Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

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.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

Importance of experimental evaluation of structural parameters for constitutive modelling of aorta

The study compares stresses and strains in the aortic wall derived using different constitutive models for various stress-strain conditions. Structure-based constitutive models with two fibre families with (GOH) and without (HGO) dispersion of collagen fibres are compared. The constitutive models were fitted to data from equibiaxial tension tests of two separated layers of the porcine aortic wall. The initial fit was evaluated with unrestricted parameters and subsequently, the mean angles of the fibre families and the angular dispersion were fixed to the values obtained from histology. Surprisingly, none of the tested models was capable to provide a good quality fit with histologically obtained structural parameters. Fitting the HGO model to experimental data resulted in two fibre families under angles close to ±45°, while the GOH model resulted in a nearly isotropic fibre distribution. These results indicate that both of these models suffer from the absence of isotropic strain stiffening. After having modified both models with corresponding additional members based on the Yeoh model of matrix, we obtained a perfect fit to the measured data while keeping the structural histology-based parameters. Finally, significant differences in compliance and resulting stresses and strains between different models are shown by means of simulations of uniaxial tension test, equibiaxial tension tests and inflation of the aorta.

Membrane curvature and connective fiber alignment in guinea pig round window membrane

The round window membrane (RWM) covers an opening between the perilymph fluid-filled inner ear space and the air-filled middle ear space. As the only non-osseous barrier between these two spaces, the RWM is an ideal candidate for aspiration of perilymph for diagnostics purposes and delivery of medication for treatment of inner ear disorders. Routine access across the RWM requires the development of new surgical tools whose design can only be optimized with a thorough understanding of the RWM's structure and properties. The RWM possesses a layer of collagen and elastic fibers so characterization of the distribution and orientation of these fibers is essential. Confocal and two-photon microscopy were conducted on intact RWMs in a guinea pig model to characterize the distribution of collagen and elastic fibers. The fibers were imaged via second-harmonic-generation, autofluorescence, and Rhodamine B staining. Quantitative analyses of both fiber orientation and geometrical properties of the RWM uncovered a significant correlation between mean fiber orientations and directions of zero curvature in some portions of the RWM, with an even more significant correlation between the mean fiber orientations and linear distance along the RWM in a direction approximately parallel to the cochlear axis. The measured mean fiber directions and dispersions can be incorporated into a generalized structure tensor for use in the development of continuum anisotropic mechanical constitutive models that in turn will enable optimization of surgical tools to access the cochlea. STATEMENT OF SIGNIFICANCE: The Round Window Membrane (RWM) is the only non-osseous barrier separating the middle and inner ear spaces, and thus is an ideal portal for medical access to the cochlea. An understanding of RWM structure and mechanical response is necessary to optimize the design of surgical tools for this purpose. The RWM geometry and the connective fiber orientation and dispersion are measured via confocal and 2-photon microscopy. A region of the RWM geometry is characterized as a hyperbolic paraboloid and another region as a tapered parabolic cylinder. Predominant fiber directions correlate well with directions of zero curvature in the hyperbolic paraboloid region. Overall fiber directions correlate well with position along a line approximately parallel to the central axis of the cochlea's spiral.

Full-Range Optical Imaging of Planar Collagen Fiber Orientation Using Polarized Light Microscopy

A novel method for semiautomated assessment of directions of collagen fibers in soft tissues using histological image analysis is presented. It is based on multiple rotated images obtained via polarized light microscopy without any additional components, i.e., with just two polarizers being either perpendicular or nonperpendicular (rotated). This arrangement breaks the limitation of 90° periodicity of polarized light intensity and evaluates the in-plane fiber orientation over the whole 180° range accurately and quickly. After having verified the method, we used histological specimens of porcine Achilles tendon and aorta to validate the proposed algorithm and to lower the number of rotated images needed for evaluation. Our algorithm is capable to analyze 5·105 pixels in one micrograph in a few seconds and is thus a powerful and cheap tool promising a broad application in detection of collagen fiber distribution in soft tissues.

