A generalized prestressing algorithm for finite element simulations of preloaded geometries with application to the aorta

Finite element models reconstructed from medical imaging data, for example, computed tomography or MRI scans, generally represent geometries under in vivo load. Classical finite element approaches start from an unloaded reference configuration. We present a generalized prestressing algorithm based on a concept introduced by Gee et al. (Int. J. Num. Meth. Biomed. Eng. 26:52-72, 2012) in which an incremental update of the displacement field in the classical approach is replaced by an incremental update of the deformation gradient field. Our generalized algorithm can be implemented in existing finite element codes with relatively low implementation effort on the element level and is suitable for material models formulated in the current or initial configurations. Applicable to any finite element simulations started from preloaded geometries, we demonstrate the algorithm and its convergence properties on an academic example and on a segment of a thoracic aorta meshed from MRI data. Furthermore, we present an example to discuss the influence of neglecting prestresses in geometries obtained from medical images, a topic on which conflicting statements are found in the literature.