rational use of the appropriate coherence selection gradients and RF pulse lengths [25].

The current study is focused on simultaneous spectral editing of lactate and alanine in the environment of lipids. Alanine is a byproduct of glutaminolysis, one of the hallmarks of cancer metabolism [26, 27]. Tumors such as diffuse large B-cell lymphoma and meningioma have exhibited alanine concentrations comparable to lactate [13, 28]. As lactate and alanine have similar molecular structures and chemical shifts, simultaneous editing of both molecules is possible with the Sel-MQC sequence. However, for successful editing of lactate and alanine in the environment of lipids, the following should be addressed: Firstly, as the lactate or alanine spins will not be exactly on-resonance with the spectrally selective pulses of the sequence, the effects of the off-resonance rotations on the coherence pathways and the product operator evolutions of lactate and alanine have to be analyzed. Secondly, the RF pulse lengths should be carefully selected along with the appropriate coherence selection gradients so that lipid signals from the various coherence pathways of J-coupled lipids [25] are effectively suppressed while lactate and alanine signals are minimally affected. Thirdly, as the phases of lactate and alanine evolve differently with their respective SQC, DQC and ZQC resonance frequencies, the sequence should be designed so that the lactate and alanine reach the same phase at the echo. This enables reliable spectral fitting and metabolite quantifications. In this study, we designed two modified Sel-MQC sequences that achieve simultaneous in-phase editing of lactate and alanine with suppression of lipids by tackling the above issues. The theoretical analysis of spin evolutions with the new sequences and comparisons with experiments are provided.

2. THEORY

2.1. Product operator formalism and coherence transfer pathways

The product operator formalism [24] enables analytically expressing the evolutions of a weakly-coupled spin system and finding the coherence levels of the system at individual periods of a sequence as needed for drawing the coherence transfer pathway (CTP) maps [25, 29, 30]. In a multi-pulse NMR experiment, the observable signals are allowed when the coherence levels of the CTP and the gradient fields during the sequence satisfy the following condition with the last coherence level of (−1) [29, 31]:

$$\sum _{i=1}^n{p}_i\cdot g_i=0$$ (1)

where i indicates the ith period which is defined as the period between the ith pulse and (i + 1)-th pulse or between the last ith pulse and acquisition. p_i is the coherence level of the spin system at the ith period, and g_i is the integrated area of gradients with polarity during the ith period. When the applied gradients do not satisfy Eq. 1, the corresponding CTP is dephased by gradients. The equation of signal attenuation by gradients for such a CTP has been derived in our previous study [25].

2.2. Chemical shifts of the J-coupled spins of lactate, alanine and lipids and the coherence pathway selection

Figure 1 shows the chemical shifts of the J-coupled spins of lactate, alanine and lipids. The J-coupled protons (indicated in boldface), the kinds of the coupled spin system, chemical shifts of I and S spins and the J-coupling constants of lactate, alanine and lipids are indicated in Table 1 [25, 32–34]. A successful MQC sequence for lactate and alanine editing should be able to pass only the desired coherence pathway of lactate and alanine while suppressing all the coherence pathways of J-coupled lipids as well as the undesired coherence pathways of lactate and alanine by a combination of the appropriate RF pulses and gradients. The Sel-MQC sequence [10] that employs multiple frequency-selective pulses and more than one coherence step during the MQ evolution time of the sequence allows for achieving the mentioned condition with modification of the original sequence. The coherence pathways of lactate, alanine and J-coupled lipids that do not have the same coherence levels as the desired coherence pathway of lactate and alanine are dephased by gradients. On the other hand, the coherence pathways of J-coupled lipids that have the same coherence levels as the desired coherence pathway of lactate and alanine can be suppressed by increasing the RF pulse lengths thereby decreasing the conversion rates of the coherence pathways of J-coupled lipids [25].

Fig. 1.

The chemical shifts of the J-coupled spins of lactate, alanine and lipids.

Table 1.

J-coupled protons, spin systems, chemical shifts and J-coupling constants of lactate, alanine and lipids.

Molecule	J-coupled protons	Spin system	I spin (ppm)	S spin (ppm)	J (Hz)
Lactate	CH3-CH	I3S	1.33	4.11	6.93
Alanine	CH3-CH	I3S	1.48	3.79	7.23
Lipids	CH2-CH2-CH3	I2S3	1.33	0.90	8.0
	OC-CH2-CH2-CH2	I2S2	1.33	1.65	7.1
	OC-CH2-CH2-CH2	I2S2	1.65	2.36	7.1
	CH-CH2-CH2	I2S2	1.33	2.07	7.14
	CH2-CH2	I2S2	2.07	2.79	10
	CH-CH2-CH2	I2S	2.07	5.38	6.2
	CH-CH2-CH	I2S	2.79	5.38	1.0
	O-CH2-CH-O	I2S	4.16	5.29	7.0
	O-CH2-CH-O	I2S	4.37	5.29	7.0
	O-CH2-CH-CH2-O	I2S2	4.16	4.37	12.4

2.3. Modified Sel-MQC sequences for simultaneous editing of lactate and alanine

We designed two different pulse sequences for simultaneous editing of lactate and alanine. Both sequences are modifications of He et al.’s original Sel-MQC sequence [10]. The first sequence (Fig. 2) adopts the structure of the revised Sel-MQC sequence, which we proposed and tested in our previous study [25], with modifications. The revised Sel-MQC sequence [25] has the following structure: 90°(I)—τ₁—90°(S)—g₂—(1/2)t₁—180°(I)—g₃—(1/2)t₁—90°(S)—g₄—τ₂—echo, where τ₁ = 1/(2J_Lac) − t₁ and g₂:g₃:g₄ = 1:0.8:2 are employed. I and S indicate the I and S spin resonance frequencies of lactate, respectively. The echo is formed at τ₂ = 1/(2J_Lac), which removes the antiphase component of lactate at the echo [25]. The amplitude of the echo is (1/2)I₀cos(πJ_Lact₁) where I₀ is the initial magnetization, excluding the T2 relaxation effect [25]. The gradient ratio g₂:g₃:g₄ = 1:0.8:2 selects the SQC→DQC→ZQC→SQC pathway (p(1, 2, 0, −1)) of lactate and effectively dephases the SQC→DQC→(SQC + DQC)→SQC pathways of J-coupled lipids that are allowed at the gradient ratio 1:0:2 [25]. For simultaneous editing of lactate and alanine, the following changes are made to the revised Sel-MQC sequence: 1) The center frequencies of the RF pulses are set to the middle of lactate and alanine chemical shifts. 2) τ₁ = 1/(2J_Avg) − t₁ is used where J_Avg is the mean J-coupling constant of lactate and alanine. The echo is formed at τ₂ = 1/(2J_Avg) as calculated by adding the background gradient g₀ to g_i in Eq. 1, leading to TE = 1/J_Avg. 3) The multiple quantum (MQ) evolution time t₁ is adjusted so that lactate and alanine have the same phase at the echo. The phase calculation and the calibration procedure are described in later subsections of this article. The gradient ratio g₂:g₃:g₄ = 1:0.8:2 again selects the SQC→DQC→ZQC→SQC pathway of lactate and alanine while dephasing the SQC→DQC→(SQC + DQC)→SQC pathways lactate, alanine and J-coupled lipids allowed at the gradient ratio 1:0:2, which are developed by off-resonance rotation effects [25].

Fig. 2. Pulse Sequence 1 (a four-pulse, modified Sel-MQC) for editing both lactate and alanine.

(A) The pulse sequence diagram. (B) The coherence transfer pathway map of lactate and alanine. g₂, g₃ and g₄ are the coherence selection gradients. WS, water suppression pulses; g_csr, crusher gradient; CSI, chemical shift imaging gradients; ACQ, acquisition window. The coherence selection gradients with the ratio g₂:g₃:g₄ = 1:0.8:2 and the CTP selected with these gradients are displayed. The center frequencies of the RF pulses are presented in the chemical shift scale in parentheses: P₁ and P₃, 1.405 ppm; P₂ and P₄, 3.95 ppm. With τ₁ = 1/(2J_Avg) − t₁, the echo is formed at τ₂ = 1/(2J_Avg).

The second sequence (Fig. 3) has the structure of 90°(I)—τ₁—90°(S)—g₂—(1/4)t₁—180°(S)—g₃—(1/2)t₁—180°(I)—g₄—(1/4)t₁—90°(S)—g₅—τ₂—echo, where I and S indicate the mean I spin resonance frequency and the mean S spin resonance frequency of lactate and alanine, respectively. The sequence was developed to reduce the signal loss by the J-coupled evolution that arises in Sequence 1. With the gradient ratio g₂:g₃:g₄:g₅ = 1:−0.8:−1:4, the sequence selects the SQC→DQC→ZQC→DQC→SQC pathway (p(1, 2, 0, −2, −1)) of lactate and alanine while dephasing the SQC→DQC→(SQC + DQC)→DQC→SQC pathways of lactate, alanine and J-coupled lipids that are allowed at g₂:g₃:g₄:g₅ = 1:0:−1:4. When τ₁ = 1/(2J_Avg) is employed, the echo from the background gradients is formed at τ₂ = 1/(2J_Avg) by Eq. 1, which leads to TE = 1/J_Avg + t₁. The condition for phase alignment of lactate and alanine is determined by the t₁ time, as will be described in a later subsection.

Fig. 3. Pulse Sequence 2 (a five-pulse, modified Sel-MQC) for editing both lactate and alanine.

