Numerical simulation and mathematical modeling of biomechanical stress distribution in poroelastic tumor tissue via magnetic field and bio-ferro-fluid.

Based on scientific evidence, it seems that bio-magnetic systems can change the process of cancer cell death by affecting the distribution of pressure and mechanical stress in the tumor tissue. Already most of the research has been done experimentally and few mathematical modeling and numerical simulations have been done to investigate the relationship between the magnetic parameters and the mechanical stress of the tumor tissue. This is despite the fact that in order to be able to make new equipment with the help of medical engineering methods, it is definitely necessary that the mathematics governing the problem and changes in the effective magnetic parameters (such as the shape of the magnetic source, magnetic flux density, magnetic source distance and ferro-fluid volume fraction) should be studied as much as possible. In this research, using numerical simulation and mathematical modeling, four common geometrical shapes (rectangular and circular) of the static magnetic field source were used to investigate the relationship between the change of the effective magnetic parameters and the mechanical stress created in the tumor tissue. The results of this research showed that when the magnetic flux density and ferro-fluid volume fraction and also the distance between the magnet and the tissue are kept constant, as well as without spending any extra energy, for a rectangular magnet, just by changing the way the source is placed on the tissue, the average biomechanical stress inside the tumor tissue causes a 25 % change. Also, for a circular magnet, just by doubling the radius of the magnet, the average biomechanical stress inside the tumor tissue causes a 73 % change.