Hyperpolarized carbon-13 MRI

{{Main|Hyperpolarization (physics)}}

Hyperpolarization of ¹³C for MRI is typically achieved using either dissolution Dynamic nuclear polarization (dDNP) or parahydrogen-induced polarization (PHIP). Although "brute force" polarization methods also exist, they are far less commonly used.{{Cite journal |last1=Hirsch |first1=Matthew L. |last2=Kalechofsky |first2=Neal |last3=Belzer |first3=Avrum |last4=Rosay |first4=Melanie |last5=Kempf |first5=James G. |date=2015-07-08 |title=Brute-Force Hyperpolarization for NMR and MRI |url=https://pubs.acs.org/doi/10.1021/jacs.5b01252 |journal=Journal of the American Chemical Society |volume=137 |issue=26 |pages=8428–8434 |doi=10.1021/jacs.5b01252 |pmid=26098752 |bibcode=2015JAChS.137.8428H |issn=0002-7863|url-access=subscription }}

In dDNP, imaging agents such as ¹³C-pyruvate are physically mixed (but not chemically reacted) with a stable free radical known as a polarizing agent (PA).{{Cite journal |last1=Ardenkjær-Larsen |first1=Jan H. |last2=Fridlund |first2=Björn |last3=Gram |first3=Andreas |last4=Hansson |first4=Georg |last5=Hansson |first5=Lennart |last6=Lerche |first6=Mathilde H. |last7=Servin |first7=Rolf |last8=Thaning |first8=Mikkel |last9=Golman |first9=Klaes |date=2003-09-02 |title=Increase in signal-to-noise ratio of > 10,000 times in liquid-state NMR |journal=Proceedings of the National Academy of Sciences |language=en |volume=100 |issue=18 |pages=10158–10163 |doi=10.1073/pnas.1733835100 |doi-access=free |issn=0027-8424 |pmc=193532 |pmid=12930897|bibcode=2003PNAS..10010158A }}{{Cite journal |last=Ardenkjaer-Larsen |first=Jan Henrik |date=March 2016 |title=On the present and future of dissolution-DNP |url=https://linkinghub.elsevier.com/retrieve/pii/S1090780716000562 |journal=Journal of Magnetic Resonance |language=en |volume=264 |pages=3–12 |doi=10.1016/j.jmr.2016.01.015|pmid=26920825 |bibcode=2016JMagR.264....3A }} This mixture is cooled to cryogenic temperatures (~1 K) and subjected to a strong magnetic field (~3 T), which causes the unpaired electron of the PA to become highly polarized. Microwave radiation is then applied near the electron resonance frequency, enabling the transfer of polarization from the electron to the ¹³C nuclei via hyperfine coupling{{Cite journal |last=Overhauser |first=Albert W. |date=1953-10-15 |title=Polarization of Nuclei in Metals |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.92.411 |journal=Physical Review |volume=92 |issue=2 |pages=411–415 |doi=10.1103/PhysRev.92.411|bibcode=1953PhRv...92..411O |url-access=subscription }} (for more details on polarization transfer mechanisms, see Dynamic nuclear polarization).