(A) The pulse sequence diagram. (B) The coherence transfer pathway map of lactate and alanine. The coherence selection gradients with the ratio g₂:g₃:g₄:g₅ = 1:−0.8:−1:4 and the CTP selected with these gradients are displayed. The center frequencies of the RF pulses are presented in the chemical shift scale in parentheses: P₁ and P₄, 1.405 ppm; P₂, P₃ and P₅, 3.95 ppm. With τ₁ = 1/(2J_Avg), the echo is formed at τ₂ = 1/(2J_Avg).

2.4. Product operator evolutions of lactate and alanine upon the modified Sel-MQC sequences

The product operator evolutions of the I₃S spin systems of lactate and alanine upon Sequence 1 (Fig. 2A) with the SQC→DQC→ZQC→SQC pathway (Fig. 2B) can be expressed in a simplified form as

$$I_z\stackrel{P_1}{\to }{I}^{+}\stackrel{J}{\to }{I}^{+}{S}_z\stackrel{P_2}{\to }{I}^{+}{S}^{+}\stackrel{P_3}{\to }{I}^{-}{S}^{+}\stackrel{P_4}{\to }{I}^{-}{S}_z\stackrel{J}{\to }{I}^{-}$$ (2)

where P₁, P₂, P₃ and P₄ are the first, second, third and fourth RF pulses, respectively. Similarly, the product operator evolutions of lactate and alanine upon Sequence 2 (Fig. 3A) with the SQC→DQC→ZQC→DQC→SQC pathway (Fig. 3B) can be expressed in a simplified form as

$$I_z\stackrel{P_1}{\to }{I}^{+}\stackrel{J}{\to }{I}^{+}{S}_z\stackrel{P_2}{\to }{I}^{+}{S}^{+}\stackrel{P_3}{\to }{I}^{+}{S}^{-}\stackrel{P_4}{\to }{I}^{-}{S}^{-}\stackrel{P_5}{\to }{I}^{-}{S}_z\stackrel{J}{\to }{I}^{-}$$ (3)

The detailed evolutions of product operators are described in the following subsections.

2.4.1. Product operator transformations by RF pulses

The spectrally selective RF pulses with their center frequencies set in the middle of the chemical shifts of lactate and alanine induce off-resonance rotations on the spins of lactate and alanine. The product operator transformations by off-resonance pulses can be calculated by using the off-resonance rotation matrices of the spin operators constituting the product operators, similar to our previous study on J-coupled lipids [25]. The total conversion factor by the product operator transformations, f_P, can be expressed as

$$f_P=2\prod f_{P_i}=\left|f_P\right|e^{i{\phi }_P}$$ (4)

where f_Pi is the conversion factor by the ith RF pulse. |f_P| and ϕ_P are the magnitude and the phase of the total conversion factor. The multiplication factor 2 was used in Eq. 4 to account for the equivalent coherence pathways to Eqs. 2 and 3 but with the (+) and (−) coherences reversed. The quadrature detector combines the signals from the final (+1) and (−1) quantum coherences [35].

2.4.2. J-coupled evolutions of the product operators

We first analyze the evolution for Sequence 1. The J-coupled evolution of the product operators of the I₃S spin system of lactate or alanine during the first period (the τ₁ time) of the sequence is expressed as [25]:

$$I^{+}\stackrel{J}{\to }{I}^{+}\text{cos}(\pi Jt)-2i{I}^{+}{S}_z\text{sin}(\pi Jt)$$ (5)

where $I^{+}=I_1^{+}+I_2^{+}+I_3^{+}$ and J is the J-coupling constant of lactate or alanine. The second RF pulse transforms the product operator $I^{+}{S}_z$ into $I^{+}{S}^{+}$, omitting the conversion factor. The J-coupled evolutions of the product operator $I_1^{+}{S}^{+}$ during the second and third periods are expressed as Eq. 6, where t = (1/2)t₁:

$$\begin{array}{l}{I}_1^{+}{S}^{+}\stackrel{J_{I_{2}S}}{\to }{I}_1^{+}{S}^{+}\text{cos}(\pi Jt)-2i{I}_1^{+}{S}^{+}{I}_{2z}\text{sin}(\pi Jt)\\ \stackrel{J_{I_{3}S}}{\to }{I}_1^{+}{S}^{+}{\text{cos}}^2(\pi Jt)-2i{I}_1^{+}{S}^{+}(I_{3z}+I_{2z})\text{cos}(\pi Jt)\text{sin}(\pi Jt)-4I_1^{+}{S}^{+}{I}_{2z}{I}_{3z}{\text{sin}}^2(\pi Jt)\\ \stackrel{P_3}{\to }{I}_1^{-}{S}^{+}{\text{cos}}^2(\pi Jt)+2i\xi I_1^{-}{S}^{+}(I_{3z}+I_{2z})\text{cos}(\pi Jt)\text{sin}(\pi Jt)-4{\xi }^2{I}_1^{-}{S}^{+}{I}_{2z}{I}_{3z}{\text{sin}}^2(\pi Jt)\\ \stackrel{J_{I_{2}S}}{\to }{I}_1^{-}{S}^{+}{\text{cos}}^3(\pi Jt)-2i{I}_1^{-}{S}^{+}{I}_{2z}{\text{cos}}^2(\pi Jt)\text{sin}(\pi Jt)\\ +2i\xi I_1^{-}{S}^{+}{I}_{3z}{\text{cos}}^2(\pi Jt)\text{sin}(\pi Jt)+4\xi I_1^{-}{S}^{+}{I}_{3z}{I}_{2z}\text{cos}(\pi Jt){\text{sin}}^2(\pi Jt)\\ +2i\xi I_1^{-}{S}^{+}{I}_{2z}{\text{cos}}^2(\pi Jt)\text{sin}(\pi Jt)+\xi I_1^{-}{S}^{+}\text{cos}(\pi J){\text{sin}}^2(\pi Jt)\\ -4{\xi }^2{I}_1^{-}{S}^{+}{I}_{2z}{I}_{3z}\text{cos}(\pi Jt){\text{sin}}^2(\pi Jt)+2i{\xi }^2{I}_1^{-}{S}^{+}{I}_{3z}{\text{sin}}^3(\pi Jt)\\ \stackrel{J_{I_{3}S}}{\to }{I}_1^{-}{S}^{+}{\text{cos}}^4(\pi Jt)-2i{I}_1^{-}{S}^{+}{I}_{3z}{\text{cos}}^3(\pi Jt)\text{sin}(\pi Jt)\\ -2i{I}_1^{-}{S}^{+}{I}_{2z}{\text{cos}}^3(\pi Jt)\text{sin}(\pi Jt)-4I_1^{-}{S}^{+}{I}_{2z}{I}_{3z}{\text{cos}}^2(\pi Jt){\text{sin}}^2(\pi Jt)\\ +2i\xi I_1^{-}{S}^{+}{I}_{3z}{\text{cos}}^3(\pi Jt)\text{sin}(\pi Jt)+I_1^{-}{S}^{+}\xi {\text{cos}}^2(\pi Jt){\text{sin}}^2(\pi Jt)\\ +4\xi I_1^{-}{S}^{+}{I}_{3z}{I}_{2z}{\text{cos}}^2(\pi Jt){\text{sin}}^2(\pi Jt)-2i\xi I_1^{-}{S}^{+}{I}_{3z}{I}_{2z}\text{cos}(\pi Jt){\text{sin}}^3(\pi Jt)\\ +2i\xi I_1^{-}{S}^{+}{I}_{2z}{\text{cos}}^3(\pi Jt)\text{sin}(\pi Jt)+4\xi I_1^{-}{S}^{+}{I}_{2z}{I}_{3z}{\text{cos}}^2(\pi Jt){\text{sin}}^2(\pi Jt)\\ +\xi I_1^{-}{S}^{+}{\text{cos}}^2(\pi Jt){\text{sin}}^2(\pi Jt)-2i\xi I_1^{-}{S}^{+}{I}_{3z}\text{cos}(\pi J){\text{sin}}^3(\pi Jt)\\ -4{\xi }^2{I}_1^{-}{S}^{+}{I}_{2z}{I}_{3z}{\text{cos}}^2(\pi Jt){\text{sin}}^2(\pi Jt)+2i{\xi }^2{I}_1^{-}{S}^{+}{I}_{2z}{I}_{3z}\text{cos}(\pi Jt){\text{sin}}^3(\pi Jt)\\ +2i{\xi }^2{I}_1^{-}{S}^{+}{I}_{3z}\text{cos}(\pi Jt){\text{sin}}^3(\pi Jt)+{\xi }^2{I}_1^{-}{S}^{+}{\text{sin}}^4(\pi Jt)\\ =I_1^{-}{S}^{+}\{{\left[{\text{cos}}^2\right(\pi Jt)+\xi {\text{sin}}^2(\pi Jt\left)\right]}^2+(\text{unobservable}\text{terms})\}\end{array}$$ (6)

In Eq. 6, the J-coupled evolutions between the S spin and the passive I spins (I₂ and I₃) during the DQC and ZQC states were applied as proposed by Kingsley [29]. The action of the third RF pulse (P₃) was expressed as the $I_1^{+}{S}^{+}$ to $I_1^{-}{S}^{+}$ transformation, omitting the conversion factor, and the transformations of $I_{2z}$ to $-\xi I_{2z}$ and $I_{3z}$ to $-\xi I_{3z}$. The transformation of $I_{2z}$ to $I_2^{+}$ and $I_2^{-}$ by the third RF pulse as well as the transformation of $I_{3z}$ to $I_3^{+}$ and $I_3^{-}$ by this pulse was ignored as they do not contribute to ZQC in the third period. The evolutions of $I_2^{+}{S}^{+}$ and $I_3^{+}{S}^{+}$ during the second and third periods are expressed in the same way as that of $I_1^{+}{S}^{+}$. The fourth RF pulse transforms $I^{-}{S}^{+}$ to $I^{-}{S}_z$, omitting the conversion factor. The J-coupled evolution of $I^{-}{S}_z$ during the fourth period is expressed as [25]:

$$-2i{I}^{-}{S}_z\stackrel{J}{\to }{I}^{-}\text{sin}(\pi Jt)-2i{I}^{-}{S}_z\text{cos}(\pi Jt)$$ (7)

The total J-coupled evolution factor f_J for the in-phase signal I⁻ at the echo is, therefore,

$$f_J=\text{sin}(\pi J{\tau }_1)\times \text{sin}(\pi J{\tau }_2)\times {[{\text{cos}}^2(\pi J{t}_1/2)+\xi {\text{sin}}^2(\pi J{t}_1/2)]}^2$$ (8)

If the third RF pulse is exactly on-resonance with the I spin, ξ = 1 and the J-coupled evolution factor during the second and the third periods reduces to 1, which is the case for the original Sel-MQC sequence [10].

