Simulation of balloon angioplasty in residually stressed blood vessels-Application of a gradient-enhanced fibre damage model

In this contribution we study the balloon angioplasty in a residually stressed artery by means of a non-local gradient-enhanced fibre damage model. The balloon angioplasty is a common surgical intervention used to extend or reopen narrowed blood vessels in order to restore the continuous blood flow in, for instance, atherosclerotic arteries. Inelastic, i.e. predominantly damage-related and elastoplastic processes are induced in the artery during its inflation resulting in an irreversible deformation. As a beneficial consequence, provided that the inelastic deformations do not exceed a specific limit, higher deformations can be obtained within the same pressure level and a continuous blood flow can be guaranteed. In order to study the mechanical response of the artery in this scenario, we make use of the non-local gradient-enhanced model proposed in Waffenschmidt et al. (2014). In this contribution, we extend this model to make use of an incompressible format in connection with a Q1Q1P0 finite element implementation. The residual stresses in the artery are also taken into account following the framework presented in Waffenschmidt (2015). From the results it becomes apparent that, when the artery is subjected to radial stresses beyond the physiological range, damage evolution is triggered in the collagen fibres. The impact of the residual stresses on the structural response and on the circumferential stress distribution along the thickness of the arterial wall is also studied. It is observed that the residual stresses have a beneficial effect on the mechanical response of the arterial wall.