A structural constitutive model considering angular dispersion and waviness of collagen fibres of rabbit facial veins

Structural parameters defining distribution of collagen fiber directions in human carotid arteries

Collagen fiber arrangement is decisive for constitutive description of anisotropic mechanical response of arterial wall. In this study, their orientation in human common carotid artery was investigated using polarized light microscopy and an automated algorithm giving more than 4·106 fiber angles per slice. In total 113 slices acquired from 18 arteries taken from 14 cadavers were used for fiber orientation in the circumferential-axial plane. All histograms were approximated with unimodal von Mises distribution to evaluate dominant direction of fibers and their concentration parameter. 10 specimens were analyzed also in circumferential-radial and axial-radial planes (2-4 slices per specimen in each plane); the portion of radially oriented fibers was found insignificant. In the circumferential-axial plane, most specimens showed a pronounced unimodal distribution with angle to circumferential direction μ = 0.7° ± 9.4° and concentration parameter b = 3.4 ± 1.9. Suitability of the unimodal fit was confirmed by high values of coefficient of determination (mean R2 = 0.97, median R2 = 0.99). Differences between media and adventitia layers were not found statistically significant. The results are directly applicable as structural parameters in the GOH constitutive model of arterial wall if the postulated two fiber families are unified into one with circumferential orientation.

Biaxial stretch can overcome discrepancy between global and local orientations of wavy collagen fibres

Most frequently used structure-based constitutive models of arterial wall apply assumptions on two symmetric helical (and dispersed) fibre families which, however, are not well supported with histological findings where two collagen fibre families are seldom found. Moreover, bimodal distributions of fibre directions may originate also from their waviness combined with ignoring differences between local and global fibre orientations. In contrast, if the model parameters are identified without histological information on collagen fibre directions, the resulting mean angles of both fibre families are close to ±45°, which contradicts nearly all histologic findings. The presented study exploited automated polarized light microscopy for detection of collagen fibre directions in porcine aorta under different biaxial extensions and approximated the resulting histograms with unimodal and bimodal von Mises distributions. Their comparison showed dominantly circumferential orientation of collagen fibres. Their concentration parameter for unimodal distributions increased with circumferential load, no matter if acting uniaxially or equibiaxially. For bimodal distributions, the angle between both dominant fibre directions (chosen as measure of fibre alignment) decreased similarly for both uniaxial and equibiaxial loads. These results indicate the existence of a single family of wavy circumferential collagen fibres in all layers of the aortic wall. Bimodal distributions of fibre directions presented sometimes in literature may come rather from waviness of circumferentially arranged fibres than from two symmetric families of helical fibres. To obtain a final evidence, the fibre orientation should be analysed together with their waviness.

Endovascular Venous Stenosis and Thrombosis Large Animal Model: angiographic, histological, and biomechanical characterization

PURPOSE

Characterize an ovine endovascular radiofrequency ablation based venous stenosis and thrombosis model for studying venous biomechanics and response to intervention.

MATERIALS AND METHODS

Unilateral short-segment (n= 2) or long-segment (n = 6) iliac vein stenoses were created in eight adult sheep using an endovenous radiofrequency (RF) ablation technique. Angiographic assessment was performed at baseline, immediately after venous stenosis creation, and after 2-week (n = 6) or 3-month (n = 2) survival. Stenosed iliac veins and contralateral healthy controls were harvested for histological and biomechanical assessment.

RESULTS

At follow-up, the short-segment RF ablation group showed stable stenosis without occlusion. The long-segment group showed complete venous occlusion/thrombosis with formation of collateral veins. Stenosed veins showed significant wall thickening (0.28 mm vs 0.16 mm; p = 0.0175) and confluent collagen deposition compared to healthy controls. Subacute non-adherent thrombi were apparent at 2 weeks, which were replaced by fibrous luminal obliteration with channels of recanalization at 3 months. Stenosed veins demonstrated increased longitudinal stiffness (448.5 ± 5.4 kPa vs. 314.6 ± 1.5 kPa, p < 0.0001) and decreased circumferential stiffness (140.8 ± 2.6 kPa vs. 246.0 ± 1.6 kPa, p < 0.0001) compared to healthy controls.

CONCLUSION

Endovenous radiofrequency ablation is a reliable technique for creating venous stenosis and thrombosis in a large animal model with histological and biomechanical attributes similar to those seen in humans. This platform can facilitate understanding of venous biomechanics and testing of venous specific devices and interventions.

