It has been well-known since the early days of NMR spectroscopy that the microscopically chaotic chemical exchange between equivalent sites of spins involved in scalar couplings lead to natural decoupling between the exchanging spins and the non-exchanging spins when the fast exchange limit is reached. Random RF decoupling is based on the similarity between the evolution of the observed heteronuclear spins when the random noise-modulated irradiation of proton spins is applied, and the chaotic chemical exchange of proton spins at the microscopically level between equivalent sites. Random RF decoupling, developed five decades ago by Ernst [10], has long been considered inferior and abandoned by the NMR community ever since the advent of modern methods that use coherent composite or adiabatic pulses for heteronuclear decoupling. The coherent heteronuclear decoupling methods are far more superior for decoupling large one-bond ¹H-¹³C couplings. Coherent composite pulse decoupling schemes are capable of decoupling a broad bandwidth (e.g., a 10 kHz bandwidth) with a γB₂ of 1–2 kHz [12, 13]. The low γB₂ required for in vivo ¹³C-MRS at high magnetic field, however, makes it impossible to use any coherent decoupling sequences, composite or adiabatic. For example, weak decoupling results were obtained when applying WALTZ-4 sequence at a very low γB₂ [28].

In contrast to coherent decoupling schemes, the repetition rate of the random RF decoupling pulse sequence determines its decoupling bandwidth [10]. The entire spectral range of proton resonances that are J-coupled to the observed ¹³C spins can be decoupled. Because the long-range ¹H-¹³C splittings are not particularly large, a moderate scaling factor can achieve perfect or nearly perfect decoupling results. We thus revived the random RF decoupling strategy of Ernst for broadband decoupling of carboxylic/amide carbons at high fields. Experimentally, a nominal γB₂ of 100 Hz is sufficient to provide effective decoupling in the carboxylic and amide carbon region at 4.7T [28]. GABA C1 (182.3 ppm) and Asp C4 (178.3 ppm) were detected from the dominant and more intense signals from Glu C5 (182.0 ppm) and Gln C5 (178.5 ppm), respectively.

The idea of coherent decoupling can be traced to the use of a spectrally-selective RF pulse for refocusing of scalar couplings. Following excitation, the evolution of the density matrix during acquisition is given by:

where C and H are the ¹³C and proton product operators, and J_CH is the scalar coupling constant. When applying a selective ¹H 180x° pulse after a delay t, the density matrix is given by:

Thus, after an additional delay t, the evolution due to scalar coupling is refocused:

The decoupled ¹³C spectrum can be obtained when the data sampling intervals are set at exact multiples of 2t.

Coherent decoupling extends the above idea by the use of a continuous and cyclic pulse train during data sampling. The goal is to make evolution of ¹³C multiplets, under the average Hamiltonian of the irradiating proton RF field, periodically indistinguishable from that of ¹³C singlets. In order to achieve broadband proton decoupling, broadband inversion pulses must be carefully designed. The composite RF pulses were the first family of the broadband inversion pulses identified. Composite pulses use pulse blocks with different nutation angles and phases. Two typical composite pulses are 90xo180yo90xo and 90xo180-xo270xo, forming the basis of MLEV [11] and WALTZ [12, 13]. Further improvements can be achieved by placing the aforementioned composite pulses into cycles. The widely used WALTZ-4 contains four successive segments: S_xS_xS_−xS_−x, where S_x is the original composite pulse 90xo180-xo270xo, and S_−x is the phase inversed version 90-xo180xo270-xo. The most popular and commonly used decoupling pulse, WALTZ-16, contains four successive segments of WALTZ-4. An advantage of cycling is that the imperfection introduced by previous pulses can be compensated for later. Due to weak γB₂ field for in vivo ¹³C-MRS especially at high magnetic fields, the resultant long pulse duration makes phase cycling and cyclic repetition of decoupling pulses much less meaningful than in high-resolution NMR spectroscopy. As such, in vivo decoupling by composite (and adiabatic for the same reason) pulses at low γB₂ suffer from markedly signal loss and accompanied side bands.

