Finite element simulation of three dimensional residual stress in the aortic wall using an anisotropic tissue growth model

Finite-element simulation of in-plane tear propagation in the dissected aorta: Implications for the propagation mechanism

Computer modeling and numerical simulation are essential for understanding the progression of aortic dissection. However, tear propagation has not been properly modeled and simulated. The in-plane dissection propagation between concentrically distributed elastic lamellae is modeled using the cohesive zone method with a bilinear traction-separation law. The parameters of cohesive elements are calibrated for the three modes of interfacial damage in the media, enabling quantitative predictions of in-plane tear propagation. An idealized cylindrical tube-shaped bilayer thick-wall model of the aorta is employed to elucidate the influence of geometrical parameters, loading conditions and residual stress on the tear propagation. While the model is capable of replicating that deeper, larger tears are associated with lower critical pressure, new findings include: (i) Larger axial stretch leads to lower critical pressure; (ii) Increased magnitude of residual stress is associated with higher critical pressure; (iii) Pressure difference between true and false lumen alters the critical pressure; (iv) The interfacial damage is mostly opening mode in the axial direction, but shear-dominated in the circumferential direction; (v) Damage due to the opening mode is associated with smaller fracture energy, which makes it easier to propagate than the shear and the mixed modes. (vi) The deformed shape of the tear, which is related to its geometrical features and loading conditions, modulates the critical pressure via two pathways: (a) deformed shapes are associated with specific modes of damage, which influences the critical pressure, and (b) deformed shapes modulate the critical pressure directly via geometrical constraints.

Fitting mechanical properties of the aortic wall and individual layers to experimental tensile tests including residual stresses

The authors have observed that a stress-strain curve for uniaxial tension of an aortic intact wall cannot be simply obtained by combining the strain energy functions of the three individual aortic layers - intima, media and adventitia - even taking into account the interaction among the three layers; the strain energy functions of the three layers are obtained fitting tensile tests on strips from the individual layers. Due to the layer separation, the residual stresses are released and thus they do not affect the stress-strain curves of the individual layers. The present study shows that it is instead possible to fit the intact wall experimental curves with the combination of the strain energy functions of the three individual layers if residual strains are added. The residual strains are used as optimization parameters with specific constraints and allowing for the buckling (wrinkling) of the intima under unpressurized condition of the aortic wall, as experimentally observed. By varying these parameters in the experimentally observed range of values, it is possible to find a solution with the combined responses of the individual layers matching the experimental stress-strain curves of the intact wall.

Local and global growth and remodeling in calcific aortic valve disease and aging

Aging and calcific aortic valve disease (CAVD) are the main factors leading to aortic stenosis. Both processes are accompanied by growth and remodeling pathways that play a crucial role in aortic valve pathophysiology. Herein, a computational growth and remodeling (G&R) framework was developed to investigate the effects of aging and calcification on aortic valve dynamics. Particularly, an algorithm was developed to couple the global growth and stiffening of the aortic valve due to aging and the local growth and stiffening due to calcification with the aortic valve transient dynamics. The aortic valve dynamics during baseline were validated with available data in the literature. Subsequently, the changes in aortic valve dynamic patterns during aging and CAVD progression were studied. The results revealed the patterns in geometric orifice area reduction and an increase in the valve stress during local and global growth and remodeling of the aortic valve. The proposed algorithm provides a framework to couple mechanobiology models of disease growth with tissue-scale transient structural mechanics models to study the biomechanical changes during cardiovascular disease growth and aging.

A novel framework for quantifying the subject-specific three-dimensional residual stress field in the aortic wall

BACKGROUND

Quantification of subject-specific residual stress field remains a challenge that prohibits accurate stress analysis and refined understanding of the biomechanical behavior of the aortic wall.

