Brownian dynamics simulation of nanoparticles and polymers with applications in drug delivery
Keywords: Mechanical Engineering.

Efficient drug delivery is important for the successful treatment of cancerous tumors. After the drug is introduced into the bloodstream, it must make its way into the target tumor at concentrations high enough to effectively treat the tumor. Unfortunately, there are numerous barriers in the tumor microenvironment that hinder this process. Three major transport steps characterize the drug delivery process. First, the drug must flow and distribute itself evenly throughout the blood vessels within the tumor. Second, the drug must extravasate through pores of the blood vessel wall. Finally, the drug must penetrate through the tumor tissue and deliver its payload. Throughout this process, both convection and Brownian diffusion are important transport mechanisms. Historically, the use of small-molecule chemotherapeutics has been the conventional method for treating tumors, however, the use of nanoparticles as drug carriers has recently emerged as a promising alternative. In this thesis, we examine some of the transport barriers that exist in the use of nanoparticles and polymers to treat tumors; where appropriate, we also extend our study to problems that are outside the scope of drug delivery. To do so, we use a combination of Brownian dynamics simulations, analytical approximations of the governing Fokker-Planck equation, and experiments to elucidate the transport processes. We begin by studying the transport of nanoparticles in the blood vessel --- the first step in the drug delivery process. It is well known that transverse velocity gradients, such as those encountered in a pressure-driven flow, can enhance the effective diffusion coefficient of the solute; this process is known as Taylor dispersion. In a blood vessel, in addition to the axial velocity field, however, hydrodynamic interactions with red blood cells drive nanoparticles toward the blood vessel walls in a direction orthogonal to the primary flow direction. Using a combination of perturbation theory and Brownian dynamics simulations, we show how this orthogonal motion, which we characterize as a "cross flow, " affects the transport of nanoparticles. Specifically, we solve for three coefficients describing the transport of nanoparticles: the effective axial dispersion coefficient, the effective velocity, and the effective mass transfer coefficient across the blood vessel wall. Next, we study the configuration and dynamics of polymers tethered to plane walls in shear flow. While this problem is not formally related to the motivating drug delivery problem, this work provides an introduction to the bead-spring model used in Brownian dynamics simulations of polymers. We study the effect of polymer contour length on the average extension of the polymer, and we develop simple scalings to interpret our results; our results are successfully compared to previously published experimental results. Motivated by engineering applications where the adsorption of polymers to walls is important, we also investigate the collision process between the polymer backbone and the wall. Finally, we return to the drug delivery problem and focus on the process of extravasation through pores of the blood vessel wall --- the second step in the drug delivery process. In the first part of this thesis, we characterized the porous blood vessel wall using an effective mass transfer coefficient; here, we zoom in on the microscale and consider transport through an individual pore. Importantly, it is well known that pores develop in the blood vessels in tumors that are significantly larger than those that occur in healthy tissue. Compared to small-molecule chemotherapeutics, which can extravasate in both healthy and tumor tissue thus causing adverse side effects, one of the noteworthy benefits of using relatively larger nanoparticles is that they passively target tumor tissue. First, we consider the extravasation of spheroidal particles, to elucidate the effect of particle shape and size. Next, we consider the effect of coating spherical particles with poly(ethylene glycol) (PEG), a polymer coating that is known to shield the nanoparticle from the body's immune system and thus minimize removal from circulation. To validate the results determined through Brownian dynamics simulations and analytical approximations, we also conduct in vitro experiments, where the extravasation rates of fluorescently-labeled unPEGylated and PEGylated bacteriophage MS2 through porous membranes are measured