Influence of a tilted external magnetic field on interstitial fluid pressure within the spherical solid tumors

In the present work, we have investigated the interstitial fluid pressure within a spherical solid tumor under a tilted external magnetic field. A proper form of the fluid flow equations, mass, and momentum conservation laws has been used in addition to the sufficient boundary conditions. The interstitial fluid pressure is analytically calculated and the effect of various parameters on the behavior of the tumor is studied. The obtained results have been compared with the experimental data. Our calculations show that in a homogeneous tumor with no necrotic core, drug particles are distributed non-uniformly. This behavior occurred due to the interstitial pressure distribution. Also, we considered the critical tumor radius and critical necrotic radius and analyzed the pressure distribution for various parameters of necrotic radii. We showed that tumor radius has a critical size, and the drug particles transport to the tumors with a radius smaller than this critical size. Also, the magnetic field has a significant effect on this drug delivery. Thus, there is a critical necrotic radius in drug delivery, and therapeutic influences have occurred. We have studied the effect of the external magnetic field on the values of the critical necrotic radius. Our results are applicable to injecting anticancer drug agents into the human body.