Paramagnetic Relaxation

How does gadolinium cause relaxation?  

MR contrast agents containing gadolinium (and other metal ions) induce both T1 and T2 relaxation in tissues where they accumulate. This results from dipolar interactions between water nuclei (in tissue) and electron spins at the metallic center. The phenomenon is known as paramagnetic relaxation enhancement (PRE).

As described in the prior Q&A gadolinium (Gd) exhibits powerful paramagnetism due to its electronic structure, possessing 7 unpaired electrons in its 4f shell. As these inner electrons are not directly involved with bonding, the paramagnetism of Gd is maintained even when formulated as a contrast agent attache to a larger molecule. 

Electronic structure of the Gd atom

A further consequence of this electron structure is that the Gd⁺³ ion typically exhibits nine coordination sites for bonding and chemical interactions. In all MR contrast agents now commercially available, a ligand group occupies eight of these sites while the ninth is available for transient bonding by a solvent water molecule. This water molecule approaches very close (mean distance ~0.25 nm) to the metallic center, fitting into a crevice of the ligand. These direct and intimate magnetic interactions between water and the Gd⁺³ ion give rise to a process known as inner sphere relaxation.

The powerful paramagnetism of the Gd ion has effects that extend well beyond this inner sphere, however. At a distance of about 0.4-0.5 nm lies another group of water molecules in a so-called second shell.  Some of the water molecules in the second shell are transiently bonded to hydroxyl and carboxyl groups on the surface of the ligand, while others are just diffusing by. Molecules in the second shell are also in continuous chemical exchange with bulk water much further away. The indirect effects of the Gd ion on this pool is known as outer sphere relaxation. 

Ball and stick model of the contrast agent Gd-DTPA (Magnevist®). The Gd⁺³ ion is coordinated with 5 oxygen atoms (blue) and 3 nitrogen atoms (red). Structural carbon atoms are black. The crevice in the molecule leaves room for a single water molecule (blue and green) to interact directly with the Gd⁺³ ion (inner sphere relaxation). Beyond this a second shell of other water molecules experience outer sphere relaxation.

Although the paramagnetically-induced static field distortions surrounding the Gd ion are sufficient to induce T2 relaxation, T1 relaxation requires field fluctuations near the Larmor frequency. Such fluctuations occur secondary to thermally-induced tumbling of the Gd-containing macromolecule as well as rotations, collisions, bonding and diffusion of the surrounding water molecules. Dipole-dipole interactions (described in prior Q&A) between the water protons and the metallic center are primarily responsible for paramagnetic relaxation in the Gd-containing contrast agents now in common use. 

Biophysical theories describing how paramagnetic contrast agents produce these effects are beyond the scope of this website. Several excellent review articles are provided in the references below for interested readers. From this complex analysis, the following general conclusions can be drawn:

     1.  Molecular size.  For efficient relaxation to occur from the dipolar mechanism, the molecular correlation time (reflecting the rotational rate of the contrast molecule) should have components near the Larmor frequency. Smaller aqueous contrast agents (like Gd-DTPA) tumble too quickly to be highly efficient at relaxation. Larger molecular weight contrast agents will therefore have slightly better relaxivity than smaller ones. If the contrast agent attaches to a very large molecule (such as albumin), its motion slows to a range much closer to the Larmor frequency and its relaxivity increases dramatically. Thus the once commercially available contrast agent Ablavar® (which was essentially Gd-DTPA with a ligand modification allowing strong binding to albumin) had a relaxivity 4-5 x higher than simple Gd-DTPA (Magnevist®).     

     2. Inner sphere effects. In the inner sphere, water molecules make a very close approach to the gadolinium center resulting in a powerful dipole-dipole interaction. The magnitude of the inner sphere effect depends on how close an approach of water is allowed by the molecule as well as the number of potential binding sites available. Currently available gadolinium agents have only one inner sphere binding site.  The size and shape of the contrast molecule also affects the mean residence time for each water molecule at this site. For most commercially available contrast agents the mean residence time is approximately 1 μsec.  This translates to a water exchange rate of approximately 1 million times per second. Thus a single gadolinium molecule can affect many, many water protons in a short period of time!

     3.  Outer sphere effects.  Outer sphere relaxation is also dipolar in nature but not as powerful as inner sphere effects on a molecule-by-molecule basis because of the larger distance of these waters from the gadolinium center. Nevertheless, a much larger number of water molecules are exposed to magnetic field fluctuations along the surface of the contrast agent than the single molecule at the inner sphere site. And water in this outer shell can exchange magnetization with others in the bulk water pool more distally.  

     4.  Relative magnitudes of inner and outer sphere effects. The relative contributions of inner and outer sphere effects to total relaxation depend on field strength, the size and type of the contrast agent molecule, and the diffusion rate of water in the surroundings. It is generally believed that for conventional Gd-based contrast agents at clinically relevant field strengths (0.5 - 3.0T) inner sphere and outer sphere contributions are roughly equal. Outer sphere relaxation is more important for smaller contrast agents without protein binding, slow translational diffusion, and lower field strengths. Conversely, inner sphere effects are more important at high fields for slowly rotating systems in the setting of fast translational diffusion.

The following educational video may clarify some of these points.

Advanced Discussion (show/hide)»

Although dipole-dipole interactions are primarily responsible for paramagnetic relaxation in the commonly used gadolinium chelates for clinical imaging, additional mechanisms may be important for other contrast agents, including non-gadolinium ones.

A second mechanism called the Fermi contact shift explains paramagnetic relaxation between an electron and nuclear spin. This involves the transfer of unpaired electron density to overlap with the s-orbitals at the center of the relaxing nucleus. It is a scalar process transmitted through bonds and very similar to nucleus-nucleus J-coupling. It is an important factor for the relaxation of certain transition element complexes such as low spin Fe (III) heme and Ni (II)-based contrast agents.

Finally, chemical exchange and magnetization transfer mechanisms can play important roles, especially explaining the properties of a new class of contrast materials called ParaCEST (Paramagnetic Chemical Exchange Saturation Transfer) agents. The paramagnetic center of these molecules is typically a non-gadolinium lanthanide-series element such as Eu (III) or Dy (III) complexed with ligands having easily exchangeable protons on −NH or −OH moieties. These ¹H protons chemically exchange first with coordinated water molecules in the outer sphere around the contrast agent, then subsequently transfer their magnetization to bulk water.

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References
     Aime S, Botta M, Fasano M, Terreno E. Lanthanide (III) chelates for NMR biomedical applications. Chem Soc Rev 1998; 27:19-29.  
     Belorizky E, Fries PH, Helm L, et al. Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field. J Chem Phys 2008; 128:052315.
     Caravan P, Ellison JJ, McMurry TJ, Lauffer RB. Gadolinium (III) chelates as contrast agents: structure, dynamics, and applications. Chem Rev 1999; 99:2293-2352.  
     De León‐Rodríguez LM, Martins AF, Pinho MC, et al. Basic MR relaxation mechanisms and contrast agent design. J Magn Reson Imaging 2015; 42:545-565.
     Kruk D, Kowalewski J. General treatment of paramagnetic relaxation enhancement associated with translational diffusion. J Chem Phy 2009; 130:174104.  
     Yang C-T, Chuang K-H. Gd(III) chelates for MRI contrast agents: from high relaxivity to "smart", from blood pool to blood-brain barrier permeable. Med Chem Commun 2012; 3:552-565.

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Related Questions
     Can you explain a little more about the dipole-dipole interaction? I still don't quite understand. 

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