Calcific aortic valve disease (CAVD) is one of the most common causes of cardiovascular disease in North America. Mechanical factors have been closely linked to the pathogenesis of CAVD and may contribute to the disease by actively regulating the mechanobiology of valve interstitial cells (VICs). Mechanical forces affect VIC function through interactions between the VIC and the extracellular matrix (ECM). Studies have shown that the transfer of mechanical stimulus during cell-ECM interaction depends on the local material properties at hierarchical length scales encompassing tissue, cell and cytoskeleton. In this thesis, biomechanical tools were developed and applied to investigate hierarchical cell-ECM interactions, using VICs and valve tissue as a model system. Four topics of critical importance to understanding VIC-ECM interactions were studied: focal biomechanical material properties of aortic valve tissue; viscoelastic properties of VICs; transduction of mechanical deformation from the ECM to the cytoskeletal network; and the impact of altered cell-ECM interactions on VIC survival. To measure focal valve tissue properties, a micropipette aspiration (MA) method was implemented and validated. It was found that nonlinear elastic properties of the top layer of a multilayered biomaterial can be estimated by MA by using a pipette with a diameter smaller than the top layer thickness. Using this approach, it was shown that the effective stiffness of the fibrosa layer is greater than that of the ventricularis layer in intact aortic valve leaflets (p<0.01). To characterize the viscoelastic properties of VICs, an inverse FE method of single cell MA was developed and compared with the analytical half-space model. It was found that inherent differences in the half-space and FE models of single cell MA yield different cell viscoelastic material parameters. However, under particular experimental conditions, the parameters estimated by the half-space model are statistically indistinguishable from those predicted by the FE model. To study strain transduction from the ECM to cytoskeleton, an improved texture correlation algorithm and a uniaxial tension release device were developed. It was found that substrate strain fully transfers to the cytoskeletal network via focal adhesions in live VICs under large strain tension release. To study the effects of cell-ECM interactions on VIC survival, two mechanical stimulus systems that can simulate the separate effects of cell contraction and cell monolayer detachment were developed. It was found that cell sheet detachment and disrupted cell-ECM signaling is likely responsible for the apoptosis of VICs grown in culture on thin collagen matrices, leading to calcification. The studies presented in this thesis refine existing biomechanical tools and provide new experimental and analytical tools with which to study cell-ECM interactions. Their application resulted in an improved understanding of hierarchical valve biomechanics, mechanotransduction, and mechanobiology.

Calcific aortic valve disease (CAVD) is one of the most common causes of cardiovascular disease in North America. Mechanical factors have been closely linked to the pathogenesis of CAVD and may contribute to the disease by actively regulating the mechanobiology of valve interstitial cells (VICs). Mechanical forces affect VIC function through interactions between the VIC and the extracellular matrix (ECM). Studies have shown that the transfer of mechanical stimulus during cell-ECM interaction depends on the local material properties at hierarchical length scales encompassing tissue, cell and cytoskeleton. In this thesis, biomechanical tools were developed and applied to investigate hierarchical cell-ECM interactions, using VICs and valve tissue as a model system. Four topics of critical importance to understanding VIC-ECM interactions were studied: focal biomechanical material properties of aortic valve tissue; viscoelastic properties of VICs; transduction of mechanical deformation from the ECM to the cytoskeletal network; and the impact of altered cell-ECM interactions on VIC survival. To measure focal valve tissue properties, a micropipette aspiration (MA) method was implemented and validated. It was found that nonlinear elastic properties of the top layer of a multilayered biomaterial can be estimated by MA by using a pipette with a diameter smaller than the top layer thickness. Using this approach, it was shown that the effective stiffness of the fibrosa layer is greater than that of the ventricularis layer in intact aortic valve leaflets (p<0.01). To characterize the viscoelastic properties of VICs, an inverse FE method of single cell MA was developed and compared with the analytical half-space model. It was found that inherent differences in the half-space and FE models of single cell MA yield different cell viscoelastic material parameters. However, under particular experimental conditions, the parameters estimated by the half-space model are statistically indistinguishable from those predicted by the FE model. To study strain transduction from the ECM to cytoskeleton, an improved texture correlation algorithm and a uniaxial tension release device were developed. It was found that substrate strain fully transfers to the cytoskeletal network via focal adhesions in live VICs under large strain tension release. To study the effects of cell-ECM interactions on VIC survival, two mechanical stimulus systems that can simulate the separate effects of cell contraction and cell monolayer detachment were developed. It was found that cell sheet detachment and disrupted cell-ECM signaling is likely responsible for the apoptosis of VICs grown in culture on thin collagen matrices, leading to calcification. The studies presented in this thesis refine existing biomechanical tools and provide new experimental and analytical tools with which to study cell-ECM interactions. Their application resulted in an improved understanding of hierarchical valve biomechanics, mechanotransduction, and mechanobiology.

In this thesis, a number of mathematical models of haptotactic cell migration are developed. The modelling of haptotaxis is presented in two distinct parts - the first comprises an investigation of haptotaxis in pre-necrotic avascular tumours, while the second consists of the modelling of adhesion-mediated haptotactic cell migration within tissue, with particular attention paid to the biological appropriateness of the description of cell-extracellular matrix adhesion. A model is developed that describes the effects of passive and haptotactic migration on the cellular dynamics and growth of pre-necrotic avascular tumours. The model includes a description of the extracellular matrix and its effect on cell migration. Questions are posed as to which cell types act as a source of the extracellular matrix, and the model is used to simulate the possible effects of different matrix sources. Simulations in one-dimensional and spherically symmetric geometry are presented, displaying familiar results such as three-phase tumour growth and tumours comprising a rim of proliferating cells surrounding a non-proliferating region. Novel effects are also described such as cell population splitting and tumour shrinkage due to haptotaxis and appropriate extracellular matrix construction. The avascular tumour model is then extended to describe the internalisation of labelled cells and inert microspheres within multicell tumour spheroids. A novel model of adhesion-receptor mediated haptotactic cell migration is presented and specific applications of the model to tumour invasion processes are discussed. This model includes a more biologically realistic description of cell adhesion than has been considered in previous models of cell population haptotaxis. Through assumptions of fast kinetics, the model is simplified with the identification of relationships between the simplified model and previous models of haptotaxis. Further simpli.cations to the model are made and travelling wave solutions of the original model are then investigated. It is noted that the generic numerical solution routine NAG D03PCF is not always appropriate for the solution of the model, and can produce oscillatory and inaccurate solutions. For this reason, a control volume numerical solver with .ux limiting is developed to provide a better method of solving the cell migration models.