An inelastic multi-mechanism constitutive equation for cerebral arterial tissue

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.

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

We present a framework for considering the gradual recruitment of collagen fibers in hyperelastic constitutive modeling. An effective stretch, which is a response variable representing the true stretch at the tissue-scale, is introduced. Properties of the effective stretch are discussed in detail. The effective stretch and strain invariants derived from it are used in selected hyperelastic constitutive models to describe the tissue response. This construction is investigated in conjunction with Holzapfel-Gasser-Ogden family strain energy functions. The ensuing models are validated against a large body of uniaxial and bi-axial stress-strain response data from human aortic aneurysm tissues. Both the descriptive and the predictive capabilities are examined. The former is evaluated by the quality of constitutive fitting, and the latter is assessed using finite element simulation. The models significantly improve the quality of fitting, and reproduce the experiment displacement, stress, and strain distributions with high fidelity in the finite element simulation.

Adaptive Remodeling in the Elastase-induced Rabbit Aneurysms

BACKGROUND

Rupture of brain aneurysms is associated with high fatality and morbidity rates. Through remodeling of the collagen matrix, many aneurysms can remain unruptured for decades, despite an enlarging and evolving geometry.

OBJECTIVE

Our objective was to explore this adaptive remodeling for the first time in an elastase induced aneurysm model in rabbits.

METHODS

Saccular aneurysms were created in 22 New Zealand white rabbits and remodeling was assessed in tissue harvested 2, 4, 8 and 12 weeks after creation.

RESULTS

The intramural principal stress ratio doubled after aneurysm creation due to increased longitudinal loads, triggering a remodeling response. A distinct wall layer with multi-directional collagen fibers developed between the media and adventitia as early as 2 weeks, and in all cases by 4 weeks with an average thickness of 50.6 ± 14.3 μm. Collagen fibers in this layer were multi-directional (AI = 0.56 ± 0.15) with low tortuosity (1.08 ± 0.02) compared with adjacent circumferentially aligned medial fibers (AI = 0.78 ± 0.12) and highly tortuous adventitial fibers (1.22 ± 0.03). A second phase of remodeling replaced circumferentially aligned fibers in the inner media with longitudinal fibers. A structurally motivated constitutive model with both remodeling modes was introduced along with methodology for determining material parameters from mechanical testing and multiphoton imaging.

CONCLUSIONS

A new mechanism was identified by which aneurysm walls can rapidly adapt to changes in load, ensuring the structural integrity of the aneurysm until a slower process of medial reorganization occurs. The rabbit model can be used to evaluate therapies to increase aneurysm wall stability.

On the optimal choice of a hyperelastic model of ruptured and unruptured cerebral aneurysm

In the last decade, preoperative modelling of the treatment of cerebral aneurysms is being actively developed. Fluid-structure interaction problem is a key point of a such modelling. Hence arises the question about the reasonable choice of the model of the vessel and aneurysm wall material to build the adequate model from the physical point of view. This study covers experimental investigation of 8 tissue samples of cerebral aneurysms and 1 tissue sample of a healthy cerebral artery. Results on statistical significance in ultimate stress for the classification of 2 cohorts of aneurysms: ruptured and unruptured described earlier in the literature were confirmed (p ≤ 0.01). We used the four most common models of hyperelastic material: Yeoh, Neo-Hookean and Mooney-Rivlin (3 and 5 parameter) models to describe the experimental data. In this study for the first time, we obtained a classification of hyperelastic models of cerebral aneurysm tissue, which allows to choose the most appropriate model for the simulation problems requirements depending on the physical interpretation of the considered problem: aneurysm status and range of deformation.

Fatigue damage of collagenous tissues: experiment, modeling and simulation studies

Mechanical fatigue damage is a critical issue for soft tissues and tissue-derived materials, particularly for musculoskeletal and cardiovascular applications; yet, our understanding of the fatigue damage process is incomplete. Soft tissue fatigue experiments are often difficult and time-consuming to perform, which has hindered progress in this area. However, the recent development of soft-tissue fatigue-damage constitutive models has enabled simulation-based fatigue analyses of tissues under various conditions. Computational simulations facilitate highly controlled and quantitative analyses to study the distinct effects of various loading conditions and design features on tissue durability; thus, they are advantageous over complex fatigue experiments. Although significant work to calibrate the constitutive models from fatigue experiments and to validate predictability remains, further development in these areas will add to our knowledge of soft-tissue fatigue damage and will facilitate the design of durable treatments and devices. In this review, the experimental, modeling, and simulation efforts to study collagenous tissue fatigue damage are summarized and critically assessed.

A 3D MODEL FOR MURAL-CELL-MEDIATED DESTRUCTIVE REMODELING DURING EARLY DEVELOPMENT OF A CEREBRAL ANEURYSM

Development of a diagnostic tool for predicting the behavior of cerebral aneurysms was the inspiration of many research groups in recent years. In the present study a fluid–solid-growth (FSG) model for the early development of a cerebral aneurysm was presented in a 3D model of the internal carotid artery (ICA). This model is the result of two parallel mechanisms: first, defining arterial wall as a living tissue with the ability of degradation, growth and remodeling and second, full coupling of the wall and the blood flow. Taking into account the shear dependent nature of elastin degradation and mural-cell-mediated destructive activities, here, the degradation process has been linked to high effective stress of the vascular wall. The evolving properties of the elastinous and collagenous constituents have been predicted during the early development of the aneurysm and the code is applicable to more complicated aneurismal growth models.

