Hyperpolarized carbon-13 MRI

Last updated
Hyperpolarized carbon-13 MRI
Purposeimaging technique for probing perfusion and metabolism

Hyperpolarized carbon-13 MRI is a functional medical imaging technique for probing perfusion and metabolism using injected substrates.

Contents

It is enabled by techniques for hyperpolarization of carbon-13-containing molecules using dynamic nuclear polarization and rapid dissolution to create an injectable solution. [1] [2] 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 lactate is increasingly being used to image cancerous tissues via the Warburg effect. [3] [4] [5]

Hyperpolarization

While hyperpolarization of inorganic small molecules (like 3He and 129Xe) is generally achieved using spin-exchange optical pumping (SEOP), compounds useful for metabolic imaging (such as 13C or 15N) 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). [6] 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 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. [3]

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. [7]

Clinical trials

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. [8]

Imaging methods

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 lactate, alanine and bicarbonate. In vivo hyperpolarized carbon 13 MRI spectra.png
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 lactate, alanine and bicarbonate.

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. [9] [10] 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, [11] [12] which enables pulse sequences to be designed that make optimal use of the limited polarization available for imaging. [13] [14]

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.

pyruvatelactatealanine
T1~46.9-65 s dependent on B0 field strength [15]
T2 (HCC Tumor)0.9 ± 0.2 s [16] 1.2 ± 0.1 s [16]
T2 (Healthy Liver)0.52 ± 0.03 s [16] 0.38 ± 0.05 s [16]

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

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

where 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 and backward rate

The differential equation describing the magnetization exchange is then

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

where is the flip angle and is the repetition time. [17] 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. [18]

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 (AUC), and taking the ratio of integrals as a proxy for rate constants of interest.

Area-under-the-curve ratio

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

of area under the product curve AUC(P) to the area under the substrate curve AUC(S) is proportional to the forward metabolic rate . [19]

Rate parameter mapping

When the assumptions under which this ratio is proportional to 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.

See also

Related Research Articles

<span class="mw-page-title-main">Magnetic resonance imaging</span> Medical imaging technique

Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes inside the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to generate images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from computed tomography (CT) and positron emission tomography (PET) scans. MRI is a medical application of nuclear magnetic resonance (NMR) which can also be used for imaging in other NMR applications, such as NMR spectroscopy.

<span class="mw-page-title-main">SQUID</span> Type of magnetometer

A SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields, based on superconducting loops containing Josephson junctions.

Hyperpolarization is the spin polarization of the atomic nuclei of a material in a magnetic field far beyond thermal equilibrium conditions determined by the Boltzmann distribution. It can be applied to gases such as 129Xe and 3He, and small molecules where the polarization levels can be enhanced by a factor of 104–105 above thermal equilibrium levels. Hyperpolarized noble gases are typically used in magnetic resonance imaging (MRI) of the lungs. Hyperpolarized small molecules are typically used for in vivo metabolic imaging. For example, a hyperpolarized metabolite can be injected into animals or patients and the metabolic conversion can be tracked in real-time. Other applications include determining the function of the neutron spin-structures by scattering polarized electrons from a very polarized target (3He), surface interaction studies, and neutron polarizing experiments.

In magnetic resonance imaging (MRI) and nuclear magnetic resonance spectroscopy (NMR), an observable nuclear spin polarization (magnetization) is created by a homogeneous magnetic field. This field makes the magnetic dipole moments of the sample precess at the resonance (Larmor) frequency of the nuclei. At thermal equilibrium, nuclear spins precess randomly about the direction of the applied field. They become abruptly phase coherent when they are hit by radiofrequency (RF) pulses at the resonant frequency, created orthogonal to the field. The RF pulses cause the population of spin-states to be perturbed from their thermal equilibrium value. The generated transverse magnetization can then induce a signal in an RF coil that can be detected and amplified by an RF receiver. The return of the longitudinal component of the magnetization to its equilibrium value is termed spin-latticerelaxation while the loss of phase-coherence of the spins is termed spin-spin relaxation, which is manifest as an observed free induction decay (FID).

