Evaluation of the surface-averaged load exerted on a blood element by the Reynolds shear stress field provided by artificial cardiovascular devices

Implantable prosthetic devices can often affect the recipient's hemostasis, with possible hemolysis and thrombus formation. Since such devices can produce turbulent flow, it is important to characterize it as accurately as possible, by means of the Reynolds stress tensor. Some parameters related to the latter have been often used to provide a quantity related to the possible damage to blood constituents: the TSS_max, for instance, has been associated with hemolysis. It can be expressed as TSS_max=(σ₁−σ₃)/2, σ₁ and σ₃ being the highest and lowest principal normal stresses (PNSs) in each point of the flow.

In the present work, the average value of the shear stress over a spherical surface, representative of a blood component, is derived. All three PNSs (σ₁, σ₂ and σ₃) are found to have an equal role in the determination of this parameter, since the relative formula shows a marked symmetry with respect to the PNSs. The average shear stress level, for a given (σ₁, σ₃) pair (hence, for a given TSS_max), has a minimum and maximum value, depending on the particular σ₂ value yielded by the local structure of the turbulent flow field. A numerical investigation on more complex geometries shows similar results. The role of the intermediate PNS is thus shown for the first time to have a physical relevance. The presented results can be useful whenever a spatial averaging of the shear field is important to be assessed, such as in the case of platelet activation. A new parameter is thus proposed, which can be correlated with prosthetic devices complications.