Page 166 - Bio Engineering Approaches to Cancer Diagnosis and Treatment

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

FIGURE 7.4 Simplified model of controlled drug delivery method based on magnetic
nanoparticles.

penetrate depth into tissue. To overcome the penetration problem two alternative
methods are utilized [9]:
Method (1) Use a few magnets to create a focal point at the desired location.
Method (2) Implant a metal near the target tissue. The metal implant is trans-
formed into a local magnet under the influence of its external magnetic field and
generates a strong magnetic field gradient.
Li et al. [9] reported higher efficiency when implant method is used compared to
the use of several magnets. One drawback is that this method may cause local injury
and may endanger the patient’s health [21].

7.4.3 Magnetic force applied to nanocarriers
Generally, Maxwell equation is used directly to determine the electromagnetic
behavior of nanocarriers and is used indirectly to obtain the force exerted on the
magnetic nanocarriers in a magnetic field. It means that the amount of force applied
to the particle obtained by using the gradient of the calculated magnetic energy. The

F→m magnetic force on a particle (F ) in a magnetic field is equal to the gradient of mag-
m
netic energy as follow [22]:

F→m=−∇Um F =−∇ U m (7.11)
m

F→m where U and F are nanocarrier magnetic energy and magnetic force vector, respec-
m
m
tively. The magnetic energy of a single object immersed in an external magnetic field
(H) is obtained from [22]:
1
⋅
U =− µ ∫ MHdv (7.12)
Um=−12µ ∫M→⋅H→dv m 2 0
0