Models of fluid dynamics in biological tissues for medical imaging and drug delivery

Fluid dynamics are essential to accurately describe the transport of any solute or particle delivered to a tumor, whether it is blood, nutrients, oxygen, systemic therapies, or a contrast agent. The purpose of this dissertation is to utilize quantitative medical imaging to inform computational fluid dynamics models of transport in biological tissues for applications in medical imaging and drug delivery, thereby improving our understanding of the imaging modalities, and providing accurate models of contrast agent and drug delivery for clinical use to maximize benefit to the individual patient. This objective is addressed in two distinct parts. First, we develop a high resolution, tissue-based model of contrast agent delivery in the mouse BT474 xenograft model of breast cancer, and simulate the acquisition of dynamic contrast enhanced magnetic resonance imaging data in this domain to test the accuracy of the standard methodology typically used to analyze such data. The results indicate that this widely used methodology for analyzing DCE-MRI data has inherent inaccuracies, as it does not account for passive delivery and distribution of the contrast agent due to diffusion within each voxel. Second, we develop, calibrate, and validate a mathematical model of convection-enhanced delivery of Rhenium-186 nanoliposomes to glioblastoma multiforme. The model is used to identify the optimal placement of the catheter within the tumor, so as to simultaneously minimize radiation exposure to healthy tissue and maximize tumor coverage. While models of convection enhanced delivery of molecular agents are currently on the market, no such models exist which are designed specifically for nanoparticle delivery, and which are calibrated and validated using clinical medical image data. Our results offer a useful model which accurately recapitulates the distribution of these liposomes, and is capable of identifying an optimal catheter placement for the delivery of these nanoparticles which avoids leakage into non-tumor regions.