METHOD

This study presents a framework combining experiments, constitutive modeling, and computer simulation to quantify the subject-specific three-dimensional residual stress field of the aortic wall. The material properties and residual deformations were acquired from the same porcine aortic sample, so that the subject-specific residual stress field was quantified analytically. Consequently, a novel stress-driven tissue growth model was developed and incorporated in a finite element aortic model to recover the subject-specific residual stress with the help of analytical solution. We then evaluated the framework's efficacy by simulating the residual stress distribution in the aortic dissection (AD).

RESULT

Subject-specific residual stress field of the aortic sample was quantified analytically. No appreciable discrepancy was observed between the numerically simulated and analytically derived residual stress distributions, indicating the effectiveness of the tissue growth model. Errors arising from the numerically simulated circumferential opening angle and axial bending angle were within 5% relative to experimental results, highlighting that the framework was accurate in terms of subject-specific residual stress estimation. Finally, numerical simulations recovered the buckling behavior of the intimal flap of the dissected aorta and revealed the expansion of the false lumen and compression of the true lumen as the tear propagates circumferentially.

CONCLUSION

The proposed framework is effective in quantifying the three-dimensional subject-specific residual stress field and it is potentially applicable in more sophisticated scenarios involving residual stress.

Computation of a probabilistic and anisotropic failure metric on the aortic wall using a machine learning-based surrogate model

Scalar-valued failure metrics are commonly used to assess the risk of aortic aneurysm rupture and dissection, which occurs under hypertensive blood pressures brought on by extreme emotional or physical stress. To compute failure metrics under an elevated blood pressure, a classical patient-specific computer model consists of multiple computation steps involving inverse and forward analyses. These classical procedures may be impractical for time-sensitive clinical applications that require prompt feedback to clinicians. In this study, we developed a machine learning-based surrogate model to directly predict a probabilistic and anisotropic failure metric, namely failure probability (FP), on the aortic wall using aorta geometries at the systolic and diastolic phases. Ascending thoracic aortic aneurysm (ATAA) geometries of 60 patients were obtained from their CT scans, and biaxial mechanical testing data of ATAA tissues from 79 patients were collected. Finite element simulations were used to generate datasets for training, validation, and testing of the ML-surrogate model. The testing results demonstrated that the ML-surrogate can compute the maximum FP failure metric, with 0.42% normalized mean absolute error, in 1 s. To compare the performance of the ML-predicted probabilistic FP metric with other isotropic or deterministic metrics, a numerical case study was performed using synthetic "baseline" data. Our results showed that the probabilistic FP metric had more discriminative power than the deterministic Tsai-Hill metric, isotropic maximum principal stress, and aortic diameter criterion.

Anisotropic residual stresses in arteries

The paper provides a deepened insight into the role of anisotropy in the analysis of residual stresses in arteries. Residual deformations are modelled following Holzapfel and Ogden (Holzapfel and Ogden 2010, J. R. Soc. Interface 7, 787-799. ( doi:10.1098/rsif.2009.0357 )), which is based on extensive experimental data on human abdominal aortas (Holzapfel et al. 2007, Ann. Biomed. Eng. 35, 530-545. ( doi:10.1007/s10439-006-9252-z )) and accounts for both circumferential and axial residual deformations of the individual layers of arteries-intima, media and adventitia. Each layer exhibits distinctive nonlinear and anisotropic mechanical behaviour originating from its unique microstructure; therefore, we use the most general form of strain-energy function (Holzapfel et al. 2015, J. R. Soc. Interface 12, 20150188. ( doi:10.1098/rsif.2015.0188 )) to derive residual stresses for each layer individually. Finally, the systematic experimental data (Niestrawska et al. 2016, J. R. Soc. Interface 13, 20160620. ( doi:10.1098/rsif.2016.0620 )) on both mechanical and structural properties of the different layers of the human abdominal aorta facilitate our discussion on (i) the importance of anisotropy in modelling residual stresses; (ii) the variability of residual stresses within the same class of tissue, the abdominal aorta; (iii) the limitations of conventional opening angle method to account for complex residual deformations; and (iv) the effect of residual stresses on the loaded configuration of the aorta mimicking in vivo conditions.