The purpose of this work is to predict the effect of impaired red blood cells (RBCs) deformability on blood flow conditions in human carotid artery bifurcation. First, a blood viscosity model is developed that predicts the steady-state blood viscosity as a function of shear rate, plasma viscosity, and mechanical (and geometrical) properties of RBC's. Viscosity model is developed by modifying the well-known Krieger and Dougherty equation for monodisperse suspensions by using the dimensional analysis approach. With the approach, we manage to account for the microscopic properties of RBC's, such as their deformability, in the macroscopic behavior of blood via blood viscosity. In the second part of the paper, the deduced viscosity model is used to numerically predict blood flow conditions in human carotid artery bifurcation. Simulations are performed for different values of RBC's deformability and analyzed by investigating parameters, such as the temporal mean wall shear stress (WSS), oscillatory shear index (OSI), and mean temporal gradient of WSS. The analyses show that the decrease of RBC's deformability decrease the regions of low WSS (i.e., sites known to be prevalent at atherosclerosis-prone regions); increase, in average, the value of WSS along the artery; and decrease the areas of high OSI. These observations provide an insight into the influence of blood's microscopic properties, such as the deformability of RBC's, on hemodynamics in larger arteries and their influence on parameters that are known to play a role in the initiation and progression of atherosclerosis.
The prediction of the arterial zero-stress state is as of yet an unresolved problem in the field of modelling the mechanical response of patientspecific arteries. This is because the configuration associated with arterial zero-stress state is impossible to obtain experimentally. However, the zero-stress configuration (or, equivalently, the residual stresses related to this configuration) represents the crucial data of any numerical analysis. In this study, the mechanical response of a pre-stressed, pressurised, hyperelastic tube (representing the artery) is determined without knowing the initial zero-stress configuration of the artery. Instead, to predict the arterial residual (bending and stretching) stresses, a corresponding thermomechanical analogy is used. As shown in the paper, the arterial residual stress state can equally be obtained by thermally loading a properly defined closed tube. Thus, based on the loaded state of the corresponding thermomechanical model, the arterial residual stress sate is constructed, from where the arterial loaded state can be obtained. The initial configuration of the thermomechanical model is defined on the basis of the arterial loaded configuration. The methodology is validated by predicting the zero-stress state of the artery. The predicted equilibrium state of the artery, when cut longitudinally and transversally, has the form of an opened-up tube with a relatively low stress state in comparison to the arterial residual stresses. The results thus demonstrate that arterial residual stresses that are predicted with the corresponding thermomechanical model exhibited the bending distribution, which proves the methodology to be adequate. Keywords: residual stresses, zero-stress state of arteries, finite element method, thermomechanics Highlights • Predicting the arterial mechanical response based on the in vivo arterial data. • Proposed methodology for predicting the arterial mechanical response. • Using thermomechanical analogy for predicting the arterial residual stress state. • Predicting the arterial zero-stress state based on the in vivo arterial data. • Determination of bending stresses by means of thermomechanical analogy.
In this work, the residual stress state of a human common carotid artery is predicted using the so-called thermomecha- nical analogy approach. The purpose of the approach is to enable consistent mapping of residual stresses and the respec- tive configuration from a circular arterial segment to a patient-specific arterial geometry. This is achieved by applying proper volumetric dilatations to the actual arterial stress-free in vivo geometry, which makes use of the analogy that states that the bending stresses can be obtained on an equivalent manner by applying proper thermal dilatations. The common carotid artery data are obtained in vivo from a healthy 28-year-old man using non-invasive methods. The pre- dicted residual stresses of the common carotid artery are in good quantitative agreement with the data from prior work in this field. The approach is validated by predicting the common carotid artery zero-stress state configuration, where a sector-like (cut-open) state is obtained. With this approach, it is thus possible to predict the residual stresses as well as the configuration of patient-specific arterial geometry without the need to model its cut-open zero-stress configuration
Reconstruction of the fiber orientation distribution function (ODF) from injection molding simulation results is commonly performed using the so-called series-based approach. However, with the development of advanced material constitutive models, the need has emerged to overcome the drawbacks of this approach, such as negative values for certain orientation states and limitations in describing highly concentrated probabilities. In this work, an approach to shift the reconstruction procedure from series-based to function-based is proposed, achieved by deducing an appropriate two-parametric form of the ODF. We demonstrate that the proposed ODF can be uniquely reconstructed from the second-order orientation tensors obtained from the injection molding simulations and that the approach does not suffer from the aforementioned limitations, being capable of accurately describing even the extreme orientation states without yielding nonphysical results. Based on the proposed ODF, a new closure approximation is also developed and used to verify the deduced form in flow-induced orientation predictions.
This paper aims to compare different heterogeneous test designs from the perspective of the confidence interval quantification of inversely identified parameters, where the influence of a DIC optical system systematic and random error are taken into account. Because the errors in optical measurement can arise from many reasons and sources, our methodology relies on the system's errors determined from initial sets of pictures acquired at the load-free state for hundreds of specimens (over 850 tests over the past three years). In this way, a prior probability distribution of systematic and random error, arisen from the system initial settings and testing procedures are determined. Further, by conducting an inverse identification procedure of linear orthotropic elastic material parameters, the influence of the error distributions is studied for different types of heterogeneous specimens. The presented methodology determines the DIC bias and random error propagation through the inverse identification procedure to individual parameters. For each specimen design, confidence intervals of identified material parameters were determined. The results show the appropriateness of a specimen design for the identification of particular material parameters.
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