Page 172 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

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

2πτ
f
χ '' = eff 2 χ 0 (7.27)
f )
+
χ’’=2πfτeff1+2πfτeff χ 1 ( 2πτ eff
2
0
τ
τeff χ 0 The effective time constant is eff and the magnetic susceptibility is χ . By insert-
0
ing Eq. (7.27) in Eq. (7.26) the residual loss is obtained by [29,31,32]:
1 ( 2π f ) 2 τ eff
P = µχ 0 H 2 2 (7.28)
f )
0
+
P=12µ χ H 2πf τeff1+2πfτeff 2 2 1 ( 2πτ eff
2
2
0 0
As stated, the eddy current heat loss negligible and can be neglected, and the
hysteresis loss and residual loss generate heat in the ferromagnetic nanoparticles.
Hence, there are two ways to achieve a significant amount of heat production [32]:
1. Using a high-frequency magnetic field (several hundred kHz) and a limited
amplitude (several kilo ampere/m) for superparamagnetic nanoparticles
(increasing the residual loss)
2. Using a limited frequency magnetic field (several hundred kHz) and a high
amplitude (several 10 kA/m) for ferromagnetic nanoparticles (increasing the
hysteresis loss)
Superparamagnetic nanoparticles do not have magnetic hysteresis and hence the
hysteresis loss doesn’t generate. As a result, the superparamagnetic nanoparticles are
the choice.
The heat in MNPs is produced due to the variable and alternative magnetic field,
and for constant field no heat generates inside the nanoparticles. Also, according to
the above equations, the heat loss is increased by increasing the amplitude magnetic
field.
Pankhurst et al. [2] reported the allowed alternative magnetic field for therapy
(Table 7.2).
Frequencies below the permissible level may stimulate bones or peripheral mus-
cles and heart muscle. However, the higher magnetic field strength causes the accu-
mulation of nanoparticles and embolism in vessels [24]. Rast et al. [24] and Dutz and
Hergt [35] reported the same range as Pankhurst et al. [2]. Also they have proposed
9
the product of the frequency in field strength up to the 5 × 10 A/(m s) for parts of
the body with a diameter of less than 30 cm.

Table 7.2 The range of allowable values for alternating magnetic fields [2].
Maximum Minimum
Frequency (kHz) 1200 50
Field amplitude (kA/m) 15 –
The product of the frequency in field 4.85 × 10 8 –
strength A (m s)