Relaxivity inner-sphere contribution

Fig. 1. Schematic representation of a Gdm complex with one inner sphere water molecule, which is the origin of the inner sphere contribution to proton relaxivity. The complex is surrounded by bulk water, giving rise to the outer sphere relaxation mechanism.

Fig. 4. Inner sphere contribution to the proton relaxivity as a function of the proton Larmor frequency. The curves were calculated on the basis of the Solomon-Bloembergen-Morgan theory for different values of the rotational correlation time, tr, and q — 1, kex — 10 x 106 s-1, tv = 20 ps, A2 = 0.1 x 102Os-2.

Finally, from Eqs. (4)-(7) it is clear that the inner sphere contribution to the relaxivity strongly depends on the observation frequency. As already discussed in the previous two chapters of this volume, the study of the field dependence of the relaxivity (NMRD technique) represents a powerful tool for extracting the values of the relaxation parameters and its application to the investigation of Gd(III) complexes of relevance as MRI CA will be discussed in Section III. 

This treatment is oversimplified because, in addition to neglecting inner sphere contributions to the reorganization energy it approximates the dielectric frequency spectrum to a single frequency, 0jo — 1011 s 1, corresponding to the Debye dielectric relaxation which probably varies in the vicinity of the ions. The cathodic current is given by... 

In the 9-coordinate TTHA complexes of the heavier Ln3+ ions, the situation is more complex, since there also the terminal N-atom bearing the uncoordinated acetate moiety is chiral. 170 NMR [49, 50], luminescence [47, 51] and NMRD measurements [46] have shown that, for both 9- and 10-coordinate Ln(TTHA)3 complexes, the inner coordination sphere of the metal ion is fully occupied by donating groups of the ligand, leaving no space for the coordination of water. Consequently, the water proton relaxation enhancement has no inner sphere contribution and the [Gd(TTHA)]3 complex is not very suitable for application... 

The inner sphere contribution to proton relaxivity results from the chemical exchange of the coordinated water protons with the bulk. The longitudinal and transverse inner sphere relaxation rates, 1IT1 and 1IT2, of the bulk solvent nuclei (the only observable NMR signal) are given by Eqs. (5) [10] and (6) [11] ... 

Another disadvantage of the small, hydrophilic agents is that they tumble very rapidly in the extracellular fluid. In water at 25 °C, for example, Gd-DTPA has a rotational correlation time (rR) of 58 ps as determined by the fitting of NMRD data [3], and 105 ps by EPR simulation in the VO++-DTPA analog [4]. This very rapid motion dominates the relaxivity of the PCA in the frequency range of typical clinical interest (42-63 MHz). The reasons for this dominance of rR can be traced to the fact that small Gd3+ chelates like Gd-DTPA have a relaxivity at clinical frequencies that is determined predominantly by an inner sphere process for Gd-DTPA at 50 MHz, Chen et al. calculate that the relaxivity in water is 43 % inner sphere, 25 % second sphere, and 32 % outer sphere [4]. In turn, the inner sphere contribution to relaxivity is often modeled by the Solomon-Bloem-bergen equations [5,6]... 

As far as the inner sphere contribution is concerned, Rip is determined by the relaxation time IM of the nuclei of the substrate-solvent complex and by its lifetime Xj, weighted by the molar ratio of the bound substrate-solvent ... 

In the case of Mn11 complexes as potential MRI contrast agents, the presence of a water molecule in the first coordination sphere is crucial to obtain reasonable relaxivity. Given the lower spin of Mn11, the outer sphere contribution to the overall relaxivity is lower than for Gdm complexes. Thus, for complexes that lack inner sphere water the relaxivity is less than 50% as compared to complexes with coordinated water (233-235). 

At variance with the aqua ion, in most manganese(II) proteins and complexes the contact contribution to relaxation is found negligible. This is clearly the case for MnEDTA (Fig. 33), the relaxivity of which indicates the presence of the dipolar contribution only, and one water molecule bound to the complex 93). Actually the profile is very similar to that of GdDTPA (see Chapter 4), and is provided by the sum of inner-sphere and outer-sphere contributions of the same order. The relaxation rate of MnDTPA is accounted for by outer-sphere relaxation only (see Section II.A.7), no water molecules being coordinated to the complex 94). 

As an example of behavior of a typical Gd-complex and Gd-macromolecule we discuss here the NMRD profiles of a derivative of Gd-DTPA with a built-in sulfonamide (SA) and the profile of its adduct with carbonic anhydrase (see Fig. 37) 100). Other systems are described in Chapter 4. The profile of Gd-DTPA-SA contains one dispersion only, centered at about 10 MHz, and can be easily fit as the sum of the relaxation contributions from two inner-sphere water protons and from diffusing water molecules. Both the reorientational time and the field dependent electron relaxation time contribute to the proton correlation time. The fit performed with the SBM theory, without... 

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