In clinical experiments, the evolution of a product concentration in tissue over time is often under study. Different products and tissues may be considered. For instance, one could analyse the evolution of drug concentration in plasma over time, by performing successive blood sampling from the subjects participating to the clinical study. One could also observe the evolution of radioactivity uptakes in different regions of the brain during a PET scan (Positron Emission Tomography). The global objective of this thesis is the modelling of such evolutions, which will be called, generically, pharmacokinetic curves (PK curves). Some clinical measures of interest are derived from PK curves. For instance, when analysing the evolution of drug concentration in plasma, PK parameters such as the area under the curve (AUC), the maximal concentration (Cmax) and the time at which it occurs (tmax) are usually reported. In a PET study, one could measure Receptor Occupancy (RO) in some regions of the brain, i.e. the percentage of specific receptors to which the drug is bound. Such clinical measures may be badly estimated if the PK curves are noisy. Our objective is to provide statistical tools to get better estimations of the clinical measures of interest from appropriately smoothed PK curves. Plenty of literature addresses the problem of PK curves fitting using parametric models. It usually relies on a compartmental approach to describe the kinetic of the product under study. The use of parametric models to fit PK curves can lead to problems in some specific cases. Firstly, the estimation procedures rely on algorithms which convergence can be hard to attain with sparse and/or noisy data. Secondly, it may be difficult to choose the adequate underlying compartmental model, especially when a new drug is under study and its kinetic is not well known. The method that we advocate to fit such PK curves is based on Bayesian Penalized splines (P-splines): it provides good results both in terms of PK curves fitting and clinical measures estimations. It avoids the difficult choice of a compartmental model and is more robust than parametric models to a small sample size or a low signal to noise ratio. Working in a Bayesian context provides several advantages: prior information can be injected, models can easily be generalized and extended to hierarchical settings, and uncertainty for associated clinical parameters are straightforwardly derived from credible intervals obtained by MCMC methods. These are major advantages over traditional frequentist approaches.

No / The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a ‘tumour cord’ geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are ‘pharmacokinetically resistant’ to chemotherapeutic strategies.

Yes / The tumour vasculature and microenvironment is complex and heterogeneous, contributing to reduced delivery of cancer drugs to the tumour. We have developed an in silico model of drug transport in a tumour cord to explore the effect of different drug regimes over a 72 h period and how changes in pharmacokinetic parameters affect tumour exposure to the cytotoxic drug doxorubicin. We used the model to describe the radial and axial distribution of drug in the tumour cord as a function of changes in the transport rate across the cell membrane, blood vessel and intercellular permeability, flow rate, and the binding and unbinding ratio of drug within the cancer cells. We explored how changes in these parameters may affect cellular exposure to drug. The model demonstrates the extent to which distance from the supplying vessel influences drug levels and the effect of dosing schedule in relation to saturation of drug-binding sites. It also shows the likely impact on drug distribution of the aberrant vasculature seen within tumours. The model can be adapted for other drugs and extended to include other parameters. The analysis confirms that computational models can play a role in understanding novel cancer therapies to optimize drug administration and delivery.

Oxytetracycline (OTC) is one of two antibiotics currently available and approved by the U.S. Food and Drug Administration for use as a chemotherapeutic agent in food fish and is widely used in the aquaculture industry. Previous pharmacokinetic studies of OTC have been conducted in cold water and warm water species of fish. However, no pharmacokinetic studies have been conducted on a cool water species such as yellow perch (Perca flavescens). The yellow perch is a cool water game and commercial species with high aquaculture potential. The pharmacokinetic profiles of oxytetracycline (OTC) was determined by measuring plasma concentrations in yellow perch following intraperitoneal (i.p.), intramuscular (i.m.), per os (p.o.), and intracardiac (i.c.) administration at a single dose of 50 mg/kg body weight. Using a modification of a high-performance-liquid-chromatographic (HPLC) technique, the plasma OTC concentrations were determined for each of the four routes of administration. Plasma concentrations were also evaluated in yellow perch exposed to a static 48-hour OTC water bath (100 mg/l). The terminal half-lives (t1/2) of OTC in yellow perch for i.p., i.m., p.o., and i.c. administrations were 112, 124, 50, and 28 h, respectively. The t1/2 for the i.m. route of administration was significantly longer than in any of the published i.m. OTC fish studies to date. However, the times of maximum OTC concentration (tmax) for the i.p., i.m. and p.o. administrations (2, 4, and 15 h, respectively) occurred relatively early in the plasma concentration-time curves. This suggests, that in yellow perch, OTC is initially absorbed very rapidly. The area under the plasma concentration-time curves (AUC) for the i.p., i.m., p.o., and i.c. routes of administration were 1718, 2659, 383, and 134 mcg·h/ml, respectively. No OTC was detected in the plasma of yellow perch following the water bath route of exposure. Finally, in yellow perch, effective therapy (plasma OTC concentrations above MIC values for most bacteria pathogenic to fish — 4 mcg/ml) would be achieved for up to 168 hours following a single i.p. or i.m. injection of 50 mg/kg and for up to 15 hours following a single p.o dose of 50 mg/kg. / Master of Science