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J Magn Reson. Author manuscript; available in PMC 2013 April 1.

Published in final edited form as:

Published online 2012 February 24. doi: 10.1016/j.jmr.2012.02.008

PMCID: PMC3326401

NIHMSID: NIHMS363495

Galen D. Reed,^{a,}^{*} Peder E. Z. Larson,^{a} Cornelius von Morze,^{a} Robert Bok,^{a} Michael Lustig,^{b} Adam B. Kerr,^{c} John M. Pauly,^{c} John Kurhanewicz,^{a} and Daniel B. Vigneron^{a}

The publisher's final edited version of this article is available at J Magn Reson

See other articles in PMC that cite the published article.

A rapid echo planar imaging sequence for dynamic imaging of [1-^{13}C] lactate and [1-^{13}C] pyruvate simultaneously was developed. Frequency-based separation of these metabolites was achieved by spatial shifting in the phase-encoded direction with the appropriate choice of echo spacing. Suppression of the pyruvate-hydrate and alanine resonances is achieved through an optimized spectral-spatial RF waveform. Signal sampling efficiency as a function of pyruvate and lactate excitation angle was simulated using two site exchange models. Dynamic imaging is demonstrated in a transgenic mouse model, and phantom validations of the RF pulse frequency selectivity were performed.

Recent studies have shown the great potential of hyperpolarized ^{13}C pyruvate for the in vivo monitoring of cellular metabolism and the characterization of disease [1–11]. Dynamic nuclear polarization (DNP) of ^{13}C labeled pyruvate followed by rapid dissolution generates an injectable contrast agent with a four order-of-magnitude signal enhancement [12] enabling the measurement of the spatial distribution of pyruvate and its conversion to lactate, alanine, and bicarbonate. The conversion of pyruvate to lactate catalyzed by the enzyme lactate dehydrogenase is of particular interest, as the kinetics of this process have been shown to be sensitive to the presence and severity of disease in preclinical models [1–8, 13–15].

Acquiring hyperpolarized ^{13}C images presents numerous challenges. Typically, multiple frequency components must be imaged in a time period short compared with the spin-lattice relaxation time *T*_{1} of the label. Spatially and temporally resolved dynamic imaging of substrate conversion requires even faster acquisition speeds. The low gyromagnetic ratio of carbon-13 (≈1070 Hz/G) requires imaging gradient lobes to have roughly four times the area to achieve the same field of view and resolution compared to proton. This limits the maximum achievable velocity through k space given the peak gradient amplitude and slew rate constraints on clinical imaging systems.

Several novel techniques have been developed to rapidly acquire ^{13}C images. A small-angle band-selective excitation radio frequency (RF) pulse [16, 17] followed by a train of rapid imaging gradient pulses such as echo planar imaging (EPI) [18] or spiral readouts [19] allows for rapid imaging of single frequencies. The transmitter frequency is offset periodically for each temporal phase, and dynamic images of multiple frequency components can be acquired in an interleaved manner. Gradient echo images acquired at multiple echo times can also be used to resolve multiple frequency components via least squares inversion of the image phase [20–22]. Although the long scan time from three dimensional phase encoding typically precludes three dimensional spatially-resolved dynamic spectroscopic imaging, echo planar spectroscopic imaging (EPSI) readouts [23] and compressive sensing acquisitions [24, 25] can sufficiently increase acquisition speed to enable dynamic imaging.

In this study, we developed an echo planar imaging sequence for dynamic imaging of [1-^{13}C] lactate and [1-^{13}C] pyruvate. Frequency separation was achieved by spatial misregistration in the phase-encoded direction by the appropriate choice of echo spacing. Suppression of the pyruvate-hydrate and alanine resonances is achieved through an optimized spectral-spatial RF waveform. The signal dynamics were simulated using two site exchange models for the pyruvate-to-lactate conversion. These models highlight the benefit of applying differential flip angles to pyruvate and lactate, and optimal combination of these angles was studied along with the signal tradeoffs. Dynamic imaging was demonstrated in a transgenic mouse model, and phantom validations of the RF pulse and imaging gradient frequency selectivity were performed. Given that this method separates frequencies using the low effective bandwidth in the phase-encoded EPI direction, imaging of resonances with small frequency separations would be challenging. This is due to the fact that echoes must be spaced far apart to generate an adequate spatial shift. However, this technique is more readily applicable to imaging two compounds with large chemical shift dispersions since the phase-encoded dimension can be aliased multiple times while still generating a small image-domain shift. The only limitation is that the frequency-encoded field of view must large enough to encode the shifts in the frequency-encoded dimension.

