Introduction

Dissolution dynamic nuclear polarization can enhance signal from [1-13C]-pyruvate by more than four orders of magnitude (1), permitting unprecedented insight into metabolism in vivo. Upregulated aerobic glycolysis (the Warburg effect) is characteristic of many cancers, and can be visualized through the conversion of hyperpolarized (HP) pyruvate into lactate. A broad and growing range of literature indicates that metabolic MRI using HP pyruvate can inform on cancer aggressiveness and provide early indications of response to therapy (2). Our long-term goal is to establish metabolic MRI using hyperpolarized pyruvate as a quantitative imaging biomarker that can be used to guide care for patients with cancer. These measurements are technically challenging because the HP magnetization is finite, non-renewable, continually relaxing towards thermal equilibrium, and depleted with each signal excitation. Excitation strategies must be carefully designed because each excitation affects all future measurements. In this work, we seek to explore temporal filtering effects of signal excitations on observed HP MRI magnetization.

Methods

The signal flow diagram for HP magnetization in tissue can be seen in Figure 1. In this hybrid discrete-continuous system, magnetization entering tissue is subjected to an excitation pulse, which controls the extent to which that magnetization is withdrawn for observation or allowed to remain and accumulate until the next excitation pulse. The transfer function for this system can be written as:
$$H(z)=\frac{z\sin\alpha}{z-E_1\cos\alpha}$$
which reveals that the low-pass filter characteristics of this system can be controlled by the excitation angle ($$$\alpha$$$) and the sampling interval ($$$E_1=e^{-TR/T_1}$$$). The observable frequency content of signals that evolve within this system are modified by this low-pass filtering effect as illustrated in Figure 2.
HP MRI signal evolution is often characterized using the normalized ratio of HP lactate signal to total HP magnetization (nLac). Kinetic models can also be used to quantify the apparent rate at which HP pyruvate is converted into lactate ($$$k_{PL}$$$). To evaluate the filtering effects of signal excitation on nLac and $$$k_{PL}$$$, we generated synthetic data using a pharmacokinetic (PK) model of HP signal evolution that includes two physical compartments and two chemical pools (3,4) and was assumed to be driven by a pyruvate arterial input function that is consistent with our prior observations in vivo. nLac was calculated as the integral of HP lactate signal over time, normalized to the sum of the integrals for HP lactate and HP pyruvate. To minimize deconvolution of the filtering effect by using a PK model that perfectly corrects for relaxation and excitation losses, we fit dynamic data synthesized from the 2-compartment model ($$$k_{PL2}$$$) to a simpler precursor-product model with one physical compartment ($$$k_{PL1}$$$). Synthetic data was generated for constant excitation angles of 1-deg to 90-deg and a pan-physiological range of $$$k_{PL2}$$$ values. All simulations and analyses were carried out using Matlab (The Mathworks, Natick, MA). For clarity, we assume ideal excitation of a uniform volume.

Results

The low-pass filter profiles illustrated in Figure 2 show that temporal averaging using low excitation angles reduces sensitivity to more rapidly evolving HP magnetization, while higher excitations have more uniform sensitivity across the sampling bandwidth (1/TR). Differences in the frequency content of HP pyruvate and lactate signals which arrive via vasculature and chemical conversion, respectively, result in nLac (Figure 3) and $$$k_{PL}$$$ values (Figure 4) that are not independent of excitation angle. nLac, which is itself a temporally averaged measure, shows strong dependence on excitation angles (Figure 3) over physiologically reasonable values for $$$k_{PL2}$$$, and less contrast to high conversion rates or sampling with high excitation angles. Pharmacokinetic analyses using a simple precursor-product model (Figure 4) shows a more modest dependence on excitation angles, and that higher apparent rate constants are observed with the use of higher excitation angles: $$$k_{PL1,max}$$$ is observed at ~21-deg for $$$k_{PL2}$$$=0.01/sec and 0.1/sec, and 34-deg and 81-deg for $$$k_{PL2}$$$=1.0/sec and 10.0/sec, respectively.

Discussion

This work explores the relationship between ideal HP MRI signal excitations and quantification methods that operate on magnetization that evolves within this system. Low excitation angles have a signal averaging effect that reduces sensitivity to rapid signal evolution that may be driven by delivery or chemical conversion, while higher excitation angles improve sensitivity to frequency content across the bandwidth defined by the sampling interval. Further study is needed to determine optimal acquisition conditions that maximize sensitivity to the expected frequency content of these signals, including effects of noise and the ability of PK models that account for this signal averaging effect to reduce bias imparted by excitations.

Acknowledgements

This work was supported in part by the National Cancer Institute of the National Institutes of Health (R01CA211150) and GE Healthcare. The content is solely the responsibility of the authors and does not necessarily represent the official views of their sponsors.