The relaxivity represents the relaxation enhancement of water protons in solutions containing the paramagnetic agent at 1 mM concentration.8 It usually refers to the value measured at the observation frequency of 20 MHz and the temperature of 25 °C or 39 °C. Much work has been done in the past 15 years or so to get an understanding of the relationships between structure and dynamics of a paramagnetic complex and the observed relaxivity.14 The observed longitudinal relaxation rate (Robs) of the water protons in an aqueous solution containing a paramagnetic complex is the sum of three contributions: (i) a diamagnetic one, whose value corresponds to the relaxation rate that would have been measured in the presence of a corresponding diamagnetic complex (R0); (ii) a paramagnetic one (R"1p), arising from the exchange of water molecules from the inner coordination sphere of the metal ion with the bulk water; and (iii) a paramagnetic one relative to the contribution of water molecules that diffuse in the outer coordination sphere of the paramagnetic centre (ROS):
Sometimes also a fourth paramagnetic contribution is taken into account that is due to the presence of mobile protons or water molecules (tightly interacting with the surface of the chelate) in the second coordination sphere of the metal ion.15
The inner-sphere contribution RI1Sp is given by:
where [C] is the concentration of the paramagnetic agent, q is the number of water molecules (generally 1 or 2) coordinated to the paramagnetic complex, rm is their exchange lifetime and T1M is the longitudinal relaxation time of their protons.
Commonly, T1M is evaluated on the basis of the expression developed earlier for simple aqua-ions:16
where S is the electron spin quantum number, 7I the proton nuclear magneto-gyric ratio, ge and mB the electronic g factor and Bohr magneton, respectively. !I and !S the proton and electron Larmor frequencies, respectively, and rc is the correlation time. rc is given by the sum:
Thus the shortest of the three correlation times (rR _ reorientational; rs _ electronic; rm _ exchange) determines rc and in turn T1M and the overall relaxivity.
The commercial CAs shown in Figure 28.1 are monohydrated (q _ 1) systems with a molecular weight of about 600-800 Da. that corresponds to rotational correlation times rR, about 60-80 ps. For this class of polyaminocarboxylate complexes, the exchange lifetime rM is typically found to be in the range 50-500 ns and T1e« 1 ns at 0.5 T; thus the inner sphere relaxivity, R^p, assumes a value of ca. 2.5-3.5mM-1 s-1, at 25 °C. Therefore, as it was recognized earlier, it is evident that at 0.5 T the overall correlation time rci is largely dominated by the rotational correlation time, whereas the contribution of both the exchange lifetime and the electronic relaxation plays an almost negligible role.
An important structural parameter that influences the 'inner sphere' relaxivity is the hydration number q. This represents a scaling factor in Equation 28.2 and therefore a higher number of coordinated water molecules (q > 1) provides a clear advantage in terms of relaxivity. The use of hepta- or hexa-dentate ligands would in principle result in Gd(III) complexes with two- and three-coordinated water molecules, respectively, but the decrease of the oleuticity of the ligand is likely to be accompanied by a decrease of their thermodynamic stability and an increase of their toxicity. Furthermore, systems with q = 2 may suffer a 'quenching' effect upon interacting with proteins, as donor atoms from Asp or Glu residues may replace the coordinated water molecules.17 However, some stable Gd(III) chelates containing two 'inner sphere' water molecules have been identified and are under intense scrutiny.
Among them, an interesting class is represented by Gd-HOPO complexes developed by Raymond and co-workers. HOPO ligands (Figure 28.3) are based on 4-carboxyamido-3,2-hydroxypyridinone chelating units and act as hepta-dentate ligands towards Gd(III), thus leaving two water molecules in the inner coordination sphere. However, the peculiar coordinating geometry of Gd-HOPO complexes does not allow an easy replacement of the two water molecules by other ligands. Moreover, the exchange rate of the coordinated water molecules is in the range of the optimal values and the electronic relaxation appears to be slow enough.18
Another system that looks very interesting in this regard is represented by the Gd(III) complex of PCP2A (Figure 28.3), a ligand based on a pyridine-containing macrocycle bearing two acetic and one methylenephosphonic arms.19 Its relax-ivity is about two times higher than the values reported for CAs currently used in clinical practice. This is the result of the presence of two water molecules in the inner coordination sphere and a significant contribution from water protons bonded to the phosphonate group.
A novel Gd(III) chelate with the heptadentate AAZTA ligand (AAZTA: 6-amino-6-methylperhydro-1,4-diazepinetetraacetic acid; Figure 28.3) has been recently characterized. AAZTA is readily obtained in high yields and its Gd(III) complex displays excellent relaxation enhancement properties so as to be considered the prototype of a new class of enhanced MRI agents. It is characterized by a quite high relaxivity value (7.1mM-1s-1, 20 MHz and 298 K), a fast exchange rate of the coordinated water molecules, a high thermo-dynamic stability in aqueous solution and a nearly complete inertness towards the influence of bidentate endogenous anions.
Figure 28.3 Schematic representations of the three heptadentate ligands (HOPO, PCP2A and AAZTA), whose Gd(III) complexes display two water molecules in the inner coordination sphere
It was earlier recognized that in the case of polyaminocarboxylate complexes of Gd(III), high relaxivities at the imaging field (0.5-1.5 T) can be obtained with long tR values. Therefore, slowly moving systems have been developed in order to reach high relaxivities. Basically, two routes have been explored to provide the Gd(III) chelates with long molecular reorientational times: (i) by forming a covalent linkage between the complex and a macromolecular substrate or (ii) by forming a non-covalent adduct between the complex and a slowly tumbling system.
The latter approach has been widely investigated by using the human serum albumin (HSA) as the interacting substrate. Research activities have been addressed along this direction to design Gd(III) chelates bearing on their surface suitable functionalities that promote the reversible binding of HSA.20,21 Representative examples of such Gd(III) complexes are shown in Figure 28.4.
Besides the attainment of high relaxivities (see R1pbound values in Figure 28.4), a high binding affinity to HSA enables the Gd(III) chelate to have a long intravascular retention time which is the property required for a good blood pool agent for MR angiography. For the reorientational time of HSA adducts (ca. 30 ns), the theory of paramagnetic relaxation foresees the attainment of relaxivity values much higher than the values actually obtained. It has been shown that the primary reason for the quenching of the relaxation enhancement
Figure 28.4 Gd(III) complexes with high binding affinity to HSA
is often associated with the occurrence of a relatively long exchange lifetime, rm, of the coordinated water.22
Slow rates of the coordinated water appear to be primarily characteristic of the complex rather than a consequence of the binding to the protein. Thus, for the attainment of high relaxivities one has to avoid Gd(III) chelates displaying slow exchange rates.
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