Inhomogeneity-free Heteronuclear iMQC

Abstract

Intermolecular dipolar interactions between proton and carbon spins can be used to indirectly detect carbon spectra with high sensitivity. In this communication, we present a modified sequence that, in addition to the high sensitivity of heteronuclear intermolecular multiple quantum coherence (iMQC) experiments, retains the line narrowing capability characteristic of homonuclear zero quantum coherences. We demonstrate that this sequence can be used to obtain high resolution ¹³C spectra in the presence of magnetic field inhomogeneities, both for thermal and hyperpolarized samples, and discuss applications to water-hyperpolarized carbon imaging.

Introduction

Intermolecular multiple quantum coherences (iMQCs) have been used for the past 20 years to obtain high resolution spectra in the presence of magnetic field inhomogeneities (1–4), and to enhance contrast in MR imaging experiments (5,6). Coherences between all spins are excited at the same time as the standard NMR signal. In the standard NMR framework, these coherences are typically ignored, since they do not give rise to any observable signal. However, in CRAZED-like experiments (Figure 1a), where the longitudinal magnetization is modulated to produce an effective non-zero dipolar field, these coherences give rise to a signal which is typically 10–50% of the standard NMR signal and therefore cannot be ignored (7). Among all coherences, intermolecular zero-quantum coherences (iZQCs) are intrinsically insensitive to inhomogeneous broadening, but combinations of other types of iMQCs can be made to have this same insensitivity (8–10).

Figure 1.

(a) CRAZED sequence used to detect the signal from intermolecular multiple quantum coherences. The ratio of the area between the second and the first pulsed field gradient designates the selected coherence. For ¹³C-¹H iDQCs, the ratio G₂/G₁ must be set to ± 5/4, while for ¹³C-¹H iZQCs, it needs to be set to ± 3/4.

(b) Modified CRAZED sequence for the detection of inhomogeneity-free heteronuclear iMQCs. The sequence allows evolution of both iDQC and iZQC coherences during the first evolution time t₁=t′+t″+t‴. During t₁, the iDQCs are transformed into iZQCs by a selective inversion of the ¹H spins. A second selective inversion pulse on the ¹H spins transforms iZQCs back into iDQCs. A mixing pulse on both the ¹³C and ¹H spins transform the iDQCs into iSQCs, which is then refocused as ¹H signal by the long-range dipolar field created by the modulated ¹³C longitudinal magnetization.

One intriguing potential application of iMQCs is in improving imaging with hyperpolarized reagents, specifically hyperpolarized carbon. Many different research groups have been examining potential uses of such hyperpolarized molecules both in vivo and in vitro (11–14). The DNP methodology, in particular, is very versatile, and hundreds of different molecules have been polarized. One limitation of virtually all in vivo work has been “incoherent imaging” (localized magnetic resonance spectroscopy after one pulse), which is dominated by T₂^* effects. For example, pyruvate and lactate in the TRAMP mouse prostate cancer model were reported as having a ≈25 Hz linewidth (15). Recent work with smaller voxels shows that proton decoupling narrows lactate linewidths slightly in vivo (10.9 Hz verses 11.8 Hz) (16), but the pixel-to-pixel standard deviation of the lactate and pyruvate linewidths (4.9 Hz and 5.8 Hz respectively) clearly reflect a strong inhomogeneous component.

Can the intrinsic iZQC compensation of inhomogeneous broadening be used to overcome this problem? Without hyperpolarization, low γ nuclei give very weak iMQC signals. The initial growth rate of iDQCs or iZQCs is proportional to γM_o², and M_o itself is proportional to γ², leading to a net γ⁵ dependence of the signal strength. In fact, the first carbon-carbon iMQCs have only recently been reported by groups using hyperpolarization (17). Heteronuclear iMQCs are a different story. The scaling relationship is much more favorable, and reference (9) shows that heteronuclear zero and double quantum coherences between ¹H and ¹³C can be observed. For these experiments, the CRAZED sequence is slightly modified to take into account the difference in the gyromagnetic ratio between ¹H and ¹³C (for example, since a ¹H-¹³C iZQC evolves at 3/4 the proton resonance frequency, it would be refocused by a 4:3 gradient ratio if ultimately detected as proton magnetization). Unfortunately, for this same reason, heteronuclear ¹³C-¹H iZQCs lead to resonance frequency lines that are only 25% narrower than those obtainable with ¹H, but three times broader than those obtainable in ¹³C homonuclear iZQC experiments.