In PHIP, hydrogen gas is cooled—typically to 77 K by passing it through a liquid nitrogen bath—resulting in a substantial population difference between the singlet (parahydrogen) and triplet (orthohydrogen) spin states.{{Cite journal |last1=Ellermann |first1=Frowin |last2=Pravdivtsev |first2=Andrey |last3=Hövener |first3=Jan-Bernd |date=2021-02-18 |title=Open-source, partially 3D-printed, high-pressure (50-bar) liquid-nitrogen-cooled parahydrogen generator |journal=Magnetic Resonance |language=English |volume=2 |issue=1 |pages=49–62 |doi=10.5194/mr-2-49-2021 |doi-access=free |pmc=10539807 |pmid=37904754}} This difference, known as singlet order (SO), is long-lived and serves as a reservoir of polarization.{{Cite journal |last1=Carravetta |first1=Marina |last2=Levitt |first2=Malcolm H. |date=2004-05-01 |title=Long-Lived Nuclear Spin States in High-Field Solution NMR |url=https://pubs.acs.org/doi/10.1021/ja0490931 |journal=Journal of the American Chemical Society |volume=126 |issue=20 |pages=6228–6229 |doi=10.1021/ja0490931 |pmid=15149209 |bibcode=2004JAChS.126.6228C |issn=0002-7863|url-access=subscription }} Parahydrogen is then chemically added to molecules such as ¹³C-pyruvate, and the singlet order is converted into ¹³C polarization using tailored radiofrequency (RF) pulses.{{Cite journal |last1=Bowers |first1=C. Russell |last2=Weitekamp |first2=D. P. |date=1987-09-01 |title=Parahydrogen and synthesis allow dramatically enhanced nuclear alignment |url=https://pubs.acs.org/doi/abs/10.1021/ja00252a049 |journal=Journal of the American Chemical Society |volume=109 |issue=18 |pages=5541–5542 |doi=10.1021/ja00252a049 |bibcode=1987JAChS.109.5541B |issn=0002-7863}}

Hyperpolarized samples of ¹³C pyruvic acid are typically dissolved in some form of aqueous solution containing various detergents and buffering reagents. For example, in a study detecting tumor response to etoposide treatment, the sample was dissolved in 40 mM HEPES, 94 mM NaOH, 30 mM NaCl, and 50 mg/L EDTA.

Hyperpolarized carbon-13 MRI is currently being developed as a potentially cost effective diagnostic and treatment progress tool in various cancers, including prostate cancer. Other potential uses include neuro-oncological applications such as the monitoring of real-time in vivo metabolic events.{{cite journal | vauthors = Miloushev VZ, Keshari KR, Holodny AI | title = Hyperpolarization MRI: Preclinical Models and Potential Applications in Neuroradiology | journal = Topics in Magnetic Resonance Imaging | volume = 25 | issue = 1 | pages = 31–7 | date = February 2016 | pmid = 26848559 | pmc = 4968075 | doi = 10.1097/RMR.0000000000000076 }}

The majority of clinical studies utilizing ¹³C hyperpolarization are currently studying pyruvate metabolism in prostate cancer, testing reproducibility of the imaging data, as well as feasibility of acquiring time.{{cite web|url=https://clinicaltrials.gov/ct2/results?term=hyperpolarized+pyruvate&Search=Search|title=Clinical Trials}}

File:In vivo hyperpolarized carbon 13 MRI spectra.png from a dynamic hyperpolarized carbon-13 MR imaging experiment in a rat model. This data set shows the evolution of magnetization in a single voxel in the rat's kidney. A strong peak from the hyperpolarized pyruvate injected in the experiment is evident, along with smaller peaks corresponding to the metabolites lactate, alanine and bicarbonate.]]

{{Main|Magnetic resonance spectroscopic imaging}}

Spectroscopic imaging techniques enable chemical information to be extracted from hyperpolarized carbon-13 MRI experiments. The distinct chemical shift associated with each metabolite can be exploited to probe the exchange of magnetization between pools corresponding to each of the metabolites.

Using techniques for simultaneous spatial and spectral selective excitation, RF pulses can be designed to perturb metabolites individually.

{{cite journal | vauthors = Lupo JM, Chen AP, Zierhut ML, Bok RA, Cunningham CH, Kurhanewicz J, Vigneron DB, Nelson SJ | title = Analysis of hyperpolarized dynamic 13C lactate imaging in a transgenic mouse model of prostate cancer | journal = Magnetic Resonance Imaging | volume = 28 | issue = 2 | pages = 153–62 | date = February 2010 | pmid = 19695815 | pmc = 3075841 | doi = 10.1016/j.mri.2009.07.007 }}

