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3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011

Non-Newtonian Models in a 3D Reconstructed Human Left Coronary Artery. Severity parameter and global importance factor. Johannes V. Soulis*, Kypriani V. Seralidou*, Yiannis S. Ch atzi z isis^, George D. Giannoglou^.

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3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011

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  1. Non-Newtonian Models in a 3D Reconstructed Human Left Coronary Artery. Severity parameter and global importance factor Johannes V. Soulis*, Kypriani V. Seralidou*, Yiannis S. Chatzizisis^, George D. Giannoglou^ *Fluid Mechanics Division, Faculty of Engineering, Democritus University of Thrace, Greece e-mail: soulis@civil.duth.gr, web page: http://www.duth.gr ^1st Cardiology Department, Cardiovascular Engineering and Atherosclerosis Laboratory, AHEPA General Hospital, Greece 3rd Micro and Nano Flows Conference Thessaloniki, Greece, 22-24 August 2011

  2. PresenterJohannes V. SOULIS B.Sc, M.Sc, Ph.DProfessor of Fluid Mechanics

  3. Abstract The capabilities and limitations of various molecular viscosity models, in the Left Coronary Artery (LCA) tree, were numerically analyzed. The vessel geometry was acquired using geometrically correct 3D Intravascular Ultrasound (3D IVUS). Seven non-Newtonian molecular viscosity models, plus the Newtonian one, were compared. The non-Newtonian Power Law and the Generalized Power Law blood viscosity models were found to approximate the molecular viscosity and Wall Shear Stress (WSS) calculations in a more satisfactory way.

  4. Geometry and computational grid of the tested LCA

  5. Computational grid of the LCA

  6. Flow equations All computational grid data as well as all physical flow data determined from the boundary conditions were imported into the main Computational Fluid Dynamics solver. The numerical code solves the governing Navier-Stokes flow equations. The assumptions made about the nature of the flow are that it is three-dimensional, steady, laminar, isothermal, with no external forces applied on it.

  7. Blood Molecular Viscosity Models Newtonian Law Carreau Law Modified Cross Law (Carreau-Yasuda Law) Power Law Non-Newtonian Power Law Generalized Power Law Casson Law Walburn-Schneck Law

  8. The mathematical equations of the tested blood molecular viscosity models Newtonian Law molecular viscosity =0.00345 kg/m s

  9. Carreau Law

  10. , Modified Cross Law (Carreau-Yasuda Law)

  11. Power Law

  12. , , Non-Newtonian Power Law , , .

  13. Generalized Power Law (Units in Poise)

  14. and Casson Law

  15. Walburn-Schneck Law (Units in Poise)

  16. Results

  17. MolecularViscosity (kg/m s) Carreau Law

  18. MolecularViscosity (kg/m s) Modified Cross Law

  19. Molecular Viscosity (kg/m s) Power Law

  20. MolecularViscosity (kg/m s)Non-Newtonian Power Law

  21. MolecularViscosity (kg/m s) Generalized Power Law

  22. MolecularViscosity (kg/m s) Casson Law

  23. MolecularViscosity (kg/m s) Walburn-Schneck Law

  24. Wall Shear Stress

  25. Area averaged Wall Shear Stress (WSS, N/m2)

  26. Wall Shear Stress (N/m2)Newtonian Law

  27. Wall Shear Stress (N/m2)Carreau Law

  28. Wall Shear Stress (N/m2) Modified Cross Law

  29. Wall Shear Stress (N/m2)Power Law

  30. Wall Shear Stress (N/m2) Non-Newtonian Power Law

  31. Wall Shear Stress (N/m2)Generalized Power Law

  32. Wall Shear Stress (N/m2)Casson Law

  33. Wall Shear Stress (N/m2)Walburn-Schneck

  34. Local Importance factor (IL) The factor IL, exhibits the degree of molecular viscosity deviation from Newtonian behaviour. (Non-Newtonian Power Law)

  35. Global non-Newtonian Importance factor (IG)

  36. Global non-Newtonian Importance factor (IG)

  37. Wall Shear Stress Gradient (WSSG, N/m3)

  38. Severity Parameter (SP, N/m3) ai is the cell area, and Ao is the total surface area

  39. Severity parameter (SP, N/m3)

  40. Conclusion The usefulness and limitations of different molecular viscosity models are compared using resting, normal and exercise flow conditions in an IVUS derived LCA tree. Results indicate that patches of highly non-Newtonian behavior are located in the concave region of the LCA bifurcation, opposite to the flow divider. The WSS distribution yields a consistent LCA tree pattern for nearly all non-Newtonian models. High molecular viscosity and low Wall Shear Stress and Wall Shear Stress Gradient values appear at proximal LCA regions at the outer walls of the major bifurcation. The Non-Newtonian Power Law, Generalized Power Law, Carreau and Casson and Modified Cross blood viscosity models give comparable molecular viscosity, WSS and WSSG values. The Power Law and Walburn-Schneck models overestimate the non-Newtonian global importance factor IG and underestimate the area averaged WSS and WSSG values. The Newtonian blood flow treatment is considered to be a good approximation at mid and high strain rates. In general, the non-Newtonian Power Law and the Generalized Power low blood viscosity models (relative to the other models) are considered to approximate the molecular viscosity and WSS calculations in a more satisfactory way.

  41. Thank you for your attention Questions, discussion and criticism are always welcome

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