Microstructural modelling of cerebral aneurysm evolution through effective stress mediated destructive remodelling

Recently, researchers have shown an increased interest in the biomechanical modelling of cerebral aneurysm development. In the present study a fluid-solid-growth model for the formation of a fusiform aneurysm has been presented in an axi-symmetric geometry of the internal carotid artery. This model is the result of two parallel mechanisms: first, defining arterial wall as a living tissue with the ability of degradation, growth and remodelling and second, full coupling of the wall and the blood flow. Here for the first time the degradation of elastin has been defined as a function of vascular wall effective stress to take into account the shear dependent nature of degradation and the mural-cell-mediated destructive activities. The model has been stabilized in size and mechanical properties and is consistent with other computational or clinical studies. Furthermore, the evolving microstructural properties of the wall during the evolution process have been predicted.

A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall

Gradual collagen recruitment has been hypothesized as the underlying mechanism for the mechanical stiffening with increasing stress in arteries. In this work, we investigated this hypothesis in eight rabbit carotid arteries by directly measuring the distribution of collagen recruitment stretch under increasing circumferential loading using a custom uniaxial (UA) extension device combined with a multi-photon microscope (MPM). This approach allowed simultaneous mechanical testing and imaging of collagen fibers without traditional destructive fixation methods. Fiber recruitment was quantified from 3D rendered MPM images, and fiber orientation was measured in projected stacks of images. Collagen recruitment was observed to initiate at a finite strain, corresponding to a sharp increase in the measured mechanical stiffness, confirming the previous hypothesis and motivating the development of a new constitutive model to capture this response. Previous constitutive equations for the arterial wall have modeled the collagen contribution with either abrupt recruitment at zero strain, abrupt recruitment at finite strain or as gradual recruitment beginning at infinitesimal strain. Based on our experimental data, a new combined constitutive model was presented in which fiber recruitment begins at a finite strain with activation stretch represented by a probability distribution function. By directly including this recruitment data, the collagen contribution was modeled using a simple Neo-Hookean equation. As a result, only two phenomenological material constants were required from the fit to the stress stretch data. Three other models for the arterial wall were then compared with these results. The approach taken here was successful in combining stress-strain analysis with simultaneous microstructural imaging of collagen recruitment and orientation, providing a new approach by which underlying fiber architecture may be quantified and included in constitutive equations.

A Structural Multi-Mechanism Damage Model for Cerebral Arterial Tissue

Early stage cerebral aneurysms are characterized by the disruption of the internal elastic lamina. The cause of this breakdown is still not understood, but it has been conjectured to be due to fatigue failure and/or by a breakdown in homeostatic mechanisms in the wall arising from some aspect of the local hemodynamics and wall tension. We propose to model this disruption using a structural damage model. It is built on a previously introduced nonlinear, inelastic multi-mechanism model for cerebral arteries (2005, “An Inelastic Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue,” Biomech. Model. Mechanobiol., 4(4), pp. 235–248), as well as a recent generalization to include the wall anisotropy (2009, “A Structural Multi-Mechanism Constitutive Equation for Cerebral Arterial Tissue,” Int. J. Solids Struct., 46(14–15), pp. 2920–2928). The current model includes subfailure damage of the elastin, represented by changes in the tissue mechanical properties and unloaded reference length. A structural model is used to characterize the gradual degradation, failure of elastin, and recruitment of anisotropic collagen fibers. The collagen fibers are arranged in two helically oriented families with dispersion in their orientation. Available inelastic experimental data for cerebral arteries are used to evaluate the constitutive model. It is then implemented in a commercial finite element analysis package and validated using analytical solutions with representative values for cerebral arterial tissue.

The mechanical response of human liver and its relation to histology: an in vivo study

The mechanical response of human liver is characterized in vivo by means of intra-operative aspiration experiments. Mechanical characterization is combined with histological evaluation of liver tissue biopsies obtained from the resected liver at the site of mechanical testing. This procedure enables a quantitative analysis of the correlation between mechanical response and tissue micro-structure of normal and diseased liver. Ten organs were tested in vivo at multiple locations, as well as ex vivo immediately after resection. Biopsies were analyzed in terms of pathology and percentage of connective tissue content. The change of the mechanical parameters from in vivo to ex vivo has been determined, with an increase of 17% of the proposed stiffness index. The relationship between mechanical parameters and various pathologic conditions affecting the tissue samples has been quantified, with fibrosis leading to a response up to three times stiffer as compared with normal tissue. Increased stiffness can be detected by digital palpation (increased "consistency") and may suggest the presence of a tumor. The present observations suggest that stiffness increase cannot be attributed to the tumoral tissue itself, but rather to the fibrotic stroma that often arise within or adjacent to the tumor. Variation of the mechanical parameters as a function of connective tissue content has been evaluated based on the histological examinations and the results confirm a direct proportionality between stiffness index and connective tissue percentage. The approach described here might eventually lead to a diagnostic procedure and complement other clinical methods, like palpation and ultrasound examination of the liver.