On Eulerian versus Lagrangian models of mechanical blood damage and the linearized damage function

Two limitations have been discovered in the derivation of the Eulerian method of hemolysis prediction using a linearized blood damage function. First is that in the transformation from the Lagrangian material volume of the original power-law model to a fixed Eulerian control volume, the spatial dependence of duration of exposure to fluid stress was neglected. This omission has the implication that the Eulerian method as reported is valid only for steady, uniaxial flow in which velocity is constant along streamlines. The second issue is related to linearization, which involves distributing an exponent across an integral. This operation is valid only for limited conditions that include the exponent being unity (which is not the case for any power-law hemolysis models) or the blood damage function being constant throughout the flow regime. These constraints severely restrict the applicability of the Eulerian method. An example problem is presented that demonstrates that the source term of the Eulerian method as reported does not account for differences in velocity between 2 similar flows. Correcting the source term to match the hemolysis prediction to that of the original, unlinearized method requires an analytical description of the flow field that may not be easily obtained for the complex flows in some cardiovascular devices.