1.1 Introduction

[2-¹³C]Pyruvate (Pyr) is an attractive choice for hyperpolarized imaging with first human studies reported recently¹. The ¹³C label at the C₂ position is both converted to [2-¹³C]Lactate (Lac) and observable from the tricarboxylic acid (TCA) cycle intermediates citrate, glutamate and acetylcarnitine, thus providing a simultaneous real-time window into glycolysis (GLY) and oxidative phosphorylation (OXPHOS)^2,3. However, imaging [2-¹³C]Lac is challenging due to blurring and ghosting artifacts arising from J-coupling between the ¹³C₂ and the ¹H nuclei. We present two techniques based on the idea of quadrature detection to resolve these artifacts. The key contribution of this work is the use of product operator formalism to derive the evolution of coherences in the presence of J-coupling as well as chemical shift to show that the combination of in-phase and anti-phase doublets resolves the peak-splitting during image acquisition. Results from simulations, phantoms and rat brain highlight the utility of this method for simultaneous assessment of GLY and OXPHOS in vivo. While these techniques are presented in the context of hyperpolarized ¹³C metabolic imaging, they are generally applicable to any spin-1/2 J-coupled spin system. Details can be found in this publication⁴.

1.2 Theory

Quadrature imaging
When imaging compounds such as [2-¹³C]Lac, J-coupling between the labeled carbon and attached proton causes a cosine modulation of k-space samples given by $$$S^{'}[k_x(t),k_y(t)]=cos⁡(πJt+φ)S[k_x(t),k_y (t)] $$$ (Fig. 1). Measuring the quadrature component via a second acquisition delayed by 1/2J can compensate for this modulation, resulting in an artifact-free image with complex combination of the two acquisitions:
$$I_{rec} (x,y)=I(x,y)*IFT(cos⁡(πJt+φ))+iI(x,y)*IFT({cos⁡(πJ(t+\frac{1}{2J})+φ) })\qquad$$
$$ =I(x,y)*IFT(cos⁡(πJt+φ))+iI(x,y)*IFT({({sin⁡(πJt+φ)})}\space\space\space$$
$$=I(x,y-Y)e^{iφ }\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\space\space\space\space [1]$$
where φ represents the phase accumulation due to the delay between excitation and data acquisition. Y is an easily corrected spatial shift given by $$$k_y Y=\frac{J.T_{readout}}{2}$$$.
Narrowband excitation
For a spin-1/2 J-coupled system ($$$\hat{I}$$$≡¹³C and $$$\hat{S}$$$≡¹H), a sufficiently narrow spectrally selective excitation pulse applied at off-resonance frequency $$$Ω_I=πJ$$$ generates the following coherences at the end of the radiofrequency pulse:
$$ \hat{σ}_{RF}=(\frac{1}{2})\hat{I}_z-(\frac{1}{2}) 2\hat{I}_z\hat{S}_z+(\frac{1}{2})\hat{I}_y+(\frac{1}{2})2\hat{I}_y\hat{S}_z\qquad\qquad\qquad [2]$$
During readout, the sum of in-phase doublet from the $$$\hat{I}_y$$$ term and anti-phase doublet from $$$2\hat{I}_y\hat{S}_z$$$ produces a singlet, eliminating all J-coupling associated artifacts (Fig. 2).

1.3 Methods

Simulation & in vitro experiments: A full-density matrix simulator for a coupled 2-spin I-S system in MATLAB (Mathworks Inc.) developed in-house was used to simulate the evolution of coherences. A syringe filled with 10ml of 0.5M [2-¹³C]Lac (or 3ml of 2.5M ¹³C Formate), doped with a Gadolinium agent, was placed in a ¹³C transmit-receive surface coil and imaged using a clinical 3T PET-MR scanner (GE Medical systems). For quadrature imaging, two images whose echo times differed by 1/2J=3.6 ms (J=140Hz for [2-¹³C]Lac) were acquired using a slice-selective fast echo-planar imaging sequence (gradient echo EPI,FOV=128mm,slice-thickness=20mm,TR=130ms,TE=22.8ms,FA=80⁰,matrix=32x32,receiver BW=41.7kHz,NEX=150). A narrowband spectrally selective radiofrequency excitation pulse (BW=100Hz,slice-thickness=20mm,70Hz off-resonance), followed by a 2D GRE-EPI image acquisition (FOV=128mm,TR=130ms,TE=22.8ms,FA=80⁰,matrix=32x32,receiver BW=41.7kHz,NEX=150) , was used to test the narrowband technique.
Hyperpolarization and in vivo imaging of [2-¹³C]Lac: 54ml of 15.5M [2-¹³C]Pyruvic acid mixed with 15mM trityl radical was polarized between 3-4 hours in GE SPINLab system and dissolved using 16g solution of 40mM tris buffer,100mg/L EDTA, and 50mM NaCl. After neutralizing with 640ul of 125mM NaOH buffer, 2.5ml of the resulting 100mM pyruvate solution was injected at a rate of 0.25mL/s into a male Wistar rat through a tail-vein catheter and imaged in a clinical GE 3T scanner 20s post injection to maximize the signal from lactate. A narrowband radiofrequency(RF) pulse centered on one of the lactate peaks followed by an EPI readout, with the same parameters as for the phantom, was used to acquire the [2-¹³C]Lac image from an axial slice through the rat-brain and overlaid on a T₁-weighted proton image for anatomical reference.
Reconstruction and post-processing: An empirical scale factor, A_corr, to compensate for the T₁ and flip angle related losses, and a relative phase factor ϕ_corr to counter the phase accumulation arising from off-resonance effects (offres) were introduced in Eq. [1], i.e., I_rec (x,y)=I₁ (x,y)+iA_corrI₂ (x,y) e^iϕ_corr. The resulting image was shifted by $$$(\frac{J}{2}+offres )*T_{readout}$$$ pixels in the slower k-space acquisition direction to offset the shift arising from the quadrature reconstruction. In the case of narrowband acquisition, the native scanner EPI reconstruction was used without any further processing.

1.4 Results

Quadrature Imaging (Fig. 3): EPI acquisitions from thermally polarized and hyperpolarized phantoms show the severity of J-modulation artifacts, which are resolved via the complex combination of two acquisitions, one delayed by 1/2J.
Narrowband Imaging: Analytically derived and simulated coherences during broadband and narrowband RF excitations are shown in Fig. 4. Data from simulations, [2-¹³C]Lac and ¹³C-formate phantoms (Fig. 4), and an in vivo [2-¹³C]Pyr rat brain study (Fig. 5), demonstrate the effectiveness of the narrowband excitation approach.

1.5 Discussion and Conclusions

The two-shot and single-shot imaging strategies described here utilize the same underlying principle of combining in-phase and quadrature components to recover the signal free of J-coupling artifacts. The two-shot method sequentially acquires the sine and cosine components, whereas the single-shot technique based on use of highly selective RF pulse simultaneously generates in-phase (cosine) and anti-phase (sine) coherences that combine to produce a singlet during imaging. Simulations, in vitro, and in vivo results demonstrate the potential utility of these methods for imaging of [2-¹³C]Lac in a hyperpolarized [2-¹³C]Pyr experiment.

Acknowledgements

The Lucas Foundation, NIH grants R01EB019018, R01CA176836, P41 EB015891.