A powerful alternative means to studying hemodynamics in diseased or healthy coronary arteries can be achieved by providing a numerical model in which blood flow can be virtually simulated, for instance, using the computational fluid dynamics (CFD) method. In fact, it is well documented that CFD allows reliable physiological blood flow simulation and measurements of flow parameters. A requisite for obtaining reliable results from coronary CFD is to use exact anatomical models and realistic boundary conditions. To date, in almost all of the modeling studies on hemodynamics of stenosed coronary arteries, a velocity based boundary conditions has been assigned. The objective of this study is to show that inlet velocity actually depends on the degree of stenosis and thus for severe constriction in coronary artery, a velocity based boundary conditions cannot be realistic. We then prove that regardless of severity of stenosis in coronary arteries, the upstream pressure, systemic pressure, is always constant, thus, should be used as boundary conditions instead. The two sets of boundary conditions are implemented to demonstrate the robustness of each in modeling of stenosed coronary artery in a CFD study. These boundary conditions are applied in a stenosed cylindrical pipe including three categories of symmetrical stenosis (mild, moderate and severe stenosis starting from 15 to 95% diameter reduction) for steady state and pulsatile flow. Results strongly indicate that inlet velocity boundary conditions are no longer valid when effective diameter in stenosis goes below approximately 2.8 mm (a healthy diameter is considered 3.2 mm) which corresponds to 10-15% diameter reduction. Further work will determine the effect of flow reduction on the oxygen tension in blood to better define conditions for clinical symptoms such as angina.
This study is an effort to produce a generic and comprehensive solution to the simulation of mass diffusion through a multiphasic and heterogeneous material model. A Galerkin-type finite element formulation is developed to solve Fick's equation for steady-state and time-dependent analysis. The effect of the interface in modelling of a liquid-solid medium is presented in this work. To show the robustness of the proposed approach, the gas exchange (oxygen and carbon dioxide) process through the capillary network between the alveolar membrane and red blood cells has been analysed and then validated with experimental data. The current work is a significant asset to modelling the diffusion of oxygen between cells and scaffolds in tissue engineering or tissue regeneration/repair studies. It is one step towards the development of high-order elements for application of the simulation of mass transfer through a multiphasic and porous model with varying degrees of interconnectivity and pore size for tissue engineering applications.
This study is an attempt to modeling a frictional gap in a crack closure process under compressive loading conditions in which the crack surfaces are in touch and the effects of friction between them are significant. An iterative finite element (FE) solution is developed to model a finite crack in an interfacial layer with varying material properties. A mere application of a Lagrange multiplier formulation (node-to-node, NTN, or node-to-segment, NTS) in a developed FE framework to fulfill the contact constraints between contacting surfaces is discussed which improves the penalty formulation used in ANSYS. We then argue that the penalty formulation allows for a certain amount of crack surface interpenetration whereas the Lagrange multiplier formulation fulfils the contact constraints more accurately. This technique is easy to implement and offers higher accuracy than the equivalent FE solution, available in commercial FE software such as ANSYS 9.0, to the same system.
The authors developed a novel numerical formulation that reduces the computational expense of solving linear and non-linear constitutive models. A finite-element constitutive law followed by a novel continuum model is discussed. The proposed approach is employed to reduce numerical errors obtained from the standard finite-element method. The continuum model is based on the Lagrange multipliers strategy along with the finite-difference method and a least-square algorithm. It is crucial to this approach that the components of either the strain or the stress tensor are known at the nodes of the finite-element mesh. The proposed model is independent of element topology which can be strongly and arbitrarily distorted.
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