Pierre Gillis

Theory of proton relaxation induced by superparamagnetic particles

Evaluating and understanding the performances of magnetic colloids as contrast agents for MRI requires a theory describing their magnetic interactions with water protons. The field dependence of the proton longitudinal relaxation rate (nuclear magnetic relaxation dispersion profiles) in aqueous colloidal suspensions of superparamagnetic particles is based on the so-called Curie relaxation, which essentially accounts for the high field part of the NMRD profiles (B0>0.02 T). The low-field part of the NMRD profiles can only be explained by the crystal’s internal anisotropy energy, a concept which clarifies the important difference between superpara- and paramagnetic compounds: the anisotropy energy modifies both the electronic precession frequencies and the thermodynamic probability of occupation of the crystal magnetic states. Our theory clearly explains why a low-field dispersion exists for suspensions of small size crystals, and why it does not for large crystals’ suspensions. This important effect is due...

Magnetic resonance relaxation properties of superparamagnetic particles.

Nanometric crystals of maghemite are known to exhibit superparamagnetism. Because of the significance of their magnetic moment, maghemite nanoparticles are exceptional contrast agents and are used for magnetic resonance imaging (of the liver, spleen, lymph nodes), for magnetic resonance angiography and for molecular and cellular imaging. The relaxivity of these agents depends on their size, saturation magnetization and magnetic field and also on their degree of clustering. There are different types of maghemite particles whose relaxation characteristics are suited to a specific MRI application. The relaxation induced by maghemite particles is caused by the diffusion of water protons in the inhomogeneous field surrounding the particles. This is well described by a theoretical model that takes magnetite crystal anisotropy and Néel relaxation into account. Another type of superparamagnetic compound is ferritin, the iron-storing protein: it contains a superparamagnetic ferrihydrite core. Even if the resulting magnetic moment of ferritin is far smaller than for magnetite nanoparticles, its massive presence in different organs darkens T(2)-weighted MR images, allowing the noninvasive estimation of iron content, thanks to MRI. The relaxation induced by ferritin in aqueous solutions has been demonstrated to be caused by the exchange of protons between bulk water protons and the surface of the ferrihydrite crystal. However, in vivo, the relaxation properties of ferritin are still unexplained, probably because of protein clustering.

On T2-shortening by strongly magnetized spheres: A partial refocusing model

Computer simulations of water transverse relaxation induced by superparamagnetic particles are shown to disagree with the available theories, covering the slow diffusion domain. Understanding these new simulations, not in the slow diffusion domain, thus requires a new theoretical approach. A “partial refocusing model” is introduced for this purpose; it is based on a spatial division between an inner region where the gradients are too strong for the refocusing pulses to be efficient and an outer region where they are efficient. This model agrees with published simulations of relaxation induced by magnetic dipoles approximated as points. The validity domains of the various models are also compared. Magn Reson Med 47:257–263, 2002.

On T2-Shortening by weakly magnetized particles : The chemical exchange model

Chemical exchange (CE) theory is compared with two theories of T2‐shortening caused by microscopic magnetic centers: inner‐ and outer‐sphere relaxation theory (long‐echo limit) and mean gradient diffusion theory (short‐echo limit). The CE equation is shown to be identical to these theories in the respective limits and appropriate parameter relationships are derived for spherical particles. The theories are then compared with computer simulations of spherical particles and with a recent general theory, with good agreement in the asymptotic regions. The CE model also reproduces the essential relaxation characteristics in the intermediate range. Finally, good agreement of a CE model with simulations for magnetized cylinders is also demonstrated. The discussion is limited to weakly magnetized particles such that the maximum phase shift during an echo interval is less than one radian, permitting the use of the Luz‐Meiboom CE equation. Magn Reson Med 45:1014–1020, 2001. Published 2001 Wiley‐Liss, Inc.

Relaxation Induced by Ferritin and Ferritin-Like Magnetic Particles: The Role of Proton Exchange

Proton T1 and T2 in solutions of ferritin and fercayl (a ferritin‐like iron‐dextran particle) solutions were measured, over a wide range of various parameters (Bo, temperature, interecho‐time and pH). The window of the previously referred linear dependence of 1/T2 on the static field was increased, up to 500 MHz, and the independence of T2 on the echo time was confirmed. Correlation times were extracted from T1 nuclear magnetic relaxation dispersion profiles. In the pH range studied, no strong variation of the relaxivities of ferritin solutions was noticed. Fercayl, which, unlike ferritin, remains stable under large pH variations, is characterized by strongly pH‐dependent relaxation rates. This feature is interpreted as due to the effect of proton exchange in the water relaxation process. Outer sphere theory, which ignores proton binding, is shown to be unable to describe the relaxation of ferritin and ferritin‐like particles solutions, first because it predicts a quadratic rate dependence on Bo, but also because it severely underestimates the relaxation rate. Explaining relaxation induced by ferritin and ferritin‐like particle solutions will likely require a model that accounts for proton binding. Magn Reson Med 43:237–243, 2000.

