Kinetic modelling of hyperpolarized13C-pyruvate metabolism in Canines using a model-based input function

Nikolaos Dikaios^{1}, Shonit Punwani^{1}, Henrik Gutte^{2}, Majbrit ME Larsen^{3}, Annemarie T Kristensen^{3}, Andreas Kjær^{2}, David Atkinson^{4}, and Adam E Hansen^{2}

Hyperpolarized
^{13}C-pyruvate MRS imaging provides metabolic information within very
short time, including relaxation ratios and enzymatically driven conversion to
pyruvate metabolites. Recently developed acquisitions substantially improved
the temporal resolution allowing for kinetic modelling. To model the chemical
exchanges a semi-classical description with the modified Bloch-McConnell
equations is used.

$$\frac{\text{d}P}{\text{d}t}=-k_{P\rightarrow X}P(t)-r_{P}P(t)+k_{X\rightarrow P}X(t)$$

$$\frac{\text{d}X}{\text{d}t}=-k_{X\rightarrow P}X(t)-r_{X}X(t)+k_{P\rightarrow X}P(t) $$

Where
k_{P→X}, k_{X→P} are the forward
and back conversion of pyruvate (P) to its metabolic products (X), r_{X}=1/T1_{X}
+ (1-cosθ)^{1/TR}, T1_{X} is the relaxation rate of each
metabolite, TR is the repetition time and θ is the flip angle. We will make the
assumption k_{X→P}~0. The PIF can be modelled with a
box-car function, based on the rate (a.u sec^{-1}) and the duration
(sec) of injection. The proposed method uses a Gaussian model PIF~f_{1}*normal(f_{2}/2,f_{2}), where
f_{1}, f_{2} are free parameters representing the height and the shape of the AIF respectively. A more complex function would be able to
delineate PIF better, but it would require the fitting of more free parameters.
Alternatively a model-free formulism can be used which approximates the
kinetics using the ratios of AUC of the injected and product metabolites, $$$
\frac{AUC(X)}{AUC(P)}\approx\frac{k_{P\rightarrow
X}}{r_{X}}$$$

[1] Zierhut ML, Yen YF, Chen AP, et al. Kinetic modeling of hyperpolarized 13C1-pyruvate metabolism in normal rats and TRAMP mice.J Magn Reson. 2010; 202(1):85-92.

[2] Nelson SJ, Kurhanewicz J, Vigneron DB, et al. Metabolic imaging of patients with prostate cancer using hyperpolarized [1-¹³C]pyruvate. Sci Transl Med. 2013; 5(198).

[3] Hill DK, Orton MR, Mariotti E, et al. Model free approach to kinetic analysis of real-time hyperpolarized 13C magnetic resonance spectroscopy data. PLoS One. 2013; 8(9):e71996.

[4] Gutte H, Hansen AE, Larsen MM, et al. Simultaneous Hyperpolarized 13C-Pyruvate MRI and 18F-FDG PET (HyperPET) in 10 Dogs with Cancer. Nucl Med. 2015; 56(11):1786-92.

Kolmogorov-Smirnov (KS) statistic test across the 10 canine dynamic peak
heights for the compartmental model using either the box-car or the Gaussian
pyruvate input function (PIF).

Examples
of box-car and Gaussian PIF, and dynamic curves of the metabolite peaks and the
modelled best fit lines.

Estimated
k_{P→X}/r_{X} across
the 10 canine dynamic peak heights using the model-free formalism and the compartmental
model using either the box-car or the Gaussian pyruvate input function (PIF).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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