Optimization in Cardiovascular Modeling

Fluid mechanics plays a key role in the development, progression, and treatment of cardiovascular disease. Advances in imaging methods and patient-specific modeling now reveal increasingly detailed information about blood flow patterns in health and disease. Building on these tools, there is now an opportunity to couple blood flow simulation with optimization algorithms to improve the design of surgeries and devices, incorporating more information about the flow physics in the design process to augment current medical knowledge. In doing so, a major challenge is the need for efficient optimization tools that are appropriate for unsteady fluid mechanics problems, particularly for the optimization of complex patient-specific models in the presence of uncertainty. This article reviews the state of the art in optimization tools for virtual surgery, device design, and model parameter identification in cardiovascular flow and mechanobiology applications. In particular, it reviews trade-offs between traditional gradient-based methods and derivative-free approaches, as well as the need to incorporate uncertainties. Key future challenges are outlined, which extend to the incorporation of biological response and the customization of surgeries and devices for individual patients.