A model of magnetic nanoparticle transport and their effects in tumor areas: Assessment of desirable magnetic properties

A mathematical model of the transport of drug loaded magnetic nanoparticles and their effects on tumor evolution is presented. The model is developed in the context of continuum mechanics and transport phenomena, with the main variables, such as interstitial fluid pressure and flow, nanoparticle, cell and oxygen concentrations, cell-phase velocities and pressures being described as continuous fields over the tumor and surrounding tissue. The evolution of tumor shape and size is obtained from the numerical solution of the model equations. Simulations are presented comparing the behavior in the absence of any drug, in the presence of drug loaded nanoparticles but without a magnetic field, and under the action of a magnetic field of varying intensity. It is observed that magnetic targeting can have a profound effect on the distribution of nanoparticles inside the tumor and a clearly apparent and quantitatively significant influence on its progression. With the aid of magnetic targeting, the otherwise almost inaccessible area, due to the effects of the interstitial fluid pressure and flow, can be exposed to significant and controlled nanoparticle concentrations. For this to be achieved, it suffices for the magnetically induced nanoparticle velocity to be a fraction of the interstitial fluid flow velocity, yet in the same order of magnitude. This assessment provides a guiding rule for the rational design of magnetic nanoparticles and the quest of suitable magnetic fields.