Ratiometric analysis in hyperpolarized NMR (I): test of the two-site exchange model and the quantification of reaction rate constants.

Conventional methods for the analysis of in vivo hyperpolarized (13) C NMR data from the lactate dehydrogenase (LDH) reaction usually make assumptions on the stability of rate constants and/or the validity of the two-site exchange model. In this study, we developed a framework to test the validity of the assumption of stable reaction rate constants and the two-site exchange model in vivo via ratiometric fitting of the time courses of the signal ratio L(t)/P(t). Our analysis provided evidence that the LDH enzymatic kinetics observed by hyperpolarized NMR are in near-equilibrium and satisfy the two-site exchange model for only a specific time window. In addition, we quantified both the forward and reverse exchange rate constants of the LDH reaction for the transgenic and mouse xenograft models of breast cancer using the ratio fitting method developed, which includes only two modeling parameters and is less sensitive to the influence of instrument settings/protocols, such as flip angles, degree of polarization and tracer dosage. We further compared the ratio fitting method with a conventional two-site exchange modeling method, i.e. the differential equation fitting method, using both the experimental and simulated hyperpolarized NMR data. The ratio fitting method appeared to fit better than the differential equation fitting method for the reverse rate constant on the mouse tumor data, with less relative errors on average, whereas the differential equation fitting method also resulted in a negative reverse rate constant for one tumor. The simulation results indicated that the accuracy of both methods depends on the width of the transport function, noise level and rate constant ratio; one method may be more accurate than the other based on the experimental/biological conditions aforementioned. We were able to categorize our tumor models into specific conditions of the computer simulation and to estimate the errors of rate quantification. We also discussed possible approaches to the development of more accurate rate quantification methods for hyperpolarized NMR.