<span class="mw-page-title-main">Spin–spin relaxation</span> Magnetic phenomenon

In physics, the spin–spin relaxation is the mechanism by which Mxy, the transverse component of the magnetization vector, exponentially decays towards its equilibrium value in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). It is characterized by the spin–spin relaxation time, known as T2, a time constant characterizing the signal decay. It is named in contrast to T1, the spin–lattice relaxation time. It is the time it takes for the magnetic resonance signal to irreversibly decay to 37% (1/e) of its initial value after its generation by tipping the longitudinal magnetization towards the magnetic transverse plane. Hence the relation

During nuclear magnetic resonance observations, spin–lattice relaxation is the mechanism by which the longitudinal component of the total nuclear magnetic moment vector (parallel to the constant magnetic field) exponentially relaxes from a higher energy, non-equilibrium state to thermodynamic equilibrium with its surroundings (the "lattice"). It is characterized by the spin–lattice relaxation time, a time constant known as T1.

<span class="mw-page-title-main">Zero field NMR</span> Acquisition of NMR spectra of chemicals

Zero- to ultralow-field (ZULF) NMR is the acquisition of nuclear magnetic resonance (NMR) spectra of chemicals with magnetically active nuclei in an environment carefully screened from magnetic fields. ZULF NMR experiments typically involve the use of passive or active shielding to attenuate Earth’s magnetic field. This is in contrast to the majority of NMR experiments which are performed in high magnetic fields provided by superconducting magnets. In ZULF experiments the sample is moved through a low field magnet into the "zero field" region where the dominant interactions are nuclear spin-spin couplings, and the coupling between spins and the external magnetic field is a perturbation to this. There are a number of advantages to operating in this regime: magnetic-susceptibility-induced line broadening is attenuated which reduces inhomogeneous broadening of the spectral lines for samples in heterogeneous environments. Another advantage is that the low frequency signals readily pass through conductive materials such as metals due to the increased skin depth; this is not the case for high-field NMR for which the sample containers are usually made of glass, quartz or ceramic. High-field NMR employs inductive detectors to pick up the radiofrequency signals, but this would be inefficient in ZULF NMR experiments since the signal frequencies are typically much lower. The development of highly sensitive magnetic sensors in the early 2000s including SQUIDs, magnetoresistive sensors, and SERF atomic magnetometers made it possible to detect NMR signals directly in the ZULF regime. Previous ZULF NMR experiments relied on indirect detection where the sample had to be shuttled from the shielded ZULF environment into a high magnetic field for detection with a conventional inductive pick-up coil. One successful implementation was using atomic magnetometers at zero magnetic field working with rubidium vapor cells to detect zero-field NMR.

Fluxomics describes the various approaches that seek to determine the rates of metabolic reactions within a biological entity. While metabolomics can provide instantaneous information on the metabolites in a biological sample, metabolism is a dynamic process. The significance of fluxomics is that metabolic fluxes determine the cellular phenotype. It has the added advantage of being based on the metabolome which has fewer components than the genome or proteome.

In vivo magnetic resonance spectroscopy (MRS) is a specialized technique associated with magnetic resonance imaging (MRI).

<span class="mw-page-title-main">Nuclear magnetic resonance</span> Spectroscopic technique based on change of nuclear spin state

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. High-resolution nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI). The original application of NMR to condensed matter physics is nowadays mostly devoted to strongly correlated electron systems. It reveals large many-body couplings by fast broadband detection and should not be confused with solid state NMR, which aims at removing the effect of the same couplings by Magic Angle Spinning techniques.

