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NMR Biomed. Author manuscript; available in PMC 2012 October 1.

Published in final edited form as:

PMCID: PMC3169748

NIHMSID: NIHMS295491

Tao Xu,^{1} Dirk Mayer,^{2,}^{3} Meng Gu,^{2,}^{3} Yi-Fen Yen,^{4} Sonal Josan,^{2,}^{3} James Tropp,^{5} Adolf Pfefferbaum,^{3} Ralph Hurd,^{4} and Daniel Spielman^{1,}^{2,}^{}

See other articles in PMC that cite the published article.

With signal-to-noise ratio enhancements on the order of 10,000-fold, hyperpolarized MR spectroscopic imaging (MRSI) of metabolically active substrates allows the study of both the injected substrate and downstream metabolic products *in vivo*. Although hyperpolarized [1-^{13}C]-pyruvate, in particular, has been used to demonstrate metabolic activities in various animal models, robust quantitation and metabolic modeling remain important areas of investigation. Enzyme saturation effects are routinely seen with commonly used doses of hyperpolarized [1-^{13}C]-pyruvate, however most metrics proposed to date, including metabolite ratios, time-to-peak of metabolic products, or single exchange rate constant fail to capture these saturation effects. In addition, the widely used small flip-angle excitation approach does not correctly model the inflow of fresh downstream metabolites generated proximal to the target slice, which is often a significant factor *in vivo*. In this work, we developed an efficient quantitation framework employing a spiral-based dynamic spectroscopic imaging approach. The approach overcomes the aforementioned limitations and demonstrates that the *in vivo* ^{13}C labeling of lactate and alanine after a bolus injection of [1-^{13}C]-pyruvate is well approximated by saturatable kinetics, which can be mathematically modeled using a Michaelis-Menten-like formulation with the resulting estimated apparent maximal reaction velocity *V _{max}* and apparent Michaelis constant

MRSI of hyperpolarized [1-^{13}C]-pyruvate is a promising technique for mapping metabolic activities *in vivo* as demonstrated in recent animal studies [1–9]. This method uses dynamic nuclear polarization (DNP) and a rapid in-field dissolution process to produce a highly polarized metabolic contrast agent [10]. In less than one minute following bolus injection, [1-^{13}C]-pyruvate and its downstream metabolic products [1-^{13}C]-lactate, [1-^{13}C]-alanine, and [1-^{13}C]-bicarbonate can be mapped at relatively high spatial resolution, with the appearance of the ^{13}C label on the various metabolites resulting from a combination of isotopic exchange and metabolic flux [11]. Several ^{13}C NMR spectroscopic imaging techniques have proven capable of monitoring the metabolism of hyperpolarized [1-^{13}C]-pyruvate as an *in vivo* biomarker for disease diagnosis and response to therapy [1,12–18].

However, the widely used small flip-angle excitation approach in combination with a multi-site exchange model [15, 19, 20] fails to adequately account for the inflow of fresh downstream metabolites generated proximal to the target slice, often a significant factor *in vivo*. In addition, to date, most proposed metrics for such hyperpolarized ^{13}C MRS studies, including metabolite ratios, time-to-peak of metabolic products, or single exchange rate constant fail to capture the saturation effect during a single bolus injection. To address these effects, Zierhut et al. [20] recently demonstrated a non-linear relationship between *in vivo* exchange rate constants and [1-^{13}C]-pyruvate dose which was mathematically well modeled using a Michaelis-Menten-like enzyme kinetics formulation parameterized by an apparent maximal reaction velocity *V _{max}* and an apparent Michaelis constant

The primary goal of the present study is the development of a robust saturatable kinetics model focusing on the ^{13}C labeling of lactate and alanine and not differentiating the labeling mechanism (net flux or isotopic exchange) or the respective contribution of various factors including organ perfusion rate, substrate transport kinetics, enzyme activities, and the size of the unlabeled lactate and alanine pools.

In this work, we developed an efficient spiral dynamic spectroscopic imaging approach such that the saturation effects can be quantified *during a single bolus injection* [21, 22]. In particular, following an injection of hyperpolarized [1-^{13}C]-pyruvate, the pyruvate concentration is time varying due to the nature of a bolus injection. Typically, the [1-^{13}C]-pyruvate signal increases rapidly, reaches a maximum shortly after the end of injection and then decays due to T_{1} relaxation, metabolic flux, isotopic exchange, and dilution into the blood and extracellular space. By exploiting this inherently time-varying pyruvate concentration in combination with an RF excitation scheme that uses all of the available magnetization within the target slice, we can obtain independent estimates of the apparent reaction velocities of ^{13}C label in each TR interval, then the respective apparent *V _{max}* and