For Sequence 2, the J-coupled evolutions of the product operators during the first and the last periods follow Eq. 5 and Eq. 7, respectively. The J-coupled evolution during the MQ evolution time t₁ is similar to that for Sequence 1. A difference is that the J-coupled evolution during the first half of the t₁ time is fully refocused by the S-spin selective 180° pulse. The J-coupled evolution during the second half of the t₁ time has the same form as in Sequence 1 except that t₁/2 should be used instead of t₁. Then, the total J-coupled evolution factor f_J for Sequence 2 is expressed as

$$f_J=\text{sin}(\pi J{\tau }_1)\times \text{sin}(\pi J{\tau }_2)\times {[{\text{cos}}^2(\pi J{t}_1/4)+\xi {\text{sin}}^2(\pi J{t}_1/4)]}^2$$ (9)

2.4.3. Phase accumulation during the free precession times

To find the condition for the phase alignment of lactate and alanine at the echo, the information on the phase accumulation during the free precession times (ϕ_free) and the phase changes during the RF pulses (ϕ_P) is needed. For Sequence 1 (see Fig. 2), ϕ_free is calculated as

$${\phi }_{\mathit{\text{free}}}=-{\omega }_I\times t_B+(-{\omega }_I-{\omega }_S)\times t_D+({\omega }_I-{\omega }_S)\times t_D+{\omega }_I\times t_F$$ (10)

where ω_I and ω_S represent the angular resonance frequencies of the I and S spins of lactate or alanine, respectively. Using t_B = 1/(2J_Avg) – t₁ – (1/2)t_A – (1/2)t_C, t_D = (1/2)(t₁ – t_C – t_E), and t_F = 1/(2J_Avg) – (1/2)t_C, Eq. 10 becomes

$${\phi }_{\mathit{\text{free}}}=({\omega }_I-{\omega }_S)\times t_1+{\omega }_I\times \frac{t_A}{2}+{\omega }_S\times (t_C+t_E)$$ (11)

For Sequence 2 (see Fig. 3), ϕ_free is calculated as

$${\phi }_{\mathit{\text{free}}}=-{\omega }_I\times t_B+(-{\omega }_I-{\omega }_S)\times t_D+(-{\omega }_I+{\omega }_S)\times t_F+({\omega }_I+{\omega }_S)\times t_H+{\omega }_I\times t_J$$ (12)

Using t_B = 1/(2J_Avg) – (1/2)t_A – (1/2)t_C, t_D = (1/4)t₁ – (1/2)(t_C + t_E), t_F = (1/2)t₁ – (1/2)(t_E + t_G), t_H = (1/4)t₁ – (1/2)(t_G + t_C), and t_I = 1/(2J_Avg) – (1/2)t_C, Eq. 12 becomes

$${\phi }_{\mathit{\text{free}}}=\frac{(-{\omega }_I+{\omega }_S)}{2}\times t_1+{\omega }_I\times \left(\frac{t_A}{2}+t_E\right)-{\omega }_S\times t_G$$ (13)

2.4.4. Condition for the phase alignment of lactate and alanine at the echo

The phase of the lactate or alanine signal at the echo is the sum of the phase ϕ_P (Eq. 4) and the phase ϕ_free (Eqs. 11 or Eq. 13):

$${\phi }_{\mathit{\text{total}}}={\phi }_P+{\phi }_{\mathit{\text{free}}}$$ (14)

Let us call the phases of lactate and alanine at the echo as ϕ_Lac and ϕ_Ala, respectively. For lactate and alanine signals to have the same phase at the echo, the following condition should be met:

$${\phi }_{Lac}-{\phi }_{Ala}=2n\pi$$ (15)

where n is an integer. On the other hand, lactate and alanine have opposite phases relative to each other if the following condition is met:

$${\phi }_{Lac}-{\phi }_{Ala}=(2n+1)\pi$$ (16)

where n is an integer. From Eqs. 4, 11, 13, 14 and 15, the t₁ times that induce the same phase of lactate and alanine at the echo can be calculated. Similarly, the t₁ times that induce opposite phases of lactate and alanine can be calculated by using Eq. 16 instead of Eq. 15. We can see that the relative phase between lactate and alanine from Sequence 1 varies with a cycle that is the inverse of the angular zero quantum coherence frequency difference between lactate and alanine. On the other hand, the relative phase between lactate and alanine from Sequence 2 varies with a cycle that is twice the inverse of the angular zero quantum coherence frequency difference between lactate and alanine.

2.5. Final signals and editing efficiencies of lactate and alanine

The theoretical total signal is calculated as

$$f_{\mathit{\text{total}}l}=\left|f_p\right|\times f_J\times f_{T2}\times f_{T1}$$ (17)

where |f_p| and f_J are from Eqs. 4, 8 and 9. f_T2 and f_T1 are

$$f_{T2}=\text{exp}(-(TE-t_1)/T{2}_{SQC})\times \text{exp}(-t_1/T{2}_{MQC})$$ (18)

$$f_{T1}=1-\text{exp}(-TR/T1)$$ (19)

where TE = 1/J_Avg for Sequence 1 and TE = 1/J_Avg + t₁ for Sequence 2. T2_MQC may differ between Sequence 1 and Sequence 2. We define the theoretical editing efficiency (E.E.(theory)) of lactate or alanine as

$$E.E.(\text{theory})=\frac{\left|f_p\right|\times f_J\times f_{T2}}{\text{exp}(-1/(J_{Avg}\times T{2}_{SQC}))}$$ (20)

where the denominator is the J-refocused spin-echo signal of lactate or alanine at TE = 1/J_Avg.

3. METHODS

3.1. MRI system:

A 3T (123.25 MHz) whole-body MRI system (Tim Trio, Siemens, Erlangen, Germany) was used for this study. The body coil of the scanner and a home-built two-channel surface coil (6 cm × 8 cm) were used for the transmitter and the receiver, respectively.

3.2. Pulse sequence:

The structures of the two modified Sel-MQC sequences (Fig. 2 and Fig. 3) were described in the Theory section. The Hamming-filtered Sinc (HSinc) and Gaussian pulses were used. The pulse shapes, pulse lengths, flip angles, bandwidths, transition widths and center frequencies in the chemical shift scale are presented in Tables 2 and 3. The pulse lengths of the employed RF pulses were chosen as a modification of those used in our previous study [25] with consideration of the changes in the center frequencies of RF pulses, to effectively suppress the coherence pathways of J-coupled lipids [25] while minimally affecting the lactate and alanine signals. Among various J-coupled lipid resonances and spin couplings (see Fig. 1 and Table 1), the 2.07 ppm lipid signal that originates from the coupling of 2.07–2.79 ppm (I = 2.07 ppm; S = 2.79 ppm) is the most affected by the center frequency changes of the pulse sequence from the previous one as both the 90° and 180° pulses are moved closer to the S and I spin resonances of this coupling respectively than the previous condition, which leads to elevation of the conversion rates of the coherence pathways for this coupling [25]. Increasing the pulse length of either the 90° or the 180° pulse or the pulse lengths of both of them can reduce the conversion rates of these coherence pathways. We chose to increase the 180° pulse (P₃) length from the previously used 5.6 ms to 8 ms and keep the 90° pulse (P₂ and P₄) length at 12 ms for Sequence 1. This helped lactate and alanine detected by the sequence better maintain their symmetric doublet lineshapes than changing the length of the other pulse. The observation is supposed to come because the quartet resonances of lactate and alanine affected by the frequency-selective 90° pulse experience more nonuniform rotation effects than the doublet resonances of lactate and alanine that are affected by the frequency-selective 180° pulse at the tested RF pulse length conditions. The bandwidths of the RF pulses (see Table 2) and the chemical shifts of the quartet (S spin) and doublet (I spin) resonances of lactate and alanine (see Table 1) are consistent with the explanation. With the 90° pulse (P₂ and P₄) length of 12 ms and the 180° pulse (P₃) length of 8 ms in Sequence 1, only minor deviations from the symmetric doublet lineshapes of lactate and alanine were observed. With these pulse lengths and the coherence selection gradient ratio of 1:0.8:2 in Sequence 1, various lipid resonance signals were kept at the noise level (see the Results and Discussion section). The 8 ms length of the P₄ pulse (1.405 ppm, 180°) of Sequence 2 was chosen to exploit the same off-resonance rotation profile as the P₃ pulse (1.405 ppm, 180°) of Sequence 1. The 6 ms length of the P₃ pulse (3.95 ppm, 180°) of Sequence 2 was chosen so that the pulse induces as uniform rotations as possible to the S spin quartet resonances of lactate and alanine while it does not affect the I spins of lactate and alanine. Simulations of spin operator transformations and the conversion rates of the coherence pathways selected by the gradients as well as experiments were used to determine these RF pulse lengths.

