Nonlinear multi-scale anisotropic material and structural models for prosthetic and native aortic heart valves
Kim, Hee Sun
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New 3D multi-scale modeling approaches for the structural analysis of native and prosthetic Aortic Valves (AV) are investigated. Three different nonlinear hyperelastic constitutive material models for the mechanical behavior of the AV tissue are introduced. The first is the well-known Holzapfel hyperelastic, anisotropic and homogeneous model. The second model, termed the Collagen Fiber Network (CFN), is a heterogeneous model that recognizes the hyperelastic collagen and elastin layers using different layered finite elements. The third hyperelastic model is implemented using a new nonlinear micromechanical formulation of the High Fidelity Generalized Method of Cells (HFGMC) originally proposed by Aboudi. The latter two material models are heterogeneous and explicitly recognize the in-situ tissue constituents. Initially, a full scale 3D structural model of a polymeric-based prosthetic AV model is studied. This model is verified using deformation metrics obtained from images taken with high speed cameras during in-vitro experiments. The predictions from the proposed polymeric AV model are in good agreement with the test data. Next, the three tissue material models are examined in their ability to predict the anisotropic material behavior of porcine AV leaflet tissue. The Holzapfel model is calibrated from the overall anisotropic uni- and biaxial stress-strain data while the in-situ elastin and collagen constituents in the CFN and HFGMC models are calibrated to match the overall effective responses. Dynamic structural analysis is performed for the porcine AV with applied transvalvular pressure measured from repeated in-vitro tests conducted in this study. Principal stretches are computed from the experimental measurements and compared with the AV material-structural predictions. The proposed multi-scale modeling approach for the native AV is capable of predicting the structural behavior during the entire cardiac cycle without suffering from numerical convergence problems. Finally, new nonlinear micromechanical formulations based on the HFGMC method are developed and applied for various types of tissue materials including the human arterial wall layers and porcine AV leaflets. The proposed hyperelastic HFGMC model is compared to the CFN model and the Holzapfel models. It is shown that the HFGMC is an effective modeling approach for the arteries especially when the collagen fiber network has a periodic microstructure.