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Stress-stretch curves of planar biaxial tests of healthy aortic tissue ( ) Average stress in a fiber family at time , see Equation 23 Undeformed collagen fiber orientation vector Deviatoric part of a constituent-specific right Cauchy-Green tensor, see Equation 3

It is now a rather common approach to perform patient-specific stress analyses of arterial walls using finite-element models reconstructed from gated medical images. However, this requires to compute for every Gauss point the deformation gradient between the current configuration and a stress-free reference configuration. It is technically difficult to define such a reference configuration, and there is actually no guarantee that a stress-free configuration is physically attainable due to the presence of internal stresses in unloaded soft tissues. An alternative framework was proposed by Bellini et al. (Ann Biomed Eng 42(3):488-502, 2014). It consists of computing the deformation gradients between the current configuration and a prestressed reference configuration. We present here the first finite-element results based on this concept using the Abaqus software. The reference configuration is set arbitrarily to the in vivo average geometry of the artery, which is obtained from gated medical images and is assumed to be mechanobiologically homeostatic. For every Gauss point, the stress is split additively into the contributions of each individual load-bearing constituent of the tissue, namely elastin, collagen, smooth muscle cells. Each constituent is assigned an independent prestretch in the reference configuration, named the deposition stretch. The outstanding advantage of the present approach is that it simultaneously computes the in situ stresses existing in the reference configuration and predicts the residual stresses that occur after removing the different loadings applied onto the artery (pressure and axial load). As a proof of concept, we applied it on an ideal thick-wall cylinder and showed that the obtained results were consistent with corresponding experimental and analytical results of the well-known literature. In addition, we developed a patient-specific model of a human ascending thoracic aneurysmal aorta and demonstrated the utility in predicting the wall stress distribution in vivo under the effects of physiological pressure. Finally, we simulated the whole process preceding traditional in vitro uniaxial tensile testing of arteries, including excision from the body, radial cutting, flattening and subsequent tensile loading, showing how this process may impact the final mechanical properties derived from these in vitro tests.

The goal of this paper is to study computationally how blood vessels adapt when they are exposed to a mechanobiological insult, namely, a sudden change of their biomechanical conditions such as proteolytic injuries or implantation.Adaptation occurs through growth and remodeling (G&R), consisting of mass production or removal of structural proteins, such as collagen, until restoring the initial homeostatic biomechanical conditions. In some circumstances, the initial conditions can never be recovered, and arteries evolve towards unstable pathological conditions, such as aneurysms, which are responsible for significant morbidity and mortality. Therefore, computational predictions of G&R under different circumstances can be helpful in understanding fundamentally how arterial pathologies progress. For that, we have developed a low-cost open-source finite-element 2D axisymmetric shell model (FEM) of the arterial wall. The constitutive equations for static equilibrium used to model the stress-strain behavior and the G&R response are expressed within the homogenized constrained mixture theory. The originality is to integrate the layer-specific behavior of both arterial layers (media and adventitia) into the model. Considering different mechanobiological insults, our results show that the resulting arterial dilatation is strongly correlated with the media thickness. The adaptation to stent implantation is particularly interesting. For large stent oversizing ratios, the artery cannot recover from the mechanobiological insult and dilates forever, whereas dilatation stabilizes after a transient period for more moderate oversizing ratios. We also show that stent implantation induces a different response in an aneurysm or in a healthy artery, the latter yielding more unstable G&R. Finally, our G&R model can efficiently predict, with very low computational cost, fundamental aspects of arterial adaptation induced by clinical procedures. KEYWORDSarterial growth and remodeling, axisymmetric shell model, homogenized constrained mixture theory, layer-specific behavior, stent implantation Int J Numer Meth Biomed Engng. 2020;36:e3282.wileyonlinelibrary.com/journal/cnm

Dissections of ascending thoracic aortic aneurysms (ATAAs) cause significant morbidity and mortality worldwide. They occur when a tear in the intima-media of the aorta permits the penetration of the blood and the subsequent delamination and separation of the wall in 2 layers, forming a false channel. To predict computationally the risk of tear formation, stress analyses should be performed layer-specifically and they should consider internal or residual stresses that exist in the tissue. In the present paper, we propose a novel layer-specific damage model based on the constrained mixture theory, which intrinsically takes into account these internal stresses and can predict appropriately the tear formation. The model is implemented in finite-element commercial software Abaqus coupled with user material subroutine. Its capability is tested by applying it to the simulation of different exemplary situations, going from in vitro bulge inflation experiments on aortic samples to in vivo overpressurizing of patient-specific ATAAs. The simulations reveal that damage correctly starts from the intimal layer (luminal side) and propagates across the media as a tear but never hits the adventitia. This scenario is typically the first stage of development of an acute dissection, which is predicted for pressures of about 2.5 times the diastolic pressure by the model after calibrating the parameters against experimental data performed on collected ATAA samples. Further validations on a larger cohort of patients should hopefully confirm the potential of the model in predicting patient-specific damage evolution and possible risk of dissection during aneurysm growth for clinical applications.

No abstract

The constrained mixture theory is an elegant way to incorporate the phenomenon of residual stresses in patient-specific finite element models of arteries. This theory assumes an in vivo reference geometry, obtained from medical imaging, and constituent-specific deposition stretches in the assumed reference state.

Healing of soft biological tissue is the process of self-recovering or self-repairing the injured or damaged extracellular matrix (ECM). Healing is assumed to be stress-driven, with the objective of returning to a homeostatic stress metrics in the tissue after replacing the damaged ECM with new undamaged one. However, based on the existence of intrinsic length scale in soft tissues, it is thought that computational models of healing should be non-local. In the present study, we introduce for the first time two gradient-enhanced constitutive healing models for soft tissues including non-local variables. The first model combines a continuum damage model with a temporally homogenized growth model, where the growth direction is determined according to local principal stress directions. The second one is based on a gradient-enhanced healing model with continuously recoverable damage variable. Both models are implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three two-dimensional situations simulating the healing process of soft tissues are modeled numerically with both models, and their application for simulation of balloon angioplasty is provided by illustrating the change of damage field and geometry in the media layer throughout the healing process.