Table 2.

The pulse shapes, pulse lengths, flip angles, bandwidths and transition widths of the employed RF pulses.

pulse shape	pulse length	flip angle	bandwidth	transition width
HSinc (7 lobes)	3 ms	90°	2,970 Hz	603 Hz
Gaussian (5% cutoff)	12 ms	90°	188 Hz	118 Hz
Gaussian (5% cutoff)	8 ms	180°	160 Hz	135 Hz
Gaussian (5% cutoff)	6 ms	180°	213 Hz	180 Hz

Table 3.

The pulse shapes, pulse lengths, flip angles and center frequencies in the chemical shift scale of the RF pulses for Sequence 1 and Sequence 2.^*

Sequence 1	Sequence 2
P1 (HSinc; 3 ms; 90°; 1.405 ppm)	P1 (HSinc; 3 ms; 90° 1.405 ppm)
P2 (Gaussian; 12 ms; 90°; 3.95 ppm)	P2 (Gaussian; 12 ms; 90°; 3.95 ppm)
P3 (Gaussian; 8 ms; 180°; 1.405 ppm)	P3 (Gaussian; 6 ms; 180°; 3.95 ppm)
P4 (Gaussian; 12 ms; 90°; 3.95 ppm)	P4 (Gaussian; 8 ms; 180°; 1.405 ppm)
	P5 (Gaussian; 12 ms; 90°; 3.95 ppm)

^*P₁, P₂, P₃, P₄ and P₅ indicate the first, second, third, fourth and fifth pulses, respectively.

For setting the pulse intervals τ₁ and τ₂ of Sequence 1 and Sequence 2, 1/J_Lac = 144 ms, 1/J_Ala = 138 ms and 1/J_Avg = 141 ms were used [36]. In Sequence 1, the g₂, g₃ and g₄ gradient durations were 1.5 ms, 1.5 ms and 3 ms, respectively, for the phantom-only experiments. They were 2 ms, 2 ms and 4 ms, respectively, for the phantom-with-subject study. The amplitudes of g₂ and g₄ gradients were 20 mT/m when the gradient ratio was 1:0:2 or 1:0.8:2. The amplitude of the g₃ gradient was 16 mT/m when the gradient ratio was 1:0.8:2. The t₁ time was varied to test the in-phase and opposite-phase conditions of the lactate and alanine. The crusher gradients (g_csr) placed before the second RF pulse and after the fourth RF pulse had amplitudes of 5 mT/m and lengths of 2 ms. The phase encoding gradients for chemical shift imaging (CSI) had 3 ms lengths. The WET water suppression pulses (bandwidth = 35 Hz) [37] were applied prior to the modified Sel-MQC sequence in the weak water suppression mode of the scanner. In Sequence 2, the g₂, g₃ and g₄ gradient durations were 1.5 ms, 1.5 ms, 1.5 ms and 6 ms, respectively. The amplitudes of g₂, g₄ and g₅ gradients were 20 mT/m, −20 mT/m and 20 mT/m, respectively, when the gradient ratio was 1:0:−1:4 or 1:−0.8:−1:4. The amplitude of the g₃ gradient was −16 mT/m when the gradient ratio was 1:−0.8:−1:4. The crusher gradients (g_csr) placed before the second RF pulse and after the fifth RF pulse had amplitudes of 5 mT/m and durations of 2 ms. Other parameters were the same as Sequence 1 except for one more spectrally-selective 180° pulse and the new t₁ times. The crusher gradients of 5 mT/m and 20 ms were applied after the acquisition window for all three axes in both sequences to dephase any remaining transverse magnetization (not shown in Figs. 2 and 3).

3.3. Calculation of product operator transformations by RF pulses:

The off-resonance rotation matrices of the spin operators of lactate and alanine upon the RF pulses of the sequence were calculated by spin nutation about an effective magnetic field on the Riemann sphere [38] as in our previous study [25]. Tables S1 and S2 of the Supplementary Materials show the off-resonance rotation matrices and the spin operator transformations of the I and S spins of lactate and alanine upon the used RF pulses. The product operator transformations (Table 4 and Table 5) were derived from them for the pathways of Eq. 2 (Sequence 1) and Eq. 3 (Sequence 2).

Table 4.

Product operator evolutions and theoretical editing efficiencies of lactate and alanine for Pulse Sequence 1.^*

Spin operator transformation	Real	Imaginary	Magnitude	Phase (radian)	fJ	fT2	fT1	E.E.
Lactate (I = 1.33 ppm, S = 4.11 ppm; I3S system, J = 6.93 Hz) SQC→DQC→ZQC→SQC
P1: Iz → I+	0.045	−0.498	0.500	−1.48	Eq. 8	Eq. 18	Eq. 19	Eq. 20
P2: I+ → I+	0.760	−0.650	1.000	−0.71
Sz → S+	0.377	0.327	0.498	0.71
P3: I+ → I−	0.991	0.005	0.991	0.00
S+ → S+	−0.107	0.994	1.000	1.68
P4: I− → I−	0.760	0.650	1.000	0.71
S+ → Sz	0.762	0.643	0.997	0.70
Total			0.492	1.61	0.729	0.846	0.635	0.344
Alanine (I = 1.48 ppm, S = 3.79 ppm; I3S system, J = 7.23 Hz) SQC→DQC→ZQC→SQC
P1: Iz → I+	−0.045	−0.498	0.500	4.62	Eq. 8	Eq. 18	Eq. 19	Eq. 20
P2: I+ → I+	−0.534	−0.846	1.000	4.15
Sz → S+	−0.377	0.327	0.498	2.43
P3: I+ → I−	0.991	−0.005	0.991	0.00
S+ → S+	−0.906	−0.423	1.000	3.58
P4: I− → I−	−0.534	0.846	1.000	2.13
S+ → Sz	−0.762	0.643	0.997	2.44
Total			0.492	19.35	0.753	0.789	0.674	0.356

^*P₁, P₂, P₃ and P₄ indicate the first, second, third and fourth pulses, respectively.

Table 5.

Product operator evolutions and theoretical editing efficiencies of lactate and alanine for Pulse Sequence 2.^*

Spin operator transformation	Real	Imaginary	Magnitude	Phase (radian)	fJ	fT2	fT1	E.E.
Lactate (I = 1.33 ppm, S = 4.11 ppm; I3S system, J = 6.93 Hz) SQC→DQC→ZQC→DQC→SQC
P1: Iz → I+	0.045	−0.498	0.500	−1.48	Eq. 9	Eq. 18	Eq. 19	Eq. 20
P2: I+ → I+	0.760	−0.650	1.000	−0.71
Sz → S+	0.377	0.327	0.498	0.71
P3: I+ → I+	0.977	0.213	1.000	0.21
S+ → S−	0.978	−0.007	0.978	−0.01
P4: I+ → I−	0.991	0.005	0.991	0.00
S− → S−	−0.107	−0.994	1.000	4.61
P5: I− → I−	0.760	0.650	1.000	0.71
S− → Sz	0.762	−0.643	0.997	−0.70
Total			0.481	4.83	0.994	0.718	0.635	0.389
Alanine (I = 1.48 ppm, S = 3.79 ppm; I3S system, J = 7.23 Hz) SQC→DQC→ZQC→DQC→SQC
P1: Iz → I+	−0.045	−0.498	0.500	4.62	Eq. 9	Eq. 18	Eq. 19	Eq. 20
P2: I+ → I+	−0.534	−0.846	1.000	4.15
Sz → S+	−0.377	0.327	0.498	2.43
P3: I+ → I+	0.898	−0.441	1.000	−0.46
S+ → S−	0.978	0.007	0.978	0.01
P4: I+ → I−	0.991	−0.005	0.991	0.00
S− → S−	−0.906	0.423	1.000	2.70
P5: I− → I−	−0.534	0.846	1.000	2.13
S− → Sz	−0.762	−0.643	0.997	3.84
Total			0.481	14.80	0.994	0.627	0.674	0.366

^*P₁, P₂, P₃, P₄ and P₅ indicate the first, second, third, fourth and fifth pulses, respectively.

3.4. Phantom-only experiments:

50 ml centrifuge tubes filled with 10 mM lactate, 10 mM alanine, 10 mM lactate + 10 mM alanine, 100 mM lactate, 100 mM alanine and 100% safflower seed oil were respectively prepared. Lithium lactate (Sigma Aldrich, 440469), L-alanine (Sigma Aldrich, 05129), PBS with Azide (Santa Cruz Biotechnology Inc., sc-296028) and safflower seed oil (Sigma Aldrich, S8281) were used for sample preparations. One of the tubes was attached to the bottom corner of a plastic container filled with water, and the receiver coil was placed adjacent to the bottom corner of the container. After scout images using a 2D fast low angle shot (FLASH) imaging sequence (TR/TE = 350/2.46 ms), a cubic voxel of (2 cm)³ was located inside the tube and the localized shimming was performed. The 90° measurement of the voxel was carried out using the Stimulated Echo Acquisition Mode (STEAM) sequence [39] (mixing time (TM) = 20 ms, echo time (TE) = 20 ms, repetition time (TR) = 1.5 s, dummy scan (DS) = 2, and the number of average (NA) = 1). The modified Sel-MQC sequences were run typically with the following parameters: slice thickness = 2 cm, field of view (FOV) = 16×16 cm, spectral width = 1,500 Hz, TR = 1,500 ms, CSI matrix = 8×8, vector size = 1,024, and NA = 2. The unedited experiment and the T1 and T2 relaxation time measurement experiments are described in the later subsections. 15 ml centrifuge tubes filled with either safflower seed oil or 10 mM lactate plus 10 mM alanine were prepared and used for the experiments with oil, lactate and alanine in the same voxel (Fig. 8).