{{cite journal | vauthors = Cunningham CH, Chen AP, Lustig M, Hargreaves BA, Lupo J, Xu D, Kurhanewicz J, Hurd RE, Pauly JM, Nelson SJ, Vigneron DB | title = Pulse sequence for dynamic volumetric imaging of hyperpolarized metabolic products | journal = Journal of Magnetic Resonance | volume = 193 | issue = 1 | pages = 139–46 | date = July 2008 | pmid = 18424203 | pmc = 3051833 | doi = 10.1016/j.jmr.2008.03.012 | bibcode = 2008JMagR.193..139C }}

This enables the encoding of metabolite-selective images without the need for spectroscopic imaging. This technique also allows different flip angles to be applied to each metabolite,

{{cite journal | vauthors = Larson PE, Kerr AB, Chen AP, Lustig MS, Zierhut ML, Hu S, Cunningham CH, Pauly JM, Kurhanewicz J, Vigneron DB | title = Multiband excitation pulses for hyperpolarized 13C dynamic chemical-shift imaging | journal = Journal of Magnetic Resonance | volume = 194 | issue = 1 | pages = 121–7 | date = September 2008 | pmid = 18619875 | doi = 10.1016/j.jmr.2008.06.010 | bibcode = 2008JMagR.194..121L | pmc = 3739981 }}{{cite journal | vauthors = Marco-Rius I, Cao P, von Morze C, Merritt M, Moreno KX, Chang GY, Ohliger MA, Pearce D, Kurhanewicz J, Larson PE, Vigneron DB | title = 13 C-MR metabolism studies | journal = Magnetic Resonance in Medicine | volume = 77 | issue = 4 | pages = 1419–1428 | date = April 2017 | pmid = 27017966 | pmc = 5040611 | doi = 10.1002/mrm.26226 }}

which enables pulse sequences to be designed that make optimal use of the limited polarization available for imaging.

{{cite journal | vauthors = Xing Y, Reed GD, Pauly JM, Kerr AB, Larson PE | title = Optimal variable flip angle schemes for dynamic acquisition of exchanging hyperpolarized substrates | journal = Journal of Magnetic Resonance | volume = 234 | pages = 75–81 | date = September 2013 | pmid = 23845910 | doi = 10.1016/j.jmr.2013.06.003 | bibcode = 2013JMagR.234...75X | pmc = 3765634 }}{{cite journal | vauthors = Maidens J, Gordon JW, Arcak M, Larson PE | title = Optimizing Flip Angles for Metabolic Rate Estimation in Hyperpolarized Carbon-13 MRI | journal = IEEE Transactions on Medical Imaging | volume = 35 | issue = 11 | pages = 2403–2412 | date = November 2016 | pmid = 27249825 | doi = 10.1109/TMI.2016.2574240 | pmc=5134417}}

In contrast with conventional MRI, hyperpolarized experiments are inherently dynamic as images must be acquired as the injected substrate spreads through the body and is metabolized. This necessitates dynamical system modelling and estimation for quantifying metabolic reaction rates. A number of approaches exist for modeling the evolution of magnetization within a single voxel.

The simplest model of metabolic flux assumes unidirectional conversion of the injected substrate S to a product P. The rate of conversion is assumed to be governed by the reaction rate constant $k\_\backslash ce\{SP\}$

{{NumBlk|:|S ->[{{} \atop {k_\ce{SP}}}] P.|{{EquationRef|1}}}}

Exchange of magnetization between the two species can then be modeled using the linear ordinary differential equation

:$\backslash frac\{d\; M\_\backslash ce\{P\}\}\{dt\}(t)\; =\; -R\_\{1\backslash ce\; P\}\; M\_P(t)\; +\; k\_\backslash ce\{SP\}\; M\_S(t)$

where $R\_\{1\backslash ce\; P\}\; =\; \backslash frac\{1\}\{T\_\{1\backslash ce\; P\}\}$ denotes the rate at which the transverse magnetization decays to thermal equilibrium polarization, for the product species P.

