Biomedical Engineering Reference
In-Depth Information
Figure 4.6
The nuclear magnetic resonance dispersion
(NMRD) profi le of typical SPIO, AMI25 (Advanced Magnetics,
Cambridge, MA, USA) at T = 310 K. Reproduced from
Ref. [170] .
diffusion of water, with the position of the
r
1
maximum determined by the char-
acteristic diffusion time,
D
=
d
2
/(4
D
), where
d
is the particle diameter and
D
is
the diffusion coeffi cient. The low-fi eld relaxation is due to fl uctuations in the
particles moment - that is, the Néel process. Muller's theory is only strictly appli-
cable to monodispersed suspensions of sub-20 nm particles. However, by using
physically acceptable values for the critical parameters - that is, the particle size,
Néel correlation time
τ
E
anis
- the theory produces a good agreement with the measured profi les of USPIO
suspensions. Among the assumptions of the model are that the magnetocrystal-
line anisotropy is uniaxial, which corresponds to a single direction for the easy-
axis. For dispersed superparamagnetic nanoparticles, the magnetic anisotropy is
usually of the order of 0.2-2.0 GHz. However, surface anisotropy and the mutual
anisotropy due to dipolar coupling between nearby crystals can complicate the
issue for USPIO and SPIO dispersions, respectively. These contributing factors
may be grouped together and referred to as the effective anisotropy energy. A
detailed analysis of the performance of the theory has also been restricted by the
polydispersity of the aqueous nanoparticle suspensions. The infl uence of the
magnetic parameters on the shape of the NMRD profi les has recently been dis-
cussed in detail [7].
In summary, for disperse suspensions the high-frequency infl ection point
is determined by
τ
N
, saturation magnetization
M
s
and anisotropy energy
Δ
D
, and the position of the maximum is sensitive to the
particle size, through its effect on
τ
D
. The value of the low-fi eld
r
1
plateau is
determined by the anisotropy energy. In cases of low anisotropy, a weak
τ
