Page 170 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

168 CHAPTER 7 Application of magnetic and electric fields for cancer therapy

material is B . The eddy current is negligible for nanoparticles with diameter of less
m
than centimeter [31].
7.5.2.2 Hysteresis loss
When the ferromagnetic material is exposed to an alternating external magnetic field,
its magnetization runs through a closed cycle. The closed cycle is characterized by
three parameters: saturation magnetization (M ), magnetic residual (M ), and coer-
r
s
civity (H ). The area inside the cycle represents the amount of energy given to the
c
substance (which becomes heat) per cycle [32].
Single domain nanoparticles release the highest amount of hysteresis loss. The
maximum amount of hysteresis loss per unit volume for each cycle (Q) is calculated
as follows [32]:
⋅
Q=4µ ⋅Ms⋅Hc Q = 4µ ⋅ MH c (7.22)
0
s
0
The coercivity is calculated from Refs. [4,33]:
H = 2 K   15 kT   (7.23)
−
b
c
Hc=2Kµ Ms1−5kbTKV µ 0 M  KV 
s
0
Anisotropic energy density is K, temperature (in Kelvin) is T, the volume of the
nanoparticle is V and the Boltzmann constant is k . The amount of thermal energy per
b
unit mass of nanoparticles (SLP) is obtained from [32]:
⋅
Qf
SLP = (7.24)
SLP=Q⋅fρ ρ
where ρ is nanoparticles density. The amount of heat generated in a metallic nanopar-
q˙p ticle ( q ) is determined from:
p
f
q˙p=f⋅∀⋅Q=4µ ⋅Ms⋅Hc⋅f⋅∀ q = f ⋅∀⋅ Q = 4µ ⋅ M ⋅ H ⋅ ⋅∀ (7.25)
0
c
p
s
0
The saturation magnetization and the anisotropy energy density of two samples
nanoparticles, iron and oxides are given in Table 7.1 [4].
The behavior of the coercivity for different nanoparticles size is shown in Fig. 7.6.
The saturation magnetization, the coercivity, and density of MNPs, particles
that are generally used in hyperthermia applications, are approximately 446,
3
30 kA/m and 5240 kg/m , respectively [32, 34]. The thermal energy of MNPs
Table 7.1 Anisotropy and crystalline parameters defining SD and SPM
critical diameters at 300 K.
3
M (kA/m) K (kJ/m )
s
Magnetite 446 13.5
Maghemite 380 4.6