In order to narrow the resonance frequency lines in the heteronuclear iZQC experiment without incurring in sensitivity loss, we apply a modified version of the CRAZED sequence that accommodates ad hoc both double and zero quantum evolutions. This sequence, shown in figure 1.b, resembles the heteronuclear iDQC (sequence in figure 1.a with G₂/G₁=5/4), with the exception of the addition of two selective inversion pulses during the iDQC evolution. These pulses are used to invert the proton magnetization in order to transform iDQC (I+S+) coherences into iZQC coherences (I−S+). With this transformation, this sequence can be made inhomogeneity free for the X-¹H correlations if the iDQC evolution is carefully compensated by the iZQC evolution. This compensation can be achieved by keeping the t‴ delay constant (Δt‴ = 0) and stepping the t′ and t″ delays so that:

$$({\gamma }_X+{\gamma }_H)\mathrm{\Delta }{t}_1^{\prime }+({\gamma }_X-{\gamma }_H)\mathrm{\Delta }{t}_1^{″}=0,$$

which means by using a

$$\mathrm{\Delta }{t}_1^{″}=\frac{({\gamma }_X+{\gamma }_H)}{({\gamma }_H-{\gamma }_X)}\mathrm{\Delta }{t}^{\prime },$$ (1)

with $\frac{1}{{SW}_{F1}}=\mathrm{\Delta }{t}_1=\mathrm{\Delta }{t}_1^{\prime }+\mathrm{\Delta }{t}_1^{″}.$

When this is accomplished, the apparent resonance frequency for the X-¹H correlation will be given by

$$\begin{array}{l}\frac{({\mathrm{\Omega }}_X+{\mathrm{\Omega }}_H)\mathrm{\Delta }{t}_1^{\prime }+({\mathrm{\Omega }}_X-{\mathrm{\Omega }}_H)\mathrm{\Delta }{t}_1^{″}}{\mathrm{\Delta }{t}^{\prime }+\mathrm{\Delta }{t}_1^{″}}=\frac{({\mathrm{\Omega }}_X+{\mathrm{\Omega }}_H)\mathrm{\Delta }{t}_1^{\prime }+({\mathrm{\Omega }}_X-{\mathrm{\Omega }}_H)\frac{({\gamma }_H+{\gamma }_H)}{({\gamma }_H-{\gamma }_X)}\mathrm{\Delta }{t}_1^{\prime }}{\mathrm{\Delta }{t}^{\prime }+\frac{({\gamma }_X+{\gamma }_H)}{({\gamma }_H-{\gamma }_X)}\mathrm{\Delta }{t}^{\prime }}\\ =\frac{({\mathrm{\Omega }}_X+{\mathrm{\Omega }}_H)({\gamma }_H-{\gamma }_X)\mathrm{\Delta }{t}_1^{\prime }+({\mathrm{\Omega }}_X-{\mathrm{\Omega }}_H)({\gamma }_X+{\gamma }_H)\mathrm{\Delta }{t}_1^{\prime }}{({\gamma }_H-{\gamma }_X)\mathrm{\Delta }{t}^{\prime }+({\gamma }_X+{\gamma }_H)\mathrm{\Delta }{t}^{\prime }}={\mathrm{\Omega }}_X-\frac{{\gamma }_X}{{\gamma }_H}{\mathrm{\Omega }}_H\end{array}$$ (2)

while the echo will be refocused at a time

$$\mathrm{\Delta }=\frac{{\gamma }_X+{\gamma }_H}{{\gamma }_H}(t_1^{\prime }+t_1^{‴})+\frac{{\gamma }_X-{\gamma }_H}{{\gamma }_H}{t}_1^{″}$$ (3)

after the mixing pulse.

If the X nucleus is a ¹³C nucleus, since the frequency of the ¹³C-¹H iDQC is −5/3 higher than that of the ¹³C-¹H iZQC, the t₁′ and t₁″ delays need to be stepped so that

$$\mathrm{\Delta }{t}_1^{″}=\frac{5}{3}\mathrm{\Delta }{t}_1^{\prime }.$$ (4)

The apparent evolution frequency will then be:

$$\frac{({\mathrm{\Omega }}_C+{\mathrm{\Omega }}_H)3\mathrm{\Delta }{t}_1^{\prime }+({\mathrm{\Omega }}_C-{\mathrm{\Omega }}_H)5\mathrm{\Delta }{t}_1^{\prime }}{3\mathrm{\Delta }{t}^{\prime }+5\mathrm{\Delta }{t}^{\prime }}={\mathrm{\Omega }}_C-\frac{{\mathrm{\Omega }}_H}{4}$$ (5)

and the signal will be refocused at a time

$$\mathrm{\Delta }=\frac{5}{4}(t_1^{\prime }+t_1^{‴})-\frac{3}{4}{t}_1^{″}$$ (6)

after the mixing pulse.

