Multi-dimensional modeling of nanoparticles transportation from capillary bed into the tumor microenvironment

In this study, we examined the extravasation of pharmaceutical inorganic nanoparticles (NPs) with a new approach from the leaky endothelium of tumor microvasculature (TMV) into the tumor microenvironment (TME) multi-dimensionally. We proposed a combination of prevailing macroscopic and microscopic methods and addressed the effect of interstitial fluid (IF) retention in solid tumor as an imperative parameter in drug delivery modeling. The Navier-Stokes equations and Darcy's law were utilized for blood flow and porous media, and the Starling's law was brought in for coupling effect. The blood flow was simulated as a non-Newtonian fluid alongside the Newtonian IF. We applied the Galerkin finite element method for the simulations. Our parametric study includes examining the effect of IF retention and TMV pressure on the distribution of tumor interstitial fluid pressure (TIFP), NPs concentration, and diameter on the penetration process, together with the time effect, on two-dimensional (2D) delivery of NPs. Our findings indicate that the IF retention in tumor cells increases TIFP depending on the amount of TMV pressure and IF retained. In addition to doubling pressure in the tumor necrotic region rather than the rest of TME, it enhances the TIFP which is an important parameter in drug delivery to solid tumors. By decreasing pressure drop within the TMV, pressure distribution within the TME becomes more uniform, creating a better condition for homogeneous penetration of NPs. Increasing both inlet pressure and NPs concentration leads to a nonlinear increase in the average concentration of tumor. Decreasing the diameter of NPs increases the penetration of NPs with a higher ratio in the TME.