A microstructurally inspired damage model for early venous thrombus

Abstract

Accumulative damage may be an important contributor to many cases of thrombotic disease progression. Thus, a complete understanding of the pathological role of thrombus requires an understanding of its mechanics and in particular mechanical consequences of damage. In the current study, we introduce a novel microstructurally inspired constitutive model for thrombus that considers a non-uniform distribution of microstructural fibers at various crimp levels and employs one of the distribution parameters to incorporate stretch-driven damage on the microscopic level. To demonstrate its ability to represent the mechanical behavior of thrombus, including a recently reported Mullins type damage phenomenon, we fit our model to uniaxial tensile test data of early venous thrombus. Our model shows an agreement with these data comparable to previous models for damage in elastomers with the added advantages of a microstructural basis and fewer model parameters. We submit that our novel approach marks another important step toward modeling the evolving mechanics of intraluminal thrombus, specifically its damage, and hope it will aid in the study of physiological and pathological thrombotic events.

Mechanical response of human female breast skin under uniaxial stretching

“…The microstructurally inspired damage model presented recently by Rausch and Humphrey (2016) will also be used to interpret the uniaxial test data. We provide a brief description of the model to facilitate the discussion; details may be found in Rausch and Humphrey (2016).…”

“…We provide a brief description of the model to facilitate the discussion; details may be found in Rausch and Humphrey (2016). In this model, the strain energy density function is represented in the following form: $$W=W_g(\mathbf{C})+\underset{S}{\int }\phi (\theta ,\mathrm{\Phi })W_f(\mathbf{C},\mathbf{N}(\theta ,\mathrm{\Phi }))d\theta d\mathrm{\Phi }-p(J-1),$$ where W g ( C ) is the strain energy density of the ground substance, C is the right Cauchy-Green tensor, φ ( θ , Φ) is the fiber bundle orientation distribution function with ( θ , Φ) representing the azimuthal and polar angles, and W f ( C , N ( θ , Φ)) is the strain energy density of the fiber bundles oriented in the direction N ( θ , Φ).…”

“…In order to evaluate this constitutive model further, it is necessary to determine the fiber bundle orientation distribution. However, this was not measured in our specimens, and therefore we will use the approximate procedure suggested by Rausch and Humphrey (2016). As the skin is stretched, fiber bundles rotate towards the stretching direction and further become uncrimped; this is the fiber recruitment process.…”

“…It is expected that ρ ( λ s ) will depend on the initial orientation of the specimen relative to the material anisotropy and the initial crimp distribution. Again, following Rausch and Humphrey (2016), we take ρ ( λ s ) to be a Weibull distribution: $$\rho \left({\lambda }_s\right)=\frac{\beta }{\delta }{\left(\frac{{\lambda }_s-\gamma }{\delta }\right)}^{\beta -1}exp\left[-{\left(\frac{{\lambda }_s-\gamma }{\delta }\right)}^{\beta }\right]$$ with the shape parameter β > 1, the scale parameter δ > 0, and the location parameter γ > 0. The ground substance and fiber are taken to be neo-Hookean, with W g = μ g ( λ 2 + 2 λ −1 −3) and W 0 = μ f ( λ̄ 2 + 2 λ̄ −1 −3), respectively, where λ̄ = λ / λ s enforces the fact that due to the initial crimp, fibers contribute to the overall energy only after they exceed the recruitment stretch.…”

“…Some of these models are derived from micromechanical considerations of the anisotropic structure of the materials, while others are purely phenomenological. Here, we consider two models, one by Hart-Smith (1966) and another by Rausch and Humphrey (2016) for interpreting experimental measurements; these models are described fully in Section 2.3.…”