<span class="mw-page-title-main">Physics of magnetic resonance imaging</span> Overview article

Magnetic resonance imaging (MRI) is a medical imaging technique mostly used in radiology and nuclear medicine in order to investigate the anatomy and physiology of the body, and to detect pathologies including tumors, inflammation, neurological conditions such as stroke, disorders of muscles and joints, and abnormalities in the heart and blood vessels among other things. Contrast agents may be injected intravenously or into a joint to enhance the image and facilitate diagnosis. Unlike CT and X-ray, MRI uses no ionizing radiation and is, therefore, a safe procedure suitable for diagnosis in children and repeated runs. Patients with specific non-ferromagnetic metal implants, cochlear implants, and cardiac pacemakers nowadays may also have an MRI in spite of effects of the strong magnetic fields. This does not apply on older devices, and details for medical professionals are provided by the device's manufacturer.

<span class="mw-page-title-main">Real-time MRI</span> Type of MRI

Real-time magnetic resonance imaging (RT-MRI) refers to the continuous monitoring of moving objects in real time. Traditionally, real-time MRI was possible only with low image quality or low temporal resolution. An iterative reconstruction algorithm removed limitations. Radial FLASH MRI (real-time) yields a temporal resolution of 20 to 30 milliseconds for images with an in-plane resolution of 1.5 to 2.0 mm. Real-time MRI adds information about diseases of the joints and the heart. In many cases MRI examinations become easier and more comfortable for patients, especially for the patients who cannot calm their breathing or who have arrhythmia.

Functional magnetic resonance spectroscopy of the brain (fMRS) uses magnetic resonance imaging (MRI) to study brain metabolism during brain activation. The data generated by fMRS usually shows spectra of resonances, instead of a brain image, as with MRI. The area under peaks in the spectrum represents relative concentrations of metabolites.

<span class="mw-page-title-main">Phase contrast magnetic resonance imaging</span> Magnetic resonance imaging to determine flow velocities

Phase contrast magnetic resonance imaging (PC-MRI) is a specific type of magnetic resonance imaging used primarily to determine flow velocities. PC-MRI can be considered a method of Magnetic Resonance Velocimetry. It also provides a method of magnetic resonance angiography. Since modern PC-MRI is typically time-resolved, it provides a means of 4D imaging.

Adiabatic radio frequency (RF) pulses are used in magnetic resonance imaging (MRI) to achieve excitation that is insensitive to spatial inhomogeneities in the excitation field or off-resonances in the sampled object.

Synthetic MRI is a simulation method in Magnetic Resonance Imaging (MRI), for generating contrast weighted images based on measurement of tissue properties. The synthetic (simulated) images are generated after an MR study, from parametric maps of tissue properties. It is thereby possible to generate several contrast weightings from the same acquisition. This is different from conventional MRI, where the signal acquired from the tissue is used to generate an image directly, often generating only one contrast weighting per acquisition. The synthetic images are similar in appearance to those normally acquired with an MRI scanner.

<span class="mw-page-title-main">MRI pulse sequence</span> A pulse sequence during a medical test

An MRI pulse sequence in magnetic resonance imaging (MRI) is a particular setting of pulse sequences and pulsed field gradients, resulting in a particular image appearance.

Hyperpolarized 129Xe gas magnetic resonance imaging (MRI) is a medical imaging technique used to visualize the anatomy and physiology of body regions that are difficult to image with standard proton MRI. In particular, the lung, which lacks substantial density of protons, is particularly useful to be visualized with 129Xe gas MRI. This technique has promise as an early-detection technology for chronic lung diseases and imaging technique for processes and structures reliant on dissolved gases. 129Xe is a stable, naturally occurring isotope of xenon with 26.44% isotope abundance. It is one of two Xe isotopes, along with 131Xe, that has non-zero spin, which allows for magnetic resonance. 129Xe is used for MRI because its large electron cloud permits hyperpolarization and a wide range of chemical shifts. The hyperpolarization creates a large signal intensity, and the wide range of chemical shifts allows for identifying when the 129Xe associates with molecules like hemoglobin. 129Xe is preferred over 131Xe for MRI because 129Xe has spin 1/2, a longer T1, and 3.4 times larger gyromagnetic ratio (11.78 MHz/T).

