Biomedical Engineering Reference
In-Depth Information
R
2
*
is always much larger than
R
2
. A unique
property of the visit-limited regime is that
R
2
exhibits a dependence on the inter-echo delay.
The appropriate regime for a given SPIO
system can be determined experimentally by
measuring the
R
2
and
R
2
*
, if using a high-fi eld
homogeneous magnet, or by measuring
R
2
as
a function of different inter-echo delays. These
curves are a representative sketch of curves
shown in Refs. [53] and [56], respectively. The
exact position and curvature of the plots
depends on the conditions used to generate
the original curves.
Figure 1.7
Sketch of the relationship between
R
2
(1/T
2
) and SPIO radius. In the motional
averaging regime (solid dark line),
R
2
increases with nanoparticle size, while in the
visit - limited regime
R
2
decreases with
nanoparticle size (dashed lines). In the
motional averaging regime,
R
2
is equal to
R
2
*
,
whereas in the visit-limited regime (also
termed the static dephasing regime)
R
2
no
longer equals
R
2
*
(gray solid line). The static
dephasing regime does not apply to most
permanent magnet systems because
R
2
*
is
dominated by their magnetic fi eld
nonuniformity; therefore, for portable systems
(
)
**
*
and
RR
2
50 nm, whereas
R
2
measured with spin echos decreased with increasing particle size, and
R
2
*
mea-
sured with a 90 ° pulse-detect reached a plateau (Figure 1.7). Subsequent experi-
mental studies and computer simulations explored the dependence of
R
2
on the
concentration of dissolved iron, magnetic susceptibility, and temperature [54].
These early investigations laid the foundations for the development of a set of
analytical models that accurately reproduced the dependence of transverse relaxiv-
ity on particle size, magnetization, iron concentration, temperature, and inter- echo
delay for both strongly [55 - 57] and weakly magnetized nanoparticles [58] .
According to developed theory, superparamagnetic nanoparticles are divided
into categories of strongly magnetized and weakly magnetized. The boundaries
between these two regimes depends on the relative magnitude of the frequency
difference between nuclei at the surface of the nanoparticle and nuclei distant
from the nanoparticle,
=
1
T
increased with particle diameter until
∼
2
2
Δ
ω
, and the inter-echo delay used in the CPMG detection
sequence,
τ
CP
.
Δ
ω
is essentially a relative measure of the effect of the dipolar