To prevent tissue overheating, SAR simulation analysis is usually performed before actual studies associated with potentially high RF power deposition. A commercial numerical simulation software package of the finite-difference time-domain (FDTD) method was used to simulate the B₁ field and SAR distribution [38, 39]. The maximum local SAR_max and spatially averaged SAR_ave are related to the timely average transmitted RF power RF_ave as:

where M is the mass of the scanned human head and SAR_10g is the maximum local SAR per 10 g tissue after normalization when the total absorbed electrical power inside the human model was 1 W at 100% duty cycle (DC). RF_ave is given by a combination of RF_DEC, the RF power used for decoupling, and RF_NOE, the RF power for NOE:

Figure 1 shows examples of the simulated B1+ field distribution of the proton coil in an axial plane at 3T (Figure 1A) and at 7T (Figure 1B). If the simulated SAR under experimental conditions is below IEC and FDA safety thresholds [22, 23], the actual experiment can be safely conducted.

The feasibility of the strategy for detecting the carboxylic/amide spectral region with low power random RF heteronuclear decoupling was first demonstrated in rhesus monkey brains at 4.7T [28]. Two decoupling schemes were tested in this study: (a) a pseudo-noise decoupling pulse with constant amplitude and randomly assigned phase (either 0° or 180°); and (b) a vectorial noise decoupling pulse with both random amplitude and phase (between 0° and 360°). The WALTZ-4 pulse with the same RF power was also evaluated as a performance benchmark. This study demonstrated that many metabolite signals, including Glu C5, Glu C1, Gln C5, Gln C1, Asp C4, Asp C1, NAA C5, and GABA C1, could be detected in the carboxylic/amide carbon spectral region (169–185 ppm) with both noise decoupling methods (Figures 2A,B). Under the same low power level, the WALTZ-4 pulse had only a negligible decoupling effect (Figure 2C). An additional advantage of this strategy is that the major metabolite resonances are not contaminated because of the absence of lipid interference. Although, fat signals pose serious spectral interference to the alkanyl spectral regions, interference due to fat signals overlapping is not an issue in the carboxylic/amide spectral region.

The same strategy for detecting carboxylic/amide spectral region with low power random RF heteronuclear decoupling has been applied to human brain studies with clinical 3T [29, 30, 32] and 7T scanners [33]. The initial human study was performed on a GE 3T Excite clinical scanner [32]. A home-built RF coil consisting of a single circular ¹³C coil and a proton quadrature surface coil was used. RF decoupling and NOE were provided by a stand-alone proton decoupler (GE Healthcare). Healthy human subjects were recruited and consented to the ¹³C-MRS infusion studies. During the experiments, [2-¹³C]glucose solution was infused into an antecubital vein using an MR-compatible infusion pump. Blood samples were withdrawn periodically to measure and monitor blood glucose levels. FASTMAP automatic high-order shimming was used to optimize static magnetic field homogeneity [40]. In vivo ¹³C spectra were acquired using the GE product sequence (FID CSI without phase encoding) during infusion. Time course spectra of Glu, Gln, Asp, and NAA turnover from intravenously infused [2-¹³C]glucose detected in the occipital lobe are shown in Figure 3A. Glu C5 and Asp C4 were spectrally resolved. GABA C1 (182.2 ppm), NAA C4 (179.4 ppm), and NAA C1 (179.6 ppm) were also detected by summing the last 17 min of data (Figure 3B). This study also compared spectra obtained at two different stochastic decoupling power levels: 7.5 and 15 W. The spectrum acquired using 7.5 W decoupling power showed similar results to the spectrum decoupled using 15 W; both achieved good spectral separation of Gln C5 and Asp C4.

