Analytical methods for characterizing magnetic resonance probes

Abstract

The efficiency of Gd(III) contrast agents in magnetic resonance image enhancement is governed by a set of tunable structural parameters. Understanding and measuring these parameters requires specific analytical techniques. This Feature describes strategies to optimize each of the critical Gd(III) relaxation parameters for molecular imaging applications and the methods employed for their evaluation.

Figure 1. An overview of MR Physics

Hydrogen nuclei, responsible for the inherent contrast of MR, have one proton and an odd atomic mass resulting in a spin of ½ and an overall magnetic moment. In the presence of an external magnetic field (B₀) the spins align parallel to the axis of the field with a slight population preference in the direction of B₀ (+ z). This induced polarization for the lower energy state (alignment with the field) is dictated by the Boltzmann distribution. The accumulation of individual proton magnetic moments results in a net nonzero magnetization in the z-direction (M_z = M₀); in the xy plane, the random alignment of each of the individual spins cancel to give an overall transverse magnetization (M_xy) of zero. (A) Excitation: The polarized nuclei are perturbed by a rotating magnetic field (B₁) perpendicular to B₀ to deliver radio frequency electromagnetic energy into the system (RF pulse). The energy of the RF pulse is equal to the Larmor frequency to facilitate resonance with the water proton spins. The duration of the RF pulse is correlated to the flip angle (a) relative to the external field. For example, a 90° RF pulse translocates the net magnetization vector into the transverse plane (M_z = 0, M_xy = M₀). (B) Relaxation: Upon removal of the RF pulse, the energized nuclear spins return to equilibrium. The nuclear spins will release this excess energy to their surroundings through molecular vibrations/rotations that occur at the Larmor frequency. The characteristic time in which the net magnetization returns to equilibrium by this mechanism is known as the spin-lattice (longitudinal) relaxation time (T₁). Alternatively, coherence of the transverse component can be lost as energy is absorbed/transferred to nearby protons with the same Larmor frequency. These intermolecular and intramolecular vibrations and rotations cause the net magnetization to fluctuate; this results in a time dependent decay [spin-spin (transverse) relaxation time, T₂]. However, inhomogeneities in the magnetic field and magnetic susceptibility differences of adjacent tissues can distort the true T₂ value; these contributions are expressed as T₂*. Pulse sequences enhance MR image contrast by exploiting differences in the T₁ and T₂ of tissues. (C) Variability in T₁ and T₂ resulting from the dissimilar water concentrations of different tissues contributes to the inherent grayscale contrast of a typical MR image. (D) An example of how Gd(III) contrast agents can enhance the contrast in an MR image of nanodiamonds through shorting T₁. T₁-weighted MR images of (1) water, (2) 1 mg/mL undecorated nanodiamonds, (3) undecorated nanodiamonds + coupling reagents, and (4)–(8) Gd(III) –nanodiamond conjugates. Reprinted with permission from Ref. . Copyright 2010 American Chemical Society.

Figure 2. Gd(III) contrast agents: design and structural parameters

(A) Common clinically approved Gd(III) contrast agents. Gd(III), a nine-coordinate lanthanide metal, is chelated by cyclic or linear ligands leaving at least one coordination site open for water exchange. Chelation by the organic framework mitigates toxicity concerns while simultaneously allowing additional synthetic modification near the paramagnetic center. (B) A schematic depiction of the parameters that govern Gd(III) relaxation enhancement. The relaxivity of a Gd(III) contrast agent is controlled by the rotational correlation time (τ_R), the number of water molecules coordinated to the Gd(III) ion (q), and the time the water remains coordinated to the metal (τ_M).

Figure 3

Strategies for q-modulated relaxation enhancement include: (A) Alternative ligand design,^{, ,} and (B) Ion-responsive contrast enhancement. Adapted with permission from Ref. . Copyright 2008 American Chemical Society. (C) Energy level diagrams for Eu(III) and Tb(III) pertaining to q measurement by luminescence lifetime decay. The denoted emission transitions are the most intense radiative transitions for each tripositive lanthanide. Radiationless decay mechanisms mediated by O-H oscillators are labeled with dotted arrows. Adapted from ref. . Copyright 1965, American Institute of Physics.

Figure 4

Strategies for τ_R modulation. (A) Schematic of a HaloTag-targeted Gd(III) contrast agent. The haloalkane tail of the Gd(III)-DO3A chelate is irreversibly bound to the mutated enzyme activity site buried deep in the interior of the protein. Upon binding, the effective radius of the small molecule is greatly increased slowing rotational motion. This τ_R-modulated relaxation enhancement strategy boosts the efficiency of the chelate almost six-fold in comparison to the unconjugated small molecule. Adapted with permission from Ref. . Copyright 2011 American Chemical Society. (B) Decreasing the number of carbons between a small molecule agent and its intended benzyl scaffold increases relaxivity via a local τ_R effect. An NMRD curve shows the characteristic bell-curve feature at field strengths corresponding to the Larmor frequency signaling a τ_R effect in the corresponding agents. Small molecule agents with short τ_R values give the relatively featureless curves at these same frequencies. The NMRD curve is reprinted with permission from Ref. . Copyright 2011 American Chemical Society.

Figure 5

Strategies to optimize of the lifetime of the bound solvent molecule (τ_M) include: (A) Steric compression via the addition of a methylene group to the coordinating acetate arms or chelate backbone, and (B) addition of sterically bulky groups to the chelate backbone.