Abstract
This study presents a variational approach with Tikhonov regularization for solving an inverse problem in hemodynamics. The functional is minimized using a gradient-based optimization algorithm, with explicit analytical derivations of the corresponding adjoint problem and the Fréchet derivative. The direct problem models blood flow in a planar vessel with a thrombus formation source on the vessel wall. Numerical results of the direct problem demonstrate that the fibrin activation function is a sensitive indicator of the thrombosis process. The inverse problem consists in reconstructing this nonlinear source function using the known results of the direct problem. The results of numerical simulations of the direct and inverse problems demonstrated satisfactory agreement, confirming the validity of the proposed approach. Moreover, the developed algorithms can be used to predict not only the fibrin activation function but also other parameters that characterize thrombus formation.