Minimization of blood damage induced by non-Newtonian fluid flows in moving domains

Abstract: Many engineering works are interested in the parametric optimization of blood pumps to minimize hemolysis (destruction of red blood cells). In order to generalize this approach, we study the shape continuity of a coupled system of PDEs modeling blood flows and hemolysis evolution in moving domains, governed respectively by generalized Navier-Stokes and transport equations.

First, the shape continuity of the blood flow solutions is shown. This development, which extends the one led in (Sokolowski, Stebel, Evol. Equ. Control Theory, 2014) to the case of shear thinning fluids, is based on the recent progress made in (Nägele, Ružička, J. Differential Equations, 2018), adapted to the present framework of a sequence of converging moving domains.

After calculating blood flows solutions, the velocity and stress fields are used as coefficients and r.h.s for the transport equation governing the evolution of the hemolysis rate. From this, the shape continuity of the hemolysis rate is also proved.

Finally, these results allow to show the existence of minimum for a class of shape optimization problems based on the minimization of the hemolysis rate, in the framework of moving domains.

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)

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