The unidirectional flux model can be extended to account for bidirectional metabolic flux with forward rate $k\_\backslash ce\{SP\}$ and backward rate $k\_\{PS\}$

{{NumBlk|:|S <=>[{{} \atop {k_\ce{SP}}}][{{k_\ce{PS}} \atop {}}] P|{{EquationRef|2}}}}

The differential equation describing the magnetization exchange is then

:$$

\frac{d M_\ce{P}}{dt}(t) = -R_{1\ce P} M_\ce{P}(t) -k_\ce{PS} M_\ce{P}(t) + k_\ce{SP} M_\ce{S}(t).

Repeated radio-frequency (RF) excitation of the sample causes additional decay of the magnetization vector. For constant flip angle sequences, this effect can be approximated using a larger effective rate of decay computed as

:$$

R_{1\ce{P, eff}} = R_{1\ce P} - \frac{\log(\cos \alpha)}{TR}

where $\backslash alpha$ is the flip angle and $TR$ is the repetition time.

{{cite journal | vauthors = Søgaard LV, Schilling F, Janich MA, Menzel MI, Ardenkjaer-Larsen JH | title = In vivo measurement of apparent diffusion coefficients of hyperpolarized ¹³C-labeled metabolites | journal = NMR in Biomedicine | volume = 27 | issue = 5 | pages = 561–9 | date = May 2014 | pmid = 24664927 | doi = 10.1002/nbm.3093 | s2cid = 29659861 }}

Time-varying flip angle sequences can also be used, but require that the dynamics be modeled as a hybrid system with discrete jumps in the system state.

{{cite journal | vauthors = Bahrami N, Swisher CL, Von Morze C, Vigneron DB, Larson PE | title = Kinetic and perfusion modeling of hyperpolarized (13)C pyruvate and urea in cancer with arbitrary RF flip angles | journal = Quantitative Imaging in Medicine and Surgery | volume = 4 | issue = 1 | pages = 24–32 | date = February 2014 | pmid = 24649432 | doi = 10.3978/j.issn.2223-4292.2014.02.02 | pmc=3947982}}

The goal of many hyperpolarized carbon-13 MRI experiments is to map the activity of a particular metabolic pathway. Methods of quantifying the metabolic rate from dynamic image data include temporally integrating the metabolic curves, computing the definite integral referred to in pharmacokinetics as the area under the curve (AUC), and taking the ratio of integrals as a proxy for rate constants of interest.

Comparing the definite integral under the substrate and product metabolite curves has been proposed as an alternative to model-based parameter estimates as a method of quantifying metabolic activity. Under specific assumptions, the ratio

:\frac{AUC(P)}{AUC(S)}

of area under the product curve AUC(P) to the area under the substrate curve AUC(S) is proportional to the forward metabolic rate $k\_\backslash ce\{SP\}$.

{{cite journal | vauthors = Hill DK, Orton MR, Mariotti E, Boult JK, Panek R, Jafar M, Parkes HG, Jamin Y, Miniotis MF, Al-Saffar NM, Beloueche-Babari M, Robinson SP, Leach MO, Chung YL, Eykyn TR | title = Model free approach to kinetic analysis of real-time hyperpolarized 13C magnetic resonance spectroscopy data | journal = PLOS ONE | volume = 8 | issue = 9 | pages = e71996 | year = 2014 | pmid = 24023724 | doi = 10.1371/journal.pone.0071996 | bibcode = 2013PLoSO...871996H | pmc=3762840| doi-access = free }}

When the assumptions under which this ratio is proportional to $k\_\{PL\}$ are not met, or there is significant noise in the collected data, it is desirable to compute estimates of model parameters directly. When noise is independent and identically distributed and Gaussian, parameters can be fit using non-linear least squares estimation. Otherwise (for example if magnitude images with Rician-distributed noise are used), parameters can be estimated by maximum likelihood estimation. The spatial distribution of metabolic rates can be visualized by estimating metabolic rates corresponding to the time series from each voxel, and plotting a heat map of the estimated rates.

• Carbon-13 nuclear magnetic resonance
• Dynamic nuclear polarization
• Functional imaging
• Magnetic resonance spectroscopic imaging

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Category:Magnetic resonance imaging