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

摘要

Conventional methods for analyzing the in vivo hyperpolarized ¹³C-NMR (HP-MR) data from the lactate dehydrogenase (LDH) reaction usually make assumptions on the stability of rate constants and/or the validity of 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 signal ratio L(t)/P(t). Our analysis provided evidence that the LDH enzymatic kinetics observed by HP-MR is in near-equilibrium and satisfies the two-site exchange model for only a specific time window. Additionally 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 fit (RF) method we developed that includes only two modeling parameters and is less sensitive to the influence of instrument settings/protocols such as flip angels, degree of polarization, and tracer dosage. We further compared the RF method with a conventional two-site exchange modeling method, i.e., the differential equations fitting (DEF) method using both the experimental and simulated HP-MR data. The RF method appeared to fit better than the DEF method for the reverse rate constant on the mouse tumor data with less relative errors on average, whereas the DEF 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 transport function (TF), noise level, and rate constant ratio; one method may be more accurate than the other one based on experimental/biological conditions aforementioned. We were able to categorize our tumor models into specific conditions of the computer simulation and estimate the errors of rate quantification. We also discussed possible approaches to developing more accurate rate-quantification methods for HP-MR.