This thesis models viscoelastic free surface and interfacial flows. Capillarity and viscoelasticity are important in many interesting problems, e.g. the deformation of droplets and blood cells, coating flows of polymer solutions, and blood flow in arteries and capillaries. The study of the combined effects of capillarity and viscoelasticity is still in its infancy due to complex physics combined with the numerical difficulties in three-dimension. This thesis extends to three-dimensional flows from the previous studies focused on two-dimensional problem. Modeling viscoelastic free surface flows presents several challenges which include modeling the liquid viscoelasticity, locating free surface boundaries, and implementing large-scale computations. Conformation tensor models are used to model the fluid viscoelasticity because they balance generality, realistic physics, and computational cost. A new, convenient open-flow boundary condition is developed for the transport equation of the conformation tensor. The domain deformation method is used to locate both two- and three-dimensional free surfaces and interfaces by treating the mesh as an elastic pseudo-solid. In addition, an isochoric domain deformation method is developed to conserve domain volumes for certain free surface flows where the volume of a liquid domain is prescribed, such as a cell deforming in shear flow. The equations for solving viscoelastic free surface flows are discretized by the finite element method. The non-linear discretized equations are solved by Newton's method and the resulting large set of linear algebraic equations is solved by parallel GMRES preconditioned by a new sparse approximate inverse preconditioner (SPAI). The parallel solver together with SPAI is scalable in a wide range of capillary and Weissenberg numbers; tests on benchmark viscoelastic free surface flows show that problems with millions of unknowns can be tackled on Linux clusters. The development of viscoelastic free surface flow modeling and isochoric domain deformation method is applied to model cell (viscoelastic drop) deformation.

Haemophilus influenzae type b (Hib) is a Gram-negative bacterium that causes meningitis in infants. Located in the outer membrane, Hib porin (342 amino acids, M$ rm sb{r}$ 37,782 daltons) forms channels that allow for the diffusion into the periplasm of small solutes up to a molecular mass of 1400 daltons. / Based on predictions of porin secondary structure, a model of Hib porin was generated. The model proposed sixteen membrane spanning $ beta$-strands connected by eight long loops on one side and eight short $ beta$-turns on the other side. To refine further this model, the epitopes of nine monoclonal antibodies specific for Hib porin were mapped precisely. Surface-exposure of these epitopes was determined by flow cytometry of intact Hib cells. Our studies identified two surface-exposed regions of Hib porin: amino acids 162 to 172, and 318 to 325. These two regions correspond to loops 4 and 8 in the Hib porin model. / Three naturally occurring Hib porin variants were purified, reconstituted into planar bilayers, and analyzed for their voltage dependency. Substitutions at Arg166 residue, which is localized to loop 4, were associated with a lowered threshold potential for the voltage gating of Hib porin. This surface-exposed loop was therefore implicated in the conformational changes that are postulated to occur during voltage gating. / Lipooligosaccharide (LOS) binds tightly to Hib porin. To generate large amounts of Hib porin devoid of LOS, the ompP2 gene was cloned into an expression vector of Bacillus subtilis. Recombinant Hib porin was produced in large quantities and it aggregated into inclusion bodies. Under denaturing conditions, recombinant porin was purified to homogeneity and subsequently refolded. To assess the fidelity of refolding of recombinant porin, four criteria were used: spectroscopic properties, channel formation in planar bilayers, resistance to trypsin digestion and formation of the conformational epitope recognized by monoclonal antibody Hb-2. We conclude that in the absence of LOS, recombinant porin was refolded into a functional form, its structure closely resembling the native state.

GEANT4 is a Monte Carlo code developed in an object-oriented environment. It provides three models of electromagnetic physics, namely Standard, Low-energy, and Penelope. In this work, we examined the accuracy of the photon and electron interactions, and developed a user code for external beam radiotherapy simulations. The code has the capabilities to collect phase space data, perform variance reduction schemes, and calculate dose distributions in a phantom. For all three models, the dose distributions of monoenergetic and clinical photon beams in water are in good agreement with the EGSnrc simulations. For electron beams, the results depend on the maximum electron step size. Significant step size artifacts are also found in the transport of electrons through a thin aluminum slab. Our studies of interface perturbation effects and Fano cavity response illustrated potential problems with the condensed history algorithm. Overall, GEANT4 can be used in applications where electron transport is not critical.

