Soft biological tissue material models in the literature are frequently limited to integer order constitutive relations where the order of differentiation of stress and/or strain is integer-valued. However, it has been demonstrated that fractional calculus theory applied in soft tissue material model formulation yields more accurate and reliable soft tissue material models. In this study, firstly a fractional order (where the order of differentation of stress in the constitutive relation is non-integer-valued) linear viscoelastic material model for soft tissues is fitted to force-displacement-time indentation test data and compared with two different integer order linear viscoelastic material models by using MATLAB&reg / optimization toolbox. After the superiority of the fractional order material model compared to integer order material models has been shown, the linear fractional order material model is extended to its nonlinear counterpart in finite deformation regime. The material model developed is assumed to be isotropic and homogeneous. v A user-subroutine is developed for the material model formulated to implement it into the commercial finite element software Msc.Marc 2010. The user-subroutine developed is verified by performing a small strain finite element analysis and comparing the results obtained with linear viscoelastic counterpart of the model on MATLAB&reg / . Finally, the unknown coefficients of the fractional order material model are identified by employing the inverse finite element method. A material parameter set with an amount of accuracy is determined and the material model with the parameters identified is capable of simulating the three different indentation test protocols, i.e., &ldquo / relaxation&rdquo / , &ldquo / creep&rdquo / and &ldquo / cyclic loading&rdquo / protocols with a good accuracy.

Small punch test (SPT) has been widely used to evaluate in-service materials in nuclear fusion facilities. Early use of SPTs is largely based on empirical relations or curve fitting from experimental data, while recent applications of SPTs take advantage of finite element methods. In this study, an improved inverse finite element analysis procedure is proposed to obtain constitutive relations from load-displacement curves recorded in SPTs. In addition, a parametric study is performed to evaluate the effects of SPT parameters including friction coefficient, punch head diameter, sample thickness, specimen scale and boundary conditions. The proposed inverse finite element (FE) method improves the accuracy of existing inverse FE methods, and the current parametric study provides a basis for the standardization of SPT procedures in the future.

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.