Two noninteracting spins that are encoded by an echo-planar readout will be spatially shifted based on their difference in chemical shift. The spins have Larmor frequencies *ω*_{1} and *ω*_{2} with a chemical shift dispersion Δ*ω* = *ω*_{2} − *ω*_{1}. The signal is spatially encoded after RF excitation using an flyback EPI gradient waveform with *N _{int}* interleaves and

$$F({k}_{x},{k}_{y})={F}_{1}({k}_{x},{k}_{y}){e}^{-i\mathrm{({k}_{y})}}$$

(1)

where *F*_{1}(*k _{x}*,

$$\mathrm{\phantom{\rule{0.16667em}{0ex}}({k}_{y})=\frac{{t}_{\mathit{esp}}\mathrm{\Delta}\omega {k}_{y}}{2{N}_{\mathit{int}}\mathrm{\Delta}{k}_{y}}.}$$

(2)

Here, Δ*k _{y}* = 1/

$$f(x,y)={f}_{1}(x,y-{y}_{s})+{f}_{2}(x,y+{y}_{s}),$$

(3)

where

$${y}_{s}=\frac{\mathrm{({k}_{y})}2\pi {k}_{y}}{=}$$

(4)

We define the quantity Φ = *y _{s}*/

$${t}_{\mathit{esp}}=\frac{4\pi (\mathrm{\Phi}+{N}_{\mathit{alias}}){N}_{\mathit{int}}}{\mathrm{\Delta}\omega}.$$

(5)

If the transmitter is at the true mean frequency, then the shift of each image will be equal and in opposite directions as shown by (3). If the resonance frequency if shifted, the images will be shifted asymmetrically about the center, but their relative shift with respect to each other will be the same.

With the appropriate choice of echo spacing, we can resolve two frequencies spatially in the phase-encoded direction. With Φ = 1/4 and *FOV _{y}* set to at least twice the object’s extent in

Although the acquisition bandwidth of the frequency-encoded direction is much greater than that of the phase-encoded dimension, these shifts can be corrected for since the images of the two frequencies are not spatially overlapping. For larger echo spacings, the readout bandwidth is lowered to increase the sampling duty cycle and SNR [27], so characterization of the shift in the frequency direction is important. With the transmitter set at the mean of the two frequencies and the frequency encoding along *x*, the shift is

$$\mathrm{\Delta}x=\frac{\mathrm{\Delta}\omega {\mathit{FOV}}_{x}}{4\pi {BW}_{\mathit{read}}}$$

(6)

where *FOV _{x}* and

$${\mathit{FOV}}_{X}\ge {L}_{x}+2\mathrm{\Delta}x.$$

(7)

Provided this condition is met, the frequency-encoded shift can be accounted for by shifting the images by ±Δ*x* from (6) similar to the technique used in [28].

This simultaneous encoding method differs from scanning individual frequencies one at a time in several important respects. Since *FOV _{y}* must be twice the object’s spatial extent, the minimum number of EPI phase encodes per scan is doubled from acquiring a single frequency. The total scan time, however, is roughly constant since the minimum number of scans is halved. The number of RF excitations applied at each frequency is doubled with simultaneous acquisition suggesting an analysis of the effects of depolarization from RF saturation and cumulative signal encoded as a function of excitation angle imparted to each frequency.

The sequence implemented uses a spectral spatial RF pulse [29] to suppress the alanine and pyruvate-hydrate signal while allowing for different excitation angles imparted to pyruvate and lactate. Qualitatively, a small flip angle on pyruvate is expected to yield a larger cumulative signal on lactate since depolarization is reduced; this effect is shown empirically in [17]. To quantify the tradeoffs in applying differential flip angles to lactate and pyruvate, a simulation was developed to study the depolarization effects from RF saturation as well as the net signal encoded as a function of flip angle. The simulation was based on a two-site exchange model for pyruvate and lactate after infusion into the animal [9, 11, 13, 14]. This model is determined by *k _{PL}* which characterizes the conversion rate from pyruvate to lactate,

