Incorporating fiber recruitment in hyperelastic modeling of vascular tissues by means of kinematic average

What does the slope of stress-stretch curves tell us about vascular tissue response?

We examined a group of 50 uniaxial stress-stretch curves obtained from human ascending aortic aneurysm tissues. The curves were believed to be associated with elastic response because the stress is monotonically increasing in all curves, and so is the slope. However, 26 curves exhibit exponential-like slope while the remaining 24 curves have sigmoid slopes. We hypothesized that the slope patterns stemmed from collage waviness distribution. A structural constitutive model was introduced to describe the responses. The model employed a unimodal density function to describe the waviness distribution, from which a two-phase response ensued. In the first phase the slope is quasi-exponential, and in the second phase the slope is sigmoid. The model fitted all 50 curves perfectly well. An exponential model was also introduced for a comparison. The model fitted the curves of quasi-exponential slope generally well, but performed worse over the curves of sigmoid slope. The work suggests that the slope may encode significant information about collagen waviness, and underscores a limitation of exponential-based models.

A waviness-centered damage model for collagenous soft tissues

This article presents a damage model for collagenous tissue under monotonic loading. Given that the true stretch of collagen fibers is not uniform and is regulated by fiber waviness, we postulate that damage commences from more stretched (i.e. straighter) fibers and progresses to less stretched (i.e. wavier) ones. The complicated nonlinear response is regarded as the outcome of two competing mechanisms: the recruitment of wavy intact fibers and the loss of taut functioning fibers. The progression of damage is modeled by an evolving damage front in the waviness domain. A power law is proposed for the evolution of damage front. The model was fitted to four groups of published uniaxial and biaxial tests data of vascular tissues. Spot-on fits were observed in all groups.

Histology-informed multiscale modeling of human brain white matter

In this study, we propose a novel micromechanical model for the brain white matter, which is described as a heterogeneous material with a complex network of axon fibers embedded in a soft ground matrix. We developed this model in the framework of RVE-based multiscale theories in combination with the finite element method and the embedded element technique for embedding the fibers. Microstructural features such as axon diameter, orientation and tortuosity are incorporated into the model through distributions derived from histological data. The constitutive law of both the fibers and the matrix is described by isotropic one-term Ogden functions. The hyperelastic response of the tissue is derived by homogenizing the microscopic stress fields with multiscale boundary conditions to ensure kinematic compatibility. The macroscale homogenized stress is employed in an inverse parameter identification procedure to determine the hyperelastic constants of axons and ground matrix, based on experiments on human corpus callosum. Our results demonstrate the fundamental effect of axon tortuosity on the mechanical behavior of the brain's white matter. By combining histological information with the multiscale theory, the proposed framework can substantially contribute to the understanding of mechanotransduction phenomena, shed light on the biomechanics of a healthy brain, and potentially provide insights into neurodegenerative processes.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

On strain-based rupture criterion for ascending aortic aneurysm: the role of fiber waviness

We propose a new approach for constructing strain-based rupture criterion for ascending thoracic aortic aneurysm. The rupture metric is formulated using an effective strain, which is a measure of net strain that the collagen bundles experience after fiber uncrimping. The effective strain is a function of the total strain and the waviness properties of the collagen fibers. In the present work, the waviness properties are obtained from fitting biaxial response data to constitutive models that explicitly consider the collagen waviness and fiber recruitment. Inflation test data from 10 ascending thoracic aortic aneurysm specimens are analyzed. For each specimen, tension-strain data at ∼2300 material points are garnered. The effective strain fields in the configuration immediately before rupture are computed. It is found that the hotspots of the effective strain match the rupture sites very well in all 10 samples. More importantly, the values of effective strain at the hotsopts are closely clustered around 0.1, in contrast to a much wider distribution of the total strain. The study underscores the importance of considering the fiber recruitment in formulating strain-based rupture metric, and suggests that ϵ¯≈0.1, where ϵ¯ is the effective strain metric defined in this work, can be considered as a criterion for assessing the imminent rupture risk of ascending aortic aneurysms.

Uniaxial properties of ascending aortic aneurysms in light of effective stretch

A constitutive model that explicitly considers the gradual recruitment of collagen fibers is applied to investigate the uniaxial properties of human ascending aortic aneurysms. The model uses an effective stretch, which is a continuum scale kinematic variable measuring the true stretch of the tissue, to formulate the fiber stress. The constitutive equation contains two shape parameters characterizing the stochastic distribution of fiber waviness, and two elastic parameters accounting for, respectively, the elastic properties of ground substance and the straightened collagen fibers. The model is applied to 156 sets of uniaxial stress-stretch data obtained from 52 aneurysm samples. Major findings include (1) the uniaxial response can be well described by a quadratic strain energy function of the effective strain; (2) the ultimate stretches, when measured in terms of the effective stretch, are closely clustered around 1.1, in contrast to a much wider range in the original stretch; and (3) the ultimate stress correlates positively with the fiber stiffness. The age dependence and directional differences of constitutive parameters are also investigated. Results indicate that only the waviness depends strongly on age; no clear alterations occur in elastic parameters. Further, the fibers are wavier and stiffer in the circumferential direction than in the longitudinal direction. No other parameters exhibit significant direction difference. STATEMENT OF SIGNIFICANCE: We introduced a constitutive model which explicitly accounts for collagen fiber recruitment to investigate the uniaxial properties of human ascending aortic aneurysm tissues. Uniaxial response data from 156 specimens were considered in the study. It was found that the seemingly dissimilar response curves are, in fact, similar if we measure the deformation using an effective stretch which factors out the uncrimping deformation. The rupture stretches in terms of the effective stretch are closely packed around 1.1. And the stress-stretch curves collapse to a canonical curve after a transformation.