The aortic valve functions in a complex mechanical environment which leads to force dependent cellular and tissue responses. Characterization of these responses provides a fundamental understanding of valve pathogenesis. The aim of this work was to develop an ex vivo organ culture system capable of simulating physiological aortic pressures and flow rates, and study the biological characteristics of native porcine aortic valves cultured in the system. Collagen, sGAG and elastin content of the valve leaflets were measured and cusp morphology, cell phenotype, cell proliferation and apoptosis were examined. Presence of endothelial cells (ECs) on the leaflet surface was also evaluated. The differences in collagen, sGAG and elastin contents were not significant (p greater than0.05) between the cultured and fresh valve leaflets. The cultured valves maintained the structural integrity of the leaflets while preserving the native morphology and cell phenotype. Cell phenotype in leaflets incubated statically under atmospheric conditions decreased compared to fresh and cultured valve leaflets, indicating the importance of mechanical forces in maintaining the natural biology of the valve leaflets. ECs were retained on the surfaces of cultured leaflets with no remodeling of the leaflets. The number of apoptotic cells in the cultured leaflets was significantly (p less than 0.05) less than in the statically incubated leaflets and comparable to fresh leaflets. The sterile ex vivo organ culture system thus maintained the viability and native biological characteristics of the aortic valves that were cultured under dynamic conditions for a period of 48 hours.

The study of wave production and propagation is a common phenomenon seen within a variety of math and physics problems. This thesis in particular will investigate the production and propagation of sound waves through musical instruments. Although this field of work has been examined since the late 1800s, approaching these types of problems can be very difficult. With the exception of the last fifty years, we have only been able to approach such problems by linearizing the necessary equations of gas dynamics. Without the use of a computer, one can only get so far in studying nonlinear acoustic problems. In addition, the numerical theory for nonlinear problems is incomplete. Proving stability is challenging and there are a variety of open problems within this field. This thesis will be examining the propagation of sound waves specifically through brass instruments. However, we will not be able to fully examine this problem in a master’s thesis because of the complexity. Instead, the objective is to provide a foundation and global picture of this problem by merge the fields of nonlinear acoustics as well as computational and analytical gas dynamics. To study the general behaviour of nonlinear wave propagation (and to verify previous findings), experiments have been carried on a trumpet. The purpose of these experiments is take measurements of the sound pressure waves at various locations along the instrument in order to understand the evolution of the wave propagation. In particular, we want to establish if the nonlinear distortion is strong enough to have musical consequences; and if there are such outcomes, what prerequisites are required for the observable behaviour. Additionally, by using the discontinuous Galerkin numerical method, a model of the system will be presented in this thesis. It will then be compared with the experimental data to verify how well we were able to describe the nonlinear wave motion within a trumpet.