Fig. 8. MR spectra of the phantom composed of (10 mM lactate + 10 mM alanine) and safflower seed oil from the modified Sel-MQC sequences.

(A) MR image of the phantom and a part of the CSI matrix. CSI FOV = 32×32 cm, 8×8 matrix, 2 cm thickness. (B-D) Data from Sequence 1 with g₂:g₃:g₄ = 0:0:0 (B), 1:0:2 (C) and 1:0.8:2 (D). t₁ = 32.7 ms. (E-G) Data from Sequence 2 with g₂:g₃:g₄:g₅= 0:0:0:0 (E), 1:0:−1:4 (F) and 1:−0.8:−1:4 (G). t₁ = 68.0 ms. Original vector size = 1,024 zero-filled to 8,192. Lb = 1 Hz.

3.5. Study with a phantom on the subject:

The study was approved by the institutional review board of the University of Pennsylvania and informed consent was obtained from the subject. A glass tube (O.D. = 2 cm) filled with 10 mM lactate plus 10 mM alanine was placed on the upper right leg of the subject and the receive coil was placed on top of the tube. The MR experiments were run using Sequence 1 with the same parameters as the phantom-only experiments except for the coherence selection gradient durations.

3.6. Data processing:

The .rda files retrieved from the scanner were read by the 3DiCSI program [40]. The free induction decay (FID) signal from the voxel of interest was extracted in the ASCII format and analyzed using the jMRUI package [41, 42]. The FID data were zero-filled to 8,196 points, Fourier-transformed and spectrally fitted using the AMARES algorithm [43] of the package. The Lorentzian lineshape was employed for fitting. For the prior knowledge of fitting, the doublet peaks of lactate were set to have the same amplitudes and linewidths. Similarly, the doublet peaks of alanine were set to have the same amplitudes and linewidths. The NUTS software (Acorn NMR Inc., Livermore, CA) was used for plotting the spectra. The data from one of the two receive channels of the coil were used for all the analyses except for the study involving the human subject. For the latter, the combined mode data retrieved from the scanner were used for analysis.

3.7. T1, T2_SQC and T2_MQC measurements:

For use in the calculation of the theoretical editing efficiency and the conversion of the metabolite to water ratio to the absolute metabolite concentration, T1 and T2 relaxation times of lactate, alanine and water were measured. For T2 relaxation times of lactate and alanine, T2_SQC, T2_MQC1 and T2_MQC2 were separately measured, where T2_SQC refers to the T2 relaxation time during the SQC state, T2_MQC1 refers to the T2 relaxation time during the I⁺S⁺ and I⁻S⁺ states of Sequence 1 (see Fig. 2) and T2_MQC2 refers to the T2 relaxation time during the I⁺S⁺, I⁺S⁻ and I⁻S⁻ states of Sequence 2 (see Fig. 3). The pulse sequences designed to measure these T1 and T2 relaxation times, experimental parameters and the least-square-fittings of data to the relaxation equations are presented in SM-1 of the Supplementary Materials. The sequences for T2 measurements were designed so that the J-coupled evolution factor becomes unity at the echo. The determined T1 and T2 values (mean±SD; n ≥ 3; room temperature (20°C)) were as follows: T1 (Lac) = 1,497±10 ms; T1 (Ala) = 1,362±29 ms; T1 (water) = 2,704±53 ms; T2_SQC (Lac) = 1,156±31 ms; T2_SQC (Ala) = 715±12 ms; T2 (water) = 1,395±57 ms; T2_MQC1 (Lac) = 453±12 ms; T2_MQC1 (Ala) = 395±9 ms; T2_MQC2 (Lac) = 316±18 ms; T2_MQC2 (Ala) = 255±2 ms.

3.8. Calculation of the experimental editing efficiencies:

The 10 mM lactate phantom and the 10 mM alanine phantom were used for the experiments. Sequence 1 and Sequence 2 were used for the edited experiments while the J-refocused spin-echo sequence (Fig. S3 of SM-1) was used for the unedited experiments. For the latter, the center frequencies of RF pulses were set to the methyl resonance frequency of lactate or alanine, and TE was set to 1/J_Avg. The experimental editing efficiency (E.E.(experiment)) of lactate or alanine was determined by the ratio of the signal from the edited experiment and the signal from the unedited experiment.

3.9. Determination of the absolute concentrations of lactate and alanine:

The modified Sel-MQC CSI sequences were run on the phantoms of 10 mM lactate plus 10 mM alanine with the outer volume saturation (OVS) bands placed around the target voxel (see Fig. 6). The OVS bands remove the signals originating from outside the target voxel to obtain the accurate metabolite to water ratio from the target voxel. The OVS pulses employed the very selective saturation (VSS) pulses of Tran et al. [44]. They were placed in front of the water suppression pulses of the sequences. Each OVS pulse had 4.5 ms length (bandwidth = 4,124 Hz; transition width = 194 Hz) and was accompanied by gradients. The center frequencies of the OVS pulses were set at 1.405 ppm which was the mean chemical shift of the methyl resonances of lactate and alanine. The flip angles for the individual OVS pulses were calculated using the interval between each OVS pulse and the first 90° pulse of the modified Sel-MQC sequences and the mean T1 relaxation time of lactate and alanine so that the longitudinal magnetizations of lactate and alanine from the OVS slabs become zero at the first 90° pulse of the main sequences. The water spin-echo CSI was run using the sequence in Fig. S3 of SM-1 with the center frequencies set at the water resonance without water suppression pulses. The water-OVS bands were placed around the target voxel. The T1 relaxation time of water was used for determining the flip angles of the water OVS pulses. Each of the OVS bands had a 3 cm thickness. The vector size used for the water spin-echo CSI experiment was 2,048 as the water signal lasted longer than the acquisition window of the 1,024 vector size. Other measurement parameters (spectral width and NA) and the zero-filled final vector size (8,192) were the same for all experiments except that TR = 1,500 ms for Sequence 1 and Sequence 2 while TR = 1,563 ms for water spin-echo CSI. The areas of lactate, alanine and water were determined by spectral fitting of the MR spectra with jMRUI. Lac/H₂O and Ala/H₂O were calculated from them. Lac/H₂O was converted to the absolute molar concentration of lactate by

$$\mathit{\text{Conc}}.(Lac)=\frac{Lac(\mathit{\text{area}})}{\mathit{\text{water}}(\mathit{\text{area}})}\times 110\times \frac{1}{3}\times \frac{1}{E.E.(\text{experiment)}}\times \frac{f_{T1}(\mathit{\text{water}})}{f_{T1}(Lac)}\times \frac{\text{exp}\left(-1/(J_{Avg}\cdot T{2}_{Lac})\right)}{\text{exp}\left(-1/(J_{Avg}\cdot T{2}_{\mathit{\text{water}}})\right)}$$ (21)

where E.E.(experiment) is the experimental editing efficiency of lactate as defined in Section 3.8. In Eq. 21, 110 is the molar concentration of protons in water and 3 is the number of protons per methyl group of lactate. Similarly, Ala/H₂O was converted to the absolute molar concentration of alanine.

Fig. 6. The CSI with the OVS bands.

(A) The multi-voxel spectra from the modified Sel-MQC-CSI sequence 1. The chemical shift range of 1.0–1.8 ppm is presented. (B) The water spin-echo-CSI. The chemical shift range of 4.4–5.2 ppm is presented. (C) The spectrum from the red voxel of (A), spectral fitting by jMRUI and the residual. Lb = 0 Hz.

4. RESULTS AND DISCUSSION

4.1. Theoretical calculation of the t₁ time for phase alignment of lactate and alanine

• Sequence 1: The off-resonance rotation matrices and spin operator transformations of lactate and alanine upon the RF pulses of Sequence 1 (Fig. 2) were calculated (see Table S1). Table 4 shows the calculation of ϕ_p (see Eq. 4) from the summation of the phase changes of the individual spin operators by RF pulses. The ϕ_p was 1.61 radians for lactate and 19.35 radians for alanine, respectively (Table 4). From Eqs. 11, 14 and 15, the condition for the phase alignment of lactate and alanine is

  $$(\Delta {\omega }_I-\Delta {\omega }_S)\times t_1+\Delta {\omega }_I\times \frac{t_A}{2}+\Delta {\omega }_S\times (t_C+t_E)+(1.61-19.35)=2n\pi$$ (22)
  Using t_A = 3 ms, t_C = 12 ms, t_E = 8 ms, Eq. 22 becomes

  $$\begin{array}{l}2\pi \times (-0.15-0.32)\times 123.25\times t_1+2\pi \times (-0.15)\times 123.25\times 1.5\times 0.001\\ +\text{2}\pi \times 0.32\times 123.25\times 20\times 0.001-17.74=2n\pi \end{array}$$ (23)

  From Eq. 23, we obtain t₁ = 33.4 ms, 50.7 ms, etc. The conditions for the opposite phase of lactate and alanine (Eq. 16) are met at t₁ = 24.8 ms, 42.0 ms, etc.

