Computational study of the optimum gradient magnetic field for the navigation of spherical particles into targeted areas

Spherical magnetic nanoparticles coated with drugs are navigated to targeted areas, for the treatment of cancer. The particles are navigated by magnetic field gradients that can be produced by an MRI device. In the present work, a computational study for the estimation of the time evolution of the gradient magnetic field is presented in order to ensure the optimum driving of the particles into the targeted area. For this purpose, the present method takes under consideration all the forces acting on the particles that make them move. The method is based on an iteration algorithm that intents to minimize the deviation of the particles from a desired trajectory. In this way, the gradient magnetic field is temporarily adjusted in a suitable way so that the particles' distances from the trajectory are decreased. Using the above mentioned method, it is clear that with the increase of the optimization parameters, i.e the modification of the gradient magnetic field, the particles are moved closer to the desired trajectory. Moreover, it is found that the present numerical model can navigate particles into the desired trajectory with efficiency above 90%.