Morphine is a commonly used analgesic in pain management. Opioid administration to a patient after surgery, such as spinal decompression surgery, can lead to adverse side effects. To demonstrate these adverse side effects could be decreased we created a model of how morphine and its metabolites are transported and excreted from the body. Using the of morphine and a standard compartment approach this thesis aimed at projecting pharmacokinetics trends of morphine overtime. A Matlab compartment model predicting the transport of morphine through the body can contribute to a better understanding of the concentrations at the systemic level, specifically with respect to a CSF, and what happens when you compare an intravenous injection to a local delivery. Other studies and models commonly utilized patient data over small periods of time2,3,5. An extended period of time will provide information into morphine’s time course after surgery. This model focuses on a compartmentalization of the major organs and the use of a simple Mechalis-Menten enzyme kinetics for the metabolites in the liver. Our results show a CSF concentration of about 1.086×〖10〗^(-12) nmol/L in 6 weeks and 1.0097×〖10〗^(-12) nmol/L in 12 weeks. The concentration profiles in this model are similar to what was expected. The implications of this suggest that patients who reported effects of morphine paste, a locally administered opioid, weeks after the surgery were due to other reasons. In creating a model we can determine important variables and dosage information. This information allows for a greater understanding of what is happening in the body and how to improve surgical outcomes. We propose this study has implications in general research in the pharmacokinetics and dynamics of pharmacology through the body.

The intervertebral disc goes through degenerative changes with age, which leads to disc thinning, bulging, or herniation. Spinal fusion treatments are ineffective as they cause quicker degeneration of adjacent discs and fail in nearly 20% of cases, so researchers have turned to tissue-engineering biocompatible intervertebral discs for transplantation. However novel and effective as this may seem, these transplanted discs still show evidence of degeneration after just 5 years. I hypothesize that these discs are degenerating due to a blockage of the cartilaginous endplates post-transplantation that is hindering nutrient transport through the intervertebral disc. In order to test this hypothesis, I developed a mathematical model of nutrient transport through the intervertebral disc in one diurnal daily loading cycle. This model was used to simulate open endplates and blocked endplates and then compare differences in nutrient concentration and nutrient transport to the center of the disc. Results from the math model simulations were then compared to in vitro experimental data collected in lab to verify the findings on a physiological level. Results showed significant differences, both in vitro and in the model, between nutrient transport in open endplates vs blocked endplates, lending support to the original hypothesis. This study only presents preliminary results, but could hold the key to preventing future disc degeneration post-transplantation.

Controlled release formulations for local, in vivo drug delivery are of growing interest to device manufacturers, research scientists, and clinicians; however, most research characterizing controlled release formulations occurs in vitro because the spatial and temporal distribution of drug delivery is difficult to measure in vivo. In this work, in vivo magnetic resonance imaging (MRI) of local drug delivery is performed to visualize and quantify the time resolved distribution of MRI contrast agents. I find it is possible to visualize contrast agent distributions in near real time from local delivery vehicles using MRI. Three dimensional T1 maps are processed to produce in vivo concentration maps of contrast agent for individual animal models. The method for obtaining concentration maps is analyzed to estimate errors introduced at various steps in the process. The method is used to evaluate different controlled release vehicles, vehicle placement, and type of surgical wound in rabbits as a model for antimicrobial delivery to orthopaedic infection sites. I are able to see differences between all these factors; however, all images show that contrast agent remains fairly local to the wound site and do not distribute to tissues far from the implant in therapeutic concentrations. I also produce a mathematical model that investigates important mechanisms in the transport of antimicrobials in a wound environment. It is determined from both the images and the mathematical model that antimicrobial distribution in an orthopaedic wounds is dependent on both diffusive and convective mechanisms. Furthermore, I began development of MRI visible therapeutic agents to examine active drug distributions. I hypothesize that this work can be developed into a non-invasive, patient specific, clinical tool to evaluate the success of interventional procedures using local drug delivery vehicles.