Chemistry Reference
In-Depth Information
Fringe-field diffusion measurements can be performed with a stimulated echo
sequence with similar principles to pulsed-field gradient NMR experiments. K opf
et al. [75] used a 9.4T superconducting magnet with a bore of 9 cm. At 26 cm axial
distance from the center of the bore, the magnetic-flux density was 3.9 T (giving a
proton Larmor frequency of 162 MHz), while the field gradient is at its maximum
value of 50 T m
−
1
. This gradient is almost constant
>
2 cm. A disadvantage of
this method is that as the gradient is constant over such a large area, only the echo
amplitude is recorded [76] and the spatial resolution is entirely lost. Therefore all
structural information is lost and distinction between the resonances of
1
H and
19
F
is impossible. There is also the problem that the available rf pulses can excite only
a thin slice of a sample in a strong gradient field. Therefore the ensemble averaged
mean-square displacement can be measured, and while it is assumed to be moving
along the contour of microscopic structure on a cellular length scale, it is not pos-
sible to be certain that the measured displacement is the actual displacement [75].
K opf and Nonnenmacher [73, 75] performed fringe-field experiments on a num-
ber of different tissue types, and discussed the use of three relaxation functions to
describe the diffusion process therein. The functions they observed are of the form
of the Debye and Kohlrausch-Williams-Watts (KWW) relations discussed below
and a power law decay.
E
=
exp(
−
Db
)
(Debye)
(84)
(
Db
)
α
E
=
exp
−
(KWW)
(85)
(
q
2
)
−
μ
E
∼
(Power law)
(86)
where
D
is the diffusion coefficient and,
4
π
2
q
2
T
b
=
q
is a wave vector that describes the length scale, and
T
is the time scale of the
measurement. Now
α
is again the anomalous exponent, with a range 0
<α<
1,
while
μ
involves the fractal dimension of the underlying geometry and has values
μ>
1. K opf et al. [73, 75] found that the observed relaxation function varied
for short, intermediate, and long time scales, and also for cellular structure. Pure
fluids and fatty tissue are well described by a Debye relaxation function. Fatty
tissue displays a low degree of compartmentation and few small cellular details.
Glandular and fibrous tissues are more structured and crowded. Their diffusion
process exhibits Debye relaxation only at very short times, due to contributions
from free cellular water. At longer times, a combination of Eqs. (84) and (85) is
required to describe the relaxation,
Db
)
α
E
=
C
1
exp(
−
Db
)
+
C
2
exp(
−
(87)
