A linearized and incompressible constitutive model for arteries

Need for transverse strain data for fitting constitutive models of arterial tissue to uniaxial tests

The study deals with the process of estimation of material parameters from uniaxial test data of arterial tissue and focuses on the role of transverse strains. Two fitting strategies are analyzed and their impact on the predictive and descriptive capabilities of the resulting model is evaluated. The standard fitting procedure (strategy A) based on longitudinal stress-strain curves is compared with the enhanced approach (strategy B) taking also the transverse strain test data into account. The study is performed on a large set of material data adopted from literature and for a variety of constitutive models developed for fibrous soft tissues. The standard procedure (A) ignoring the transverse strain test data is found rather hazardous, leading often to unrealistic predictions of the model exhibiting auxetic behaviour. In contrast, the alternative fitting method (B) ensures a realistic strain response of the model and is proved to be superior since it does not require any significant demands of computational effort or additional testing. The results presented in this paper show that even the artificial transverse strain data (i.e., not measured during testing but generated ex post based on assumed Poisson's ratio) are much less hazardous than total disregard of the transverse strain response.

Fiber orientation and crimp level might control the auxetic effect of biological tissues

We propose an analytical micromechanical model for studying the lamellar-composite-like structure of fibrous soft tissue. The tissue under consideration is made up of several lamellae, and is designed to resemble the annulus fibrosus (AF) tissue or media layer of arterial tissue, for example. The collagen fibers are arranged in parallel in each lamella and the fiber orientation differs from one lamella to its neighbors. The parallel fibers in each lamella of AF tissue, for example, have been observed to have a crimped microstructure. The proposed model incorporates this quality, considering fiber waviness as a sinusoidal shape and taking into account the fiber dispersion in different layers, where both fiber and matrix are considered as solid phases. We find that collagen-fiber waviness and layer orientation have a significant influence on Poisson's ratio. The effective Poisson's ratio predicted by the proposed model demonstrates that the crimped collagen fiber microstructure might weaken the auxetic effect of fibrous soft tissue, which might explain why, as the literature suggests, the auxetic behavior is more difficult to observe than large Poisson's ratios. As opposed to the many studies that use the well-known hyperelastic fiber-based constitutive model, in which out-of-plane expansion is often observed, the present work explains the auxetic response found in modeling and in experimental data from the perspective of collagen fiber microstructure.

Compressibility of arterial wall - Direct measurement and predictions of compressible constitutive models

Volumetric compressibility and Poisson's ratios of fibrous soft tissues are analyzed in this paper on the basis of constitutive models and experimental data. The paper extends the previous work of Skacel and Bursa (J Mech Behav Biomed Mater, 54, pp. 316-327, 2016), dealing with incompressible behaviour of constitutive models, to the area of compressibility. Both recent approaches to structure-based constitutive modelling of anisotropic fibrous biomaterials (based on either generalized structure tensor or angular integration) are analyzed, including their compressibility-related aspects. New experimental data related to compressibility of porcine arterial layer are presented and compared with the theoretical predictions of analyzed constitutive models. The paper points out the drawbacks of recent models with distributed fibres orientation since none of the analyzed constitutive models seems to be capable to predict the experimentally observed Poisson's ratios and volume change satisfactory.

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

STUDY OF PLAQUE VULNERABILITY IN CORONARY ARTERY USING MOONEY–RIVLIN MODEL: A COMBINATION OF FINITE ELEMENT AND EXPERIMENTAL METHOD

Atherosclerosis is a disease in which plaque builds up inside arteries. It is also considered as one of the most serious and common forms of cardiovascular disease which can lead to heart attack and stroke. In the current research, finite element method is used to anticipate plaque vulnerability based on peak plaque stress using human samples. A total of 23 healthy and atherosclerotic human coronary arteries, including 14 healthy and 9 atherosclerotic are removed within 5 h postmortem. The samples are mounted on a uniaxial tensile test machine and the obtained mechanical properties are used in finite element models. The results, including the Mooney–Rivlin hyperelastic constants of the samples as well as peak plaque stresses, are computed. It is demonstrated that the atherosclerotic human coronary arteries have significantly (p < 0.05) higher stiffness compared to healthy ones. The hypocellular plaque, in addition, has the highest stress values compared to the cellular and calcified ones and, consequently, is so prone to rupture. The calcified plaque type, nevertheless, has the lowest stress values and, remains stable. The results of this study can be used in the plaque vulnerability prediction and could have clinical implications for interventions and surgeries, such as balloon angioplasty, bypass and stenting.

Biaxial deformation of collagen and elastin fibers in coronary adventitia

The microstructural deformation-mechanical loading relation of the blood vessel wall is essential for understanding the overall mechanical behavior of vascular tissue in health and disease. We employed simultaneous mechanical loading-imaging to quantify in situ deformation of individual collagen and elastin fibers on unstained fresh porcine coronary adventitia under a combination of vessel inflation and axial extension loading. Specifically, the specimens were imaged under biaxial loads to study microscopic deformation-loading behavior of fibers in conjunction with morphometric measurements at the zero-stress state. Collagen fibers largely orientate in the longitudinal direction, while elastin fibers have major orientation parallel to collagen, but with additional orientation angles in each sublayer of the adventitia. With an increase of biaxial load, collagen fibers were uniformly stretched to the loading direction, while elastin fibers gradually formed a network in sublayers, which strongly depended on the initial arrangement. The waviness of collagen decreased more rapidly at a circumferential stretch ratio of λθ = 1.0 than at λθ = 1.5, while most collagen became straightened at λθ = 1.8. These microscopic deformations imply that the longitudinally stiffer adventitia is a direct result of initial fiber alignment, and the overall mechanical behavior of the tissue is highly dependent on the corresponding microscopic deformation of fibers. The microstructural deformation-loading relation will serve as a foundation for micromechanical models of the vessel wall.