Let *M _{z}*

$${M}_{z}(t)=\left(\begin{array}{c}{M}_{z,P}\\ {M}_{z,L}\end{array}\right).$$

(8)

Combining with a continuous model for RF saturation and *T*_{1} decay with the chemical dynamics, the state space model can be represented as

$$\frac{d}{dt}{M}_{z}(t)={AM}_{z}(t),$$

(9)

with

$$A=\left(\begin{array}{cc}-{\rho}_{P}-{k}_{PL}+{\scriptstyle \frac{1}{TR}}(cos{\theta}_{P}-1)& {k}_{LP}\\ {k}_{PL}& -{\rho}_{L}-{k}_{LP}+{\scriptstyle \frac{1}{TR}}(cos{\theta}_{L}-1)\end{array}\right),$$

(10)

where *TR* is the repetition time. The solution to (9) is a matrix exponential that can be calculated using inverse Laplace transforms:

$$\begin{array}{l}{M}_{z}(t)={e}^{At}{M}_{z}(0)\\ ={\mathcal{L}}^{-1}{[sI-A]}^{-1}{M}_{z}(0).\end{array}$$

(11)

Here, *s* is the complex frequency variable, *I* is the 2 × 2 identity matrix, and

$${M}_{z}(0)=\left(\begin{array}{c}1\\ 0\end{array}\right)$$

(12)

The cumulative signal for pyruvate and lactate can be modeled as

$${S}_{P}=\sum _{k=1}^{{N}_{\mathit{acqs}}}sin{\theta}_{P}\xb7{M}_{z,P}(k\xb7TR)$$

(13)

$${S}_{L}=\sum _{k=1}^{{N}_{\mathit{acqs}}}sin{\theta}_{L}\xb7{M}_{z,L}(k\xb7TR).$$

(14)

The initial conditions represented by equation (12) imply that the pulse sequence begins immediately after substrate infusion, and the function describing the time dependence of the substrate delivery is ignored. This could be accounted for as in [14] but was not performed here since we are only concerned with getting an estimate of signal intensity as a function of flip angle.

The signal of the hyperpolarized pyruvate and lactate as acquired with this sequence were simulated in Mathematica (Wolfram Research, Champaign, Il, USA). The solution (11) to equation (9) and the signal intensities (14) and (13) were computed as functions of both *θ _{P}* and

Total encoded signal of pyruvate (*S*_{P} ) and lactate (*S*_{L}) given by equations (13) and (14) respectively. Simulations were computed assuming *T*_{1,}_{L} = *T*_{1,}_{P} = 25s. *S*_{L} and *S*_{P} both show maxima as functions of *θ*_{L} and *θ*_{P}, respectively (a,c). However, **...**

Since the *T*_{1,}* _{L}* and

a) the ratio of *S*_{L} calculated for a lactate flip angle of *θ*_{L} = 15° to the *S*_{L} value computed with the optimal angle for the given lactate relaxation time *T*_{1,}_{L}. The optimal flip angle is shown in b). Both plots assume *T*_{1,}_{P} = 25 s. The acquired **...**

The mean repetition time was used in simulations:

$$TR=\frac{{N}_{\mathit{int}}{TR}_{\mathit{act}}+{t}_{\mathit{delay}}}{{N}_{\mathit{int}}},$$

(15)

where *TR _{act}* is the actual repetition time used in the scan and

A spectral-spatial pulse giving a nominal excitation flip angle of 7.5° to pyruvate, 15° to lactate, and 0° to both alanine and pyruvate hydrate was designed for this sequence (Figure 4). This choice of flip angles was based on the simulation results of the cumulative lactate signal as a function of both *θ _{P}* and

This sequence was demonstrated in a single slice in the coronal plane. The phase encoding was set along the left/right dimension, and frequency was set along superior/inferior. The phase field-of-view *FOV _{y}* was set to at least twice the extent of the object. For mouse imaging, this was always possible using

