Simulation of transport and extravasation of nanoparticles in tumors which exhibit enhanced permeability and retention effect

Determining the factors that influence the delivery of sub-micron particles to tumors and understanding the relative importance of each of these factors is fundamental to the optimization of the particle delivery process. In this paper, a model that combines random walk with the pressure driven movement of nanoparticles in a tumor vasculature is presented. Nanoparticle movement in a cylindrical tube with dimensions similar to the tumor's blood capillary with a single pore is simulated. Nanoparticle velocities are calculated as a pressure driven flow over imposed to Brownian motion. The number and percentage of nanoparticles leaving the blood vessel through a single pore is obtained as a function of pore size, nanoparticle size and concentration, interstitial pressure, and blood pressure. The model presented here is able to determine the importance of these controllable parameters and thus it can be used to understand the process and predict the best conditions for nanoparticle-based treatment. The results indicate that the nanoparticle delivery gradually increases with pore size and decreases with nanoparticle size for tumors with high interstitial fluid pressure (in this work we found this behavior for head and neck carcinoma and for metastatic melanoma with interstitial pressures of 18 mmHg and 19 mmHg, respectively). For tumors with lower interstitial fluid pressure (rectal carcinoma with 15.3 mmHg) however, delivery is observed to have little sensitivity to particle size for almost the entire nanoparticle size range. Though an increase in nanoparticle concentration increases the number of nanoparticles being delivered, the efficiency of the delivery (percentage of nanoparticles delivered) is found to remain closely unaffected.