• Sequence 2: Table 5 shows the calculation of ϕ_p for Sequence 2 (Fig. 3) using the spin operator transformations of lactate and alanine for this sequence (Tables S1 and S2). The ϕ_p was 4.83 radians for lactate and 14.80 radians for alanine, respectively (Table 5). From them, Eqs. 13, 14 and 15 lead to

  $$\frac{(-\Delta {\omega }_I+\Delta {\omega }_S)}{2}\times t_1+\Delta {\omega }_I\times \left(\frac{t_A}{2}+t_E\right)-\Delta {\omega }_S\times t_G+(4.83-14.80)=2n\pi$$ (24)

  for the in-phase condition of lactate and alanine. Using t_A = 3 ms, t_C = 12 ms, t_E = 6 ms, t_G = 8 ms, Eq. 24 becomes

  $$\begin{array}{l}2\pi \times (-0.15-0.32)\times 123.25\times (t_1/2)+2\pi \times (-0.15)\times 123.25\times (1.5+6)\times 0.001\\ -\text{2}\pi \times 0.32\times 123.25\times 8\times 0.001+(4.83-14.80)=2n\pi \end{array}$$ (25)

  From Eq. 25, we obtain t₁ = 70.5 ms and 105.0 ms for in-phase condition. Similarly, we obtain t₁ = 53.2 ms and 87.7 ms for the opposite phase condition of lactate and alanine.

4.2. Experimental test and correction of the t₁ times

MR experiments were performed using a phantom consisting of 10 mM lactate plus 10 mM alanine with Sequence 1 and Sequence 2. Figure 4A shows a part of the MR image, CSI matrix and the selected voxel. Figure 4B shows the MR spectrum from the indicated voxel with Sequence 1 at t₁ = 32.7 ms. The t₁ time was fine-adjusted from the theoretically calculated 33.4 ms to achieve the best alignment of the phases of lactate and alanine. The 0.7 ms difference between the experiment and the theoretical calculation comes from the limitations of the product operator analysis applied to spectrally-selective pulses. These pulses do not uniformly excite the multiplets of lactate and alanine (the methyl (CH₃) doublet resonances of lactate and alanine; the methine (CH) quartet resonances of lactate and alanine), and it is difficult to incorporate such non-uniform excitation effects on multiplets into the product operator analysis. Nonetheless, Eq. 23 indicates that the mismatch can be corrected by calibration of the t₁ time as we did. The opposite phases of lactate and alanine were achieved by applying the same calibration (0.7 ms) to the theoretically calculated t₁ time (24.8 ms) for the opposite phase condition. Figure 4C shows the spectrum at t₁ = 24.1 ms which demonstrates the opposite phases of lactate and alanine. In the experiments with Sequence 2, the t₁ times were also experimentally calibrated from the theoretically calculated t₁ times (70.5 ms and 53.2 ms) to achieve the in-phase and opposite-phase conditions as expected from Eq. 25. Figures 4D–4E show spectra at t₁ = 68.0 ms (in-phase condition) and t₁ = 50.7 ms (opposite phase condition), respectively. The calibration of 2.5 ms was required for these experiments. A larger calibration required for the experiment with Sequence 2 than with Sequence 1 is understandable considering that the additional Gaussian 180° pulse (the P₃ pulse of Fig. 3) centered in the middle of the methine (CH) quartet resonances of lactate and alanine in Sequence 2 produces substantial nonuniform rotations on the individual quartet resonances of lactate and alanine that are centered at 4.11 ppm and 3.79 ppm, respectively. The significant distortions of the lactate doublet shapes for the spectra in Figs. 4D and 4E obtained with Sequence 2 are attributable to this effect. The lactate signal with Sequence 2 was slightly bigger than with Sequence 1 (Fig. 4D vs Fig. 4B). On the other hand, the alanine signal intensities and doublet shapes were similar between the spectra from the two sequences (Fig. 4D vs Fig. 4B).

Fig. 4. MR spectra of (lactate + alanine) from Pulse Sequence 1 and Pulse Sequence 2.

(A) MR image of the (lactate + alanine) phantom and a part of the CSI matrix. (B) The MR spectrum from Pulse Sequence 1 at t₁ = 32.7 ms. (C) The MR spectrum from Pulse Sequence 1 at t₁ = 24.1 ms. (D) The MR spectrum from Pulse Sequence 2 at t₁ = 68.0 ms. (E) The MR spectrum from Pulse Sequence 2 at t₁ = 50.7 ms. Original vector size = 1,024 zero-filled to 8,192. Line broadening (Lb) = 0.5 Hz.

4.3. Editing efficiencies of lactate and alanine with Sequence 1 and Sequence 2

To quantitatively analyze the editing efficiencies of lactate and alanine with the modified Sel-MQC sequences, the edited and unedited experiments were performed on a 10 mM lactate phantom and a 10 mM alanine phantom separately. The experimental setup and the voxel selection were the same as in Fig. 4A except that the tube was filled with lactate only or alanine only. A reason for the need for such separate experiments is that the unedited experiment (I spin-selective refocused spin echo; TE = 1/J_Avg) with the center frequency of the 180° pulse set in the middle of the methyl resonances of lactate and alanine induces phase difference between lactate and alanine at the echo when both molecules are simultaneously detected. By performing experiments on lactate only and alanine only, such an issue is removed. Figure 5A shows the alanine spectrum from the unedited experiment (TE = 141 ms) while Fig. 5B and Fig. 5C show the alanine spectra from Sequence 1 (t₁ = 32.7 ms) and Sequence 2 (t₁ = 68.0 ms), respectively. Similarly, Fig. 5D shows the lactate spectrum from the unedited experiment (TE = 141 ms) while Fig. 5E and Fig. 5F show the lactate spectra from Sequence 1 (t₁ = 32.7 ms) and Sequence 2 (t₁ = 68.0 ms), respectively.

Fig. 5. Comparison of the unedited and edited spectra of alanine and lactate.

An unedited spectrum (A), the edited spectrum with Sequence 1 (B), and the edited spectrum with Sequence 2 (C) from a 10 mM alanine phantom. An unedited spectrum (D), the edited spectrum with Sequence 1 (E), and the edited spectrum with Sequence 2 (F) from a 10 mM lactate phantom. TE = 141 ms for all experiments. Original vector size = 1,024 zero-filled to 8,192. Lb = 0.5 Hz.

The experimental editing efficiencies (mean±SD) of lactate and alanine as determined by the spectrally fitted area ratios between the edited spectra and the unedited spectra were (33.3±0.0)% for lactate and (34.2±0.5)% for alanine, respectively, with Sequence 1. They were (36.6±0.4)% for lactate and (34.8±0.8)% for alanine, respectively, with Sequence 2. Therefore, the experimental editing efficiency of lactate from Sequence 2 was 10% bigger than that from Sequence 1, while the experimental editing efficiencies of alanine from Sequence 1 and Sequence 2 were almost the same.

The theoretical editing efficiencies of lactate and alanine were calculated by Eq. 20. We first analyze the editing efficiencies with Sequence 1. Table 4 shows various signal modulation factors that contribute to the editing efficiencies. The magnitude of the product operator transformation factor |f_P| was 0.492 for both lactate and alanine. The value is just 1.6% smaller than 0.50, the maximum obtainable at the on-resonance condition [25], indicating that the signal losses of lactate and alanine by the off-resonance rotations with the employed pulse lengths are very small. For calculation of f_J (Eq. 8), ξ of 0.982 from Table S1 was used for both lactate and alanine. Other parameters to calculate f_J were: t₁ = 32.7 ms, τ₁ = 70.5 ms – 32.7 ms = 37.8 ms, τ₂ = 70.5 ms. From these parameters, the followings are calculated: [cos²(πJ_Lact₁/2) + ξsin²(πJ_Lact₁/2)]² = 0.996, [cos²(πJ_Alat₁/2) + ξsin²(πJ_Alat₁/2)]² = 0.995, sin(πJ_Lacτ₁)×sin(πJ_Lacτ₂) = 0.730, sin(πJ_Alaτ₁)×sin(πJ_Alaτ₂) = 0.754. From them, f_J was 0.729 for lactate and 0.753 for alanine, respectively. Also, using the measured T2_SQC and T2_MQC1 of lactate and alanine (see SM-1), f_T2 (Lac) = 0.846 and f_T2 (Ala) = 0.789 are obtained by Eq.18. From them, the theoretical editing efficiencies (Eq. 20) were 34.4% for lactate and 35.6% for alanine, respectively (Table 4). The analysis of editing efficiencies with Sequence 2 was performed similarly. Equation 20 and Table 5 were used. The individual factors for the editing efficiencies were: |f_P| (Lac) = 0.481, f_J (Lac) = 0.994, f_T2 (Lac) = 0.718, |f_P| (Ala) = 0.481, f_J (Ala) = 0.994, and f_T2 (Ala) = 0.627. The T2_SQC and T2_MQC2 were used for the f_T2 calculation. From them, the theoretical editing efficiencies (Eq. 20) of lactate and alanine were 38.9% and 36.5%, respectively.

The experimental and theoretical editing efficiencies of lactate and alanine well matched each other for both sequences within 3–6%. Signal loss by the J-coupled evolution factor in Sequence 1 (~25%) was almost eliminated in Sequence 2 (<1%). However, the long TE time in Sequence 2 required for phase alignment of lactate and alanine increased the signal loss by the T2 relaxation factor. Resultantly, the signal gain by Sequence 2 relative to Sequence 1 was limited; ~10% for lactate and ~2% for alanine.