Half-volume transceiver coils and surface coils have been used in in vivo ¹³C-MRS studies for proton decoupling to keep RF power deposition within an acceptable range. However, surface coil efficiency is usually degraded under inhomogeneous B₁ fields. In addition, and as noted above, frontal lobe regions are often avoided in ¹³C studies because the required high power for proton decoupling may cause heating of the poor perfused eyes. The strategy of using [2-¹³C]glucose infusion to detect metabolites in the carboxyl/amide region requires only very low RF power for decoupling. Using this strategy, in vivo ¹³C-MRS studies were conducted in human brain using volume coil decoupling at 3T [30]. The average and local SARs were evaluated using numerical simulations under experimental conditions before the actual experiments. The experimental settings in the volume coil study were the same as in the previously described surface coil study [29]. A GE 3T Excite clinical scanner (GE Healthcare, Milwaukee, WI, USA) and home-built RF coil system were used. Spectra obtained from the occipital lobe and frontal lobe of five different healthy volunteers are shown in Figure 4. In both regions, the resonances of Glu C5 (182.0 ppm), Glu C1 (175.4 ppm), Gln C5 (178.5 ppm), Gln C1 (174.9 ppm), Asp C4 (178.3 ppm), Asp C1 (175.0 ppm), and NAA C5 (174.3 ppm) were clearly detected. The occipital lobe spectra have better spectra resolution compared with that of frontal lobe spectra. This was due to the stronger B₀ distortion caused by the nasal cavity, frontal sinus, and sphenoid sinus in the frontal lobe region.

Recently, the low RF power carboxylic/amide ¹³C-MRS technique was safely applied to the occipital lobe human brain studies at 7T on five healthy volunteers [33]. An in-house built RF coil assembly consisting of a circular ¹³C coil, a proton quadrature surface coil, and a slotted RF shield were used in this study. RF power of the ¹³C coil and in the proton channel were calibrated before actual data acquisition. In vivo ¹³C-MRS experiments were conducted on a Siemens Magneton 7T scanner during infusion of [2-¹³C]glucose. The infusion process was similar to the 3T studies. In vivo data were acquired using a modified Siemens FID sequence with low power broadband stochastic proton decoupling. The simulated B1+ field distribution is shown in Figure 1B. Based on the SAR calculation equations, the maximum local SAR per 10 g of tissue was 5.6 W/kg, and the average SAR was 0.9 W/kg. Both maximum and averaged SAR were well below the limits set by the IEC [22] and FDA [23]. Figure 5 shows the spectral results under three different conditions: (1) with neither NOE nor decoupling; (2) with NOE only; and (3) with decoupling and NOE. The signal peak amplitude of Glu C5 increased significantly when the combination of NOE and decoupling was used. Figure 6 shows the time course spectra of several metabolites detected in the occipital lobe with intravenous infusion of [2-¹³C] glucose. In addition to the spectrally resolved signals of Glu C5 and C1, Gln C5 and C1, Asp C4 and C1 at 3T, GABA C1 (182.2 ppm) was also observed in the time course spectra at 7T. Figure 7 shows the spectra obtained from four different subjects with the same experimental settings of NOE and decoupling power. Very similar spectra were observed among different subjects, demonstrating the reliability of the strategy with [2-¹³C] glucose infusion and low RF power stochastic decoupling. In general, GABA C1 and Glu C5 were clearly separated and distinguishable.

Another study also applied carboxylic/amide ¹³C-MRS to rat brain on a Bruker microimaging spectrometer interfaced to an 11.7T 89-mm bore vertical magnet [31]. Pseudo-stochastic ¹H decoupling was used with constant RF amplitude and randomly inverted phases. Because carboxylic and amide carbons are presented at the end of the carbon skeleton of a molecule, only singlets (doublets) ¹³C signals are showing from carboxylic/amide spectral regions when the neighboring carbon is ¹²C (¹³C). The carboxylic/amide spectrum is much simpler than the corresponding aliphatic carbon spectrum. Therefore, simultaneous detection of the metabolism contribution from different substrates can be easily determined in vivo from the carboxylic/amide region. Three groups of two co-infused ¹³C labeled substrates were used in this study: Group A, [¹³C₆] glucose and [2-¹³C] lactate; Group B, [¹³C₆]glucose and [1,3-¹³C₂]β- hydroxybutyrate (BHB); and Group C, [¹³C₆]glucose and [1-¹³C]acetate. Co-infusion of the different ¹³C-labeled substrates in brain demonstrated that the cerebral metabolic changes resulting from different substrates could be simultaneously measured in vivo. Figure 8 shows the accumulated in vivo ¹³C spectra of intravenous co-infusion from the three groups of ¹³C labeled substrates. [1-¹³C] acetate is the only glia-specific substrate among [¹³C₆]glucose, [2-¹³C]lactate, [1,3-¹³C₂] (BHB), and [1-¹³C] acetate. It labels Gln C5 in glial cells before transferring to neuronal Glu. As a result, the signal intensity of the Gln C5 singlet was much higher than that of the Glu C5 singlet (Figure 8C). Analysis of Glu C5, Gln C5, and Asp C4 signals quantified brain's selection of its fuels for activities and functions.