Microstructural and mechanical characterization of the layers of human descending thoracic aortas

The mechanical properties of human aortas are linked to the layered tissue and its microstructure at different length scales. Each layer has specific mechanical and structural properties. While the ground substance and the elastin play an important role in tissue stiffness at small strain, collagen fibers carry most of the load at larger strains, which corresponds to the physiological conditions of the aorta at maximum pulsatile blood pressure. In fact, collagen fibers are crimped in the unloaded state. Collagen fibers show different orientation distributions when they are observed in a plane that is tangent to the aortic wall (in-plane section) or along a direction orthogonal to it (out-of-plane section). This was systematically investigated using large images (2500 × 2500 µm) with high resolution obtained by second harmonic generation (SHG) in order to homogenize tissue heterogeneity after a convergence analysis, which is a main goal of the study. In addition, collagen fibers show lateral interactions due to entanglements and the presence of transverse elastin fibers, observed on varying length scales using atomic force microscopy and a three-dimensional rendering obtained by stacking a sequence of SHG and two-photon fluorescence images; this is another important contribution. Human descending thoracic aortas from 13 heartbeat donors aged 28 to 66 years were examined. Uniaxial tensile tests were carried out on the longitudinal and circumferential strips of the aortic wall and the three separated layers (intima, media and adventitia). A structurally-motivated material model with (i) a term to describe the combined response of ground substance and elastin and (ii) terms to consider four families of collagen fibers with different directions was applied. The exclusion of compressed fibers was implemented in the fitting process of the experimental data, which was optimized by a genetic algorithm. The results show that a single fiber family with directional and dispersion parameters measured from SHG images can describe the mechanical response of all 39 layers (3 layers for each of the 13 aortas) with very good accuracy when a second (auxiliary) family of aligned fibers is introduced in the orthogonal direction to account for lateral fiber interaction. Indeed, all observed distributions of collagen directions can be accurately fitted by a single bivariate von Mises distribution. Statistical analysis of in-plane and out-of-plane dispersion of fiber orientations reveals structural differences between the three layers and a change of collagen dispersion parameters with age. STATEMENT OF SIGNIFICANCE: The stiffness of healthy young aortas is adjusted so that a diameter expansion of about 10 % is possible during the heartbeat. This creates the Windkessel effect, which smooths out the pulsating nature of blood flow and benefits organ perfusion. The specific elastic properties of the aorta that are required to achieve this effect are related to the microstructure of the aortic tissue at different length scales. An increase in the aortic stiffness, in addition to reducing cyclic expansion and worsening perfusion, is a risk factor for clinical hypertension. The present study relates the microstructure of healthy human aortas to the mechanical response and examines the changes in microstructural parameters with age, which is a key factor in increasing stiffness.

Inflation instability in the lung: an analytical model of a thick-walled alveolus with wavy fibres under large deformations

Inflation of hollow elastic structures can become unstable and exhibit a runaway phenomenon if the tension in their walls does not rise rapidly enough with increasing volume. Biological systems avoid such inflation instability for reasons that remain poorly understood. This is best exemplified by the lung, which inflates over its functional volume range without instability. The goal of this study was to determine how the constituents of lung parenchyma determine tissue stresses that protect alveoli from instability-related overdistension during inflation. We present an analytical model of a thick-walled alveolus composed of wavy elastic fibres, and investigate its pressure-volume behaviour under large deformations. Using second-harmonic generation imaging, we found that collagen waviness follows a beta distribution. Using this distribution to fit human pressure-volume curves, we estimated collagen and elastin effective stiffnesses to be 1247 kPa and 18.3 kPa, respectively. Furthermore, we demonstrate that linearly elastic but wavy collagen fibres are sufficient to achieve inflation stability within the physiological pressure range if the alveolar thickness-to-radius ratio is greater than 0.05. Our model thus identifies the constraints on alveolar geometry and collagen waviness required for inflation stability and provides a multiscale link between alveolar pressure and stresses on fibres in healthy and diseased lungs.

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.

Venous Biomechanics of Angioplasty and Stent Placement: Implications of the Poisson Effect

PURPOSE

To characterize the Poisson effect in response to angioplasty and stent placement in veins and identify potential implications for guiding future venous-specific device design.

MATERIALS AND METHODS

In vivo angioplasty and stent placement were performed in 3 adult swine by using an established venous stenosis model. Iron particle endothelium labeling was performed for real-time fluoroscopic tracking of the vessel wall during intervention. A finite-element computational model of a vessel was created with ADINA software (version 9.5) with arterial and venous biomechanical properties obtained from the literature to compare the response to radial expansion.

RESULTS

In vivo angioplasty and stent placement in a venous stenosis animal model with iron particle endothelium labeling demonstrated longitudinal foreshortening that correlated with distance from the center of the balloon (R² = 0.87) as well as adjacent segment narrowing that correlated with the increase in diameter of the treated stenotic segment (R² = 0.89). Finite-element computational analysis demonstrated increased Poisson effect in veins relative to arteries (linear regression coefficient slope comparison, arterial slope 0.033, R² = 0.9789; venous slope 0.204, R² = 0.9975; P < .0001) as a result of greater longitudinal Young modulus in veins compared with arteries.

