Magnetic Drug Targeting in Blood Vessels

Magnetic Field Control

External magnetic field guidance

Nanoparticle Dynamics

2nm, 5nm, and 10nm diameter particles

CFD Simulation

Blood flow and particle transport

$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x_i}(\rho V_i) = 0$

$\frac{\partial}{\partial t}(\rho V_i) + \frac{\partial}{\partial x_j}(\rho V_i V_j) = -\frac{\partial p}{\partial x_i} + \frac{\partial}{\partial x_j}\mu\left(\frac{\partial V_i}{\partial x_j} + \frac{\partial V_j}{\partial x_i}\right) + \mu_0 M_i \frac{\partial H_j}{\partial x_i}$

$\frac{\partial \alpha}{\partial t} + \frac{\partial}{\partial x_j}(\alpha V_j) = \frac{\partial J_j}{\partial x_j}$

where

$J_j = \Gamma\left(\frac{\partial \alpha}{\partial x_j} + S_T\frac{\partial T}{\partial x_j} - \frac{\alpha}{H}\xi L(\xi)\frac{\partial H_j}{\partial x_j}\right)$

$\Gamma = \frac{K_B T}{3\pi\mu_b d_p}$

$\xi = \frac{m_i\mu_0 H_i}{K_B T}$

$L(\xi) = \coth\xi - \frac{1}{\xi}$

$m_i = \frac{4\mu_B\pi d_p^3}{6 \times 91.25 \times 10^{-30}}$

$M_i = Nm_i L(\xi)$

Without Magnetic Field

With Magnetic Field

Diameter: d = 5nm

Diameter: d = 2nm

Mnf = 32.8, Re = 100, X = x1

Mnf = 328, Re = 100, X = x2