Chemistry Reference
In-Depth Information
gadolinium complexes tend to be
T
1
relaxation agents (i.e., they give rise to large changes in
T
1
and relatively small
changes in
T
2
, and
T
1
weighted images produce the most effective results), and for all subsequent discussion of the factors
affecting inner sphere contrast, we will refer to
T
1
for simplicity.
2
To obtain a more detailed understanding of contrast agent behaviour, paramagnetic relaxation can be divided up in other
ways, that is
IS
OS
(/ )
1
T
para
=
(
1
/
T
)
+
(/
1
T
)
(8.12)
1
1
1
where
T
1
IS
and
T
1
OS
refer to contributions to
T
1
from inner and outer sphere solvent molecules respectively. Even complexes
with q = 0 give rise to a significant increase in contrast as a consequence of solvation of the molecule as a whole: Outer
sphere solvent molecules are more numerous than inner sphere solvent molecules and, by their nature, tend to exchange
more rapidly with bulk solvent [42, 43]. To a first approximation, and given the similarity in structure of complexes in
current use, the outer sphere contribution is likely to be similar for all complexes. Inner sphere solvents (i.e., water molecules
bound directly to the lanthanide) will have a much greater effect, provided that they are in rapid exchange on the NMR time-
scale. The relationship between
T
1
IS
and q, the number of inner sphere water molecules, is given by:
1
qP
m
=
(8.13)
IS
T
+τ
T
1
1
mm
where
P
m
is the mole fraction of bound solvent molecules relative to bulk (and thus related to the concentration of the com-
plex under study),
τ
m
is the reciprocal of the rate of exchange of bound solvent molecules (i.e., the residence lifetime of a
bound solvent molecule), and
T
1
m
is the relaxation rate enhancement for a coordinated solvent molecule [44, 45]. There is
thus a clear relationship between the number of inner sphere solvent molecules bound to an individual gadolinium complex
and the magnitude of the relaxivity. Furthermore, where
T
1
m
> >
τ
m
,
T
1
m
will dominate the observed relaxivity.
In practice, this equation represents a slight simplification, because a given complex may not always have a single value for
q; indeed, non-integer values are often reported in the literature as a consequence of population weighted averaging for differ-
ent inner sphere hydration states of a complex. It might be more strictly correct to think of 1/
T
1
IS
being represented by a sum of
terms that reflect the populations of all possible q values for a given complex. However, the equation above stands up well in
practice, and a more complicated treatment would usually be over-parameterised. The value of q can be determined in the solid
state using crystallographic techniques. In solution, time-resolved luminescence measurements have been used to determine
the luminescence lifetimes of the europium and terbium complexes, which are then used to determine q using the relations:
q
=
12
.(
τ
−
τ
−
0250075
.
−
.
x
)
and
(8.14)
Eu
HO
2
dO
2
q
Tb
= 5
(
τ−τ−
0 06
.
)
(8.15)
HO
2
dO
2
where τ
H2O
and τ
d2O
are the luminescence lifetimes of the complex under study in ms in H
2
O and d
2
O respectively, and x is
the number of close diffusing amide N-H oscillators [46]. The lanthanide contraction means that the value of q for a gado-
linium complex is likely to be between those of its europium and terbium analogues. Alternatively, q can be determined by
measurements of the induced shifts in the
17
O NMR spectrum for dysprosium complexes; for complexes in which the bound
solvent is in fast exchange, it has been shown that there is a linear relationship between the dysprosium induced shift to the
bulk water resonance and q [47].
This simple treatment allows us to rationalise the behaviour of contrast agents in a general sense and illustrates that the
inner sphere solvation at the metal centre is clearly very important in determining the effectiveness of a contrast agent.
Values of r
1
at 20 MHz are shown in Table 8.2. It is clear from these data that, while hydration is clearly important, other
factors also play a role in determining the relaxivity.
The Solomon-Bloembergen-Morgan (SBM) equations have been used to provide some rationalisation of the properties
of lanthanide complexes [18, 48]. These divide the contributions to 1/
T
im
into contributions from dipole-dipole (dd) and
contact, or scalar (SC), pathways: Since rates are additive.
1
1
1
=
+
(8.16)
DD
SC
T
TT
im
i
i
2
For those who wish to understand T
2
in more detail, refer to [18] P. Caravan, J.J. Ellison, T.J. McMurry, R.B. Lauffer,
Chem. Rev.
99
, 2293‒2352 (1999).
