Adjoint-based estimation of sensitivity of clinical measures to boundary conditions for arteries

The use of adjoint solvers is considered in order to obtain the sensitivity of clinical measures in aneurysms to incomplete (or unknown) boundary conditions and/or geometry. It is shown that these techniques offer interesting theoretical insights and viable computational tools to obtain these sensitivities. A optimization framework with Navier-Stokes equations (in the laminar regime) as constraints is introduced. Sensitivities with respect to inflow and inflow position are derived. In the specific case of inflow normal to the boundary, the sensitivities are shown to be the function of adjoint pressure. For the Poiseuille flow through a channel, explicit expressions for all the underlying quantities such as solution to the state equations, adjoint equations and sensitivites are derived, which are further confirmed by numerical experiments. In the next two examples, flow inside aneurysm geometries is considered.

Automated summary

This article introduces the use of adjoint solvers to obtain the sensitivity of clinical measures in aneurysms to incomplete boundary conditions and geometry, providing theoretical insights and computational tools. The authors derived sensitivities with respect to inflow and inflow position, and demonstrated the explicit expressions for underlying quantities in numerical experiments.