Mathematical modeling of chemotherapy strategies in vascular tumor growth using nanoparticles

摘要

Throughout various fields of science and technology, a push towards the use of nanoscale technology is well underway. One area where nanoscale work is already well underway is within the field of drug delivery. Nanoscale devices carrying chemotherapeutic drugs could extravasate from blood vessels and even diffuse through the tissue and enter tumor cells. Drug delivery through nanoparticles presents significant potential advantages over traditional delivery via bolus injection. Drug release kinetics at the tumor site is an important aspect of chemotherapy.In this paper, we have developed a mathematical model that describes the chemotherapy strategies in spherically symmetric tumor. A system of partial differential equations is used to describe the drug concentration in the tumor cell, the cell movement whose divergence defines the local specific mass growth rate and the expression for the radius of the tumor cell.The analytical and numerical techniques are used to illustrate the tumor’s response to various chemotherapeutic strategies (i.e. for 10 nm and 100 nm) and the analytic expressions are also developed.