Kevin Michael Brindle,, is a British biochemist, currently Professor of Biomedical Magnetic Resonance in the Department of Biochemistry at the University of Cambridge and a Senior Group Leader at Cancer Research UK. He is known for developing magnetic resonance imaging (MRI) techniques for use in cell biochemistry and new imaging methods for early detection, monitoring, and treatment of cancer.

Hyperpolarized gas MRI, also known as hyperpolarized helium-3 MRI or HPHe-3 MRI, is a medical imaging technique that uses hyperpolarized gases to improve the sensitivity and spatial resolution of magnetic resonance imaging (MRI). This technique has many potential applications in medicine, including the imaging of the lungs and other areas of the body with low tissue density.

References

  1. ↑ Ardenkjaer-Larsen JH, Fridlund B, Gram A, Hansson G, Hansson L, Lerche MH, Servin R, Thaning M, Golman K (September 2003). "Increase in signal-to-noise ratio of > 10,000 times in liquid-state NMR". Proceedings of the National Academy of Sciences of the United States of America. 100 (18): 10158–63. Bibcode:2003PNAS..10010158A. doi: 10.1073/pnas.1733835100 . PMC   193532 . PMID   12930897.
  2. ↑ Golman K, Ardenkjaer-Larsen JH, Petersson JS, Mansson S, Leunbach I (September 2003). "Molecular imaging with endogenous substances". Proceedings of the National Academy of Sciences of the United States of America. 100 (18): 10435–9. Bibcode:2003PNAS..10010435G. doi: 10.1073/pnas.1733836100 . PMC   193579 . PMID   12930896.
  3. 1 2 Day SE, Kettunen MI, Gallagher FA, Hu DE, Lerche M, Wolber J, Golman K, Ardenkjaer-Larsen JH, Brindle KM (November 2007). "Detecting tumor response to treatment using hyperpolarized 13C magnetic resonance imaging and spectroscopy". Nature Medicine. 13 (11): 1382–7. doi:10.1038/nm1650. PMID   17965722. S2CID   11576068.
  4. ↑ Sriram R, Kurhanewicz J, Vigneron DB (2014). "Hyperpolarized Carbon-13 MRI and MRS Studies". EMagRes. 3: 1–14. doi:10.1002/9780470034590.emrstm1253. ISBN   9780470034590.
  5. ↑ 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 (August 2013). "Metabolic imaging of patients with prostate cancer using hyperpolarized [1-¹³C]pyruvate". Science Translational Medicine. 5 (198): 198ra108. doi:10.1126/scitranslmed.3006070. PMC   4201045 . PMID   23946197.
  6. ↑ Jóhannesson H, Macholl S, Ardenkjaer-Larsen JH (April 2009). "Dynamic Nuclear Polarization of [1-13C]pyruvic acid at 4.6 tesla". Journal of Magnetic Resonance. 197 (2): 167–75. Bibcode:2009JMagR.197..167J. doi:10.1016/j.jmr.2008.12.016. PMID   19162518.
  7. ↑ Miloushev VZ, Keshari KR, Holodny AI (February 2016). "Hyperpolarization MRI: Preclinical Models and Potential Applications in Neuroradiology". Topics in Magnetic Resonance Imaging. 25 (1): 31–7. doi:10.1097/RMR.0000000000000076. PMC   4968075 . PMID   26848559.
  8. ↑ "Clinical Trials".
  9. ↑ Lupo JM, Chen AP, Zierhut ML, Bok RA, Cunningham CH, Kurhanewicz J, Vigneron DB, Nelson SJ (February 2010). "Analysis of hyperpolarized dynamic 13C lactate imaging in a transgenic mouse model of prostate cancer". Magnetic Resonance Imaging. 28 (2): 153–62. doi:10.1016/j.mri.2009.07.007. PMC   3075841 . PMID   19695815.
