A Coupled Fiber-Matrix Model Demonstrates Highly Inhomogeneous Microstructural Interactions in Soft Tissues Under Tensile Load

Abstract

A soft tissue’s macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a non-fibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to quantify fully the internal stress field within such a tissue and to explore interactions between the collagen fiber network and non-fibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed to couple the two tissue components, and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, Poisson’s ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of in homogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure, that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

A Multiscale Approach to Modeling the Passive Mechanical Contribution of Cells in Tissues

“…proteoglycans) represented as a solid Neo-Hookean material. This framework has been successfully used to model tissues and tissue equivalents, e.g., arteries [24], collagen-agarose cogels [25,26], as well as model tissue damage [27]. A significant gap in this model, however, is the absence of cells, which are integral components in most tissues.…”

Computational modeling of the arterial wall based on layer-specific histological data

“…According to Zhang et al (2013) and D'Amore et al (2014), fiber stretching is one of the dominant deformation modes and truss elements are very effective in capturing it. Moreover, the primary unknowns of truss elements are the coordinates of the two endpoints that can be expressed by the finite element nodal displacements and interpolation functions via the isoparametric relationship (Eq.…”

“…The EF approach directly incorporates the microscopic arrangement of fibers that are modeled as truss elements in the numerical simulation with the assumption that fiber stretching is the main deformation mode (Zhang et al 2013;D'Amore et al 2014). The fibers are embedded in the surrounding matrix and the two material components deform together.…”

“…An alternative to homogenization relies on directly incorporating the microscopic arrangement of fibers in the modeling process (Lake et al 2012;Zhang et al 2013;Jin and Stanciulescu 2015). The fiber arrangement can either be directly obtained using image processing from real tissues (D'Amore et al 2014;Carleton et al 2015) or synthetically generated (Huisman et al 2007;Barocas 2007;Sander et al 2009;Liu et al 2013;Heidemann et al 2015).…”

Determination and Finite Element Validation of the WYPIWYG Strain Energy of Superficial Fascia from Experimental Data

“…Since fibers are statistically distributed in the specimen, it is also frequent to propose a distribution function, which can be integrated either fiber-by-fiber in Angular Integration models (AI) [7,8,9] or somehow averaged in Generalized Structure Tensor (GST) approaches [9,10,11]. Other approaches include homogeneization methods or explicit structural finite element modelling of the constituents [12,13].…”