Peder Eric Zufall Larson^{1}, Hsin-Yu Chen^{1}, Jeremy W. Gordon^{1}, John Maidens^{2}, Daniele Mammoli^{1}, Mark Van Criekinge^{1}, Robert Bok^{1}, Rahul Aggarwal^{3}, Marcus Ferrone^{4}, James B. Slater^{1}, John Kurhanewicz^{1}, and Daniel B. Vigneron^{1}

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 reconstruction^{1}. 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
time^{2}.

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 input^{4}.

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 point^{5}. 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.

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
function^{6-8}.

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.

1. Larson PEZ, Hu S, Lustig M, Kerr AB, Nelson SJ, Kurhanewicz J, Pauly JM, Vigneron DB. Fast dynamic 3D MR spectroscopic imaging with compressed sensing and multiband excitation pulses for hyperpolarized 13C studies. Magn Reson Med. 2011 Mar;65(3):610–9. PMID: 20939089

2. Xing Y, Reed GD, Pauly JM, Kerr AB, Larson PEZ. Optimal variable flip angle schemes for dynamic acquisition of exchanging hyperpolarized substrates. J Magn Reson. 2013 Sep;234:75–81. PMID: 23845910

3. Hill DK, Orton MR, Mariotti E, Boult JKR, Panek R, Jafar M, Parkes HG, Jamin Y, Miniotis MF, Al-Saffar NMS, Beloueche-Babari M, Robinson SP, Leach MO, Chung Y-L, Eykyn TR. Model free approach to kinetic analysis of real-time hyperpolarized 13C magnetic resonance spectroscopy data. PLoS One. 2013;8(9):e71996. PMID: 24023724

4. Zierhut ML, Yen Y-F, Chen AP, Bok R, Albers MJ, Zhang V, Tropp J, Park I, Vigneron DB, Kurhanewicz J, Hurd RE, Nelson SJ. Kinetic modeling of hyperpolarized 13C1-pyruvate metabolism in normal rats and TRAMP mice. J Magn Reson. 2010 Jan;202(1):85–92. PMID: 19884027

5. Khegai O, Schulte RF, Janich MA, Menzel MI, Farrell E, Otto AM, Ardenkjaer-Larsen JH, Glaser SJ, Haase A, Schwaiger M, Wiesinger F. Apparent rate constant mapping using hyperpolarized [1-(13)C]pyruvate. NMR Biomed. 2014 Oct;27(10):1256–65. PMID: 25156807

6. Bankson JA, Walker CM, Ramirez MS, Stefan W, Fuentes D, Merritt ME, Lee J, Sandulache VC, Chen Y, Phan L, Chou P-C, Rao A, Yeung S-CJ, Lee M-H, Schellingerhout D, Conrad CA, Malloy C, Sherry AD, Lai SY, Hazle JD. Kinetic Modeling and Constrained Reconstruction of Hyperpolarized [1-13C]-Pyruvate Offers Improved Metabolic Imaging of Tumors. Cancer Res. 2015 Nov;75(22):4708–17. PMID: 26420214

7. Maidens J, Gordon JW, Arcak M, Larson PEZ. Optimizing flip angles for metabolic rate estimation in hyperpolarized carbon-13 MRI. IEEE Trans Med Imaging. 2016 May; PMID: 27249825

8. Sun C, Walker CM, Michel KA, Venkatesan AM, Lai SY, Bankson JA. Influence of parameter accuracy on pharmacokinetic analysis of hyperpolarized pyruvate. Magn Reson Med. 2017.

9. Larson PEZ, Kerr AB, Chen AP, Lustig MS, Zierhut ML, Hu S, Cunningham CH, Pauly JM, Kurhanewicz J, Vigneron DB. Multiband excitation pulses for hyperpolarized 13C dynamic chemical-shift imaging. J Magn Reson. 2008 Sep;194(1):121–7. PMID: 18619875

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 time^{9} histograms.