A structural finite element model for lamellar unit of aortic media indicates heterogeneous stress field after collagen recruitment

doi:10.1016/j.jbiomech.2016.03.034

Journal of Biomechanics

Volume 49, Issue 9, 14 June 2016, Pages 1562-1569

https://doi.org/10.1016/j.jbiomech.2016.03.034 Get rights and content

Abstract

Incorporation of collagen structural information into the study of biomechanical behavior of ascending thoracic aortic (ATA) wall tissue should provide better insight into the pathophysiology of ATA. Structurally motivated constitutive models that include fiber dispersion and recruitment can successfully capture overall mechanical response of the arterial wall tissue. However, these models cannot examine local microarchitectural features of the collagen network, such as the effect of fiber disruptions and interaction between fibrous and non-fibrous components, which may influence emergent biomechanical properties of the tissue. Motivated by this need, we developed a finite element based three-dimensional structural model of the lamellar units of the ATA media that directly incorporates the collagen fiber microarchitecture. The fiber architecture was computer generated utilizing network features, namely fiber orientation distribution, intersection density and areal concentration, obtained from image analysis of multiphoton microscopy images taken from human aneurysmal ascending thoracic aortic media specimens with bicuspid aortic valve (BAV) phenotype. Our model reproduces the typical J-shaped constitutive response of the aortic wall tissue. We found that the stress state in the non-fibrous matrix was homogeneous until the collagen fibers were recruited, but became highly heterogeneous after that event. The degree of heterogeneity was dependent upon local network architecture with high stresses observed near disrupted fibers. The magnitude of non-fibrous matrix stress at higher stretch levels was negatively correlated with local fiber density. The localized stress concentrations, elucidated by this model, may be a factor in the degenerative changes in aneurysmal ATA tissue.

Introduction

Biomechanical response of the ascending thoracic aortic (ATA) wall tissue plays an important role in the pathophysiology of the thoracic aorta. Primary load-bearing components of the ATA media are lamellar units (LU) consisting of elastic lamellae encompassing vascular smooth muscle cells (VSMC), interposed with collagen fiber network (Fig. 1b). Incorporation of the above mentioned structural features of the lamellar units are thus essential in the study of biomechanical response of ATA wall tissue. A number of structurally motivated constitutive models for the arterial wall have recently appeared in the literature that augment the strain energy expression with additional terms incorporating experimentally observed collagen fiber tortuosity and orientation (Ferruzzi et al., 2011, Gasser et al., 2006, Holzapfel et al., 2004, Wan et al., 2012, Weisbecker et al., 2015, Zulliger and Stergiopulos, 2007). These constitutive models are a major improvement over purely phenomenological models, and are quite successful in fitting the overall stress-strain response of arterial wall tissue specimens. However, these models are not fully structural representations of the aortic wall. Thus they cannot examine, for example, the effect of physiological fiber network architecture and fiber-nonfibrous matrix interaction on the biomechanical state of the wall tissue. These lamellar scale details can give rise to locally heterogeneous stress distribution within the elastic lamellae and may influence structural and functional remodeling of the extracellular matrix by the VSMCs mediated by local mechanical stimuli.

Our goal in this study was to develop a finite element based modeling framework leading towards true structural representation of the ATA media lamellar unit. To achieve this goal, we developed a novel fiber reinforced finite element method capable of embedding 1D fibers of arbitrary orientation within 3D finite elements. Using this framework, we created a representation of the lamellar unit of the human aortic media that directly included structural features of the tissue. The developed model could recapitulate the uniaxial constitutive response of the media successfully. Additionally, our model revealed that stress state in the non-collagenous matrix is homogeneous at low stretch, but becomes highly heterogeneous at higher stretch levels after collagen fiber recruitment. Magnitude of non-collagenous matrix stress depends on the local architecture of the collagen network. Further, collagen fibers oriented themselves in the loading direction, and created distinct “stress paths” that were the primary load-bearing mechanism at high stretch.

Section snippets

Computational domain and finite element simulation methodology

We constructed a 3D representative volume element (RVE) to simulate the biomechanical response of a single LU within the ATA media (Fig. 1c). Thickness of the elastic lamellae and spacing between them vary radially within the media. Depth-averaged values of these parameters, namely lamella thickness of 1.5 μm and interlamellar (IL) spacing of 11 μm were thus chosen (O׳Connell et al., 2008). We exploited lamellar unit symmetry in the radial (RAD) direction by modeling only half of it. A network of

Stress distribution in the interlaminar non-fibrous matrix

The CIRC component of Cauchy stress tensor in the IL region on the CIRC-LONG plane in the immediate vicinity of the collagen network at different applied stretches is presented in Fig. 5. The fiber network was superimposed in white in all panels to reveal the features of the non-fibrous matrix stress distribution in relation to the spatial arrangement of collagen fibers. Fig. 5 demonstrates that the stress state in the non-fibrous matrix was homogeneous up to recruitment stretch of the collagen

Structural model of lamellar unit of aortic media recapitulates its constitutive behavior

Elastic lamellar units, the primary load-bearing structure of human ATA media, are arranged radially in a repetitive fashion in 40–60 layers (Benninghoff, 1928). Accordingly, we modeled a portion of the LU as the representative volume element of the aortic media (Fig. 1). A representative collagen fiber network, constructed using empirically derived fiber network features from multi-photon microscopy, was directly incorporated in the RVE. Network features in addition to orientation distribution

Conclusions

We have presented a finite element structural model of the aortic media considering its lamellar architecture. An important aspect of our approach is the use of only experimentally-derived information as model parameters. The model correctly reproduced nonlinear mechanical response of the wall tissue and importantly, revealed a heterogeneity in the stress state of fibers and matrix throughout the entire stretching event. We found that fiber-matrix interaction, combined with local fiber

Conflict of interest

The authors do not have any financial interest or other relationship (grant, research support, consultant, etc.) with any manufacturer(s) of any commercial product(s) to disclose.

Acknowledgments

Research reported in this publication was supported in part by the National Heart, Lung and Blood Institute of the National Institutes of Health under Award Number R01HL109132 (TGG), the National Science Foundation under Award Number CBET 1511504 (JRT and SM), and an NPSC fellowship (JRT).

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A structural finite element model for lamellar unit of aortic media indicates heterogeneous stress field after collagen recruitment

Abstract

Introduction

Section snippets

Computational domain and finite element simulation methodology

Stress distribution in the interlaminar non-fibrous matrix

Structural model of lamellar unit of aortic media recapitulates its constitutive behavior

Conclusions

Conflict of interest

Acknowledgments

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