4.4. Determination of the absolute metabolite concentrations of lactate and alanine

The modified Sel-MQC sequences and the water spin-echo sequence with the OVS pulses (see Section 3.9) were applied to the phantom of 10 mM lactate plus 10 mM alanine. Figure 6A shows a 3×3 section of the CSI grid from Sequence1, and Fig. 6B shows the corresponding CSI grid from the water spin-echo sequence. The OVS pulses successfully suppressed the signals originating from the voxels outside the target voxel. The remnant signals outside the target voxels are the bled-over signals coming from the point spread function of the target voxel. Figure 6C shows the spectrum from the target voxel of Fig. 6A, the spectral fitting by the AMARES routine of jMRUI and the residual. Lac/H₂O and Ala/H₂O of the target voxel (see Section 3.9 for details) were converted into absolute concentrations by Eq. 21. From the experiments with three different samples, the metabolite concentrations (mean±SD) determined by Sequence 1 were 10.0±0.4 mM for lactate and 10.1±0.3 mM for alanine, respectively. The metabolite concentrations determined by Sequence 2 were 10.2±0.2 mM for lactate and 10.3±0.2 mM for alanine, respectively. Therefore, the concentrations of lactate and alanine determined from both Sequence 1 and Sequence 2 reasonably matched the prepared sample concentrations.

4.5. Suppression of J-coupled lipid signals

Sequence 1 and Sequence 2 without water suppression pulses were applied to the safflower seed oil phantom (Fig. 7A). For this study, the receive coil was placed directly on the 50 ml tube filled with the seed oil without immersing the tube in the water container. Figures 7B–7D show the data with Sequence 1 (t₁ = 32.7 ms). The chemical shift of the biggest peak of lipids was referenced at 1.33 ppm and the center frequencies of the RF pulses of Sequence 1 (1.405 ppm and 3.95 ppm; see Fig. 2) were set accordingly. The coherence selection gradient ratios of g₂:g₃:g₄ = 0:0:0 (Fig. 7B), 1:0:2 (Fig. 7C) and 1:0.8:2 (Fig. 7D) were tested. The 1.33 ppm lipid signal decreased 660-fold at the gradient ratio 1:0:2 compared to the signal at the gradient ratio 0:0:0 (Fig. 7B vs. Fig. 7C). The 1.33 ppm lipid signal decreased 8-fold further with the gradient ratio 1:0.8:2 compared to the gradient ratio 1:0:2 (Fig. 7C vs. Fig. 7D), reaching a total of 5,410-fold decrease compared to the signal at the gradient ratio 0:0:0 (Fig. 7B vs. Fig. 7D). This trend of lipid signal decreases is similar to that in our previous study where the center frequencies of RF pulses were set at 1.33 ppm and 4.11 ppm and the coherence selection gradient ratios 0:0:0, α:−1:2 and 1:β:2 with varied α and β were tested [25]. At the gradient ratio of 0:0:0, the lipid signals come mostly from the spins that stay in the SQC state. The corresponding coherence pathway has the coherence levels of p(1, 1, −1, −1) [25]. At the gradient ratio 1:0:2, the lipid spins that stay in the SQC state are dephased by gradients while the lipid spins that evolve through the SQC→DQC→SQC→SQC pathway (p(1, 2, −1, −1)) dominate [25]. The 1.33 ppm lipid signal at this gradient ratio comes mostly from the spin coupling of 1.33–2.07 ppm as can be found from the conversion rate calculations of the coherence pathways from three different spin couplings relevant to the 1.33 ppm lipid resonance [25]. The lipid signals around the chemical shift of 4 ppm are from the spin couplings of 4.16–4.37, 4.16–5.29 and 4.37–5.29 ppm. How these spin couplings lead to observable signals at the gradient ratio of 0:−1:2 were explained in our previous study [25], and a similar principle applies at the gradient ratio of 1:0:2. At the gradient ratio of 1:0.8:2, the signals from the SQC→DQC→SQC→SQC pathway are dephased and only the signals from the SQC→DQC→ZQC→SQC pathway (p(1, 2, 0, −1)) survive. The left signals were almost negligible (Fig. 7D). The advantage of using β = 0.8 over other β values of the gradient ratio 1:β:2 to effectively suppress the signals from the various coherence pathways of J-coupled lipids as well as from the SQC pathway of water is understood in a similar way the gradient ratio α:−1:2 with α = −0.8 does in our previous study [25]. The 2.07 ppm lipid signal that was observed at the gradient ratio 0:0:0 disappeared at the gradient ratios 1:0:2 and 1:0.8:2. This indicates that the signal contributions by the coherence pathways, SQC→DQC→SQC→SQC and SQC→DQC→ZQC→SQC, that are allowed at these gradient ratios from the couplings of 2.07–2.79 ppm and 2.07–5.38 ppm were negligible with the employed pulse lengths.

Fig. 7. MR spectra of the safflower seed oil phantom from the modified Sel-MQC sequences.

(A) MR image of the oil phantom and a part of the CSI matrix. (B-D) Data from Sequence 1 with g₂:g₃:g₄ = 0:0:0 (B), 1:0:2 (C) and 1:0.8:2 (D). t₁ = 32.7 ms. (E-G) Data from Sequence 2 with g₂:g₃:g₄:g₅= 0:0:0:0 (E), 1:0:−1:4 (F) and 1:−0.8:−1:4 (G). t₁ = 68.0 ms. Original vector size = 1,024 zero-filled to 8,192. Lb = 1 Hz.

Figures 7E–7G show data with Sequence 2 (t₁ = 68.0 ms) from the same phantom (Fig. 7A). As for the experiments in Figs. 7B–7D, the center frequencies of RF pulses were set with the biggest lipid signal referenced at 1.33 ppm. The coherence selection gradient ratios of g₂:g₃:g₄:g₅ = 0:0:0:0 (Fig. 7E), 1:0:−1:4 (Fig. 7F) and 1:−0.8:−1:4 (Fig. 7G) were tested. The overall signal intensities of the lipid peaks at the gradient ratio of 0:0:0:0 (Fig. 7E) were similar to those at the gradient ratio of 0:0:0 with Sequence 1 (Fig. 7B). When the gradient ratio of 1:0:−1:4 or 1:−0.8:−1:4 was applied, all the lipid peaks decreased to the noise level (Figs. 7F and 7G). The coherence pathways allowed at the gradient ratio g₂:g₃:g₄:g₅ = 1:0:−1:4 are SQC→DQC→(ZQC + SQC + DQC)→DQC→SQC. The coherence pathway allowed at the gradient ratio g₂:g₃:g₄:g₅ = 1:−0.8:−1:4 is SQC→DQC→ZQC→DQC→SQC. The data of Figs. 7F–7G indicate that the third pulse of Sequence 2 (the Gaussian 180° pulse of 6 ms centered at 3.95 ppm) filtered out all three MQC pathways of J-coupled lipids that were allowed at g₂:g₃:g₄:g₅ = 1:0:−1:4 and 1:−0.8:−1:4.

Next, we performed experiments with both an oil phantom and a lactate-plus-alanine phantom in the same voxel of CSI. Two 15 ml centrifuge tubes filled with either safflower seed oil or 10 mM lactate plus 10 mM alanine were immersed in a water container. The MR experiments were performed as in Fig. 4 except that a FOV of 32×32 cm and a voxel size of 4×4 cm were employed. The lactate doublet was referenced at 1.33 ppm and the center frequencies of the RF pulses were set accordingly. Figure 8A shows the chosen voxel. Figures 8B–8D and 8E-8G show data with Sequence 1 (t₁ = 32.7 ms) and Sequence 2 (t₁ = 68.0 ms), respectively. Figures 8B, 8C and 8D are spectra upon the application of the gradient ratios 0:0:0, 1:0:2 and 1:0.8:2, respectively, with Sequence 1. At the gradient ratio of 0:0:0, lipid signals overwhelmed the spectrum (Fig. 8B). The biggest peak of lipids appeared at 1.51 ppm. The chemical shifts of lipids are temperature-dependent. The chemical shift difference of ~0.20 ppm between lactate and the biggest peak of lipids is typical at room temperature, while the chemical shifts of lactate and the biggest peak of lipids almost coincide in the in vivo condition [45]. At the gradient ratio of 1:0:2, lactate and alanine signals dominated while they were contaminated by the J-coupled lipid signals that come from the coherence pathway SQC→DQC→SQC→SQC (Fig. 8C). At the gradient ratio of 1:0.8:2, the above-mentioned coherence pathway of J-coupled lipids is dephased, which resulted in a clean spectrum of lactate and alanine (Fig. 8D). Figures 8E, 8F and 8G are spectra with Sequence 2 upon the application of the gradient ratios 0:0:0:0, 1:0:−1:4 and 1:−0.8:−1:4, respectively. At the gradient ratio of 0:0:0:0, lipid signals overwhelmed (Fig. 8E). At both the gradient ratio of 1:0:−1:4 (Fig. 8F) and 1:−0.8:−1:4 (Fig. 8G), lipid-free clean signals of lactate and alanine were observed. The data of Figs. 8B–8G indicate that both Sequence 1 and Sequence 2 can be used to selectively detect lactate and alanine in the environment of lipids. As the lactate signal from Sequence 2 exhibited a significant unbalance in the doublet shape (see Fig. 8G), we employed Sequence 1 for the study on the phantom with a human subject in the next subsection.