All measurements were performed on a clinical 3 T Signa MR scanner (GE Healthcare, Waukesha, WI) equipped with self-shielded gradients (40 mT/m, 150 mT/m/ms). A custom-built dual-tuned (^{1}H/^{13}C) quadrature rat coil (inner diameter: 80 mm, length: 90 mm), operating at 127.7 MHz and 32.1 MHz, respectively, was used for both RF excitation and signal reception. Four healthy male Wistar rats (350–390 g body weight) were anesthetized with 1–3% isoflurane in oxygen (1.5 l/min). The rats were injected in a tail vein with the 80-mM solution of ^{13}C-pyruvate that was hyperpolarized via DNP. For each experimental run, the 2–4 ml of the hyperpolarized pyruvate solution were injected via a bolus at a rate of 0.2 ml/sec.

The spectroscopic imaging experiments were designed to measure the total hyperpolarized [1-^{13}C]-pyruvate, [1-^{13}C]-lactate, and [1-^{13}C]-alanine signals within an excited slice each TR interval. The ^{13}C-bicarbonate signal was quite small in the rat kidney and thus not quantified in this study. Because about 20% of rat blood volume flows through the kidneys, the perfusion of these organs is high. Therefore, we assume the pyruvate signal at the end of each TR represents a snapshot of the newly inflowing pyruvate concentration within the slice, i.e., new hyperpolarized pyruvate completely replenishes the slice each TR interval. In addition, during each TR, a fraction of this pyruvate is metabolically converted to, or isotopically exchanged with, lactate and alanine. In contrast to pyruvate, eflux of lactate and alanine signals during each TR was assumed to be negligible. To verify the validity of these influx and eflux assumptions, a series of experiments with TR values ranging from 1.5 to 5 sec were performed and the corresponding ^{13}C-pyruvate, ^{13}C-lactate, and ^{13}C-alanine signals were recorded (see *TR selection experiment* part of *Results* section). To approximate the dynamic nature of pyruvate concentration within each TR interval, we employed the arithmetic average of pyruvate concentration at the beginning and end of each TR interval to approximate the *effective* pyruvate concentration within this TR interval.

Exploiting the fact that the pyruvate concentration is inherently time-varying following a bolus injection, independent estimation of apparent reaction velocities of lactate and alanine ^{13}C label within each TR interval can be used to plot the relationship between apparent reaction velocity of ^{13}C label and pyruvate concentration. Based on this non-linear relationship, the apparent *V _{max}* and

Dynamic imaging data were obtained using an extension of our prior fast multi-shot spiral-based MRSI acquisition and reconstruction algorithm [23] optimized for imaging of hyperpolarized [1-^{13}C]-pyruvate and its downstream metabolic products. Specifically, three clustered slice-selective pulses with variable flip angles (35.3°, 45°, 90°) [24], each followed by an interleaved spiral readout trajectory, were used to repeatedly excite a slice through rat kidneys and measure the resulting spectroscopic signals from pyruvate, lactate, and alanine with the following parameters: 5 × 5 mm^{2} nominal in-plane resolution, 10 mm slice thickness, FOV = 8 cm, TR = 5 s, TE = 5 ms, 8.6 Hz nominal spectral resolution, and 276.24 Hz spectral bandwidth. The three flip angles were chosen to achieve equal transverse magnetization for each of the three interleaves. Initial *in vivo* experiments showed significant hyperpolarized lactate, produced outside of the target slice (likely produced in the heart) flowing into the kidney slice during the imaging experiment. To minimize this undesired lactate inflow, we added a lactate-selective saturation pulse at the beginning of each TR interval. Therefore, the lactate signal we observed at the end of each TR was almost the locally generated lactate within that TR. Data were processed as described in [23] and metabolic images were calculated by peak integration in absorption mode with integration intervals of 36 Hz for pyruvate, lactate, and alanine. Figure 1 depicts the overall spectroscopic imaging pulse sequence we developed for the study, and Figure 2 shows representative *in vivo* spectroscopic imaging results.