A finite element investigation on plaque vulnerability in realistic healthy and atherosclerotic human coronary arteries

Atherosclerosis is the most common arterial disease. It has been shown that stresses that are induced during blood circulation can cause plaque rupture and, in turn, lead to thrombosis and stroke. In this study, finite element method is used to predict plaque vulnerability based on peak plaque stress using human samples. A total of 23 healthy and atherosclerotic human coronary arteries of 14 healthy and 9 atherosclerotic patients are excised within 5 h postmortem. The samples are mounted on an uniaxial tensile test machine, and the obtained mechanical properties are used in two-dimensional and three-dimensional finite element models. The results including the Neo-Hookean hyperelastic coefficients of the samples as well as peak plaque stresses are analyzed. The results indicate that the atherosclerotic human coronary arteries have significantly (p < 0.05) higher stiffness compared with the healthy ones. The hypocellular plaque also has the highest stress values and, as a result, is most likely (vulnerable) to rupture, while the calcified type has the lowest stress values and, consequently, is expected to remain stable. The results could be used in the plaque vulnerability anticipation and have clinical implications in interventions and surgeries, including balloon angioplasty, bypass, and stenting.

Measurement of the uniaxial mechanical properties of healthy and atherosclerotic human coronary arteries

Atherosclerosis is a common arterial disease which alters the stiffness of arterial wall. Arterial stiffness is related to many cardiovascular diseases. In this investigation, maximum stress and strain as well as physiological and maximum elastic modulus of 22 human coronary arteries are measured. In addition, the force-displacement diagram of human coronary artery is obtained to discern the alterations between the healthy and atherosclerotic arterial wall stiffness. The age of each specimen and its effect on the elastic modulus of human coronary arteries is also considered. Twenty-two human coronary arteries, including eight atherosclerotic and fourteen healthy arteries are excised within 5 hours post-mortem. Samples are mounted on a tensile-testing machine and force is applied until breakage occurs. Elastic modulus coefficient of each specimen is calculated to compare the stiffness of healthy and atherosclerotic coronary arteries. The results show that the atherosclerotic arteries bear 44.55% more stress and 34.61% less strain compared to the healthy ones. The physiological and maximum elastic moduli of healthy arteries are 2.53 and 2.91 times higher than that of atherosclerotic arteries, respectively. The age of specimens show no correlation with the arterial wall stiffness. A combination of biomechanics and mathematics is used to characterize the mechanical properties of human coronary arteries. These results could be utilized to understand the extension and rupture mechanism of coronary arteries and has implications for interventions and surgeries, including balloon-angioplasty, bypass, and stenting.

The layered structure of coronary adventitia under mechanical load

The mechanical loading-deformation relation of elastin and collagen fibril bundles is fundamental to understanding the microstructural properties of tissue. Here, we use multiphoton microscopy to obtain quantitative data of elastin and collagen fiber bundles under in situ loading of coronary adventitia. Simultaneous loading-imaging experiments on unstained fresh coronary adventitia allowed morphometric measurements of collagen and elastin fibril bundles and their individual deformation. Fiber data were analyzed at five different distension loading points (circumferential stretch ratio λ(θ) = 1.0, 1.2, 1.4, 1.6, and 1.8) at a physiological axial stretch ratio of λ(axial) = 1.3. Four fiber geometrical parameters were used to quantify the fibers: orientation angle, waviness, width, and area fraction. The results show that elastin and collagen fibers in inner adventitia form concentric densely packed fiber sheets, and the fiber orientation angle, width, and area fraction vary transmurally. The extent of fiber deformation depends on the initial orientation angle at no-distension state (λ(θ) = 1.0 and λ(axial) = 1.3). At higher distension loading, the orientation angle and waviness of fibers decrease linearly, but the width of collagen fiber is relatively constant at λ(θ) = 1.0-1.4 and then decrease linearly for λ(θ) ≥ 1.4. A decrease of the relative dispersion (SD/mean) of collagen fiber waviness suggests a heterogeneous mechanical response to loads. This study provides fundamental microstructural data for coronary artery biomechanics and we consider it seminal for structural models.

A novel arterial constitutive model in a commercial finite element package: Application to balloon angioplasty

Recently, a novel linearized constitutive model with a new strain measure that absorbs the material nonlinearity was validated for arteries. In this study, the linearized arterial stress-strain relationship is implemented into a finite element method package, ANSYS, via the user subroutine USERMAT. The reference configuration is chosen to be the closed cylindrical tube (no-load state) rather than the open sector (zero-stress state). The residual strain is taken into account by analytic calculation and the incompressibility condition is enforced with Lagrange penalty method. Axisymmetric finite element analyses are conducted to demonstrate potential applications of this approach in a complex boundary value problem where angioplasty balloon interacts with the vessel wall. The model predictions of transmural circumferential and compressive radial stress distributions were also validated against an exponential-type Fung model, and the mean error was found to be within 6%.