A computational framework for derivative-free optimization of cardiovascular geometries

Predictive simulation and optimization-based design tools have great potential to improve the design of surgeries and interventions used in cardiovascular medicine. The present work builds upon recent advances in blood flow simulation capabilities to develop tools for optimization. A framework for coupling optimal shape design to time-accurate three-dimensional blood flow simulations in idealized cardiovascular geometries is presented. The optimization method employed is a tailored version of the surrogate management framework, a method that was developed previously for expensive functions with little or no gradient information. In this method, we employ a derivative-free approach using surrogates for increased efficiency together with mesh adaptive direct search to guarantee convergence to a local minimum. The optimization procedure has been fully automated to include the generation and parameterization of three-dimensional solid geometries, mesh generation, finite element flow computation, post processing and optimization. This methodology is demonstrated on three model problems that are representative of typical cardiovascular geometries: a stenosis, a vessel bifurcation modeled on Murray’s law, and an end-to-side anastomosis. These problems are used to illustrate the importance of the choice of cost function and the performance of the optimization algorithm. This framework for treatment optimization will be applicable to a wide range of cardiovascular surgical or catheter-based interventions in future work.