This means that, in the presence of one proton species, the indirectly detected spectrum will be equivalent to the ¹³C spectrum, shifted by −1/4 of the proton resonance frequency offset Ω_H. In other words, the carbon resonance frequency offset, as well as its inhomogeneous resonance frequency spreading is renormalized by the proton resonance frequency offset rescaled by the gyromagnetic ratio between the carbon and proton nuclei.

Results and Discussion

For all experiments we use a 7T small animal magnetic resonance tomograph with a 210 mm inner bore diameter, interfaced to a Bruker Biospec console (Bruker BioSpin MRI GmbH, Ettlingen, Germany). The system is equipped with a gradient coil system (maximum gradient strength 42Gauss/cm) and a dual ¹H/¹³C transmitter-receive coil with a 72mm inner diameter.

A 2D spectrum is then acquired from a sample of 1M ¹³C enriched urea dissolved in water. This spectrum is acquired with the sequence in figure 1.b, with a number of averages NA=80, a repetition time (TR) of 15s and a spectral bandwidth along the directly detected dimension F2 of SW_F2=1602Hz. The first excitation pulse and the mixing pulse is set on both ¹³C and ¹H channels to a 90° Hermite pulses, with a duration of 900μs, while a 1.9ms Hermite pulse is used to refocus both ¹³C and ¹H spins during the t₂ delay. A 3.5ms hyperbolic secant pulse is used only on the ¹H channel to invert ¹H spins during the t₁ delay. The t′₁, t″₁, t₁‴ and ξ delays are set to 10.25, 17, 1.15 and 60 ms, respectively. The t′₁ and t″₁ delays are then incremented 64 times (NR=64) such that $\mathrm{\Delta }{t}_1^{\prime }=937.5\mu s,\mathrm{\Delta }{t}_1^{″}=1562.5\mu s$, according to equation (4), leading to an indirect spectral bandwidth of $S{W}_{F1}=\frac{1}{\mathrm{\Delta }{t}_1}=\frac{1}{\mathrm{\Delta }{t}_1^{\prime }+\mathrm{\Delta }{t}_1^{″}}=\frac{1}{2500\mu s}=400Hz$. The water resonance frequency offset is then set at +400Hz, while the carbon offset is set at +200Hz.

We also acquire a ¹³C-¹H iZQC spectrum on the same sample with the sequence in figure 1.a, with G₂/G₁= − ¾, t₁=28.4ms and Δt₁ = 2500μs. All other parameters are the same as for the previous experiment except for the resonance frequency offset, which in this case is set at 400Hz for the proton and at 300Hz for the carbon. In both experiments, the magnetic field is intentionally de-shimmed to produce a linewidth of about 200Hz on the ¹H spectrum and 50Hz on the ¹³C spectrum (Figure 2.c).

Figure 2.

Experimental demonstration of inhomogeneity-free heteronuclear ¹³C-¹H iMQCs on the urea deshimmed sample. (a) Spectrum acquired with the sequence in figure 1.b (b) Projection along the indirectly detected dimension F1. (c) Standard 1D ¹³C and ¹H spectrum of the urea de-shimmed sample. (d) 2D ¹³C-¹H iZQC spectrum acquired with the pulse sequence in figure 1.a with G₂/G₁= − ¾. (e) Projection of (d) along the indirectly detected dimension F1. (f) Comparison between the standard 1D ¹³C spectrum and the inhomogeneity-free ¹³C-¹H iMQC spectrum.

The spectrum acquired with the modified sequence is shown in Figure 2.a, while the spectrum acquired with the ¹³C-¹H iZQC sequence is shown in Figure 2.d. As expected, the ¹³C-¹H correlation appears at $(F1,F2)={\left({\mathrm{\Omega }}_C-\frac{{\mathrm{\Omega }}_H}{4},{\mathrm{\Omega }}_H\right)}_{\begin{array}{l}{\mathrm{\Omega }}_C=200Hz\\ {\mathrm{\Omega }}_C=400Hz,\end{array}}=(100Hz,400Hz)$ as expected from equation (2), while for the iZQC sequence the peak appears at $(F1,F2)={\left({\mathrm{\Omega }}_C-{\mathrm{\Omega }}_H,{\mathrm{\Omega }}_H\right)}_{\begin{array}{l}{\mathrm{\Omega }}_C=300Hz\\ {\mathrm{\Omega }}_H=400Hz,\end{array}}=(-100Hz,400Hz)$. A clear line narrowing can be observed between the indirectly detected spectrum of the modified sequence (Figure 2.b) and the standard 1D ¹³C spectrum (Figure 2.f) and the ¹³C-¹H CRAZED iZQC spectrum (Figure 2.e). While the ¹³C-¹H iZQC resonance frequency line is much broader than the standard 1D ¹³C resonance frequency line (~75Hz), the ¹³C-¹H line for the modified sequence appears much narrower than both (~ 20Hz). In this case the spreading of the ¹³C resonance frequency is somewhat reduced by subtracting a “renormalized” spreading of the nearby proton spins.

