A mathematical model of drug delivery by modifying the tumor microenvironment:MMP activation

Cancer modeling has become one of the challenging frontiers of applied mathematics mostly for two decades. Drug delivery to solid tumors also attracts both theorists and experimentalists due to its significance in cancer therapy. Recent studies have revealed that drug responses of tumor cells are determined both by intrinsic characteristics and by regulation of tumor microenvironment. The irregularity tumor blood vessel structure results in disorganized blood flow within the tumor and increased leakage which causes increased interstitial fluid pressure (IFP). This IFP forms a barrier for drug transport and it could be seen as an apparent obstacle to the delivery of therapeutic molecules. The basis of this thesis is the effects of the delivery of matrix metalloproteinases (MMPs) to the tumor tissue, which in turn, increased hydraulic conductivity, improved interstitial transport and enhanced distribution of nanotherapeutics. In the light of Mok et al.'s researches, a mathematical model which associates the effect of MMPs to convective transport and to drug distribution in tumors is constructed. Governing equations in the model with suitable boundary conditions involve the principles for transvascular and interstitial drug transport and conservation laws. Finally, these equations are discretized with finite element method (FEM) and the simulation results are discussed comparing to the literature.