The aim of stereotactic radiosurgery is to deliver a high and uniform radiation dose to the target volume and a minimized dose to the surrounding healthy tissue. Various linac-based radiosurgical techniques are used clinically: multiple non-coplanar converging arcs, dynamic arc rotation, and conical rotation. The techniques differ in their beam distribution over the patient's head. / A study of the beam distribution characteristics for the clinical linac-based radiosurgical techniques is presented. Two spiral linac-based radiosurgical techniques are developed: the uniform dose-rate spiral irradiation and the dose-rate-weighted spiral irradiation. Both exhibit the same spiraling beam entry trace over the patient's head; however, they differ in their beam distribution along the spiral. The dose-rate-weighted spiral irradiation provides a uniform beam distribution over the 2pi solid angle available in radiosurgery. / The currently existing techniques and the spiral techniques are then compared using the cumulative dose-volume histogram (CDVH) tools available with the McGill Treatment Planning System (MPS). The dose-rate-weighted spiral technique leads to lower dose inhomogeneities within the target volume and better dose conformity within the target. Moreover, it also encompasses smaller volumes of tissue at all isodose levels with larger differences at low isodose levels. A conclusion is reached that the dose-rate-weighted spiral irradiation technique offers interesting advantages over the currently used clinical linac-based techniques.

Algorithms for optimization and verification of radiation treatments have been developed. The first one, an active set algorithm for inverse treatment planning employs a conjugate gradient routine for subspace minimization in order to achieve a higher rate of convergence than the widely used constrained steepest descent method at the expense of a negligeable amount of overhead calculations and storage. The active set algorithm is found to be superior to the constrained steepest descent in terms of both its convergence properties and the residual value of the cost functions at termination. The active set approach can significantly accelerate the process of inverse treatment planning by decreasing the number of time consuming dose calculations. / The second algorithm employs a continuous penalty function method to solve approximately a large-scale constrained minimization problem which reflects the goal of sparing healthy tissues as much as possible while delivering the necessary tumorcidal dose. The performance of the continuous penalty function method is optimized by a numerical investigation of a few integration schemes and a pair of weighting functions which influence the performance of the method. Clinical examples are presented that illustrate possible applications of the techniques in the context of multi-objective optimization. / An image correlation based algorithm for automatic registration of pairs of portal images has also been developed. Accounting for both in-plane translations and rotations, the algorithm uses fast-Fourier-transforms and a sequential approach to speed up the registration without degrading the accuracy of the match. The technique has also been applied to the automatic registration of portal images to digitally reconstructed radiographs (DRRs) which have been modified to resemble megavoltage images. The results indicate the feasibility of this approach as a tool for treatment setup verification.

To increase the effectiveness of conventional radiotherapy in the treatment of cancer, different drugs can be administered. The aim of this project is to investigate biodegradable polyanhydride carrier matrices (PCPP-SA; 20:80) as a localized slow release delivery system for halogenated pyrimidines, in our case Bromodeoxyuridine (BrdU). Our in vitro experiments show that RIF-1 cells which have incorporated BrdU into their DNA over 4 doublings show significant increase in the initial slope (alpha-value) of their radiation cell survival curves, indicating an increase in radiosensitivity. To investigate the radiosensitization potential of BrdU in vivo, biodegradable BrdU/polymer combinations (20% w/w) were prepared and implanted directly into RIF-1 tumors, grown subcutaneously on the backs of C3H/Km mice. Clonogenic/excision assays were done with these tumors exposed to BrdU/polymer implants for several cell cycles before irradiation in situ to determine the extent of radiosensitization on the basis of cell survival. Tumor growth delay (TGD) measurements were also used as an index of tumor control following different treatments (single dose or fractionated doses) with and without the drug/polymer implants. All results indicate that BrdU, combined with radiation, increases TGD, while having no effect on non-irradiated tumors. The extent of substitution of thymidine by BrdU in DNA were also determined. This project was supported by the National Cancer Institute of Canada.

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