Inner-sphere relaxation

The longitudinal inner-sphere relaxation rate, l/Ti, of bulk water protons is given by Equation (2) 13... 

The Gd-H distance, /-GdH, which enters at the inverse sixth power into the expression of inner-sphere relaxivity, is a difficult parameter to obtain experimentally. It is generally estimated on the basis of Gd-coordinated water oxygen distances, determined by solid-state X-ray analysis. Solid-state distances are good estimates of the aqueous solution state, as was experimentally proven by an X-ray absorption fine-structure study on [Gd(D0TA)(H20)] and [Gd(DTPA)(H20)]2, which gave identical values for the Gd-0 distances for both complexes in solid and solution states.20... 

The Gd-H distance, rGdII, which enters on the inverse sixth power into the expression of inner sphere relaxivity, remains a difficult parameter to obtain experimentally. Most often it has been estimated on the basis of Gdm - coordinated water-oxygen... 

Fig. 3. Simulation curves of the inner sphere relaxivity as function of Xji/ for a mono-aquo Gd(III) complex at 25°C and 20 MHz for increasing values of the rotational correlation time. The other relaxation parameters were set as follows = 5.0 x 10 s ...

Another important parameter that influences the inner sphere relaxivity of the Gd(III)-based contrast agents is the electronic relaxation time. Both the longitudinal and transverse electron spin relaxation times contribute to the overall correlation times xa for the dipolar interaction and are usually interpreted in terms of a transient zero-field splitting (ZFS) interaction (22). The pertinent equations [Eqs. (6) and (7)] that describe the magnetic field dependence of 1/Tie and 1/T2e have been proposed by Bloembergen and Morgan and... 

Because of the dependence of the inner sphere relaxivity on l/r, the Gd-water proton distance is extremely important in determining the efficacy of a CA. In Fig. 8 the experimental profile of [GdDTPA(H20)] is shown and also the best-fit curve obtained with a th value of 3.1 A, compared with two calculated profiles corresponding to th values of 2.95 (upper curve) and 3.25 A. A variation of this parameter of only 0.15 A changes the relaxivity about 16% at low fields. Estimates from X-ray data of the Gd-0 distance are affected by some errors as the tilt angle of the water molecule in solution is not defined with precision. 

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 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] ... 

More precisely, the paramagnetic contribution of the longitudinal relaxation rate is composed of the inner-sphere relaxation, the second-sphere relaxation, and the outer-sphere relaxation. The model used to describe these interactions is shown in Figure 10.4. The various parameters that influence the observed longitudinal relaxivity will be discussed using Gd-based CAs as illustrative examples. 

The inner-sphere relaxation refers to the contribution from the water molecules that are directly bound to the gadolinium, and is expressed by the Solomon-Bloembergen equations (Equations 10.3-10.6) [15, 16],... 

Clinical CAs have one inner-sphere water molecule, and thus an increase in q will directly increase the inner-sphere relaxivity. However, this leads to a trade-off in stability by decreasing the coordination number. Desirable modifications of Gd-DTPA or Gd-DOTA to optimize the relaxivity would be to use octadentate or heptadentate chelates. Scientists have designed many different chelates to increase q [19-21]. Raymond and coworkers reported a novel class of chelate, HOPO (tris[(3-hydroxy-l-methyl-2-oxo-l,2-didehydropyridine-4-carboxamido)-ethyl] amine), which can accommodate two or more inner-sphere water molecules and have a good thermodynamic stability and relaxivity [22-25]. The observed r of some HOPO-Gd complexes can be as high as 11.1 mM s at 298 K and 20 MHz [26]. The g value of Gd complexes in solution can be estimated by luminescence lifetime studies of Eu or Tb analogs, according to the Horrocks equation. 

This contribution to the PRE is called inner-sphere relaxation. The ligand or solvent molecules can also experience PRE without ever entering the inner coordination sphere of the paramagnetic species. This second mechanism, referred to as outer-sphere (OS) relaxation, is usually less important and more... 

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