A mathematical model for understanding nanoparticle biodistribution after intratumoral injection in cancer tumors

To exploit the benefits of a multifunctional nanomaterial as theranostics, drug carriers, and adjuvant therapeutics, tissue parameters affecting in-vivo transport, intratumoral diffusion, need to be understood properly. Literature has reported different regions of tumor such as necrotic core, viable tumor which are surrounded by healthy tissue. Transvascular exchange of the fluid and solute plays a crucial role in nanoparticle retention in the tumors. Modeling fluid and solute transport phenomenon in tissue considering in-vivo tumor architecture is essential. In this study, the influence of necrotic core presence, transvascular transport, nanoparticle size, and vascular normalization have been investigated to better understand the nanoparticle distribution in tumors. A three-dimensional numerical model has been developed to study the interstitial fluid flow and nanoparticle distribution in tumors considering the reported in-vivo scenario. The effects of nanoparticle size, intratumoral single-site, and multi-site injection methods, and vascular normalization on the distribution were investigated. In-silico investigations were carried out with respective parameters of tumor and healthy tissues using finite element based COMSOL Multiphysics 5.6® software. Interstitial fluid pressure, velocity, and nanoparticle concentration in interstitial space were predicted by solving the developed models. It was found that the interstitial fluid pressure is elevated and uniform throughout the tumor region, inhibiting the convective transport of the nanoparticles. Post-injection distribution patterns of nanoparticles revealed that the smaller nanoparticles show faster diffusion and rapid clearance from the tissues, while larger particles are retained for longer periods. The multi-site infusion method is more efficacious than the single-site method, gives better distribution patterns in the tumor. Vascular normalization does not affect the distribution of larger particles while it has shown a profound effect on the 10 nm particle distribution. Considering necrotic core and transvascular transport is inevitable in modeling to replicate the in-vivo scenario in in-silico investigations. Based on the results obtained, it is found that very fine particles of the size 10 nm will lead to lower therapeutic concentrations due to vascular clearance, despite faster diffusion rates. Particle sizes larger than 30 nm will not diffuse into the tumor due to lower diffusion coefficients and retained at the injected site. This study proposes 15 nm–30 nm as the suitable size for hyperthermia considerations.