View source for Hyperpolarized carbon-13 MRI

{{Short description|Medical imaging technique}}
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'''Hyperpolarized carbon-13 MRI''' is a [[functional imaging|functional medical imaging]] technique for probing [[perfusion]] and [[metabolism]] using injected [[Substrate (chemistry)|substrates]].

It is enabled by techniques for [[hyperpolarization (physics)|hyperpolarization]] of [[carbon-13]]-containing molecules using [[dynamic nuclear polarization]] and rapid dissolution to create an [[injection (medicine)|injectable]] solution.<ref>
{{cite journal | vauthors = Ardenkjaer-Larsen JH, Fridlund B, Gram A, Hansson G, Hansson L, Lerche MH, Servin R, Thaning M, Golman K | title = Increase in signal-to-noise ratio of > 10,000 times in liquid-state NMR | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 100 | issue = 18 | pages = 10158–63 | date = September 2003 | pmid = 12930897 | pmc = 193532 | doi = 10.1073/pnas.1733835100 | bibcode = 2003PNAS..10010158A | doi-access = free }}
</ref><ref>
{{cite journal | vauthors = Golman K, Ardenkjaer-Larsen JH, Petersson JS, Mansson S, Leunbach I | title = Molecular imaging with endogenous substances | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 100 | issue = 18 | pages = 10435–9 | date = September 2003 | pmid = 12930896 | pmc = 193579 | doi = 10.1073/pnas.1733836100 | bibcode = 2003PNAS..10010435G | doi-access = free }}</ref> Following the injection of a hyperpolarized substrate, metabolic activity can be mapped based on enzymatic conversion of the injected molecule. In contrast with other metabolic imaging methods such as [[positron emission tomography]], hyperpolarized carbon-13 MRI provides chemical as well as spatial information, allowing this technique to be used to probe the activity of specific metabolic pathways. This has led to new ways of imaging disease. For example, metabolic conversion of hyperpolarized [[pyruvate]] into [[lactic acid|lactate]] is increasingly being used to image [[cancer]]ous tissues via the [[Warburg effect (oncology)|Warburg effect]].<ref name="pmid17965722">
{{cite journal | vauthors = Day SE, Kettunen MI, Gallagher FA, Hu DE, Lerche M, Wolber J, Golman K, Ardenkjaer-Larsen JH, Brindle KM | title = Detecting tumor response to treatment using hyperpolarized 13C magnetic resonance imaging and spectroscopy | journal = Nature Medicine | volume = 13 | issue = 11 | pages = 1382–7 | date = November 2007 | pmid = 17965722 | doi = 10.1038/nm1650 | s2cid = 11576068 }}</ref><ref>{{cite journal| vauthors = Sriram R, Kurhanewicz J, Vigneron DB | title=Hyperpolarized Carbon-13 MRI and MRS Studies | journal=EMagRes| year=2014| volume=3| pages=1–14| doi=10.1002/9780470034590.emrstm1253| isbn=9780470034590 }}
</ref><ref>{{cite journal | vauthors = Nelson SJ, Kurhanewicz J, Vigneron DB, Larson PE, Harzstark AL, Ferrone M, van Criekinge M, Chang JW, Bok R, Park I, Reed G, Carvajal L, Small EJ, Munster P, Weinberg VK, Ardenkjaer-Larsen JH, Chen AP, Hurd RE, Odegardstuen LI, Robb FJ, Tropp J, Murray JA | title = Metabolic imaging of patients with prostate cancer using hyperpolarized [1-¹³C]pyruvate | journal = Science Translational Medicine | volume = 5 | issue = 198 | pages = 198ra108 | date = August 2013 | pmid = 23946197 | pmc = 4201045 | doi = 10.1126/scitranslmed.3006070 }}
</ref>

==Hyperpolarization==
{{Main|Hyperpolarization (physics)}}
While hyperpolarization of inorganic small molecules (like <sup>3</sup>He and <sup>129</sup>Xe) is generally achieved using [[Hyperpolarization (physics)#Spin-Exchange Optical Pumping|spin-exchange optical pumping]] (SEOP), compounds useful for metabolic imaging (such as <sup>13</sup>C or <sup>15</sup>N) are typically hyperpolarized using [[dynamic nuclear polarization]] (DNP). DNP can be performed at operating temperatures of 1.1-1.2 K, and high magnetic fields (~4T).<ref>{{cite journal | vauthors = Jóhannesson H, Macholl S, Ardenkjaer-Larsen JH | title = Dynamic Nuclear Polarization of [1-13C]pyruvic acid at 4.6 tesla | journal = Journal of Magnetic Resonance | volume = 197 | issue = 2 | pages = 167–75 | date = April 2009 | pmid = 19162518 | doi = 10.1016/j.jmr.2008.12.016 | bibcode = 2009JMagR.197..167J }}</ref> The compounds are then thawed and dissolved to yield a room temperature solution containing hyperpolarized nuclei which can be injected.

