Kinetic modelling of dissolution dynamic nuclear polarisation 13 C magnetic resonance spectroscopy data for analysis of pyruvate delivery and fate in tumours

Abstract

Dissolution dynamic nuclear polarisation (dDNP) of ¹³ C-labelled pyruvate in magnetic resonance spectroscopy/imaging (MRS/MRSI) has the potential for monitoring tumour progression and treatment response. Pyruvate delivery, its metabolism to lactate and efflux were investigated in rat P22 sarcomas following simultaneous intravenous administration of hyperpolarised ¹³ C-labelled pyruvate (¹³ C₁ -pyruvate) and urea (¹³ C-urea), a nonmetabolised marker. A general mathematical model of pyruvate-lactate exchange, incorporating an arterial input function (AIF), enabled the losses of pyruvate and lactate from tumour to be estimated, in addition to the clearance rate of pyruvate signal from blood into tumour, K_ip , and the forward and reverse fractional rate constants for pyruvate-lactate signal exchange, k_pl and k_lp . An analogous model was developed for urea, enabling estimation of urea tumour losses and the blood clearance parameter, K_iu . A spectral fitting procedure to blood time-course data proved superior to assuming a gamma-variate form for the AIFs. Mean arterial blood pressure marginally correlated with clearance rates. K_iu equalled K_ip , indicating equivalent permeability of the tumour vasculature to urea and pyruvate. Fractional loss rate constants due to effluxes of pyruvate, lactate and urea from tumour tissue into blood (k_po , k_lo and k_uo , respectively) indicated that T₁ s and the average flip angle, θ, obtained from arterial blood were poor surrogates for these parameters in tumour tissue. A precursor-product model, using the tumour pyruvate signal time-course as the input for the corresponding lactate signal time-course, was modified to account for the observed delay between them. The corresponding fractional rate constant, k_avail , most likely reflected heterogeneous tumour microcirculation. Loss parameters, estimated from this model with different TRs, provided a lower limit on the estimates of tumour T₁ for lactate and urea. The results do not support use of hyperpolarised urea for providing information on the tumour microcirculation over and above what can be obtained from pyruvate alone. The results also highlight the need for rigorous processes controlling signal quantitation, if absolute estimations of biological parameters are required.

Keywords: P22 rat sarcoma; dynamic nuclear polarisation; mathematical modelling; precursor-product; pyruvate metabolism; rate constant; tumour microcirculation; urea.