On an adjoint-based numerical approach for time-dependent optimal control problems of biomedical interest

This work develops a rigorous numerical framework for solving time-dependent Optimal Control Problems (OCPs) of interest for biomedical applications. The focus is on drug delivery problems. The approach deals with adjoint-based Lagrangian methodology, which enables efficient gradient computation and systematic derivation of optimality conditions for both distributed and concentrated control formulations. The proposed framework is first verified using a time-dependent advection-diffusion equation, endowed with a manufactured solution to assess accuracy and convergence properties. Subsequently, two representative applications involving drug delivery are investigated. Numerical experiments demonstrate the accuracy of the approach, as well as its flexibility and robustness.