Of course, when high resolution two-dimensional spectroscopy is possible, there are other methods to use iMQCs to effectively remove the inhomogeneous broadening, such as the IDEAL sequence (9). While 2-D spectroscopy with hyperpolarization has been demonstrated (18), the technique generally relies on uniform resonance frequencies within the sample region, and is thus challenging to extend to imaging.

Aside from 2-D spectroscopy, there is real value in cleaning up the homogeneity of points of the hyperpolarized compounds FID where large signals are expected from the scalar coupling, thereby differentiating nominally similar species. In this spirit, we use the same sequence to collect the echo from a 10mM hyperpolarized pyruvate sample. For this experiment, the sample is hyperpolarized using the Hypersense Hyperpolarizer from Oxford Instruments. The sample, dissolved in 4.5mL of DI water with 25mM EDTA, is polarized for 4 hours at a microwave frequency of 94.105 GHz. Just after polarization, the sample is inserted in a 7T small animal imager with a Bruker console. In this case, the delays are set at t′=13ms, t″=20ms, and t‴=3ms, while the time delay ξ between the mixing pulse and the last 180 refocusing pulse is kept constant at 75ms. The same experiment is run twice, with and without the selective refocusing pulse on the proton spins (Figure 3. a–b). The different time at which these two signals refocused confirms the different coherence pathways traveled by the spins. Unlike in the iDQC CRAZED sequence, where the signal evolves at 5/4 of the ¹H resonance frequency, in the modified sequence the signal evolves during t″ at −3/4 of the ¹H resonance frequency. This leads to a different refocusing time, which is given by (5/4− (−3/4)*t″ = 40ms, as observed in our case (Figure 3. c–d). The same experiments are run again 5 minutes after dissolution, after the spin system has reached thermal equilibrium (Figure 3. e–f). In this case, almost no signal is observed for both sequences, as expected. This is because the loss of the ¹³C polarization, for this very low concentration solution, leads to a longer dipolar demagnetization time on the order of several seconds (17), which inherently diminishes the observable signal.

Figure 3.

Comparison between the signal acquired with the ¹³C-¹H iDQC sequence and the signal acquired with the modified sequence for the pyruvate sample under DNP-enhanced and normal thermal polarization conditions. The ¹³C-¹H iDQC sequence (a) and the modified sequence (b) have the same iMQC evolution time t₁=t′+t″+t‴ and the same delay ξ between the mixing pulse and the 180 refocusing pulse. Unlike in (a), the sequence in (b) presents two extra inversion pulses on the ¹H that are used to transform iDQCs into iZQCs and vice-versa. (c) Signal acquired with the sequence in figure (a) which refocuses at $\xi -\mathrm{\Delta }=\xi -\frac{5}{4}(t^{\prime }+t^{\prime \prime }+t^{\prime \prime \prime })=30ms$ after the last refocusing pulse. (d) Signal acquired with the sequence in figure (b) which refocuses at $\xi -\mathrm{\Delta }=\xi -\left(\frac{5}{4}(t^{\prime }+t^{\prime \prime \prime })-\frac{3}{4}{t}^{\prime \prime }\right)=70ms$ after the last refocusing pulse. A difference in the refocusing time of 40ms is noticeable. (e) and (f) are analogous to (c) and (d), but recorded after the sample’s magnetization has returned to equilibrium.

Conclusions

We have introduced a modified version of the heteronuclear CRAZED sequence that can be used to indirectly detect inhomogeneity-free spectra from low γ nuclei. We have demonstrated this technique in both thermally polarized samples and in hyperpolarized reagents. Although in the case of hyperpolarized reagents, the sequence needs to be modified to allow the acquisition of an entire 2D spectrum in a single shot, as in (19), our results suggest applications to improving specificity in the detection of hyperpolarized reagents at long echo times, in intrinsically inhomogeneous environments, such as those encountered in standard proton imaging.