Topology optimization for blood flow considering a hemolysis model

Abstract

In the past years, topology optimization has been studied for designing fluid flow devices, such as channels, valves and pumps, and also considering non-Newtonian fluid flows, such as blood. When considering blood flow devices, it is important to quantify and minimize the blood damage (given mainly by hemolysis). However, up to now, in topology optimization, hemolysis has been minimized in an indirect manner, by considering shear stress (or even energy dissipation) as the objective function to indirectly minimize hemolysis. This approach may give a general idea of where hemolysis may or may not appear, but the actual distribution of hemolysis can not be easily correlated. Therefore, a more direct measure may be better to evaluate hemolysis. The direct way to measure hemolysis is by considering the hemolysis index, which is given from a differential equation model (a “hemolysis model”). In this work, the hemolysis index computed though a hemolysis model is included in the topology optimization formulation. In order to illustrate this approach, the design of a 2D swirl flow device, which is based on an axisymmetric fluid flow with or without rotation around an axis, is considered. One relevant example in the field of blood flow devices is the design of blood pumps, which has been previously considered in topology optimization with the aim of indirectly reducing hemolysis. More specifically in terms of pump design for 2D swirl flow, the design of a Tesla-type blood pump is considered. A Tesla-type pump is a bladeless fluid flow device, in which the boundary layer effect is used for pumping the fluid. This principle of operation may lead to a smaller induction of blood damage. Together with the hemolysis index, the topology optimization is formulated by considering the relative energy dissipation for indirectly maximizing efficiency. The fluid is modeled considering a non-Newtonian fluid model, and the fluid flow is solved with the finite element method. In order to model the solid material to block the fluid flow, the traditional formulation of fluid topology optimization is augmented with the “Brinkman-Forchheimer model”. Also, an additional penalization is considered in the non-Newtonian viscosity. The optimization problem is solved with IPOPT (Interior Point Optimization algorithm).