MRI using hyperpolarized (HP) carbon-13 pyruvate is being investigated in clinical trials to provide non-invasive measurements of metabolism for cancer and cardiac imaging. In this project, we applied HP [1- C]pyruvate dynamic MRI in prostate cancer to measure the conversion from pyruvate to lactate, which is expected to increase in aggressive cancers. The goal of this work was to develop and test analysis methods for improved quantification of this metabolic conversion. In this work, we compared specialized kinetic modeling methods to estimate the pyruvate-to-lactate conversion rate, k , as well as the lactate-to-pyruvate area-under-curve (AUC) ratio. The kinetic modeling included an "inputless" method requiring no assumptions regarding the input function, as well as a method incorporating bolus characteristics in the fitting. These were first evaluated with simulated data designed to match human prostate data, where we examined the expected sensitivity of metabolism quantification to variations in k , signal-to-noise ratio (SNR), bolus characteristics, relaxation rates, and B variability. They were then applied to 17 prostate cancer patient datasets. The simulations indicated that the inputless method with fixed relaxation rates provided high expected accuracy with no sensitivity to bolus characteristics. The AUC ratio showed an undesired strong sensitivity to bolus variations. Fitting the input function as well did not improve accuracy over the inputless method. In vivo results showed qualitatively accurate k maps with inputless fitting. The AUC ratio was sensitive to bolus delivery variations. Fitting with the input function showed high variability in parameter maps. Overall, we found the inputless k fitting method to be a simple, robust approach for quantification of metabolic conversion following HP [1- C]pyruvate injection in human prostate cancer studies. This study also provided initial ranges of HP [1- C]pyruvate parameters (SNR, k , bolus characteristics) in the human prostate.
We present a connection between the viability kernel and maximal reachable sets. Current numerical schemes that compute the viability kernel suffer from a complexity that is exponential in the dimension of the state space. In contrast, extremely efficient and scalable techniques are available that compute maximal reachable sets. We show that under certain conditions these techniques can be used to conservatively approximate the viability kernel for possibly high-dimensional systems. We demonstrate the results on two practical examples, one of which is a seven-dimensional problem of safety in anesthesia.
Hyperpolarized carbon-13 magnetic resonance imaging has enabled the real-time observation of perfusion and metabolism in vivo. These experiments typically aim to distinguish between healthy and diseased tissues based on the rate at which they metabolize an injected substrate. However, existing approaches to optimizing flip angle sequences for these experiments have focused on indirect metrics of the reliability of metabolic rate estimates, such as signal variation and signal-to-noise ratio. In this paper we present an optimization procedure that focuses on maximizing the Fisher information about the metabolic rate. We demonstrate through numerical simulation experiments that flip angles optimized based on the Fisher information lead to lower variance in metabolic rate estimates than previous flip angle sequences. In particular, we demonstrate a 20% decrease in metabolic rate uncertainty when compared with the best competing sequence. We then demonstrate appropriateness of the mathematical model used in the simulation experiments with in vivo experiments in a prostate cancer mouse model. While there is no ground truth against which to compare the parameter estimates generated in the in vivo experiments, we demonstrate that our model used can reproduce consistent parameter estimates for a number of flip angle sequences.
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