Daniele Mammoli^{1}, Jeremy Gordon^{1}, Adam Autry^{1}, Peder EZ Larson^{1}, Hsin-Yu Chen^{1}, Mark Van Criekinge^{1}, Lucas Carvajal^{1}, Ilwoo Park^{2}, James B Slater^{1}, Robert Bok^{1}, Jason Crane^{1}, Markus Ferrone^{3}, John Kurhanewicz^{1}, Susan Chang^{4}, and Daniel B Vigneron^{1}

We show preliminary results of
hyperpolarized [1-^{13}C]pyruvate injected in 9 patients
affected with glioma.

Raw data showed excellent SNR. Variable bolus delivery and magnitude images introduced errors in modeling the conversion of pyruvate into lactate: kinetic models were presented and compared quantitatively to address these issues.

Finally, reliable and spatially-resolved maps of *k _{PL}*
rates were obtained, which can be useful in future to assess the clinical
relevance of the method for both diagnosis and response to therapy.

Dissolution
Dynamic Nuclear Polarization (dDNP)^{[1] }is a powerful technique
enhancing nuclear polarization by up to 5 orders of magnitude and its clinical
potential is being investigated.

Pyruvate is intensively studied
for dDNP *in-vivo* applications because of its long *T _{1}*(

The goal of this
work was to develop, implement and test methods for calculating reliable *k _{PL}*
maps describing the label exchange from [1-

A GE SpinLab^{[4] }polarizer was used to enhance
the polarization of [1-^{13}C]pyruvate up to about 40% in the solid
state at cryogenic temperatures.

Experiments were
carried on a 3T MRI scanner equipped with either a 8 or 32 channels ^{13}C
RF coil for detection. The acquisition
scheme consisted of an EPI dynamic sequence^{[5]
}with: 8 slices, 2 cm thick axial slice, TR=0.13 s, TE=6.1 ms, 20 time points, 3 s
time resolution, variable in-plane resolution of 1.2x1.2 cm^{2} or 2x2
cm^{2}. Temporal magnitude images of
pyruvate, lactate and bicarbonate were acquired (figure 1).
Excellent peak SNR of 600 and 100 was
achieved for pyruvate and lactate; the SNR of
bicarbonate varied among data sets. See figure 2 for examples in a voxel.

Overall, 15 data sets were acquired on 9 glioma patients.

Consider the general model $$$\frac{\text{d}}{\text{d}t}\widehat{M}(t)=\widehat{\widehat{K}}\cdot\widehat{M}(t)+\widehat{Γ}(t)$$$, where:

$$$\widehat{\widehat{K}}=\begin{bmatrix}-R_{1}-k_{PL}-k_{PB} & k_{LP} & k_{BP} \\k_{PL} & -R_{1}-k_{LP} & 0 \\k_{PB} & 0 & -R_{1}-k_{BP} \end{bmatrix}$$$

$$$\widehat{M}(t)=\begin{bmatrix}M^{pyr}(t) \\M^{lac}(t) \\M^{bic}(t) \end{bmatrix}$$$, $$$\widehat{Γ}(t)=\begin{bmatrix}Γ(t) \\Γ(t) \cdot c_{lac}\\Γ(t) \cdot c_{bic} \end{bmatrix}$$$ and $$$Γ(t)=\alpha\cdot e^{\beta t} \cdot t^{\gamma}$$$

We tested 6 different approaches:

A) $$$Γ(t)=0$$$, $$$k_{LP}=k_{BP}=0$$$, $$$M^{pyr}(t)=M^{pyr}_{EXP}(t)$$$, $$$\widehat{M}(0)=\widehat{M}_{EXP}(0)$$$, $$$\widehat{M}(\infty)=\widehat{M}_{EXP}(\infty)$$$. Fitted parameters: $$$k_{PL}$$$, $$$k_{PB}$$$, $$$R_{1}$$$.

B) Same as A) except for having now $$$k_{LP}=k_{PL}\neq0$$$ and $$$k_{BP}=k_{PB}\neq0$$$. Fitted parameters: $$$k_{PL}$$$, $$$k_{PB}$$$, $$$R_{1}$$$.

C) Same as A) except for having now $$$k_{LP}\neq0$$$ and $$$k_{BP}\neq0$$$. Fitted parameters: $$$k_{PL}$$$, $$$k_{PB}$$$, $$$k_{LP}$$$, $$$k_{BP}$$$, $$$R_{1}$$$.

D) Same as A) except for having now $$$\widehat{M}^{T}(\infty)=\begin{bmatrix}{M}^{fit}_{\infty} & {M}^{fit}_{\infty} &{M}^{fit}_{\infty} \end{bmatrix}$$$. Fitted parameters: $$$k_{PL}$$$, $$$k_{PB}$$$, $$$R_{1}$$$, $$${M}^{fit}_{\infty} $$$.

E) Same as A) except for having now $$$\widehat{M}^{T}(\infty)=\begin{bmatrix}{M}^{fit}_{\infty} & {M}^{fit}_{\infty} &{M}^{fit}_{\infty} \end{bmatrix}$$$ and $$$\widehat{M}^{T}(0)=\begin{bmatrix}{M}^{fit}_{0} & {M}^{fit}_{0} &{M}^{fit}_{0} \end{bmatrix}$$$.

Fitted
parameters: $$$k_{PL}$$$, $$$k_{PB}$$$, $$$R_{1}$$$,
$$${M}^{fit}_{\infty} $$$, $$${M}^{fit}_{0} $$$.

F) $$$k_{LP}=k_{BP}=0$$$,
$$$\widehat{M}(0)=\widehat{M}_{EXP}(0)$$$, $$$\widehat{M}(\infty)=\widehat{M}_{EXP}(\infty)$$$.
Fitted parameters: $$$k_{PL}$$$, $$$k_{PB}$$$, $$$R_{1}$$$, $$$\alpha$$$, $$$\beta$$$, $$$\gamma$$$, $$$c_{lac}$$$, $$$c_{bic}$$$.

Custom MATLAB routines were used to
fit data to the models.

Modeling suffered from errors induced by variable bolus delivery ($$$\pm3$$$ s) and magnitude images (non-zero mean noise) and discarding
voxels with poor fitting was found to be critical to provide reliable *k _{PL}*
maps.

In this section, we describe and compare kinetic models and fitting criteria to address these issues.

First, we adopted the "error criterion": initially all voxels were
allowed to be fitted, then we discarded those with an error on the fitted *k _{PL}*
bigger than the

Then, we
compared the "error criterion" with the "SNR criterion" in which voxels with peak SNR lower than a threshold are discarded in *k _{PL}* maps. We tested model
A with 3 sets of SNR thresholds for pyruvate and lactate (figure 4): 5
and 2 (case I), 10 and 2 (case II), 5 and 5 (case III).

Finally, bias introduced by magnitude images were estimated with model A and power images^{[6]}: $$$\triangle k_{PL}^{perc}$$$=62% suggests that ignoring bias likely leads to underestimating *k _{PL}*s.

Model A, "error criterion" and power images are optima from the discussed perspectives.

Preliminary studies of hyperpolarized pyruvate injected in patients affected with glioma demonstrated the feasibility for quantifying metabolic rates in the human brain.

Comparison of kinetic models provided quantitative and spatially-resolved maps
of *k _{PL}* rates of conversion of pyruvate into lactate, which will be useful in future studies to assess the clinical importance of the
method as for diagnosis and response to treatment.

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