Plasticity and Enzymatic Degradation Coupled With Volumetric Growth in Pulmonary Hypertension Progression

Pulmonary hypertension (PH) is one of the least understood and highly elusive cardiovascular conditions associated with elevated pulmonary arterial pressure. Although the disease mechanisms are not completely understood, evidence has accumulated from human and animal studies that irreversible processes of pulmonary arterial wall damage, compensated by stress-mediated growth, play critical roles in eliciting the mechanisms of disease progression. The aim of this study is to develop a thermodynamic modeling structure of the pulmonary artery to consider coupled plastic-degradation-growth irreversible processes to investigate the mechanical roles of the dissipative phenomena in the disease progression. The proposed model performs a model parameter study of plastic deformation and degradation processes coupled with dissipative growth subjected to elevated pulmonary arterial pressure and computationally generates in silico simulations of PH progression using the clinical features of PH, found in human morphological and mechanical data. The results show that considering plastic deformation can provide a much better fitting of the ex vivo inflation tests than a widely used pure hyperelastic model in higher pressure conditions. In addition, the parameter sensitivity study illustrates that arterial damage and growth cause the increased stiffness, and the full simulation (combining elastic-plastic-degradation-growth models) reveals a key postpathological recovery process of compensating vessel damage by vascular adaptation by reducing the rate of vessel dilation and mediating vascular wall stress. Finally, the simulation results of luminal enlargement, arterial thickening, and arterial stiffness for an anisotropic growth are found to be close to the values from the literature.

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.

Unraveling the multilayer mechanical response of aorta using layer-specific residual stresses and experimental properties

To test the capability of the multilayer model, we used previously published layer-specific experimental data relating to the axial pre-stretch, the opening angle, the fiber distribution obtained by polarized light microscopy measurements, and the uniaxial and biaxial response of the porcine descending and abdominal aorta. We fitted the mechanical behavior of each arterial layer using Gasser, Holzapfel and Ogden strain energy function using the dispersion parameter κ as phenomenological parameter obtained during the fitting procedure or computed from the experimental fiber distribution. A multilayer finite element model of the whole aorta with the dimensions of the circumferential and longitudinal strips were then built using layer-specific material parameters previously fitted. This model was used to capture the whole aorta response under uniaxial and biaxial stress states and to reproduce the response of the whole aorta to internal pressure. Our results show that a model based on a multilayer structure without residual stresses is unable to render the uniaxial and biaxial mechanical response of the aorta (R²=0.6954 and R²=0.8582 for descending thoracic aorta (DTA) and infrarenal abdominal aorta (IAA), respectively). Only an appropriate multilayer model that includes layer-specific residual stresses can reproduce the response of the whole aorta (R²=0.9787 and R²=0.9636 for DTA and IAA respectively). In addition, a multilayer model without residual stresses produces the same stress distribution as a monolayer model without residual stresses where the maximal value of circumferential and longitudinal stresses appears at the inner radius of the intima. Finally, if layer-specific residual stresses are not available, there is less error the stress distribution using a monolayer model with residual stresses that a multilayer model without residual stresses.

In vitro histomechanical effects of enzymatic degradation in carotid arteries during inflation tests with pulsatile loading

In this paper, the objective is to assess the histomechanical effects of collagen proteolysis in arteries under loading conditions reproducing in vivo environment. Thirteen segments of common porcine carotid arteries (8 proximal and 5 distal) were immersed in a bath of bacterial collagenase and tested with a pulsatile tension/inflation machine. Diameter, pressure and axial load were monitored throughout the tests and used to derive the stress-stretch curves and to determine the secant circumferential stiffness. Results were analysed separately for proximal and distal segments, before and after 1, 2 and 3 h of enzymatic degradation. A histological analysis was performed to relate the arterial microstructure to its mechanical behavior under collagen proteolysis. Control (before enzymatic degradation) and treated populations (after 1, 2 or 3 h of enzymatic degradation) were found statistically incomparable, and histology confirmed the alteration of the fibrous structure of collagen bundles induced by the collagenase treatment. A decrease of the secant circumferential stiffness of the arterial wall was noticed mostly at the beginning of the treatment, and was less pronounced after 1 h. These results constitute an important set of enzymatically damaged arteries that can be used to validate biomechanical computational models correlating structure and properties of blood vessels.

Ultrasound assessment of tensile stress in carotid arteries of healthy human subjects with varying age

Background

Arterial remodeling is thought to reflect the adaptation of the vessel wall to mechanical and hemodynamic stimuli and contributes to the progression of cardiovascular and cerebrovascular diseases. Tensile stress (TS) is one of the mechanical properties of the artery wall. The purpose of this study was to investigate the tensile stress change (TS) of carotid artery with varying viscoelasticity in healthy subjects within two groups of different ages.

