Topology optimization study of arterial bypass configurations using the level set method

We studied the arterial bypass design problem using a level set based topology optimization method. The blood flow in the artery was considered as the non-Newtonian flow governed by the Navier–Stokes equations coupled with the modified Cross model for the shear dependent viscosity. The fluid–solid interface is immersed in the design domain by the level set method and the fictitious porous material method. The sensitivity velocity derived by the level set based continuous adjoint method was utilized to control the evolution of the level set function. In order to accommodate the irregular analysis domains, the flow equations and the level set equations were computed on two different unstructured grids respectively. Three idealized arterial bypass configurations problems with the minimum flow shear stress objective were studied in the numerical examples. The results indicated that the optimal arterial bypass designs can effectively reduce integral of the squared shear rate in the artery and have a superior performance for the arterial grafting.