This work is directed to scientists that are developing methods for estimating apparent metabolic conversion rates by dynamic spectroscopy of hyperpolarized substrates.

Imaging of hyperpolarized (HP) agents such as [1-¹³C] pyruvate is of great interest in oncology because metabolism is often affected by cancer and therapy¹. The metabolic state of a tumor can be partially reflected by the chemical conversion of HP pyruvate to HP lactate. For quantifying this apparent rate of conversion, a pharmacokinetic model with two chemical and two physical compartments has been proposed². Evaluation of effects of noise and bias in signal and different parameters in the kinetic model is challenging due to complex and confounding biology and the dynamic nature of the HP signal. In this work, use simulation to examine the effects of signal to noise ratio (SNR) on estimation of the apparent rate of conversion of HP pyruvate into lactate (kpl).The simulated HP data was generated using a Bloch-McBonnell simulator³ that has been modified to include perfusion effects. A simple dynamic pulse-acquire sequence (FA = 20°, TR = 2s, SW = 4096 Hz, NOP = 2048) was used to simulate HP data; a perfectly homogeneous B0 of 3T was assumed with a radio frequency excitation pulse modeled as a five-lobed sinc pulse with 5-kHz bandwidth centered halfway between the lactate and pyruvate resonances. T1 for pyruvate and lactate were assumed as 56 and 30 seconds, respectively. The vascular input function was modeled as a gamma-variate function with α=2.8, β=4.5. The rate of extravasation (kve) was set to be 0.02/s and the vascular blood volume fraction (vb) was 0.09. The ground truth of kpl was set to be 0.1/s. The model was tested with a variety of SNRs (10~50) by adding Gaussian noise to the simulated free induction decays. Here SNR was defined as the maximum spectral peak value divided by the standard deviation of the Gaussian noise. The full width at half height (FWHH) of the spectral peaks (Figure 1) were calculated at each TR to generate dynamic metabolite curves (Figure 2) for kinetic analysis. For each noise level, the experiments were repeated 100 times. The Fourier transformation of simulated data of noise free, SNR=15 and SNR=30 are shown in Figure 1. Degradation in data quality is evident here and in the dynamic metabolite curves shown in Figure 2. Results of kinetic analysis (Figure 2, curves) agree with noisy observations, but fitting error is introduced by Gaussian noise. For quantifying the effects of noise on the estimation of kpl by the kinetic model, 95% confidence interval, mean and standard deviation of kpl estimated by the kinetic model are calculated and compared between different SNRs (Figure 3). SNR correlates inversely with the width of the 95% confidence interval and the standard deviation, while the mean of the kpl is relatively stable. A small 3% underestimate of the mean of kpl was observed for all SNRs, which is attributed in part to the approximation of excitation losses as averaged over TR in analysis.As expected, the SNR affects the reproducibility of the estimation of kpl by kinetic analysis. According to confidence intervals observed in these simulation experiments, the reproducibility of kpl estimates decreases quickly below an SNR threshold of ~25. These kinds of simulations will also be to explore noise and bias in other kinetic parameters and their effects on measurement of kpl .