Methods

Forty-five subjects were recruited and randomly assigned into the group at the age above 50 years and below 50 years. The carotid arteries were examined by ultrasonography, using the techniques of shear wave elastography (SWE), shear wave dispersion (SWD) and radiofrequency (RF) -based ultrasound. The following values, including elastic modulus (SWER) and viscous index (SWDR), as well as the peak and mean TS of the left and right carotid arteries (L-PTS, R-PTS, L-MTS and R-MTS) were measured. The correlations between SWER, SWDR and tensile stress were evaluated.

Results

The SWE_R and SWD_R of carotid arteries are lower in the subjects ≥50 years old than the subjects younger than 50 years (SWE_R, 10.29 ± 9.57 kPa VS 17.24 ± 14.07 kPa; SWD_R, 11.99 ± 3.51 (m/s)/kHz VS 13.97 ± 3.71 (m/s)/kHz, P < 0.05). The R-PTS was lower in the group with younger age (P < 0.05). Pearson correlation analysis showed that SWE_R of carotid artery was positively correlated with the parameters of tensile stress, R-PTS, R-MTS, L-PTS and L-MTS(r = 0.218, r = 0.359, r = 0.209 and r = 0.369, respectively, P < 0.05). However, SWD_R of carotid arteries was not significantly associated with TS.

Conclusion

Ultrasonic shear wave imaging could be used to quantitatively assess carotid viscoelasticity. The carotid TS was related to its elasticity while little related to its viscosity, suggesting that mechanical properties of the arterial wall might be better revealed.

Trial registration

Date of our trial registration: 2018-06-11. Registered with the official website of China Clinical Trial Registration Center (ChiCTR1800016590)

A discrete fibre dispersion method for excluding fibres under compression in the modelling of fibrous tissues

Recently, micro-sphere-based methods derived from the angular integration approach have been used for excluding fibres under compression in the modelling of soft biological tissues. However, recent studies have revealed that many of the widely used numerical integration schemes over the unit sphere are inaccurate for large deformation problems even without excluding fibres under compression. Thus, in this study, we propose a discrete fibre dispersion model based on a systematic method for discretizing a unit hemisphere into a finite number of elementary areas, such as spherical triangles. Over each elementary area, we define a representative fibre direction and a discrete fibre density. Then, the strain energy of all the fibres distributed over each elementary area is approximated based on the deformation of the representative fibre direction weighted by the corresponding discrete fibre density. A summation of fibre contributions over all elementary areas then yields the resultant fibre strain energy. This treatment allows us to exclude fibres under compression in a discrete manner by evaluating the tension-compression status of the representative fibre directions only. We have implemented this model in a finite-element programme and illustrate it with three representative examples, including simple tension and simple shear of a unit cube, and non-homogeneous uniaxial extension of a rectangular strip. The results of all three examples are consistent and accurate compared with the previously developed continuous fibre dispersion model, and that is achieved with a substantial reduction of computational cost.

The use of small angle light scattering in assessing strain induced collagen degradation in arterial tissue ex vivo

Collagen is the predominant load bearing component in many soft tissues including arterial tissue and is therefore critical in determining the mechanical integrity of such tissues. Degradation of collagen fibres is hypothesized to be a strain dependent process whereby the rate of degradation is affected by the magnitude of strain applied to the collagen fibres. The aim of this study is to investigate the ability of small angle light scattering (SALS) imaging to identify strain dependent degradation of collagen fibres in arterial tissue ex vivo, and determine whether a strain induced protection mechanism exists in arterial tissue as observed in pure collagen and other collagenous tissues. SALS was used in combination with histological and second harmonic generation (SHG) analysis to determine the collagen fibre architecture in arterial tissue subjected to strain directed degradation. SALS alignment analysis identified statistically significant differences in fibre alignment depending on the strain magnitude applied to the tissue. These results were also observed using histology and SHG. Our findings suggest a strain protection mechanism may exist for arterial collagen at intermediate strain magnitudes between 0% and 25%. These findings may have implications for the onset and progression of arterial disease where changes in the mechanical environment of arterial tissue may lead to changes in the collagen degradation rate.

