A new pre-stressing algorithm for patient-specific simulations of growth and remodeling using the homogenized constrained mixture theory

The homogenized constrained mixture theory has been implemented in different Finite-Element software packages for almost ten years to simulate growth and remodeling in soft biological tissues. In these models, it is essential to determine the pre-stresses of each constituent of the mixture in the reference configuration. However, no efficient numerical solution has been proposed so far to solve this problem. We propose to address this lack with a new algorithm based on the concept of anisotropic thermal contraction. In this algorithm, the pre-stretch tensor is incrementally updated by applying a series of anisotropic thermal contractions to each representative volume element of the model to restore its reference configuration. These contractions are proportional to the inverse of the local right stretch tensor, obtained through the polar decomposition of the deformation gradient. We implemented the algorithm in the Abaqus Finite-Element package through a UMAT subroutine and verified it on examples including growth and remodeling of a patient-specific aorta. We demonstrate that the model captures the residual stresses in good agreement with experimental results. To highlight the potential clinical relevance of the proposed algorithm, we expanded our model predictions to investigate the influence of the aortic axial pre-stretch on morphological and microstructural evolutions of the aorta under hypertensive conditions. Our simulations show that loss of axial tension, induced by hypertension, increases aortic length and may lead to pathological deformations such as aortic tortuosity. These findings highlight the importance of efficiently determining pre-stresses for simulating long-term vascular growth and remodeling.