Relaxivity outer-sphere contribution

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). 

Fig. 25. Outer-sphere contribution to the water proton relaxation rate, calculated for a distance of closest approach, d, of 3 A and different values of S (1/2,1, 3/2, 2, 5/2).

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). 

The NMRD profiles of water solution of Ti(H20)g" have been shown in Section I.C.7 and have been already discussed. We only add here that the best fit procedures provide a constant of contact interaction of 4.5 MHz (61), and a distance of the twelve water protons from the metal ion of 2.62 A. If a 10% outer-sphere contribution is subtracted from the data, the distance increases to 2.67 A, which is a reasonably good value. The increase at high fields in the i 2 values cannot in this case be ascribed to the non-dispersive term present in the contact relaxation equation, as in other cases, because longitudinal measurements do not indicate field dependence in the electron relaxation time. Therefore they were related to chemical exchange contributions (see Eq. (3) of Chapter 2) and indicate values for tm equal to 4.2 X 10 s and 1.2 X 10 s at 293 and 308 K, respectively. 

The smaller contribution to solvent proton relaxation due to the slow exchanging regime also allows detection of second and outer sphere contributions (62). In fact outer-sphere and/or second sphere protons contribute less than 5% of proton relaxivity for the highest temperature profile, and to about 30% for the lowest temperature profile. The fact that they affect differently the profiles acquired at different temperature influences the best-fit values of all parameters with respect to the values obtained without including outer and second sphere contributions, and not only the value of the first sphere proton-metal ion distance (as it usually happens for the other metal aqua ions). A simultaneous fit of longitudinal and transverse relaxation rates provides the values of the distance of the 12 water protons from the metal ion (2.71 A), of the transient ZFS (0.11 cm ), of the correlation time for electron relaxation (about 2 x 10 s at room temperature), of the reorienta-tional time (about 70 x 10 s at room temperature), of the lifetime (about 7 x 10 s at room temperature), of the constant of contact interaction (2.1 MHz). A second coordination sphere was considered with 26 fast exchanging water protons at 4.5 A from the metal ion (99), and the distance of closest approach was fixed in the range between 5.5 and 6.5 A. 

For monomer Gd(III) complexes the inner and outer sphere mechanisms contribute more or less to the same extent to the overall paramagnetic relaxation enhancement. The development of high relaxivity contrast agents mainly involves increasing the inner sphere term, since the outer sphere contribution can hardly be modified. For the new generation macromolecular agents, therefore, the inner sphere relaxivity becomes much more significant (over 90% of total relaxivity). 

The relaxivity induced by gadolinium chelates due to inner-sphere water molecules, riIS, is well understood on the microscopic scale as can be seen from the above discussion. The contribution to the overall relaxation enhancement due to all other water molecules is normally summed up in the term r, generally called the outer-sphere contribution. The interaction between the water proton nuclear spin I and the gadolinium electron spin S is supposed to be a dipolar intermolecular interaction whose fluctuations are governed by random translational motion. The corresponding relaxation rate, l/Tly for unlike spins is given by Eq. (23) [88-90]... 

The second contribution to paramagnetic relaxation is the outer-sphere relaxation. It is explained by dipolar interactions at longer distances between the spins of the paramagnetic center and the nuclear spin. This intermolecular mechanism is modulated by the translational correlation time Tp, which takes into account the relative diffusion constant (D) of the Gd center and of the solvent molecule and their distance of closest approach (d). The outer-sphere contribution has been described by Freed and is given by equations (10) and (11) ... 

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.

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