Magic angles and fibre stretch in arterial tissue: Insights from the linear theory

This work is motivated by the current widespread interest in modelling the mechanical response of arterial tissue. A widely used approach within the context of anisotropic nonlinear elasticity is to use an orthotropic incompressible hyperelasticity model which, in general, involves a strain-energy density that depends on seven independent invariants. The complexity of such an approach in its full generality is daunting and so a number of simplifications have been introduced in the literature to facilitate analytical tractability. An extremely popular model of this type is where the strain energy involves only three invariants. While such models and their generalisations have been remarkably successful in capturing the main features of the mechanical response of arterial tissue, it is generally acknowledged that such simplified models must also have some drawbacks. In particular, it is intuitively clear that the correlation of such models with experiment will suffer limitations due to the restricted number of invariants considered. Our purpose here is to use the linearised theory for infinitesimal deformations to provide some guidelines for the development of a more robust nonlinear theory. The linearised theory for incompressible orthotropic materials is developed and involves six independent elastic constants. The general stress-strain law is inverted to provide an expression for the fibre stretch in terms of the stress. We examine the linearised response for simple tension in two mutually perpendicular directions corresponding to the axial and circumferential directions in the artery, obtaining an explicit expression for the fibre stretch in terms of the applied tension, fibre angle and linear elastic constants. The focus is then on determining the range of fibre orientation angles that ensure that the fibres are in tension in these simple tension tests. It is shown that the fibre stretch is positive for both simple tension tests if and only if the fibre angle is restricted to lie between two special angles called generalised magic angles. For the special case where the strain-energy function for the nonlinear model depends only on the three invariants I₁,I₄,I₆, it is shown that the corresponding linearised model, called the standard linear model (SLM), depends on three elastic constants and the fibre stretch is positive only in the small range of fibre angles between the classic magic angles 35.26° and 54.74°. However, when the two additional invariants I₅,I₇ are included in the nonlinear strain energy so that the corresponding linear model involves four elastic constants, it is shown that the domain of fibre angle for which the stretch is positive is much larger and that the fibre stretch is monotonic with respect to the fibre angle in this range.

Biomechanical relevance of the microstructure in artery walls with a focus on passive and active components

The microstructure of arteries, consisting, in particular, of collagen, elastin, and vascular smooth muscle cells, plays a very significant role in their biomechanical response during a cardiac cycle. In this article, we highlight the microstructure and the contributions of each of its components to the overall mechanical behavior. We also describe the changes of the microstructure that occur as a result of abdominal aortic aneurysms and disease, such as atherosclerosis. We also focus on how the passive and active constituents are incorporated into a mathematical model without going into detail of the mathematical formulation. We conclude by mentioning open problems toward a better characterization of the biomechanical aspects of arteries that will be beneficial for a better understanding of cardiovascular pathophysiology.

Assessing Collagen and Elastin Pressure-dependent Microarchitectures in Live, Human Resistance Arteries by Label-free Fluorescence Microscopy

The pathogenic contribution of resistance artery remodeling is documented in essential hypertension, diabetes and the metabolic syndrome. Investigations and development of microstructurally motivated mathematical models for understanding the mechanical properties of human resistance arteries in health and disease have the potential to aid understanding how disease and medical treatments affect the human microcirculation. To develop these mathematical models, it is essential to decipher the relationship between the mechanical and microarchitectural properties of the microvascular wall. In this work, we describe an ex vivo method for passive mechanical testing and simultaneous label-free three-dimensional imaging of the microarchitecture of elastin and collagen in the arterial wall of isolated human resistance arteries. The imaging protocol can be applied to resistance arteries of any species of interest. Image analyses are described for quantifying i) pressure-induced changes in internal elastic lamina branching angles and adventitial collagen straightness using Fiji and ii) collagen and elastin volume densities determined using Ilastik software. Preferably all mechanical and imaging measurements are performed on live, perfused arteries, however, an alternative approach using standard video-microscopy pressure myography in combination with post-fixation imaging of re-pressurized vessels is discussed. This alternative method provides users with different options for analysis approaches. The inclusion of the mechanical and imaging data in mathematical models of the arterial wall mechanics is discussed, and future development and additions to the protocol are proposed.

Evaluation of microstructurally motivated constitutive models to describe age-dependent tendon healing

Tendon injuries are common to all ages. Injured tendons typically do not recover full functionality. The amount and organization of tendon constituents dictate their mechanical properties. The impact of changes in these constituents during (patho)physiologic processes (e.g., aging and healing) are not fully understood. Toward this end, microstructurally motivated strain energy functions (SEFs) offer insight into underlying mechanisms of age-dependent healing. Several SEFs have been adapted for tendon; however, most are phenomenological. Therefore, the aims of this study are: (1) evaluate the descriptive capability of SEFs in age-dependent murine patellar tendon healing and (2) identify a SEF for implementation in a growth and remodeling (G&R) model. To accomplish these aims, models were fitted to patellar tendon tensile data from multiple age groups and post-injury timepoints. Model sensitivity to parameters and the determinability of the parameters were assessed. A two-way analysis of variance was used to identify changes in parameters and the feasibility of implementing each model into a G&R model is discussed. The evaluated SEFs exhibited adequate descriptive capability. Parameter determinability and sensitivity analysis, however, highlighted the need for additional data to inform and validate the models to increase physiologic relevance and enable G&R model formulation to determine underlying mechanisms of age-dependent healing. This work, as a first, evaluated changes in tendon mechanical properties both as functions of age and injury in an age-dependent manner using microstructurally motivated models, highlights inherent dependencies between parameters of widely used hyperelastic models, and identified unique post-injury behavior by the aging group compared to the mature and aged groups.

