Stress-driven collagen fiber remodeling in arterial walls

Hariton, I.; deBotton, Gal; Gasser, Thomas C.; Holzapfel, Gerhard

doi:10.1016/s0021-9290(06)84245-4

Cited by 23 publications

(22 citation statements)

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“…8). The derived angle aligns with the largest principal stress directions, which is in agreement with the theory proposed by Hariton et al (2007), which hypothesized that the collagen remodeling is modulated by principal stresses.…”

Section: Discussionsupporting

confidence: 90%

The fiber orientation in the coronary arterial wall at physiological loading evaluated with a two-fiber constitutive model

Horst

Broek

Vosse

et al. 2011

Biomech Model Mechanobiol

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A patient-specific mechanical description of the coronary arterial wall is indispensable for individualized diagnosis and treatment of coronary artery disease. A way to determine the artery's mechanical properties is to fit the parameters of a constitutive model to patient-specific experimental data. Clinical data, however, essentially lack information about the stress-free geometry of an artery, which is necessary for constitutive modeling. In previous research, it has been shown that a way to circumvent this problem is to impose extra modeling constraints on the parameter estimation procedure. In this study, we propose a new modeling constraint concerning the in-situ fiber orientation (β phys ). β phys , which is a major contributor to the arterial stress-strain behavior, was determined for porcine and human coronary arteries using a mixed numerical-experimental method. The in-situ situation was mimicked using in-vitro experiments at a physiological axial pre-stretch, in which pressure-radius and pressure-axial force were measured. A single-layered, hyperelastic, thick-walled, two-fiber material model was accurately fitted to the experimental data, enabling the computation of stress, strain, and fiber orientation. β phys was found to be almost equal for all vessels measured (36.4 ± 0.3) • , which theoretically can be explained using netting analysis. In further research, this finding can be used as an extra modeling constraint in parameter estimation from clinical data.

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Section: Discussionsupporting

confidence: 90%

The fiber orientation in the coronary arterial wall at physiological loading evaluated with a two-fiber constitutive model

Horst

Broek

Vosse

et al. 2011

Biomech Model Mechanobiol

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“…So far, several computational G&R models have been developed to investigate the effect of timedependent biomechanical characteristics of an aneurysm (such as stress-mediated collagen fibers generation, degradation, and orientation) on its expansion, stress distribution, and strength [20,21,[25][26][27][28]. Here, we use a previously developed membrane G&R model, with the details presented in Ref.…”

Section: Methodsmentioning

confidence: 99%

Computational Growth and Remodeling of Abdominal Aortic Aneurysms Constrained by the Spine

Farsad

Zeinali‐Davarani

Choi

et al. 2015

Journal of Biomechanical Engineering

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Abdominal aortic aneurysms (AAAs) evolve over time, and the vertebral column, which acts as an external barrier, affects their biomechanical properties. Mechanical interaction between AAAs and the spine is believed to alter the geometry, wall stress distribution, and blood flow, although the degree of this interaction may depend on AAAs specific configurations. In this study, we use a growth and remodeling (G&R) model, which is able to trace alterations of the geometry, thus allowing us to computationally investigate the effect of the spine for progression of the AAA. Medical image-based geometry of an aorta is constructed along with the spine surface, which is incorporated into the computational model as a cloud of points. The G&R simulation is initiated by local elastin degradation with different spatial distributions. The AAA-spine interaction is accounted for using a penalty method when the AAA surface meets the spine surface. The simulation results show that, while the radial growth of the AAA wall is prevented on the posterior side due to the spine acting as a constraint, the AAA expands faster on the anterior side, leading to higher curvature and asymmetry in the AAA configuration compared to the simulation excluding the spine. Accordingly, the AAA wall stress increases on the lateral, posterolateral, and the shoulder regions of the anterior side due to the AAA-spine contact. In addition, more collagen is deposited on the regions with a maximum diameter. We show that an image-based computational G&R model not only enhances the prediction of the geometry, wall stress, and strength distributions of AAAs but also provides a framework to account for the interactions between an enlarging AAA and the spine for a better rupture potential assessment and management of AAA patients.

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“…HARITON ET AL. [3], the gradients of the electric or magnetic field or other characteristic directions is thinkable. In this contribution we concentrate on a reorientation in terms of the principal strain direction.…”

Section: Constitutive Equationsmentioning

confidence: 99%

Theory and Implementation of Time‐Dependent Fibre Reorientation in Transversely Isotropic Materials

Himpel

Menzel

Kuhl

et al. 2006

Proc Appl Math and Mech

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Transversely isotropic materials are commonly described by one characteristic direction in the material configuration, which commonly is assumed to be constant. However, for some applications it makes sense to consider a reorientation of the characteristic direction, as for instance the orientation of biological materials adapts to the mechanical loading, see e.g. KUHL ET AL. [4]. Other examples are piezoelectric materials, which reorient due to electric or mechanical loading, as described in SMITH [7], and liquid crystals changing their orientation on account of electric or magnetic fields, see ERICKSEN [1]. Furthermore simulations with a reorientation of the characteristic direction can be used in the context of optimisation of composites. In this contribution we restrict ourselves to the modelling of hyper-elasticity and assume a time dependent reorientation of the characteristic direction with respect to the principal strain directions, see for instance MENZEL [5]. Thereby we concentrate on the numerical implementation into a finite element code. Constitutive EquationsTransverse isotropy can be described by the characteristic direction n A or respectively by the structural tensor A = n A ⊗ n A . In this contribution we assume a reorienting characteristic direction n A . Thus, insertion of the standard free energy density ψ 0 = ψ 0 (C, A) and the Piola-Kirchhoff stresses S = 2∂ C ψ 0 into the dissipation inequality yields the reduced dissipation inequalitywith the extra entropy source S 0 satisfying the second law of thermodynamics, see for instance HIMPEL ET AL. [2]. Analogous to the director in the theory of shells a rotation of the characteristic direction n A is assumed, so that its evolution becomeṡFor the definition of the angular velocity ω an alignment with the principal strain directions, see e.g. MENZEL [5], the principal stress directions, see e.g. HARITON ET AL.[3], the gradients of the electric or magnetic field or other characteristic directions is thinkable. In this contribution we concentrate on a reorientation in terms of the principal strain direction. It can be shown that the critical state of free energy can be reached for coaxial stress and strain tensors. The Piola-Kirchhoff stresses for transverse isotropy can be depicted asdepending on the scalars S i=1,...5 = ∂ Ii ψ. Thus it can easily be observed, that for an alignment of n A with one of the principal strain directions, the Piola-Kirchhoff stresses S and the right Cauchy-Green tensor C become coaxial. Hence, following to MENZEL [5] we assume an alignment of n A with the maximum principal strain directionTo avoid drilling rotation the angular velocity is defined orthogonal to n A and n Cwith the material parameter t acting as time relaxation parameter. Implementation into a Finite Element CodeFor the implementation into a finite element code the characteristic direction has been introduced as internal variable. Due to the EULER-theorem exp(−ε · ω ∆t) is a rotation about ω by the angle ω ∆t. Thus we apply an implicit exponential map fo...

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Stress-driven collagen fiber remodeling in arterial walls

Cited by 23 publications

References 0 publications

The fiber orientation in the coronary arterial wall at physiological loading evaluated with a two-fiber constitutive model

The fiber orientation in the coronary arterial wall at physiological loading evaluated with a two-fiber constitutive model

Computational Growth and Remodeling of Abdominal Aortic Aneurysms Constrained by the Spine

Theory and Implementation of Time‐Dependent Fibre Reorientation in Transversely Isotropic Materials

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