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WIREs Nanomed Nanobiotechnol
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Magnetic resonance relaxation induced by superparamagnetic particles used as contrast agents in magnetic resonance imaging: a theoretical review

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Superparamagnetic nanoparticles are used as contrast agents in magnetic resonance imaging and allow, for example, the detection of tumors or the tracking of stem cells in vivo. By producing magnetic inhomogeneities, they influence the nuclear magnetic relaxation times, which results in a darkening, on the image, of the region containing these particles. A great number of studies have been devoted to their magnetic properties, to their synthesis and to their influence on nuclear magnetic relaxation. The theoretical and fundamental understanding of the behavior of these particles is a necessary step in predicting their efficiency as contrast agents, or to be able to experimentally obtain some of their properties from a nuclear magnetic resonance measurement. Many relaxation models have been published, and choosing one of them is not always easy, many parameters and conditions have to be taken into account. Relaxation induced by superparamagnetic particles is generally attributed to an outersphere relaxation mechanism. Each model can only be used under specific conditions (motional averaging regime, static regime, high magnetic field, etc.) or for a particular sequence (Carr‐Purcell‐Meiboom‐Gill, spin echo, free‐induction decay, nuclear magnetic relaxation dispersion profile, etc.). The parameters included in the equations must be carefully interpreted. In some more complex conditions, simulations are necessary to be able to predict the relaxation rates. A good agreement is usually observed between the theoretical predictions and the experimental results, although some data still cannot be fully understood, such as the dependence of the transverse relaxation on the magnetic field. WIREs Nanomed Nanobiotechnol 2017, 9:e1468. doi: 10.1002/wnan.1468 This article is categorized under: Diagnostic Tools > Diagnostic Nanodevices Diagnostic Tools > In Vivo Nanodiagnostics and Imaging
(a) Hysteresis curve of a ferro‐ or ferrimagnetic material. (b) Magnetic Langevin curve of a sample containing superparamagnetic nanoparticles. (c) A magnetic material is composed of Weiss domains. The arrows represent the electronic moment or spin of each structure. A superparamagnetic nanoparticle (SPM NP) is a particle composed of a single magnetic domain in which the electron spins are all aligned in the same direction.
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Clustered and unclustered systems with their associated parameters.
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Simulation results and theoretical prediction of the transverse relaxation rate at a high magnetic field. Each model fits well its region of validity except for the spin echo model which seems to fit only the static dephasing regime (SDR) regime (the value of κ = 0.002395 for f = 3.14 10−6 was obtained by numerically solving the transcendental equation in Ref ).
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Nuclear magnetic relaxation dispersion (NMRD) profiles for the transverse relaxation for (a) the low anisotropy model and (b) the Rigid Dipole model. Parameters used for the graphs: RSPM = 5 nm, D = 3 × 10−9 m2 s−1, Msat = 2 × 105 A m−1, CFe = 1 mM, T = 310 K, η = 0.6915 Pa s, τN = 10−9 s, and P = 0.8.
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Nuclear magnetic relaxation dispersion (NMRD) profiles of the Rigid Dipole relaxation model for (a) different radii RSPM and (b) different magnetizations Msat for magnetite. If not explicitly mentioned on the graph, the used parameters are: RSPM = 10 nm, D = 3 × 10−9 m2 s−1, Msat = 2 × 105 A m−1, CFe = 1 mM, T = 310 K, and η = 0.6915 Pa s. In (a), the last inflection point of each curve is also circled.
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Nuclear magnetic relaxation dispersion (NMRD) profiles predicted by the low anisotropy model (dominant Néel relaxation). If not explicitly mentioned the used parameters are: RSPM = 5 nm, D = 3 × 10−9 m2 s−1, Msat = 2 × 105 A m−1, CFe = 1 mM, τN = 10−9 s, and P = 0.8. (a) NMRD profiles for different radii. The circled last inflection point is shifted to a low magnetic field when the radius increases. (b) When the saturation magnetization increases, the maximum position is shifted to lower fields. (c) The region of influence of the different parameters on the curve.
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(a) Red arrows represent local magnetic fields and green arrows the proton spins. Each proton is exposed to its own local magnetic field. After the 90°‐pulse of a T2* sequence, all the proton spins are aligned in the transverse plane and the proton magnetization is thus maximum. (b) After a while, with each proton rotating at its own frequency and neglecting proton diffusion, a dephasing occurs and the magnetization is zero. (c) In a more realistic case, such as the superparamagnetic nanoparticle (SPM NP) case, magnetic inhomogeneities are produced by the SPM NP dipolar field and fluctuations come from the proton diffusion and the SPM magnetic moment fluctuation due to Néel or Brownian rotational relaxations.
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