Kinetic Modeling and Constrained Reconstruction of Hyperpolarized [1-13C]-Pyruvate Offers Improved Metabolic Imaging of Tumors

Abstract

Hyperpolarized [1-(13)C]-pyruvate has shown tremendous promise as an agent for imaging tumor metabolism with unprecedented sensitivity and specificity. Imaging hyperpolarized substrates by magnetic resonance is unlike traditional MRI because signals are highly transient and their spatial distribution varies continuously over their observable lifetime. Therefore, new imaging approaches are needed to ensure optimal measurement under these circumstances. Constrained reconstruction algorithms can integrate prior information, including biophysical models of the substrate/target interaction, to reduce the amount of data that is required for image analysis and reconstruction. In this study, we show that metabolic MRI with hyperpolarized pyruvate is biased by tumor perfusion and present a new pharmacokinetic model for hyperpolarized substrates that accounts for these effects. The suitability of this model is confirmed by statistical comparison with alternates using data from 55 dynamic spectroscopic measurements in normal animals and murine models of anaplastic thyroid cancer, glioblastoma, and triple-negative breast cancer. The kinetic model was then integrated into a constrained reconstruction algorithm and feasibility was tested using significantly undersampled imaging data from tumor-bearing animals. Compared with naïve image reconstruction, this approach requires far fewer signal-depleting excitations and focuses analysis and reconstruction on new information that is uniquely available from hyperpolarized pyruvate and its metabolites, thus improving the reproducibility and accuracy of metabolic imaging measurements.

Figure 1

Relationship between the normalized HP lactate signal (nLac) and tissue perfusion (K^trans) assessed by DCE- MRI in a murine model of ATC. Although differences in nLac were not quite statistically significant (p = 0.08; t-test), and no differences in K^trans were observed between groups, strong correlation between perfusion and nLac is evident.

Figure 2

Candidate kinetic models to describe dynamic signal evolution of HP pyruvate and lactate in vivo. All models include two chemical pools and (a) one spatial compartment; (b) two spatial compartments (intravascular and extravascular) with exchange limited to extravascular region; or (c) three spatial compartments (intravascular, extravascular/extracellular, and intracellular) with exchange restricted to the intracellular region.

Figure 3

Comparison of model fits to observed data. The area under the spectral peaks (a) associated with pyruvate and lactate were integrated to generate dynamic summary curves. (b) Representative fits show subtle differences between models. (c) In 55 datasets, models B-C (Figs 2b, 2c) score significantly better (lower) than model A (Fig. 2a). Model B scored better than model C but not to statistical significance.

Figure 4

Graphical summary of the model-based constrained reconstruction algorithm. (a) Temporal information from the kinetic model is combined with priors from ¹H MRI to eliminate unknowns. The constrained reconstruction solves for model parameters that minimize the mean-square difference between estimates and (b) under-sampled observations. (c) Estimates of signal at arbitrary time and position can then be calculated.

Figure 5

Prior information and representative images from model-based constrained reconstruction algorithm. (a) Segmentation of ¹H MRI allows identification of the left ventricle for constrained estimation of (b) the pyruvate vascular input function. Once parameters are found, the kinetic model assists reconstruction of the distribution of HP substrates at arbitrary points in their observable life. Here, estimates for (c) pyruvate and (d) lactate are shown for t=6.4s after the start of data acquisition, which followed injection and flush of HP pyruvate. Red arrow indicates tumor.

Figure 6

Overlay of representative parametric maps, derived from constrained reconstruction of radially encoded data from the double spin-echo MBFE sequence with interleaved measurement of the pyruvate vascular input function. (a) P₀ and (b) L₀ reflect the initial distribution of HP pyruvate and lactate at the start of data acquisition; (c) k_pl, the rate constant (1/s) describing chemical conversion of pyruvate to lactate; (d) v_b, the unitless fraction of tissue volume ascribed to the intravascular compartment; (e) k_ve, the rate constant (1/s) for pyruvate extravasation. (f) The background reference T₂-weighted image with ATC tumor indicated by red arrow. All images were scaled to the maximum value of the associated parameter for ease of visualization, except for (a) and (b) which were both normalized to the same value. Colorbars along the right edge of these panels show the relative intensity scale.

Figure 7

Overlay of representative parametric maps derived from constrained reconstruction of gradient-echo radMBFE data with prior information from DCE-MRI. High resolution parametric maps of (a) K^trans and (b) v_b from ¹H DCE-MRI were used to eliminate unknowns for perfusion/extravasation and vascular volume fraction in the kinetic model for HP substrate evolution. (c) k_pl, the apparent rate constant for chemical conversion of pyruvate to lactate.