==Dissolution and injection==
Hyperpolarized samples of <sup>13</sup>C 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 [[Sodium chloride|NaCl]], and 50&nbsp;mg/L [[EDTA]].<ref name="pmid17965722" />

===Preclinical models===
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.<ref>{{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 }}</ref>

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

==Imaging methods==
[[File:In vivo hyperpolarized carbon 13 MRI spectra.png|thumb| Sequence of [[NMR spectra]] 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 [[lactic acid|lactate]], [[alanine]] and [[bicarbonate]].]]

===Spectroscopic imaging===
{{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.

===Metabolite-selective excitation===
Using techniques for simultaneous spatial and spectral selective excitation, RF pulses can be designed to perturb metabolites individually.<ref>
{{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 }}</ref><ref>
{{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 }}</ref>
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,<ref>
{{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 }}</ref><ref>{{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 }}</ref>
which enables pulse sequences to be designed that make optimal use of the limited polarization available for imaging.<ref>
{{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 }}</ref><ref>{{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}}</ref>

==Dynamic imaging models==

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. 
{| class="wikitable"
!
!pyruvate
!lactate
!alanine
|-
|T1
|~46.9-65 s dependent on B0 field strength<ref>{{cite journal | vauthors = Chattergoon N, Martínez-Santiesteban F, Handler WB, Ardenkjaer-Larsen JH, Scholl TJ | title = Field dependence of T1 for hyperpolarized [1-13C]pyruvate | journal = Contrast Media & Molecular Imaging | volume = 8 | issue = 1 | pages = 57–62 | date = January 2013 | pmid = 23109393 | doi = 10.1002/cmmi.1494 | doi-access =  }}</ref>
|
|
|-
|T2 ([[Hepatocellular carcinoma|HCC Tumor]])
|
|0.9 ± 0.2 s<ref name=":0">{{cite journal | vauthors = Yen YF, Le Roux P, Mayer D, King R, Spielman D, Tropp J, Butts Pauly K, Pfefferbaum A, Vasanawala S, Hurd R | title = T(2) relaxation times of (13)C metabolites in a rat hepatocellular carcinoma model measured in vivo using (13)C-MRS of hyperpolarized [1-(13)C]pyruvate | journal = NMR in Biomedicine | volume = 23 | issue = 4 | pages = 414–23 | date = May 2010 | pmid = 20175135 | pmc = 2891253 | doi = 10.1002/nbm.1481 }}</ref>
|1.2 ± 0.1 s<ref name=":0" /> 
|-
|T2 (Healthy Liver)
|
|0.52 ± 0.03 s<ref name=":0" /> 
|0.38 ± 0.05 s<ref name=":0" />
|}

===Two-species model with unidirectional flux===

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

Exchange of magnetization between the two species can then be modeled using the linear ordinary differential equation 
:<math chem>\frac{d M_\ce{P}}{dt}(t) = -R_{1\ce P} M_P(t) + k_\ce{SP} M_S(t)</math>
where <math chem>R_{1\ce P} = \frac{1}{T_{1\ce P}}</math> denotes the rate at which the transverse [[magnetization]] decays to thermal equilibrium polarization, for the product species P.

===Two-species model with bidirectional flux===

The unidirectional flux model can be extended to account for bidirectional metabolic flux with forward rate <math chem>k_\ce{SP}</math> and backward rate <math>k_{PS}</math> 
{{NumBlk|:|<chem>S <=>[{{} \atop {k_\ce{SP}}}][{{k_\ce{PS}} \atop {}}] P</chem>|{{EquationRef|2}}}}
The differential equation describing the magnetization exchange is then
:<math chem>
\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).  
</math>

===Effect of radio-frequency excitation===

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
:<math chem>
R_{1\ce{P, eff}} = R_{1\ce P} - \frac{\log(\cos \alpha)}{TR}
</math>
where <math>\alpha</math> is the flip angle and <math>TR</math> is the repetition time.<ref>
{{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 }}
</ref>
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.<ref>
{{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}}
</ref>

==Metabolism mapping==

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 ([[Area under the curve (pharmacokinetics)|AUC]]), and taking the ratio of integrals as a proxy for rate constants of interest.

===Area-under-the-curve ratio===
Comparing the [[Area under the curve (pharmacokinetics)|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 
:<chem>\frac{AUC(P)}{AUC(S)}</chem>
of area under the product curve AUC(P) to the area under the substrate curve AUC(S) is proportional to the forward metabolic rate <math chem>k_\ce{SP}</math>.<ref>
{{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 }}
</ref>

===Rate parameter mapping===
When the assumptions under which this ratio is proportional to <math>k_{PL}</math> 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 distribution|Gaussian]], parameters can be fit using [[non-linear least squares]] estimation. Otherwise (for example if magnitude images with [[Rice distribution|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.

== See also ==
* [[Carbon-13 nuclear magnetic resonance]]
* [[Dynamic nuclear polarization]]
* [[Functional imaging]]
* [[Magnetic resonance spectroscopic imaging]]

== References ==
{{Reflist}}

[[Category:Magnetic resonance imaging]]