In the carboxylic/amide ¹³C-MRS studies, protons that were scalarly coupled to carboxylic/amide carbons were clustered in two separate spectral regions by the resonating frequencies from alkyl protons and amide protons: 1.91 (GABA H3)-3.9 (Asp H2) ppm and 6.83 (Gln H_z)-7.6 (Gln H_E) ppm [41]. A considerable amount of RF power is wasted in the empty spectral window between these two regions. According to Rayleigh's theorem, the total power in a signal is conserved under Fourier transform [35]. Based on this theorem, a large reduction in RF power deposition could be achieved by removing the empty spectral window spanning the 3.90–6.83 ppm region from the effective band of the stochastic decoupling sequences. To explore this possibility, Xiang and colleagues developed a windowed stochastic proton decoupling technique that multiplies a double bandpass filter to the frequency spectrum of the stochastic decoupling pulse [34]. This method skips decoupling frequency components within the empty spectral window spanning the 3.90–6.83 ppm region, thus reduced a significant amount of decoupling RF power deposition.

This technique was evaluated on rat brain at 11.7T. Ernst's pseudo-stochastic decoupling scheme was used as reference [10]. The original pseudo-stochastic decoupling sequence and the windowed version are shown in Figure 9. The double bandpass filter removes frequency components between 3.90 and 6.83 ppm. NOE was accomplished via a train of nonselective hard pulses spaced at 100 ms apart, and each with a nominal flip angle of 180°. Figure 10 compares the proton-decoupled ¹³C-MRS spectra using Ernst's pseudo-stochastic decoupling and the windowed stochastic decoupling sequence. Decoupling power was reduced by 51.4% in windowed stochastic decoupling compared to original stochastic decoupling sequence. An essentially similar spectral decoupling effect was shown with very similar metabolite linewidth. Another comparison was also made between two decoupling methods under very low decoupling power. Figure 11 shows the proton-decoupled ¹³C-MRS spectra acquired at a decoupling power that was 12.8% of that used in Figure 10. The decoupling effect was significantly degraded using Ernst's stochastic decoupling method, as the linewidths of Glu C5 and Gln C5 were broadened by 60.6% and 51.8%, respectively, compared to Figure 10. In contrast, much smaller linewidth increases were measured from the spectra using windowed stochastic decoupling with the same low decoupling power. This is because the RF power used for actual decoupling used in the windowed stochastic decoupling was much higher than that used in the original Ernst's stochastic decoupling, where almost half of the decoupling power was deposited in the empty region spanning the 3.90–6.83 ppm range. As a result, the windowed stochastic decoupling method performed much better than the original stochastic decoupling method at very low RF power deposition. The further ~50% reduction in decoupling power deposition in the windowed stochastic proton decoupling method suggests that it is possible to conduct in vivo ¹³C-MRS studies of human brain at very high magnetic field strengths.

The frequency-domain windowing method discussed above requires a particular signal distribution of protons that are scalarly coupled to the carbons. A more general method, based on time-domain under-sampling that does not rely on specific proton signal distribution was proposed by Li et al. [36]. In contrast to the crowded short-TE proton spectra of brain, typical in vivo ¹³C spectra are sparsely populated. Because sparsity of the frequency domain translates into redundant information in the time domain, a time domain under-sampling strategy was developed to further reduce the RF power deposition of proton decoupling. This new strategy used a pseudo-randomly windowed decoupling scheme in the time domain in which decoupling was only needed for randomly selected segments of data sampling. The spectra were reconstructed with an iterative algorithm using those randomly selected segments only. The random under-sampling scheme began with a fully sampled core followed by randomly sampled data segments throughout acquisition. The under-sampling rate was defined as the percentage of sampled data over the full data length.

