Kinetic modeling of hyperpolarized ¹³C pyruvate metabolism in tumors using a measured arterial input function

Abstract

Mathematical models are required to estimate kinetic parameters of [1-(13)C] pyruvate-lactate interconversion from magnetic resonance spectroscopy data. One- or two-way exchange models utilizing a hypothetical approximation to the true arterial input function (AIF), (e.g. an ideal 'box-car' function) have been used previously. We present a method for direct measurement of the AIF in the rat. The hyperpolarized [1-(13)C] pyruvate signal was measured in arterial blood as it was continuously withdrawn through a small chamber. The measured signal was corrected for T1 relaxation of pyruvate, RF pulses and dispersion of blood in the chamber to allow for the estimation of the direct AIF. Using direct AIF, rather than the commonly used box-car AIF, provided realistic estimates of the rate constant of conversion of pyruvate to lactate, kpl, the rate constant of conversion of lactate to pyruvate klp, the clearance rate constant of pyruvate from blood to tissue, Kip, and the relaxation rate of lactate T1la. Since no lactate signal was present in blood, it was possible to use a simple precursor-product relationship, with the tumor tissue pyruvate time-course as the input for the lactate time-course. This provided a robust estimate of kpl, similar to that obtained using a directly measured AIF.

Kinetic Modeling and Constrained Reconstruction of Hyperpolarized [1-13C]-Pyruvate Offers Improved Metabolic Imaging of Tumors

“…2a). Kazan et al (16) recently examined kinetic models for HP pyruvate that incorporate a vascular input function, but observed no statistically significant differences in k pl when comparing results from the simple precursor-product relationship (Case 6, in (16)) to those derived from the model fed by an explicitly measured input function (Case 1, Eqs. 6–9).…”

“…HP pyruvate is converted into lactate at an apparent rate that depends on the intracellular equilibrium concentrations of pyruvate, lactate, LDH, and NADH (11, 12). Several groups have integrated terms to account for inflow of HP agents (13–15), including direct measurement of the vascular input function (VIF) (16). With no separation between physical pools, these models assume that all observed HP agents are in direct chemical contact with enzymes that catalyze exchange, leading to over-estimation of chemically active HP pyruvate and under-estimation of the apparent rate of conversion.…”

A novel perfused Bloch–McConnell simulator for analyzing the accuracy of dynamic hyperpolarized MRS

“…The T 1 values used for pyruvate and lactate were assumed to be 43 and 33-s, respectively, following the results in Ref. 35, and T 2 * was set to 20-ms for both metabolites. In the perfused system, the vascular input function was modeled as a gamma variate; extravasation (k ve ) was assumed to be 0.02-s −1 (Ref.…”

Alternating Acquisition Technique for Quantification of in vitro Hyperpolarized [1-13C] Pyruvate Metabolism

“…Additionally, the robustness of these model-based approaches can be compromised by the arterial input function (AIF), and also by the chosen signal acquisition window. It was shown that error in AIF could have significant influence in estimating the apparent rate constants from kinetic modeling (23), and some have investigated methods for direct measurement of the AIF (24) or for minimization of its effect on kinetic modeling (25)(26)(27). Also, it was shown that the calculated rate constants can vary depending on the signal acquisition timing (28), and that careful determination of optimal acquisition window is necessary for increasing the results' reproducibility.…”