Conference Agenda

The Growth and Remodeling (G&R) mechanisms in the arterial wall have been extensively investigated over the past two decades, with particular focus on their involvement in disease progression such as aneurysms. The arterial wall's microstructure is composed of various cellular and extracellular matrix elements. From a mechanical standpoint, collagen and elastin represent the most essential extracellular constituents. Collagen fibers provide structural reinforcement to the tissue. Additionally, as with most soft biological tissues, the arterial wall preserves a specific preferred mechanical state (mechanical homeostasis) [1,2]. Although computational constrained mixture models of arterial G&R have significantly enhanced our comprehension of this complex phenomenon, their clinical use—such as in computer-assisted treatment or surgical planning—remains unfulfilled. When the tissue deviates from this preferred mechanical state, G&R processes, involving modifications in mass and internal organization, work to reestablish homeostasis. The G&R mechanism alters the collagen fiber orientation distribution in the tissue, leading to time-dependent degradation and deposition of fibers. Consequently, incorporating G&R behavior into models is fundamental for understanding the arterial wall’s mechanical response and aneurysm formation. Building on previous studies where the authors introduced a statistical framework offering analytical insights into the evolution of collagen fiber alignment in soft tissues during G&R under uniaxial loads [3], the present work aims to apply that theoretical framework to explore G&R in both healthy and aneurysmatic arterial walls. The arterial wall is modeled as a mixture of multiple constituents deforming collectively. By employing the homogenized constrained mixture theory [3] along with the principle of mechanical homeostasis [1], a probabilistic law for fiber-mass evolution is formulated and solved numerically. As collagen fibers are not oriented uniformly but follow a statistical distribution, this formulation includes a probability distribution of fiber orientations [4], assumed to follow a Von Mises-type distribution. To facilitate analysis, the Von Mises distribution is taken to have the same mean and variance as the fiber mass density distribution. The homogenized constrained mixture model from [3] is then used to analyze G&R in both healthy and aneurysmal arterial walls. A novel set of differential equations describing elastic and inelastic deformations in the circumferential, radial, and longitudinal directions is derived. Once the evolution of the fiber probability density is known, the remodeling behavior of the tissue in both healthy and pathological states can be evaluated. Numerical simulations and comparison with experimental data highlight the method’s effectiveness. The proposed method offers a promising strategy for modeling G&R processes in arterial tissue under various conditions. Preliminary simulations show strong correlation with experimental data, and a qualitative comparison with existing G&R models is also presented.

Introduction

The treatment of cardiovascular disease places a substantial burden on global healthcare systems [1]. Vascular pathologies such as aortic dissection, stroke, and aneurysm can lead to the rupture of the vascular wall, often with fatal consequences. Predicting and preventing such ruptures requires a deep understanding of the mechanics governing fracture behavior in vascular tissue [2]. Given its hierarchical structure, vascular tissue exhibits complex mechanical properties, necessitating robust and efficient numerical tools for identifying its fracture mechanics. While the elastin network facilitates vessel wall recoil, collagen fibers play a crucial role in non-linear viscoelasticity, supporting large deformations and providing both stiffness and toughness. The orientation of these fibers varies within the vascular wall and across different aortic locations, influencing its macroscopic mechanical properties.

Material and Methods

This study focuses on characterizing the fracture properties of the aortic media, a vessel wall layer where collagen fibers are primarily aligned in the circumferential direction. Our previously established in-vitro symmetry-constrained Compact Tension (symconCT) test [3] serves as ground truth data for Finite Element Modeling (FEM). In an attempt to overcome drawbacks of our more classical fracture modeling approaches (cohesive zones [4], extended FEM [5]), we now explored phase-field approaches [6,7].

The vessel wall shows anisotropic mechanical behaviour [8], a property which relation to fracture propagation is not well understood. We therefore described vessel wall bulk properties with both, the isotropic Yeoh constitutive model and the anisotropic Gasser-Ogden-Holzapfel (GOH) model and explored its implications. As viscoelasticity has a paramount implication in tissue fracture [9], a five-element Maxwell description captured the time-dependent tissue properties. Similarly to the description of the bulk material properties, isotropic and anisotropic phase field description have been tested. All our models have been realized within FEAP (Univ. of California at Berkeley, US).

