Page 210 - Computational Modeling in Biomedical Engineering and Medical Physics

Magnetic drug targeting 199

Figure 6.25 The magnetic field produced by the array of magnets and the magnetic forces in the MDT
therapy at the knee level. (A) The magnetic flux density and forces. (B) The magnetic energy density—
surface map. The swarms indicate the permanent magnets positions. MDT, Magnetic drug targeting.

6.6 The magnetic drug transfer from the larger blood vessel to the
region of interest
The magnetic drug transfer to the ROI occurs through two mechanisms: convection and
diffusion. In the larger vessels the transfer is dominated by convection, whereas diffusion is
prevalent for the vessels walls and in the adjacent microvascularized tissue. To these adds
the magnetic field, which intervenes through magnetic body forces. Proportional to and
led by the magnetic energy density gradient, its motive action adds as a control means in
targeting the MD, directing it to higher energy density regions, that is, toward the mag-
netic source. Therefore qualitatively, the ROI has to be “on the path” from the delivery
location to the higher magnetic energy region for this magnetic control to have the
desired positive targeting effect.
Several transfer stages are discussed next: the MD transfer in larger vessels, where
the blood flow is pulsatile; the transfer through smaller size vessels, where flow is sta-
tionary, and the transfer through the vessel wall and the adjacent region. The blood
flow (larger and smaller blood vessels) is assumed laminar and incompressible.

Biorheological models in magnetic drug transfer
So far, in this chapter, the MAF was assimilated with a Newtonian fluid and its flow
was assumed stationary. This line of study may be consistent with venous flows, and
larger vessels. Arterial flows are pulsatile, and for small size vessels, the Newtonian
rheological model is no longer representative. The low shear stress observed in the
hemodynamic of microvessels with diameter less than 1300 μm shows off a blunted
plug-flow type profile (Xu et al., 2005). Its constituents (red and white blood cells,
and platelets suspended in the fluid) make the blood a complex fluid. Its mechanical