Structure and dynamics of water in tendon from NMR relaxation measurements

Nuclear magnetic relaxation times were measured in collagen tissue when varying the orientation of the fiber with respect to the static field. T1 was found to be only slightly dependent on theta, the fiber-to-field angle, but T2 was very sensitive to the orientation, with a maximum value at the magic angle. The transverse decay curves were multiexponential. Their deconvolution displayed four components; the ones that decayed most slowly were almost independent of theta, but the two fastest ones showed a strong angular dependence that was interpreted with a cross-relaxation model. Quadrupolar dips were visible in the 1/T1 dispersion curves. These dips were independent of theta, so that the magnetization transfer could also be assumed to be independent of the fiber orientation. Finally, each component was assigned to a fraction of protons localized in the macromolecular structure and characterized by particular dynamics. The model of Woessner was applied to the water molecules tightly bound into the macromolecules, which resulted in a dynamical description of this water fraction. This description is compatible with the two-sites model of Ramachandran based on x-ray diffraction and with the extensive studies of Berendsen. However, the important indications obtained from the deconvolution lead to a less static representation of the tissue.

Dy-DTPA derivatives as relaxation agents for very high field MRI: The beneficial effect of slow water exchange on the transverse relaxivities

Proton longitudinal and transverse relaxivities of Dy(DTPA)2− and Dy‐DTPA bisamide derivatives (Dy(DTPA‐BA): Dy‐DTPA bisamide, Dy(DTPA‐BEA): Dy‐DTPA bisethylamide, Dy(DTPA‐BnBA): Dy‐DTPA bis‐n‐butylamide, and Dy(DTPA‐BBMA): Dy‐DTPA bisbismethylamide) were analyzed between 0.47 T and 18.8 T. Curie longitudinal relaxation was clearly observed at magnetic fields larger than 2.4 T, but the longitudinal relaxivities are limited by the fast rotation of the complexes. Rotational correlation times were separately assessed by deuterium relaxometry of the diamagnetic deuterated lanthanum analogs. Transverse relaxivity, which depends on the square of the magnetic field and on the residence time of the coordinated water molecule (τM), was more than 7.5 times larger at 18.8 T and 310 K for Dy(DTPA‐BA) and Dy(DTPA‐BEA) as compared to Dy(DTPA)2−. This difference is mainly related to the slower water exchange of the bisamide complexes, as confirmed by the values of τM measured by oxygen‐17 relaxometry. Such Dy‐complexes, characterized by relatively long τM values (τ M 310 larger than 100 ns but smaller than 1 μs), thus appear to be useful as negative T2 (or transverse) contrast agents for high‐field imaging. This was demonstrated by the spin‐echo images of phantoms obtained at 4.7 T on samples containing Dy(DTPA)2− and Dy(DTPA‐BEA). Magn Reson Med 47:1121–1130, 2002.

Fiber-to-field angle dependence of proton nuclear magnetic relaxation in collagen

Longitudinal and transverse proton relaxation times were measured on pig tendon. For T1, dispersion curves and more accurate measurements at 20 MHz are presented. Values of T2 were obtained from CPMG pulse sequences, at 20 MHz. The dependence of relaxation times against the fiber-to-field angle was particularly investigated. Longitudinal relaxation rate was found to be almost orientation independent, and presented quadrupolar peaks between 1 and 4 MHz. On the contrary, transverse relaxation, that was well fitted by the sum of four exponentials, was highly orientation dependent. Deconvolution showed that the exponentials decaying most quickly are most orientation dependent. For those two fractions, a cross-relaxation model allowed explaining the fiber-to-field angle dependence, and the specially low rate corresponding to the magic angle of 55 degrees. Finally, each decaying mode was assigned to a fraction of protons localized in the macromolecular structure and characterized by particular dynamics.

Monte Carlo simulation and theory of proton NMR transverse relaxation induced by aggregation of magnetic particles used as MRI contrast agents

Superparamagnetic particles are widely used in MRI as R2 contrast agents. In this last decade, different studies have focused on aggregation of superparamagnetic particles for important applications such as multimodal agents. A complete study--via simulations--of the influence of aggregation on the MR efficiency of these particles at high magnetic field is presented here. First, an empirical expression is proposed for R2 in the presence of uniformly distributed nanoparticles, taking into account two regimes at once (motional averaging and slow motion regimes). Three cluster shapes are simulated: Sphere, shell and line. An analytical model is proposed to understand water transverse relaxation induced by spherical and shell aggregates. Simulations lead to the conclusion that, in the motional averaging regime, the most efficient aggregate contrast agent is the densest sphere or shell.

Anomalous nuclear magnetic relaxation of aqueous solutions of ferritin: an unprecedented first-order mechanism.

Ferritin, the iron‐storing protein, speeds up proton transverse magnetic relaxation in aqueous solutions. This T2 shortening is used in MRI to quantify iron in the brain and liver. Current theoretical models underestimate the relaxation enhancement by ferritin at imaging fields, and they do not predict the measured dependence of the rate enhancement on the magnetization of the particles. Here it is shown that a proton exchange dephasing model (PEDM) overcomes these limitations by allowing a first‐order relaxation mechanism. The PEDM considers proton exchange between bulk water and exchangeable protons located at the surface of the hydrated iron oxide nanometric core of the protein. Relaxation is shown to depend on the distribution of the frequency shifts of the adsorption sites; the observed properties agree with a Lorentzian distribution. Computer simulations utilizing recent Mössbauer spectroscopy data show that the distribution of these shifts is effectively Lorentzian. Magn Reson Med 48:959–964, 2002.