Magnetic Drug Targeting

Magnetic Drug Targeting#

Magnetic Drug Targeting involves the use of magnetic fields to guide drug-carrying particles to a specific target within the body. This application combines principles of magnetohydrodynamics (MHD) with drug delivery. Below are the mathematical models and example test cases for Magnetic Drug Targeting:

Mathematical Models#

  1. MHD Continuity Equation: $\( \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) = 0 \)\( where \)\rho\( is the fluid density, and \)\mathbf{v}$ is the fluid velocity.

  2. MHD Momentum Equation: $\( \rho \frac{D\mathbf{v}}{Dt} = -\nabla p + \rho \mathbf{g} + \nabla \cdot \boldsymbol{\tau} + \mathbf{J} \times \mathbf{B} + \nu \nabla^2 \mathbf{v} \)\( incorporating the viscous term (\)\nu \nabla^2 \mathbf{v}$) for fluid viscosity.

  3. Magnetic Particle Motion Equation: $\( m_p \frac{d\mathbf{u}_p}{dt} = \mathbf{F}_p + \mathbf{F}_{\text{magnetic}} \)\( where \)m_p\( is the particle mass, \)\mathbf{u}_p\( is the particle velocity, \)\mathbf{F}p\( is the sum of external forces, and \)\mathbf{F}{\text{magnetic}}$ is the magnetic force.

  4. Magnetic Force Equation: $\( \mathbf{F}_{\text{magnetic}} = \nabla (\mathbf{m} \cdot \mathbf{B}) \)\( where \)\mathbf{m}$ is the magnetic moment of the drug-carrying particle.

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