Results and conclusions

Phase field modelling allows to deal with most complexity of vascular tissue fracture, requires however significant numerical resources. An anisotropic description of the bulk properties of the normal vessel had a minor implication on the fracture propagation direction. In highly diseased specimens from the aneurysmatic aorta, fracture is often diverted along the circumferential direction [10], an experimental observation that could only be captured by an anisotropic phase field description, and which was challenged by sever FEM mesh distortion.

References

1. (WHO), "W.H.O.: Cardiovascular Diseases (CVDs)"

2. Timmis, A et al., Eur. Heart J. 41, 12–85 (2020)

3. Alloisio, M et al., Acta Biomaterialia 167, 147-157 (2023)

4. Alloisio, M et al., Acta Biomaterialia 167, 158-170 (2023)

5. Miller, et al, Computational Mechanics 73 (6), 1421-1438 (2024)

6. Teichtmeister S et al., Int. J. of Non-Lin. Mech. 97, 1-21 (2017)

7. Aldakheel F., Leibniz Universität Hannover – Habilitation: https://doi.org/10.15488/11367 (2021)

8. Gasser TC, 1st edn. Springer https://doi.org/10.1007/978-3-030 (2021)

9. Forsell C, et al., Journal of biomechanics 44 (1), 45-51(2011)

10. Alloisio M, et al., Scientific Reports 15 (1), 667 (2025)

Introduction

The human aorta undergoes lifelong morphological changes driven by mechanical and biological factors. Aging and hypertension, in particular, increase aortic tortuosity, disrupting flow and wall stresses and raising the risk of cardiovascular complications. A key driver of these changes is the progressive loss of axial pre-stretch, a crucial factor for maintaining biomechanical stability. While previous studies have linked reduced axial pre-stretch to aortic elongation and altered mechanical behavior, its precise role in growth and remodeling (G&R) and its potential to induce pathological deformations, such as aortic buckling, remain poorly understood. This study aims to elucidate the influence of axial pre-stretch on aortic morphology evolution using a patient-specific finite element simulation.

Method

A computational model of the human ascending aorta was developed based on the constrained mixture theory, accounting for the distinct mechanical contributions of elastin, collagen, and smooth muscle cells. The model captures the tissue’s capacity to restore homeostatic stress via biological adaptation mechanisms such as mass growth and structural remodeling. It was implemented in Abaqus through a UMAT subroutine to simulate the G&R of the ascending aorta.

Using age-related physiological axial loading conditions, we considered two cases to evaluate effects of axial pre-stretch on the G&R of the ascending aorta in hypertensive patients. In the first case, representing a 70-year-old patient, the model was subjected only to 80 mmHg without axial pre-stretch. In the second case, corresponding to a 40-year-old patient, the same pressure was applied with 20% axial pre-stretch. After computing the pre-stress fields, both models were subjected to a 40% increase in pressure to simulate hypertensive conditions.

Results

The simulations revealed distinct remodeling patterns between the two scenarios. In both cases, the model predicted increases in aortic diameter and wall thickness, consistent with clinical observations of hypertension-related remodeling. However, the presence or absence of axial pre-stretch had a significant impact on aortic morphology and mechanical stability.

In the model without axial pre-stretch, the ascending aorta exhibited localized kinking along the inner curvature under elevated pressure, indicative of pathological deformation and reduced structural integrity. In contrast, the model with 20% axial pre-stretch preserved a smoother geometry, even following a 40% increase in blood pressure.

An analysis of stress evolution during G&R revealed a gradual reduction in axial stress over time in both models. This effect was more pronounced in the non-pre-stretched aorta, where the loss of axial tension led to localized pathological deformations. These findings are consistent with prior studies suggesting that buckling pressure decreases as axial pre-stretch diminishes. Our results confirm that insufficient axial tension compromises the mechanical stability of the aortic wall, increasing the risk of tortuous geometries.

Overall, the results underscore the critical biomechanical role of axial pre-stretch in maintaining aortic structure under hypertensive loading. The loss of axial tension appears to drive maladaptive remodeling and may serve as a key factor in the onset of tortuosity and buckling in hypertensive patients.