Experiments were performed on a GE 3T Signa MRI system (GE Health-care, Waukesha, WI, USA). A custom dual-tuned ^{1}H/^{13}C, transmit/receive mouse coil was used for carbon and proton imaging. Prior to infusion of the hyperpolarized contrast, the transmitter attenuation was calibrated by obtaining images at multiple attenuation settings from a syringe containing 0.7 mL of 8 M ^{13}C-urea placed next to the animal. 24 uL of 99 % [1-^{13}C] pyruvate was mixed with the OX063 radical (GE Healthcare, Oslo, Norway) and polarized in an Oxford Instruments Hyperpsense polarizer (Oxford Instruments Biotools, Oxford, UK) operating at 3.35 T and 1.2 K. After approximately one hour of 94.114 GHz microwave irradiation, the sample was rapidly dissolved in 4.25 mL of a heated TRIS/NaOH solution giving a final concentration of 80 mM. A transgenic prostate tumor bearing mouse [35] was injected with 350 *μ*L of the hyperpolarized solution over 8 seconds. Imaging was started 20 seconds after the beginning of injection. A 3 second delay period is inserted between slices giving a temporal resolution of *t _{delay}* +

The pulse sequence produces the pyruvate and lactate images side by side in the left/right dimension. The image was shifted by +*FOV _{y}*/4 and multiplied by an ideal filter with width

Figure 2 shows plots summarizing the simulation results. The integrated lactate signal intensity from Figure 2a has a maximum at approximately *θ _{L}* ≈ 15° and is approximately independent of

Figures 5, ,6,6, and and77 show preliminary data acquired from infusion of hyperpolarized pyruvate into a TRAMP mouse. Figure 5 shows the coronal spin echo localizer (left) and a representative pyruvate/lactate image (right). Figure 6 shows anoverlay of the color-mapped SNR values of the hyperpolarized images. For ease of viewing, only every other dynamic repetition is displayed. Figure 7 shows the average SNR of all the pixels within two ROIs drawn around the prostate tumor and the thorax of the mouse. This figure highlights how multiband excitation with the EPI sequence generates comparable SNR for lactate and pyruvate (≈ 25 in the prostate tumor and ≈ 9 in the thorax).

Every other dynamic repetition overlaid on a coronal FSE localizer. Pyruvate and lactate SNR values represented as overlays. Concordant with prior studies in the TRAMP model, the tumor shows persistent lactate signal at the later time points.

Coronal FSE localizer on the left shows the locations of the two ROIs. The mean SNR of all the pixels within each ROI is plotted at each repetition on the right. The comparable SNR values between pyruvate and lactate in the early time points highlight **...**

Some limitations of the pulse sequence presented are discussed. Ghosting artifacts stemming from interleaving strongly degrades the images in this simultaneous encoding strategy since these artifacts appear along the same dimension in which the different frequencies are resolved. Although this effect was largely mitigated by the echo shifting strategy, some persistent ghosts were visible in early time points. This was likely due to the fact that in the early time points, the contrast is largely concentrated in the vasculature, and the echo shifting cannot fully correct the phase errors from flowing spins. Setting *t _{esp}* to a value larger than the minimum does make the sequence more susceptible to geometric distortion from

Simultaneous encoding of pyruvate and lactate using a flyback echo planar sequence is demonstrated. This method spatially resolves the two frequencies by deliberate chemical shift misregistration based on proper selection of the echo spacing. Robust performance of the pulse sequence was observed in phantom and in vivo hyperpolarized experiments. Simulations of the combined exchange, excitation, saturation, and relaxation effects of hyperpolarized compounds were implemented. These simulations show promise in determining optimum flip angle for the metabolic product as well as elucidating the tradeoff in product signal encoded versus substrate flip angle. Possible drawbacks of the pulse sequence presented as well as some interesting extensions are discussed.

- EPI sequence for simultaneous imaging of two hyperpolarized compounds was developed
- Two site exchange models were used to optimize flip angles.
- In vivo validation was performed with 13C pyruvate in a transgenic mouse.

The authors would like to thank Simon Hu, Christine Leon, Michael Ohliger, Kayvan Keshari, Subramaniam Sukumar, Douglas Kelley, Mark van Criekinge, and Bertram Koelsch for numerous helpful discussions, Hikari Yoshihara for substrate preparation, Kristen Scott for preparation of the animals used in this study, and Jim Tropp for the construction of the animal transmit/receive coil. The authors gratefully acknowledge funding from R01 EB007588, P41 EB013598, and UC Discovery Grant ITL-BIO04-10148 in conjunction with GE Healthcare. G. R. acknowledges funding from the ARCS foundation and offers particular thanks to Bruce and Betty Alberts, whose family serves as the role model for all of his scientific endeavors.

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