Dynamic Modeling of Drug Transport in Solid Tumors and Optimal Chemotherapy Regimen

Abstract

One of the most common therapies for treatment of cancer patients is chemotherapy. Therapeutic agents (drugs) can kill cancer cells by damaging their DNA and interrupting their extensive proliferation. Successful chemotherapy depends on the injected drug dosages and their timings. A high dosage of the therapeutic agents is toxic to normal cells, whereas a low dosage leads to an unsuccessful treatment. Distribution of drugs within solid tumors and their efficacy depend on the drug biophysical properties as well as physiological properties of solid tumor under treatment; therefore, the chemotherapy regimen should be determined and personalized for a specific patient and drug. Finding the optimal scheduling of chemotherapy for a specific drug and tumor condition using clinical or preclinical studies is almost impossible, as many parameters are involved and examining all of them is costly and lengthy. Mathematical models, instead, can be used to overcome these limitations. The objective of this study is to introduce a method for finding the optimal chemotherapy regimen that can be applied to a wide range of tumor microenvironments. We first use transport phenomena equations such as Darcy's law, the continuity equation, and Startling's equation to model the fluid flow within a tumor microenvironment. Two main mechanisms of drug transport is convection and diffusion; thus, an advection-diffusion equation is utilized to calculate spatio-temporal distribution of chemotherapeutic drugs. Then, a novel algorithm is developed to calculate the distribution of fluid and drug within an ideal image of a solid tumor, in which the tumor boundary and vasculature are perfectly recognized. Using this computational framework, we study the effects of important features of tumor microenvironment such as microvascular density and vessel locations on the drug macromolecule distribution. Finally, built upon these computations, we develop an algorithm for finding the optimal regimen for injection of drug nanoparticles to a specific tumor microenvironment. Firstly, different drug delivery steps including traveling within blood vessels, penetration from vessel walls to tumor tissue, distribution within tumor tissue, binding to cancer cell receptors, and internalization within cancer cells are mathematically modeled. Then, an objective function is defined based on the efficiency of drug macromolecules in killing cancer cells. We use an optimization algorithm to find an optimal dosage regimen that maximizes the eradication of cancer cells over treatment period while satisfying specific constraints. Constraints are set to make sure the toxicity level of drugs is tolerable by the patient. This computational framework is applied to conventional chemotherapy and chemotherapy using drugs encapsulated in liposomes. Moreover, the efficacy of two delivery approaches, bolus injection and continuous infusion, when optimal dosages are applied is investigated.