4.6. Lactate and alanine editing in the environment of large lipids of a human body

A phantom of 10 mM lactate plus 10 mM alanine (a glass tube with an outer diameter of 2 cm) was placed on the upper leg of a subject and Sequence 1 was run; FOV = 16×16 cm and an 8×8 matrix. Figures 9A-9C show CSI data (0.8 – 2.2 ppm) from three different conditions (different gradient ratios or t₁ times) and Figs. 9D-9F show the corresponding spectra from the red voxels of Figs. 9A–9C. The first condition had g₂:g₃:g₄ = 0:0:0 and t₁ = 32.7 ms (Figs. 9A and 9D). The second condition had g₂:g₃:g₄ = 1:0.8:2 and t₁ = 32.7 ms (Figs. 9B and 9E). The third condition had g₂:g₃:g₄ = 1:0.8:2 and t₁ = 24.1 ms (Figs. 9C and 9F). The first condition corresponds to Fig. 8B, the second condition corresponds to Fig. 8D and the third condition corresponds to Fig. 4C. In the first condition, large lipid signals are observed in the various voxels of CSI (Fig. 9A), which are mostly the contribution of the SQC pathway signals. The signal at the phantom voxel (Fig. 9D) was dominated by lipid signals that bled over from the nearby lipid-rich tissue voxels. In the second condition, lipid signals from all the CSI voxels of the leg were suppressed to the noise level (Fig. 9B) while the phantom voxel exhibited lipid-free lactate and alanine signals that were in phase with each other (Fig. 9E). Some bled-over lactate and alanine signals were observed in the voxels outside the phantom voxel due to the point spread function of CSI. In the third condition, the phantom voxel exhibited lactate and alanine signals having opposite phases with each other while lipid signals from all the voxels were suppressed to the noise level (Figs. 9C and 9F). These data demonstrate that in-phase and opposite-phase spectral editings of lactate and alanine with suppression of J-coupled lipid signals in vivo were achieved.

Fig. 9. MR spectra from the modified Sel-MQC sequence 1 with the (lactate + alanine) phantom on the upper leg of a volunteer.

(A) CSI at g₂:g₃:g₄ = 0:0:0 and t₁ = 32.7 ms. CSI FOV = 16×16 cm, 8×8 matrix, 2 cm thickness. (B) CSI at g₂:g₃:g₄ = 1:0.8:2 and t₁ = 32.7 ms. (C) CSI at g₂:g₃:g₄ = 1:0.8:2 and t₁ = 24.1 ms. (D) The spectrum from the phantom voxel of (A). (E) The spectrum from the phantom voxel of (B). (F) The spectrum from the phantom voxel of (C). Original vector size = 1,024 zero-filled to 4,096. Lb = 0 Hz. The biggest peak of lipids was within 0.1 ppm of the lactate methyl resonance peak of the phantom for all the voxels of CSI.

4.7. Summary and further discussions

In this study, we provided the theoretical basis and experimental demonstration of in-phase spectral editing of lactate and alanine with suppression of J-coupled lipid signals by the modified Sel-MQC sequences. The information of both the magnitudes and phases of the product operator evolutions was exploited. The calculation of the phase evolutions of the product operators of lactate and alanine during the RF pulses and the free precession times of the modified Sel-MQC sequences enabled the prediction of the MQ evolution times that induce in-phase and opposite-phase conditions of lactate and alanine, which were fine-tuned with experiments. The contributions of the various signal modulation factors, i.e., off-resonance rotation effects, J-coupled evolution effects and T1 and T2 relaxation effects, to the final signals of lactate and alanine were determined, which allowed for deriving the absolute concentrations of lactate and alanine from the MQC editing data. Two different pulse sequences that achieve the in-phase editing of lactate and alanine with suppression of J-coupled lipid signals were developed. Although the signal losses of lactate and alanine by J-coupled evolution in Sequence 1 were almost removed in Sequence 2, the increased MQ evolution time required for phase alignment of lactate and alanine in Sequence 2 resulted in the prolonged TE and larger signal attenuation by T2 relaxation than in Sequence 1. Consequently, the final signal intensities of lactate and alanine from Sequence 1 and Sequence 2 were similar.

Our previous study applied the off-resonance rotations to the transformation of product operators for the first time [25]. While only the magnitude information of product operator transformations was exploited in that study to calculate the conversion rates of the individual coherence pathways [25], the current study, in addition, exploited the phase information of the product operator transformations upon the off-resonance rotation pulses for the first time, to calculate the condition for phase alignment of lactate and alanine.

Moreover, the current study measured the T2 relaxation times of lactate and alanine separately during the SQC states and the MQC states for the first time by designing appropriate pulse sequences. T2_MQC was smaller than T2_SQC, and T2_MQC of Sequence 2 was smaller than T2_MQC of Sequence 1. While we measured T2_SQC of lactate and alanine by the I-spin selective refocused spin-echo sequence, that method will not be applicable in vivo due to the overlapping lipid signals. In such a case, the T2_SQC can be measured by placing the I-spin selective refocused spin-echo pulse train before the modified Sel-MQC sequences as Muruganandham et al. [12]. In vivo T1 relaxation times of lactate and alanine can also be measured by placing an adiabatic inversion pulse before the modified Sel-MQC sequences. Such information can be used to determine the absolute concentrations of lactate and alanine from in vivo tissues such as tumors.

van Dijk had previously proposed a method to extract the lactate-only or alanine-only signals from a mixed solution of lactate and alanine by using a conventional MQC editing sequence that employs the SQC→DQC→SQC pathway of lactate and alanine [5]. The method adds or subtracts spectra from two different t₁ times, exploiting the fact that the phase difference between lactate and alanine varies with the MQ evolution time t₁ of the sequence and has a cycle that is the inverse of the DQC frequency difference between lactate and alanine [5]. However, the addition/subtraction method requires accurate correction of the T2 relaxation and J-coupled evolution effects on the lactate and alanine signals at the two different t₁ times, which can entail a substantial error. In contrast, our study has determined the t₁ times of the modified Sel-MQC sequences that can eliminate the phase difference between lactate and alanine without the need for addition/subtraction. Moreover, both of the modified Sel-MQC sequences exhibited excellent lipid suppression.

Our previous study [25] and the current study set an important foundation for lactate and alanine editing in vivo, which can be exploited in future studies with high clinical significance. Cancer cells heavily rely on glucose and glutamine metabolism for making building blocks of cellular proliferation such as nucleic acids, fatty acids and adenosine triphosphate [26, 27, 46, 47]. Fluorodeoxyglucose-positron emission tomography (FDG-PET), the well-known cancer imaging tool, monitors glucose metabolism by measuring the glucose uptake rate of tumors. However, the method does not provide information on other metabolic pathways. The glucose uptake rates from the FDG-PET often did not match the progression of tumors [48, 49], which is understandable considering that metabolic pathways not directly related to glucose uptake also play crucial roles in the proliferation of cancer cells. Glutaminolysis and reductive glutamine metabolism are representative of such pathways [27, 50, 51]. As alanine is a byproduct of glutaminolysis and reductive glutamine metabolism [52], the concentration of alanine in cancer cells can reflect glutamine metabolism [52]. By measuring the lactate (a product of glucose metabolism) and alanine (a product of glutamine metabolism) concentrations from tumors, the metabolic characteristics and activities of tumors can be probed much better than from lactate or glucose uptake alone. Such information can be used to help plan the most suitable therapy options for individual cancer patients and to predict early in a treatment time course whether a given therapy will work or not because metabolic changes precede tumor cell proliferation changes [13, 18, 52].

While we employed the CSI localization in this study, a single voxel spectroscopy (SVS) localization will be a more robust method when motion-concerned body regions are to be studied because frequency- and phase-corrections of the individual transients of MR signals can be more easily implemented with the SVS method by using the retrospective and prospective motion correction strategies [53]. The SVS localization can be achieved by adding the adiabatic refocusing pulses with slice gradients during the first and last periods of our sequences as the semi-LASER (Localization by Adiabatic Selective Refocusing) scheme [54]. The adiabatic pulses are needed to ensure the large bandwidths for refocusing both the I and S spins of lactate and alanine with minimal chemical shift displacement error. On the other hand, the first 90° pulse of our sequences has only to rotate the I spins of lactate and alanine. The S spin rotation with the first 90° pulse was irrelevant to the final I spin signal of lactate in our previous analysis of the product operator evolution of lactate from the Sel-MQC sequence [25]. The same applies to the lactate and alanine signals from the modified Sel-MQC sequences. A property of the adiabatic refocusing pulse (comprising two adiabatic inversion pulses for a refocusing) is that the phase evolution during the refocusing pulse becomes zero regardless of the off-resonance frequencies [55]. This indicates that the total ϕ_p will not change after adding the adiabatic refocusing pulses. Also, as the adiabatic refocusing pulses will be applied when the quantum coherence levels of the spin system are +1 (the first period of the sequence) and −1 (the last period of the sequence), there is no net change in ϕ_free for either lactate or alanine. Then, the t₁ times we determined for phase alignment of lactate and alanine in the current study will be able to be applied without changes, in principle. An issue is that a normal hyperbolic secant pulse used for adiabatic inversion [55] requires a long pulse length (e.g., we used an 18 ms hyperbolic secant pulse in the inversion recovery experiment for T1 relaxation time measurements in SM-1) for B1_max to be within the allowed limit of the MRI system. As two adiabatic inversions are required for a refocusing pulse, such long RF pulses do not fit into the τ₁ time of Sequence 1. The gradient-modulated adiabatic refocusing pulses developed for short TE experiments such as FOCI, GOIA, etc. [54] will be suitable options in that case.

5. CONCLUSION

Two modified Sel-MQC sequences that can align the phases of lactate and alanine signals and suppress J-coupled lipid signals were designed and tested. The magnitude and phases of lactate and alanine signals on the two sequences were theoretically analyzed using product operator evolutions and compared with experiments. The phase alignment of lactate and alanine with suppression of J-coupled lipid signals was achieved in phantom experiments and a phantom with a subject study.