Mathematical Analysis of Casson Fluid Model for Blood Rheology in Stenosed Narrow Arteries

Venkatesan, Jayavelu; Sankar, D. S.; Hemalatha, K.; Yatim, Yazariah Mohd

doi:10.1155/2013/583809

Cited by 99 publications

(60 citation statements)

References 14 publications

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“…The Casson model takes into account not only the shear thinning behavior but also the yield stress of the blood. Specifically, this model is used for blood flow at low shear rates in narrow arteries [32]. Following equation gives the dynamic viscosity with regards to this viscosity model…”

Section: Methodsmentioning

confidence: 99%

Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging

Gharahi

Zambrano

Zhu

et al. 2016

Int J Adv Eng Sci Appl Math

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Blood flow patterns and local hemodynamic parameters have been widely associated with the onset and progression of atherosclerosis in the carotid artery. Assessment of these parameters can be performed noninvasively using cine phase-contrast (PC) magnetic resonance imaging (MRI). In addition, in the last two decades, computational fluid dynamics (CFD) simulation in three dimensional models derived from anatomic medical images has been employed to investigate the blood flow in the carotid artery. This study developed a workflow of a subject-specific CFD analysis using MRI to enhance estimating hemodynamics of the carotid artery. Time-of-flight (TOF) MRI scans were used to construct three-dimensional computational models. PC-MRI measurements were utilized to impose the boundary condition at the inlet and a 0-dimensional lumped parameter model was employed for the outflow boundary condition. The choice of different viscosity models of blood flow as a source of uncertainty was studied, by means of the axial velocity, wall shear stress, and oscillatory shear index. The sequence of workflow in CFD analysis was optimized for a healthy subject using PC-MRI. Then, a patient with carotid artery stenosis and its hemodynamic parameters were examined. The simulations indicated that the lumped parameter model used at the outlet gives physiologically reasonable values of hemodynamic parameters. Moreover, the dependence of hemodynamics parameters on the viscosity models was observed to vary for different geometries. Other factors, however, may be required for a more accurate CFD analysis, such as the segmentation and smoothness of the geometrical model, mechanical properties of the artery’s wall, and the prescribed velocity profile at the inlet.

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Section: Methodsmentioning

confidence: 99%

Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging

Gharahi

Zambrano

Zhu

et al. 2016

Int J Adv Eng Sci Appl Math

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“…The Casson model is widely used to model blood flow in narrow arteries at low strain rates [22]. The apparent viscosity of this model is given as follows [23]:…”

Section: Methodsmentioning

confidence: 99%

Variability of hemodynamic parameters using the common viscosity assumption in a computational fluid dynamics analysis of intracranial aneurysms

Suzuki

Takao

Suzuki

et al. 2017

THC

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Variability of hemodynamic parameters using the common viscosity assumption in a computational fluid dynamics analysis of intracranial aneurysms Takashi Abstract. BACKGROUND: In most simulations of intracranial aneurysm hemodynamics, blood is assumed to be a Newtonian fluid. However, it is a non-Newtonian fluid, and its viscosity profile differs among individuals. Therefore, the common viscosity assumption may not be valid for all patients. OBJECTIVE: This study aims to test the suitability of the common viscosity assumption. METHODS: Blood viscosity datasets were obtained from two healthy volunteers. Three simulations were performed for three different-sized aneurysms, two using measured value-based non-Newtonian models and one using a Newtonian model. The parameters proposed to predict an aneurysmal rupture obtained using the non-Newtonian models were compared with those obtained using the Newtonian model. RESULTS:The largest difference (25%) in the normalized wall shear stress (NWSS) was observed in the smallest aneurysm.Comparing the difference ratio to the NWSS with the Newtonian model between the two Non-Newtonian models, the difference of the ratio was 17.3%. CONCLUSIONS: Irrespective of the aneurysmal size, computational fluid dynamics simulations with either the common Newtonian or non-Newtonian viscosity assumption could lead to values different from those of the patient-specific viscosity model for hemodynamic parameters such as NWSS.

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“…Here we followed the standard non-newtonian assumption of a blunt velocity profile across the vessel wall, which is typical for blood flow in large arteries. Alternative (and more realistic) models for the rheology of the blood (such as Casson model, [18], [23], which assumes a nonlinear stress strain relation for the fluid) will lead to different expressions for the friction forces in the reduced model and to different nonlinear terms for the momentum equation. While these models are worth considering for a more realistic mathematical model (see also comments in the conclusion section), for the scope of the present paper it is sufficient to stay with simplest model for the fluid and fluid structure interactions, since we do not expect significantly different qualitative conclusions if we were to incorporate other models.…”

Section: Mathematical Modelmentioning

confidence: 99%

Boundary Control for an Arterial System

Cascaval¹,

D’Apice²,

D'Arienzo³

et al. 2016

JFFHMT

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-We consider a boundary control problem arising in the study of the dynamics of an arterial system which consists of one arterial segment (modeling the aorta in the cardiovascular system) coupled at the inflow with a pressurized chamber (modeling the left ventricle) via a valve. The opening and closing of the valve is dynamically determined by the pressure difference between the left ventricular and aortic pressures. Mathematically, this is described by a 1D system of coupled PDEs for the pressure and flow in the arterial segment, with a Dirichlet boundary condition imposed on the flow (when valve is closed) or on the pressure (when valve is open). At the outflow we impose a peripheral resistance model, which leads to a non-homogeneous Dirichlet condition. A numerical scheme based on the discontinuous Galerkin method is used to approximate the solution of the resulting system. We then use this methodology to simulate the heart rate variability observed in real physiological systems, by optimizing the timing of the heartbeat and the peripheral resistance, modeled using a terminal reflection coefficient, with the goal of achieving a prescribed mean pressure in the system.

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Mathematical Analysis of Casson Fluid Model for Blood Rheology in Stenosed Narrow Arteries

Cited by 99 publications

References 14 publications

Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging

Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging

Variability of hemodynamic parameters using the common viscosity assumption in a computational fluid dynamics analysis of intracranial aneurysms

Boundary Control for an Arterial System

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