Study of blood flow patterns in a stenosed artery through the combined effect of body acceleration and generalized womersley solution

Figures

• 

  Fig. 1. Schematic of the two-dimensional Geometrical models. The three-dimensional viewpoint is for visualization purposes only. (a) Different shapes of stenosis, (b) Arterial domain inclined at an angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta$$\end{document}Θ with the horizontal.

• 

  Fig. 2. Comparison with the result obtained in the works of Sarifuddin et al.75, by fixing, Re = 300, 48% area reduction in the stenosis region.

• 

  Fig. 3. Time-averaged axial velocity (w) measured in the radial direction at the throat of stenosis for various angles in each case. We observe a direct proportional relation between the angle and the velocity magnitude.

• 

  Fig. 4. Time-averaged WSS (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ) measured along the arterial wall for various angles in each case. We observe a direct proportional relation between the angle and the WSS peak for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{e}$$\end{document}Se and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{hs}$$\end{document}Shs. The reverse trend is observed for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}…

• 

  Fig. 5. Time-averaged axial velocity (w) measured at three different axial locations, (a) Pre-stenosis (upstream to stenosis), (b) Stenosis (throat of stenosis), (c) Post-stenosis (downstream to stenosis). As expected, the velocity almost remains the same before the constriction for all shapes; however, it increases significantly at the throat and post-stenosis for the stenosis shape (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{o}$$\end{document}So).

• 

  Fig. 6. Time-averaged radial velocity (u) measured at three different axial locations, (a) Pre-stenosis (upstream to stenosis), (b) Stenosis (throat of stenosis), (c) Post-stenosis (downstream to stenosis). The velocity profiles nearly overlap before the constriction for all shapes; however, for the stenosis shape (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{o}$$\end{document}So), the profile shoots to a positive value at the center line and remains positive with a higher magnitude downstream of the stenosis.

• 

  Fig. 7. Time-averaged WSS (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ) measured along the arterial wall with the stenosis shapes as the parameter of interest. We observe maximum fluctuations with the maximum peak and drop for stenosis with the shape (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{o}$$\end{document}So).

• 

  Fig. 8. Phase-averaged WSS (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ) measured along the arterial wall with the stenosis shapes as the parameter of interest at (a) Phase 1, (b) Phase 2, (c) Phase 3, (d) Phase 4, (e) Phase 5.

• 

  Fig. 9. Time-averaged plots for (a) axial velocity, w (b) radial velocity, u (c) WSS \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ. We observe that the non-Newtonian case with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=0.7$$\end{document}n=0.7 exhibits a dominant behavior in terms of magnitude in the near wall region.

• 

  Fig. 10. Phase-averaged contour plots for different test cases (a) Rest condition with normal viscosity (b) Rest condition with high viscosity (first row) (c) Exercise condition with normal viscosity (d) Exercise condition with high viscosity (second row).

• 

  Fig. 11. Phase-averaged WSS (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau$$\end{document}τ) measured along the arterial wall with the stenosis shapes as the parameter of interest at (a) Phase 1, (b) Phase 2, (c) Phase 3, (d) Phase 4, (e) Phase 5.

• 

  Fig. 12. Time-averaged OSI measured along the arterial wall for different case studies. (a) Variation of OSI for four stated physiological states, (b) Tuning of Reynolds number over time, (c) Variation of OSI for different transition rates.