An immersed boundary framework for modeling flow-induced large deformation of compliant vessels

Classic diffusive IBM is widely used for biomedical flows but less established for compliant vessel walls due to challenges handling motion-constrained vessel portions, which include the inlet and outlet segments for applying boundary conditions, as well as the longitudinal motion of the deformable segment due to the tethering effects from surrounding tissues. Here, we propose a hybrid approach: wall forces from unconstrained portions are still computed by membrane constitutive laws, while motion constraints are modeled by the iterative multi-direct forcing method to enforce zero velocity. By reusing correction forces from previous time steps, convergence typically occurs in 1-2 iterations, even with significant wall deformation. Validation against analytical theories shows excellent agreement in predicting vessel inflation and collapse with large deformation. Effects of nonlinear constitutive models are also discussed. Unlike many IBM implementations, our method avoids free parameters from virtual springs, enhancing physiological accuracy and generalizability. Compared to sharp interface formulations, our approach simplifies implementation without computationally expensive procedures for updating boundary intercepts, requiring minimal changes to the widely adopted classic IBM framework.