  10. ↑ Cunningham CH, Chen AP, Lustig M, Hargreaves BA, Lupo J, Xu D, Kurhanewicz J, Hurd RE, Pauly JM, Nelson SJ, Vigneron DB (July 2008). "Pulse sequence for dynamic volumetric imaging of hyperpolarized metabolic products". Journal of Magnetic Resonance. 193 (1): 139–46. Bibcode:2008JMagR.193..139C. doi:10.1016/j.jmr.2008.03.012. PMC   3051833 . PMID   18424203.
  11. ↑ Larson PE, Kerr AB, Chen AP, Lustig MS, Zierhut ML, Hu S, Cunningham CH, Pauly JM, Kurhanewicz J, Vigneron DB (September 2008). "Multiband excitation pulses for hyperpolarized 13C dynamic chemical-shift imaging". Journal of Magnetic Resonance. 194 (1): 121–7. Bibcode:2008JMagR.194..121L. doi:10.1016/j.jmr.2008.06.010. PMC   3739981 . PMID   18619875.
  12. ↑ Marco-Rius I, Cao P, von Morze C, Merritt M, Moreno KX, Chang GY, Ohliger MA, Pearce D, Kurhanewicz J, Larson PE, Vigneron DB (April 2017). "13 C-MR metabolism studies". Magnetic Resonance in Medicine. 77 (4): 1419–1428. doi:10.1002/mrm.26226. PMC   5040611 . PMID   27017966.
  13. ↑ Xing Y, Reed GD, Pauly JM, Kerr AB, Larson PE (September 2013). "Optimal variable flip angle schemes for dynamic acquisition of exchanging hyperpolarized substrates". Journal of Magnetic Resonance. 234: 75–81. Bibcode:2013JMagR.234...75X. doi:10.1016/j.jmr.2013.06.003. PMC   3765634 . PMID   23845910.
  14. ↑ Maidens J, Gordon JW, Arcak M, Larson PE (November 2016). "Optimizing Flip Angles for Metabolic Rate Estimation in Hyperpolarized Carbon-13 MRI". IEEE Transactions on Medical Imaging. 35 (11): 2403–2412. doi:10.1109/TMI.2016.2574240. PMC   5134417 . PMID   27249825.
  15. ↑ Chattergoon N, Martínez-Santiesteban F, Handler WB, Ardenkjaer-Larsen JH, Scholl TJ (January 2013). "Field dependence of T1 for hyperpolarized [1-13C]pyruvate". Contrast Media & Molecular Imaging. 8 (1): 57–62. doi:10.1002/cmmi.1494. PMID   23109393.
  16. 1 2 3 4 Yen YF, Le Roux P, Mayer D, King R, Spielman D, Tropp J, Butts Pauly K, Pfefferbaum A, Vasanawala S, Hurd R (May 2010). "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". NMR in Biomedicine. 23 (4): 414–23. doi:10.1002/nbm.1481. PMC   2891253 . PMID   20175135.
  17. ↑ Søgaard LV, Schilling F, Janich MA, Menzel MI, Ardenkjaer-Larsen JH (May 2014). "In vivo measurement of apparent diffusion coefficients of hyperpolarized ¹³C-labeled metabolites". NMR in Biomedicine. 27 (5): 561–9. doi:10.1002/nbm.3093. PMID   24664927. S2CID   29659861.
  18. ↑ Bahrami N, Swisher CL, Von Morze C, Vigneron DB, Larson PE (February 2014). "Kinetic and perfusion modeling of hyperpolarized (13)C pyruvate and urea in cancer with arbitrary RF flip angles". Quantitative Imaging in Medicine and Surgery. 4 (1): 24–32. doi:10.3978/j.issn.2223-4292.2014.02.02. PMC   3947982 . PMID   24649432.
  19. ↑ 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 (2014). "Model free approach to kinetic analysis of real-time hyperpolarized 13C magnetic resonance spectroscopy data". PLOS ONE. 8 (9): e71996. Bibcode:2013PLoSO...871996H. doi: 10.1371/journal.pone.0071996 . PMC   3762840 . PMID   24023724.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.