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1.7.2 Shear Stress Calculation

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At the regions of stasis and flow reversals, there is an important role of motion and deformation in the shear stress calculation [110, 111], concept of the rigid wall condition was assumed due to the negligible effect of shear stress on total DF [112]. The distribution of stresses within the blood was estimated. The stresses tσij at time “t” is equal

(1.4)

where

(1.5)

is the viscous stress, tμ is viscosity corresponding to the velocity vector tv at a spatial point within the blood domain. The viscous stresses are represented by (1.5).

The wall shear stress is calculated as:

(1.6)

where tvt denotes the tangential velocity, and n is the normal direction at the vessel wall. At the integration points near the wall surface, the tangential velocity was estimated first, and then the velocity gradient tvt/∂n was calculated. Finally, the viscosity coefficient tμ using the average velocity was evaluated. Blood was taken as an incompressible Newtonian fluid, appropriate for larger arteries [110]. The kinematic viscosity was ν = 3.5e−6 m2/s and the blood density was ρ = 1050 kg/m3.

Computational Modeling and Simulation Examples in Bioengineering

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