3D Fiber Orientation in Atherosclerotic Carotid Plaques

Atherosclerotic plaque rupture is the primary trigger of fatal cardiovascular events. Fibrillar collagen in atherosclerotic plaques and their directionality are anticipated to play a crucial role in plaque rupture. This study aimed assessing 3D fiber orientations and architecture in atherosclerotic plaques for the first time. Seven carotid plaques were imaged ex-vivo with a state-of-the-art Diffusion Tensor Imaging (DTI) technique, using a high magnetic field (9.4Tesla) MRI scanner. A 3D spin-echo sequence with uni-polar diffusion sensitizing pulsed field gradients was utilized for DTI and fiber directions were assessed from diffusion tensor measurements. The distribution of the 3D fiber orientations in atherosclerotic plaques were quantified and the principal fiber orientations (circumferential, longitudinal or radial) were determined. Overall, 52% of the fiber orientations in the carotid plaque specimens were closest to the circumferential direction, 34% to the longitudinal direction, and 14% to the radial direction. Statistically no significant difference was measured in the amount of the fiber orientations between the concentric and eccentric plaque sites. However, concentric plaque sites showed a distinct structural organization, where the principally longitudinally oriented fibers were closer to the luminal side and the principally circumferentially oriented fibers were located more abluminally. The acquired unique information on 3D plaque fiber direction will help understanding pathobiological mechanisms of atherosclerotic plaque progression and pave the road to more realistic biomechanical plaque modeling for rupture assessment.

On arterial fiber dispersion and auxetic effect

There are two polar contemporary approaches to the constitutive modeling of arterial wall with anisotropy induced by collagen fibers. The first one is based on the angular integration (AI) of the strain energy on a unit sphere for the analytically defined fiber dispersion. The second one is based on the introduction of the generalized structure tensors (GST). AI approach is very involved computationally while GST approach requires somewhat complicated procedure for the exclusion of compressed fibers. We present some middle ground models, which are based on the use of 16 and 8 structure tensors. These models are moderately involved computationally and they allow excluding compressed fibers easily. We use the proposed models to study the role of the fiber dispersion in the constitutive modeling of the arterial wall. Particularly, we study the auxetic effect which can appear in anisotropic materials. The effect means thickening of the tissue in the direction perpendicular to its stretching. Such an effect was not observed in experiments while some simple anisotropic models do predict it. We show that more accurate account of the fiber dispersion suppresses the auxetic effect in a qualitative agreement with experimental observations.

A validated 3D microstructure-based constitutive model of coronary artery adventitia

A structure-based model that accurately predicts micro- or macromechanical behavior of blood vessels is necessary to understand vascular physiology. Based on recently measured microstructural data, we propose a three-dimensional microstructural model of coronary adventitia that incorporates the elastin and collagen distributions throughout the wall. The role of ground substance was found to be negligible under physiological axial stretch λz = 1.3, based on enzyme degradation of glycosaminoglycans in swine coronary adventitia (n = 5). The thick collagen bundles of outer adventitia (n = 4) were found to be undulated and unengaged at physiological loads, whereas the inner adventitia consisted of multiple sublayers of entangled fibers that bear the majority of load at higher pressures. The microstructural model was validated against biaxial (inflation and extension) experiments of coronary adventitia (n = 5). The model accurately predicted the nonlinear responses of the adventitia, even at high axial force (axial stretch ratio λz = 1.5). The model also enabled a reliable estimation of material parameters of individual fibers that were physically reasonable. A sensitivity analysis was performed to assess the effect of using mean values of the distributions for fiber orientation and waviness as opposed to the full distributions. The simplified mean analysis affects the fiber stress-strain relation, resulting in incorrect estimation of mechanical parameters, which underscores the need for measurements of fiber distribution for a rigorous analysis of fiber mechanics. The validated structure-based model of coronary adventitia provides a deeper understanding of vascular mechanics in health and can be extended to disease conditions.