Three-shot spiral-based pulse sequence diagram. At the beginning of each TR, the lactate-selective saturation pulse eliminates all hyperpolarized lactate signal existing within the rat body, allowing fresh hyperpolarized [1-^{13}C]-pyruvate subsequently **...**

Our proposed approach first estimates the apparent reaction velocities of lactate and alanine ^{13}C label within each TR interval, and then extracts the apparent *V _{max}* and

We first assume the backward exchange rate constant *k _{LP}* of

$$\begin{array}{l}{k}_{PL}=\frac{\widehat{L}}{P\xb7\text{TR}}\\ {k}_{LP}=\frac{\mathrm{\Delta}P}{\widehat{L}\text{TR}}\\ {k}_{LP}=\alpha \xb7{k}_{PL}\\ \widehat{L}-\mathrm{\Delta}P=L\end{array}$$

(1)

By solving these four equations with four unknowns *k _{PL}*,

$${k}_{PL}=\frac{P-\sqrt{{P}^{2}-4\alpha P\xb7L}}{2\alpha P\xb7\text{TR}}$$

(2)

In [20], the backward exchange rate of ^{13}C label, here denoted by *k _{LP}*, was assumed to be negligible as compared to the forward exchange rate of

Ignoring the backward reaction of ^{13}C label, i.e., *α* → 0, the apparent reaction velocity of lactate ^{13}C label *V _{PL}* which is estimated as the product of the effective pyruvate

$${V}_{PL}={k}_{PL}\xb7P=\frac{L}{\text{TR}}$$

(3)

Repeating the aforementioned calculation for each of *N* TR intervals yields
${V}_{PL}^{i}$ and *P ^{i}* (

$${V}_{PL}^{i}={V}_{\mathit{max}}\frac{{P}^{i}}{{P}^{i}+{K}_{M}}\phantom{\rule{0.38889em}{0ex}}\phantom{\rule{0.38889em}{0ex}}\phantom{\rule{0.38889em}{0ex}}i=1,2\dots N$$

(4)

where *V _{max}* is the apparent maximal reaction velocity of lactate

For our experiments, we included an external 8-M ^{13}C-enriched urea phantom to quantify the *in vivo* metabolite concentrations. To obtain absolute quantitation, both percentage polarization and T_{1} relaxation must be taken into account. The basic idea is to use the proportionality between the readout signal and the *in vivo* concentration as shown below:

$$\begin{array}{l}{S}_{P}=\beta \xb7{\text{pol}}_{P}(\%)\xb7P\\ {S}_{U}=\beta \xb7{\text{pol}}_{U}(\%)\xb7U\end{array}$$

(5)

where *S _{P}* and

Metabolite signal intensity *S _{P}* and urea phantom signal

(a) The target slice is positioned through the center of the right kidney. (b) A Region of Interest (ROI) from the right kidney is selected. The ROI is carefully chosen to avoid major renal blood vessels. (c) The metabolite signal from the ROI within **...**

Pyruvate percentage polarization at dissolution
${\text{pol}}_{P}^{\text{diss}}(\%)$ is estimated from the solid-state polarization value and the amount of the pyruvic acid (PA) placed in the polarizer. Starting from
${\text{pol}}_{P}^{\text{diss}}(\%)$ after dissolution, the pyruvate percentage polarization pol* _{P}* (%) first experiences an

The relationship between the pyruvate percentage polarization at dissolution
${\text{pol}}_{P}^{\text{diss}}(\%)$ and the pyruvate acid amount is determined for several samples of polarized and dissolved PA mix using the ratio of the polarized signal to its thermal equilibrium signal. Then, the relationship is extrapolated back to the time of dissolution using an estimate of pyruvate T_{1} and correlated with the solid state signal level. The empirical formula for the pyruvate percentage polarization at dissolution in our experiment setup is found to be

$${\text{pol}}_{P}^{\text{diss}}(\%)=\frac{\text{SS}}{4.17\times \text{PA}}$$

(6)

where SS is the solid state polarization value (A.U.), PA is the amount (umol) of the pyruvic acid placed in the polarizer and 4.17 is the regressed constant multiplier determined from our measurements.

Urea percentage polarization pol* _{U}* (%) was estimated from the thermal polarization definition as shown below:

$${\text{pol}}_{U}(\%)=\frac{1-exp(-h\nu /\text{KT})}{1+exp(-h\nu /\text{KT})}$$

(7)

where *h* is the Plank constant, *ν* is the urea resonant frequency (approximately 32.1 MHZ at 3T), K is the Boltzmann constant, T is the absolute temperature of urea.

After estimating pyruvate signal *S _{P}*, urea signal

To verify the selected pulse sequence and metabolic modeling equations, a series of *in vivo* experiments were conducted on normal adult male Wistar rats. Specifically, dynamic spectroscopic imaging data were acquired from a 10-mm thick slice through the center of the right kidney as shown in Figure 3. Pyruvate, lactate, and alanine peak integrals were computed from Region of Interests (ROIs) in the right kidney, carefully chosen to avoid major renal blood vessels. Pyruvate signal was typically 10 times larger than lactate and alanine as shown in Figure 3(c).

