Chemistry Reference
In-Depth Information
111
τ
=+
(8.21)
T
τ
ei
ie
m
Influencing
T
1
e
,
τ
m
and
τ
r
raises the possibility of optimising r
1
relaxivities. As we will see in the subsequent sections,
τ
m
can
be varied by controlling both ligand structure and hydrogen bonding to bound solvent molecules, while
τ
r
can be optimised
by making large rigid molecules that tumble slowly in solution.
4
The electronic relaxation time also has potential to be varied
between structures, but is hard to predict - not least because it is itself dependent upon the applied field [49].
8.5
strategIes for IncreasIng reLaxIvIty
We have already seen that the observed relaxivity for a contrast agent can be influenced by changes to the number of inner
sphere solvent molecules (q); by the residence time of solvent (
τ
m
); and by the variety of factors that influence
T
1
m
, namely
the separation between the gadolinium ion and a proton on the coordinated water (r), the electronic relaxation time (
T
1
e
), and
the rotational correlation time (
τ
r
). Of these, the electronic relaxation time is the most difficult to predict, measure, and con-
trol - indeed, related gadolinium complexes can exhibit very different zero field splittings and electronic relaxation times
[50], and a much larger body of data is required before a rational design approach can be applied to optimise
T
1
e
. Until that
time, the variability in this parameter represents a potential pitfall for those engaged in contrast agent design.
Variation in r is also difficult to predict (and measure), but changes in this separation induced by changes in the equilibrium
position between SAP and TSAP isomers can have a profound influence upon both r and
τ
m
. In the TSAP isomer, the upper
plane of donor atoms imposes a smaller space for access by an axial ninth donor. Accordingly, the separation of the gado-
linium and the bound water protons is increased, while the greater gd-O separation increases the relative rate of water
exchange. Indeed, in the TSAP isomer, the rate of water exchange has been shown to be up to 50 times faster than in the SAP
isomer of the same complex [29, 51, 52]. Thus, the two effects compete in that an increase in r would be expected to lead to
a decrease in relaxivity, while the decrease in τ
M
should increase relaxivity. In fact, the changes in separation are relatively
small, and the large change in residence time dominates the observed relaxivity. Indeed, in complexes where both SAP and
TSAP forms are present, the TSAP form can provide the dominant contribution to the relaxivity even in cases where the SAP
form is the major isomer; effectively, a weighted average is observed in which the dramatic difference in exchange rates
ensures that TSAP dominates exchange with bulk water.
At high fields, the usefulness of lanthanide complexes will be determined chiefly by q, τ
M
and τ
R
[18]. Accordingly, we
will consider these in greater detail. τ
M
can also vary dramatically between complexes. The residual charge upon the metal
centre determines its affinity for inner sphere water. Thus solvent exchange rates in [gd.dOTA]
-
(k
ex
(SAP) = 4.1 × 10
6
s
-1
;
k
ex
(TSAP) = 24 × 10
6
s
-1
) are dramatically faster than in tetraamide complexes such as [gd.dOTAM]
3+
(k
ex
(SAP) = 0.05 ×
10
6
s
-1
), while the fastest rates of all are observed with highly anionic complexes such as [gd.
RRRR
-gdOTA]
5-
(k
ex
(SAP) = 15.4 ×
10
6
s
-1
; k
ex
(TSAP) = 22 × 10
6
s
-1
) [29, 53-55]. There are exceptions to this simple trend. For instance, [gd.dOTAgly]
-
(Figure 8.5) exhibits slow exchange of water on the NMR timescale despite the overall negative charge on the complex - to
the point where other lanthanide analogues of this complex have been used in saturation transfer imaging [56]. This is a
consequence of the position of the glycine pendant residues in this complex, because hydrogen bonding with these residues
stabilises the bound solvent molecules and slows exchange.
At first sight, the benefits of increasing q seem straightforward. Relaxivity should increase more or less in proportion with
the increase in number of bound water molecules at the gadolinium centre (provided the residence time and relaxation rate of
the bound water remain approximately the same). However, all clinical agents in current use have q = 1. There are a variety of
reasons for this. First, the stability of lanthanide complexes decreases as the denticity of the ligand donor set is reduced from
eight to seven. Indeed, while dO3A forms stable complexes with lanthanide ions, we have already seen that the thermody-
namic and kinetic stability of such complexes is significantly reduced compared to dOTA complexes. Furthermore, while
uncharged donor ligands (such as dOTA-tetraamides) form highly stable complexes with lanthanides, dO3A-triamide
complexes tend to be more labile in solution. While a number of stable complexes with seven coordinate ligands exist, the
story does not end here. It is also necessary to consider displacement of coordinated water by endogenous bidentate anions. It
is widely known that phosphate, hydrogencarbonate, and other anions can displace water from the inner coordination sphere
in a range of dO3A derivatives [57]. In the case of gadolinium complexes, this displacement clearly negates the advantage
of having q = 2 in the first place, and the anion bound forms effectively behave like outer sphere contrast media. Parker and
4
It should also be noted that the rotational correlation time will vary between tissue types, because viscosity can vary significantly between intra- and
extracellular fluids and between biological domains.