CONCLUSIONS

Clinically observed adjacent segment narrowing during venous angioplasty and stent placement is a result of the Poisson effect, with redistribution of radially applied force to the longitudinal direction. The Poisson effect is increased in veins relative to arteries as a result of unique venous biomechanical properties, which may be relevant to consider in the design of future venous interventional devices.

On fibre dispersion modelling of soft biological tissues: a review

Collagen fibres within fibrous soft biological tissues such as artery walls, cartilage, myocardiums, corneas and heart valves are responsible for their anisotropic mechanical behaviour. It has recently been recognized that the dispersed orientation of these fibres has a significant effect on the mechanical response of the tissues. Modelling of the dispersed structure is important for the prediction of the stress and deformation characteristics in (patho)physiological tissues under various loading conditions. This paper provides a timely and critical review of the continuum modelling of fibre dispersion, specifically, the angular integration and the generalized structure tensor models. The models are used in representative numerical examples to fit sets of experimental data that have been obtained from mechanical tests and fibre structural information from second-harmonic imaging. In particular, patches of healthy and diseased aortic tissues are investigated, and it is shown that the predictions of the models fit very well with the data. It is straightforward to use the models described herein within a finite-element framework, which will enable more realistic (and clinically relevant) boundary-value problems to be solved. This also provides a basis for further developments of material models and points to the need for additional mechanical and microstructural data that can inform further advances in the material modelling.

Iliac Vein Stent Placement: Acute Venographic Changes and Relevance to Venous Biomechanics

PURPOSE

To describe acute venographic changes of external iliac vein (EIV) after ipsilateral common iliac vein (CIV) stent placement.

MATERIALS AND METHODS

Retrospective review was performed of 17 cases with placement of a single CIV stent. Central CIV stent diameter and minimal ipsilateral EIV diameter were measured on venogram; vein diameter was measured at the same 2 anatomic locations on venogram obtained before intervention. Relative CIV diameter increase was defined as the ratio of change in central CIV diameter after stent placement to CIV diameter before intervention. Relative EIV diameter reduction was defined as the ratio of change in diameter of EIV after stent deployment in CIV to EIV diameter before intervention. Diameters before and after intervention were compared using a 2-tailed, paired sample t test. Pearson coefficient was calculated for correlations.

RESULTS

There was a significant reduction of EIV diameter after ipsilateral CIV stent placement compared with before stent placement (mean 9.3 mm ± 3.1 vs 11.9 mm ± 3.8; P < .01); mean decrease in EIV diameter was 21.7% ± 15.8. There was a correlation between relative CIV diameter increase and relative EIV diameter reduction (r = .8917).

CONCLUSIONS

Significant venographic narrowing of the EIV occurs after placement of an adjacent CIV stent, and the degree of narrowing is associated with the relative increase in CIV diameter. These findings may be explained by the inherent anisotropic elasticity of veins. Further study is warranted to guide future venous interventions.

Modelling non-symmetric collagen fibre dispersion in arterial walls

New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new non-symmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structural features of the material, extending our rotationally symmetric dispersion model (Gasser et al. 2006 J. R. Soc. Interface 3, 15-35. (doi:10.1098/rsif.2005.0073)). We provide specific ranges for the dispersion parameters and show how previous models can be deduced as special cases. We also provide explicit expressions for the stress and elasticity tensors in the Lagrangian description that are needed for a finite-element implementation. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from human abdominal aortic adventitia. In a finite-element example, we analyse the influence of the fibre dispersion on the homogeneous biaxial mechanical response of aortic strips, and in a final example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. It has recently become apparent that this more general model is needed for describing the mechanical behaviour of a variety of fibrous tissues.

Contribution of collagen fiber undulation to regional biomechanical properties along porcine thoracic aorta

As major extracellular matrix components, elastin, and collagen play crucial roles in regulating the mechanical properties of the aortic wall and, thus, the normal cardiovascular function. The mechanical properties of aorta, known to vary with age and multitude of diseases as well as the proximity to the heart, have been attributed to the variations in the content and architecture of wall constituents. This study is focused on the role of layer-specific collagen undulation in the variation of mechanical properties along the porcine descending thoracic aorta. Planar biaxial tensile tests are performed to characterize the hyperelastic anisotropic mechanical behavior of tissues dissected from four locations along the thoracic aorta. Multiphoton microscopy is used to image the associated regional microstructure. Exponential-based and recruitment-based constitutive models are used to account for the observed mechanical behavior while considering the aortic wall as a composite of two layers with independent properties. An elevated stiffness is observed in distal regions compared to proximal regions of thoracic aorta, consistent with sharper and earlier collagen recruitment estimated for medial and adventitial layers in the models. Multiphoton images further support our prediction that higher stiffness in distal regions is associated with less undulation in collagen fibers. Recruitment-based models further reveal that regardless of the location, collagen in the media is recruited from the onset of stretching, whereas adventitial collagen starts to engage with a delay. A parameter sensitivity analysis is performed to discriminate between the models in terms of the confidence in the estimated model parameters.