The selection of TR is critical for these experiments. An overly short TR does not allow appreciable accumulation of ^{13}C label on the downstream products of lactate and alanine and also invalidates the assumed complete replenishment of hyperpolarized [1-^{13}C]-pyruvate between measurements. In contrast, a too long TR would result in undesirable T_{1} decay for hyperpolarized metabolite signals and invalidate the assumption that products come from the imaging slice.

Figure 4 shows the measured metabolite signals from the same ROI in a rat kidney acquired with different TR values (5 sec, 3 sec, and 1.5 sec respectively). Figure 4(a) indicates that pyruvate signal is largely unchanged when TR value changes from 5 sec to 3 sec while lactate and alanine signals decrease in proportion to the TR reduction. When TR is reduced to 1.5 sec, the assumption of the complete replenishment of the fresh hyperpolarized [1-^{13}C]-pyruvate between measurements breaks down (as shown by decreased pyruvate signal) and lactate and alanine signals decrease further. Hence, for subsequent studies, we chose 5 sec as a reasonable compromise among lactate and alanine ^{13}C labeling process, the pyruvate replenishment, and T_{1} decay.

To assess the validity of ignoring the backward exchange rate, we performed a series of simulations and quantified the change of the estimated apparent *V _{max}* and

In particular, focusing on the flow of the ^{13}C-labeled fraction in organs with large preexisting lactate pools, ^{12}C lactate backward reaction dominates the backward reaction so little ^{13}C lactate label will go back. The worst case is where there is no or low preexisting unlabeled lactate pool. Our simulation results showed the numerical effect of ignoring the backward exchange rate of ^{13}C-labeled lactate on the estimated parameters in the worst case (i.e, no preexisting lactate pool) is small. As shown in Figure 5, *V _{max}* is insensitive to the inclusion of the backward reaction. Even if

Using the pulse sequence, mathematical modeling, and absolute quantitation procedures described in *Methods*, experimental results demonstrate that a Michaelis-Menten-like formulation for saturatable enzyme kinetics provides a good model for fitting the observed relationship between the reaction velocities and the effective pyruvate concentration as shown in Figure 6. Table 1 shows that the regression results of apparent *V _{max}* and

Representative saturatable kinetics between reaction velocities of ^{13}C label and effective pyruvate concentration and the best-fit curves. The relationship can be mathematically approximated as shown in Equation 4. Although the saturatable model has similar **...**

We also repeated our experiments on four rats to study the intra- and inter-subject variability of the estimated apparent *V _{max}* and

Intra- and inter-subject variability of the estimated apparent *V*_{max} and *K*_{M} parameters. For the intra-subject variability study, we repeated the 80 mM pyruvate injections three times (2.3 ml, 2.7 ml, and 2.7 ml respectively) with a single rat. The different **...**

One attractive feature of this mathematical formulation is the estimated apparent *V _{max}* and

The saturatable kinetics between reaction velocities of ^{13}C label and effective pyruvate concentrations with different 80-mM pyruvate dosages (2 ml, 3 ml, and 4 ml respectively) for (a) pyruvate to lactate and (b) pyruvate to alanine. The dashed curve **...**

*In vivo* results clearly demonstrate the proposed dynamic spectroscopic imaging approach overcomes limitations of widely used small flip-angle approaches. The described technique explicitly exploits the inflow of fresh hyperpolarized [1-^{13}C]-pyruvate, suppresses undesired contributions from [1-^{13}C]-lactate generated proximal to the target slice, and estimates the apparent *V _{max}* and

The estimated apparent *V _{max}* and

For the rat kidney, a well perfused organ, we exploited the rapid inflow of fresh hyperpolarized [1-^{13}C]-pyruvate during each TR interval. The validity of this high inflow assumption and subsequent rapid metabolic conversion and isotopic exchange depends on the key physiological parameters such as the organ perfusion rate, substrate transport kinetics, enzyme activities, and pool sizes of unlabeled substrates. For other organs and tissues, as well as substrates other than pyruvate, such modeling assumptions will need to be verified and modified where appropriate. In particular, a set of acquisitions with varying TR intervals, as depicted in Figure 4, would likely be required to choose the optimum acquisition parameters. In future work, we will extend our current single-slice approach to the multi-slice version to provide volumetric apparent *V _{max}* and

We gratefully acknowledge support from NIH grants RR-09784, EB-009070, AA005965, AA018681, and AA013521-INIA, the Lucas foundation, and General Electric Healthcare.

- MRSI
- Magnetic Resonance Spectroscopic Imaging
- DNP
- Dynamic Nuclear Polarization
- ROI
- Region of Interest
- PA
- Pyruvic Acid
- A.U
- Arbitrary Unit

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