The iterative reconstruction method began by assigning un-sampled data points s̄  (where no decoupling power is applied) with zero values:

Because of the sparsity of the spectra, a significant number of data points had zero amplitude after baseline removal. All frequency domain data points of an in vivo ¹³C spectrum can be classified into two different groups: (1) the signal group P, where all data points were from a metabolite peak; (2) the empty frequency group Z, where all data points had zero amplitude after baseline removal. Using this information, the iterative algorithm replaced the data in group Z by zero in the frequency domain after the forward Fourier transform  (F) of the under-sampled data starting from the second iteration:

The updated frequency domain data were transformed back into the time-domain by inverse Fourier transform (F-1).

An error term ε_n, defined as the absolute norm difference between the updated time domain data and the under-sampled-experimental data (30), was computed:

The iteration algorithm ended only if ε_n was smaller than a manually set threshold [a very small number (<10⁻⁶)]. Otherwise, the algorithm proceeded by replacing the time domain data in the sampled segments with experimental data and continued to the next iteration:

A maximum iteration number (>5,000) was also set to automatically end the algorithm when it failed to converge. This usually occurred when the under-sampling rate was too high.

Numerical simulations were conducted to evaluate the performance of the iterative reconstruction method compared to under-sampled data obtained with different under-sampling rates and strategies. Figure 12 shows examples of spectra reconstructed using the total random sampling pattern and coherent sampling pattern with gradually decreasing under-sampling rates. In general, spectra reconstructed using the total random sampling strategy yielded fewer residuals and fewer mean signal intensity errors compared to the coherent under-sampling strategy. Therefore, total random under-sampling strategies were used in the rest of the study. Monte Carlo simulation was used to assess the SNR from the full sampling and random under-sampling for the same total number of sampled data points (therefore, the same decoupling SAR). Monte Carlo simulations demonstrated that the SNR per unit power deposition obtained via the random under-sampling strategy was significantly higher than that obtained with full sampling (Figure 13).

The performance of the iterative algorithm was also evaluated on four sets of in vivo ¹³C human brain data acquired using a Siemens Magnetom 7T scanner [33]. A non-linear fitting algorithm developed in-house was used to generate a ¹³C baseline model from all four in vivo datasets [42]. The very low frequency baseline model was removed from all datasets before iterative reconstruction. Figure 14 shows the reconstructed spectra from all four in vivo datasets with an under-sampling rate of 30%. Visual inspection indicates only small differences between the reconstructed spectra from under-sampled data and those using the fully sampled data. Figure 15 shows the mean signal intensity error for Glu C5, Gln C5, and Asp C4 averaged from all subjects as a function of under-sampling rates. As expected, increases in the under-sampling rate led to increases in signal intensity errors. Weaker signals tended to have larger signal intensity errors.

Both simulations and in vivo experiments found that excellent spectral reconstruction could be achieved with a >30% under-sampling rate. This corresponded to reductions of 30% or more in RF power deposition from proton decoupling, which largely dominated the local and averaged SAR values. As no particular spectral distribution of proton signals is required for this strategy, therefore, it can be applied to alkanyl ¹³C-MRS as well. For other ¹³C regions where the signal peaks are contaminated by the broad lipid signal (e.g., muscle tissue), the usefulness of this method would be limited.

Because the SAR increases quadratically with field strength, it is always beneficial to use the lowest RF power deposition at high fields, especially for frontal lobe ¹³C studies of human subjects. The frequency-domain windowing method enhances decoupling power deposition by avoiding RF irradiation in the empty spectral region without using time-domain windowing. In contrast, the time-domain under-sampling method, in general, does not require particular spectral distributions of protons that are scalarly coupled to the carbons. Therefore, it is possible to combine the frequency-domain and time-domain windowing methods to further reduce RF power deposition for ¹³C-MRS at very high magnetic fields.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.