Bio-Chemo-Mechanical Models of Vascular Mechanics

Models of vascular mechanics are necessary to predict the response of an artery under a variety of loads, for complex geometries, and in pathological adaptation. Classic constitutive models for arteries are phenomenological and the fitted parameters are not associated with physical components of the wall. Recently, microstructurally-linked models have been developed that associate structural information about the wall components with tissue-level mechanics. Microstructurally-linked models are useful for correlating changes in specific components with pathological outcomes, so that targeted treatments may be developed to prevent or reverse the physical changes. However, most treatments, and many causes, of vascular disease have chemical components. Chemical signaling within cells, between cells, and between cells and matrix constituents affects the biology and mechanics of the arterial wall in the short- and long-term. Hence, bio-chemo-mechanical models that include chemical signaling are critical for robust models of vascular mechanics. This review summarizes bio-mechanical and bio-chemo-mechanical models with a focus on large elastic arteries. We provide applications of these models and challenges for future work.

Characterization of biaxial mechanical behavior of porcine aorta under gradual elastin degradation

Arteries are composed of multiple constituents that endow the wall with proper structure and function. Many vascular diseases are associated with prominent mechanical and biological alterations in the wall constituents. In this study, planar biaxial tensile test data of elastase-treated porcine aortic tissue (Chow et al. in Biomech Model Mechanobiol 2013) is re-examined to characterize the altered mechanical behavior at multiple stages of digestion through constitutive modeling. Exponential-based as well as recruitment-based strain energy functions are employed and the associated constitutive parameters for individual digestion stages are identified using nonlinear parameter estimation. It is shown that when the major portion of elastin is degraded from a cut-open artery in the load-free state, the embedded collagen fibers are recruited at lower stretch levels under biaxial loads, leading to a rapid stiffening behavior of the tissue. Multiphoton microscopy illustrates that the collagen waviness decreases significantly with the degradation time, resulting in a rapid recruitment when the tissue is loaded. It is concluded that even when residual stresses are released, there exists an intrinsic mechanical interaction between arterial elastin and collagen that determines the mechanics of arteries and carries important implications to vascular mechanobiology.

Arterial stiffness identification of the human carotid artery using the stress-strain relationship in vivo

Arterial stiffness is well accepted as a reliable indicator of arterial disease. Increase in carotid arterial stiffness has been associated with carotid arterial disease, e.g., atherosclerotic plaque, thrombosis, stenosis, etc. Several methods for carotid arterial stiffness assessment have been proposed. In this study, in vivo noninvasive assessment using applanation tonometry and an ultrasound-based motion estimation technique was applied in seven healthy volunteers (age 28±3.6years old) to determine pressure and wall displacement in the left common carotid artery (CCA), respectively. The carotid pressure was obtained using a calibration method by assuming that the mean and diastolic blood pressures remained constant throughout the arterial tree. The regional carotid arterial wall displacement was estimated using a 1D cross-correlation technique on the ultrasound radio frequency (RF) signals acquired at a frame rate of 505-1010Hz. Young's moduli were estimated under two different assumptions: (i) a linear elastic two-parallel spring model and (ii) a two-dimensional, nonlinear, hyperelastic model. The circumferential stress (σ(θ)) and strain (ɛ(θ)) relationship was then established in humans in vivo. A slope change in the circumferential stress-strain curve was observed and defined as the transition point. The Young's moduli of the elastic lamellae (E(1)), elastin-collagen fibers (E(2)) and collagen fibers (E(3)) and the incremental Young's moduli before ( [Formula: see text] ) and after the transition point ( [Formula: see text] ) were determined from the first and second approach, respectively, to describe the contribution of the complex mechanical interaction of the different arterial wall constituents. The average moduli E(1), E(2) and E(3) from seven healthy volunteers were found to be equal to 0.15±0.04, 0.89±0.27 and 0.75±0.29MPa, respectively. The average moduli [Formula: see text] and [Formula: see text] of the intact wall (both the tunica adventitia and tunica media layers) were found to be equal to 0.16±0.04MPa and 0.90±0.25MPa, respectively. The average moduli [Formula: see text] and [Formula: see text] of the tunica adventitia were found to be equal to 0.18±0.05MPa and 0.84±0.22MPa, respectively. The average moduli [Formula: see text] and [Formula: see text] of the tunica media were found to be equal to 0.19±0.05MPa and 0.90±0.25MPa, respectively. The stiffness of the carotid artery increased with strain during the systolic phase. In conclusion, the feasibility of measuring the regional stress-strain relationship and stiffness of the normal human carotid artery was demonstrated noninvasively in vivo.