Analysis Methods for Human Hyperpolarized 13C-pyruvate Studies
Peder Eric Zufall Larson1, Hsin-Yu Chen1, Jeremy W. Gordon1, John Maidens2, Daniele Mammoli1, Mark Van Criekinge1, Robert Bok1, Rahul Aggarwal3, Marcus Ferrone4, James B. Slater1, John Kurhanewicz1, and Daniel B. Vigneron1

1Radiology and Biomedical Imaging, University of California - San Francisco, San Francisco, CA, United States, 2Electrical Engineering and Computer Science, University of California - Berkeley, Berkeley, CA, United States, 3Medicine, University of California - San Francisco, San Francisco, CA, United States, 4Pharmacy, University of California - San Francisco, San Francisco, CA, United States


A major challenge for human Hyperpolarized 13C metabolic MRI is to develop informative, accurate and robust methods for measuring metabolic conversion, while accounting for a broad range of experimental characteristics and without gold-standard experiments for evaluating accuracy and precision. We present a simulation framework to evaluate analysis strategies and show that an “input-less” kPL fitting method is a promising approach for accurate and robust measurements of metabolism in human hyperpolarized 13C-pyruvate MRI. We evaluate this method in human prostate cancer studies, where we observed variability of ±5-10s in the bolus delivery that can lead to errors in other analysis methods.


Hyperpolarized 13C-pyruvate MRI is now entering more widespread clinical trials for studies of metabolism in cancer as well as heart disease. The interpretation of this study data requires informative, accurate and robust methods for measuring metabolic conversion tailored to human studies, which have shown a much broader range of bolus characteristics and perfusion compared to preclinical studies. Furthermore, multi-site studies will soon be conducted to evaluate this modality more broadly.

A major challenge in developing analysis methods is there is no gold-standard for evaluating accuracy, while analyzing precision requires an impossibly large number of studies. To address this, we propose a Monte Carlo simulation framework in which to evaluate to performance of analysis methods in response to expected experimental variability and unknown parameters. The results were evaluated in human hyperpolarized 13C-pyruvate MRI of primary prostate cancer.


Data were acquired with a 3D dynamic MRSI sequence covering the entire prostate using a blipped EPSI acquisition with a compressed sensing reconstruction1. Other 3D MRSI sequence parameters included 12x12x16 matrix size, TE = 4.0 ms, TR = 150 ms, 8 mm isotropic resolution, and 2 sec between timepoints. Multiband spectral-spatial RF excitation pulses were used, combined with a variable flip angle strategy in time2.

Analysis methods used assumed uni-directional conversion from pyruvate to lactate with a rate constant kPL (kLP = 0), and metabolite decay rates R1L and R1P. All methods were modified to allow for arbitrary flip angle schemes, and are available in the hyperpolarized-mri-toolbox: https://github.com/LarsonLab/hyperpolarized-mri-toolbox

Area Under Curve ratio (AUCratio)3: For this method the ratio of the area under the lactate to area under pyruvate curves is used as a simple surrogate for metabolic conversion. A calibrated AUCratio was computed based on the nominal expected experimental parameters.

Boxcar-input kPL fitting: This fitting approach assumes a box-car input shape, including start time of the bolus, bolus duration, and the injection rate to characterize the input4.

Input-less kPL fitting: In this approach, we only fit the lactate magnetization, not the pyruvate magnetization, where the measured pyruvate magnetization is used as the input for the kinetic model at each time point5. This model requires fitting just kPL and the metabolite decay rates, R1L and R1P.

Simulated data was generated based the two-site model, with a gamma-variate input function. Monte Carlo simulations were performed by adding random noise to evaluate the precision and accuracy of the fitting methods. Ranges of simulated values were chosen based on what we observed or estimated in human prostate cancer studies.

Results & Discussion

The Monte Carlo simulation results with approximately equivalent SNR to human prostate experiments show the input-less fitting outperforms both the AUCratio and boxcar-input fitting methods, with typical expected errors < 10%.

The variable flip strategy causes the AUCratio approach to have systematic biases when there is variation in the bolus timing (Tarrive), bolus duration (Tbolus), and when the pyruvate decay rate, R1P, deviates from the assumed value. The boxcar-input is more robust to the variations in the bolus timing and duration, but has a bias with deviations in R1P. Meanwhile, the input-less method is robust to R1P deviations as well. The performance of the boxcar-input fitting may improve by using a measured input function6-8.

All methods have systematic bias when there are deviations in the lactate decay rate, R1L, which was fixed to an assumed value. R1L can additionally be fit with the kPL fitting methods, but this leads to substantial increases in the expected error of > 20 % (would not appear on range plotted). This error when fitting R1L is greater than the bias+error across the range of R1L from 15 to 35 s when R1L is fixed, suggesting it is not a favorable tradeoff to include R1L in the kinetic model fitting.

In human studies, we observed inter-subject variations in pyruvate delivery times to the prostate. AUCratio and input-less kPL fits show good agreement of spatial distributions but differ by apparent scaling factors, which can be explained by variations in bolus delivery. The mean pyruvate time, a measure of delivery time, shows ±5-10 s in arrival to the prostate. This variation, if unknown, is expected to lead to errors in the AUCratio, while the kPL fits should be unaffected.


An input-less kPL fitting method is a promising approach for accurate and robust measurements of metabolism in human hyperpolarized 13C-pyruvate MRI. This method is particularly advantageous for human studies, where we observed variability of ±5-10s in the bolus delivery that can lead to errors in the AUCratio method. The simulation framework provides a way to evaluate analysis strategies in response to potential experimental variations and unknown factors.


This work was supported by grants from the NIH (R01EB017449, R01EB013427, R01CA166655, and P41EB013598).


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Multiband variable flip angle strategy in time, and resulting simulated dynamic curves including noise chosen to approximately match in vivo human prostate cancer data. The effective flip angles summarize the net effect of multiple RF pulses applied to create an image every 2 s.

Simulation results showing the sensitivity of metabolic rate estimates for sample data using the clinical prostate acquisition parameters. Sensitivity plots on top show the relative kPL accuracy from the kinetic models. These are plotted over kPL, noise level, bolus arrival time (Tarrive), bolus duration (Tbolus), and metabolite relaxation rates (R1P, R1L). Accuracy is shown by the solid lines, which are the average fit across the simulation. Precision is shown by the dashed lines, which plot ±1 standard deviation in the simulation fits.

Selected prostate voxel data and input-less kPL fits chosen from regions of high kPL with variable bolus delivery. For these variable flip angle schemes, the signal dynamics increase throughout most of the experiment, while the state magnetization more clearly shows the bolus arrival, metabolic conversion, and relaxation decay.

Comparison on AUCratio and kPL maps (from input-less fitting with a fixed R1L) across 5 patients. The maps are identically windowed with the colorscale shown.

Summary of in vivo quantifications across human prostate studies, where each color represents a different study. The plots of these two parameterizations show differences across studies, which can be explained by the varying bolus delivery, characterized by the mean pyruvate time9 histograms.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)