Elsevier

Acta Biomaterialia

Volume 33, 15 March 2016, Pages 183-193
Acta Biomaterialia

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

https://doi.org/10.1016/j.actbio.2016.01.030Get rights and content

Abstract

Background

Mechanical characteristics of vascular tissue may play a role in different arterial pathologies, which, amongst others, requires robust constitutive descriptions to capture the vessel wall’s anisotropic and non-linear properties.Specifically, the complex 3D network of collagen and its interaction with other structural elements has a dominating effect of arterial properties at higher stress levels.The aim of this study is to collect quantitative collagen organization as well as mechanical properties to facilitate structural constitutive models for the porcine carotid artery.This helps the understanding of the mechanics of swine carotid arteries, being a standard in clinical hypothesis testing, in endovascular preclinical trials for example.

Method

Porcine common carotid arteries (n = 10) were harvested and used to (i) characterize the collagen fiber organization with polarized light microscopy, and (ii) the biaxial mechanical properties by inflation testing.The collagen organization was quantified by the Bingham orientation density function (ODF), which in turn was integrated in a structural constitutive model of the vessel wall.A one-layered and thick-walled model was used to estimate mechanical constitutive parameters by least-square fitting the recorded in vitro inflation test results.Finally, uniaxial data published elsewhere were used to validate the mean collagen organization described by the Bingham ODF.

Results

Thick collagen fibers, i.e.the most mechanically relevant structure, in the common carotid artery are dispersed around the circumferential direction.In addition, almost all samples showed two distinct families of collagen fibers at different elevation, but not azimuthal, angles.Collagen fiber organization could be accurately represented by the Bingham ODF (κ1,2,3=[13.5,0.0,25.2] and κ1,2,3=[14.7,0.0,26.6]; average error of about 5%), and their integration into a structural constitutive model captured the inflation characteristics of individual carotid artery samples.Specifically, only four mechanical parameters were required to reasonably (average error from 14% to 38%) cover the experimental data over a wide range of axial and circumferential stretches.However, it was critical to account for fibrilar links between thick collagen fibers.Finally, the mean Bingham ODF provide also good approximation to uniaxial experimental data.

Conclusions

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, the collagen fiber orientations measured from polarized light microscopy, alone, seem to be insufficient structural information. Alternatively, a larger dispersion of collagen fiber orientations, that is likely to arise from analyzing larger wall sections, could have had a similar effect, i.e. could have avoided coupling amongst thick collagen fibers.

Statement of Significance

The applied structural constitutive model, based on individually measured collagen orientation densities, was able to capture the biaxial and uniaxial properties of the common carotid artery. Since the model required coupling amongst thick collagen fibers, an effective orientation density that accounts for cross-links between the main collagen fibers has been porposed. The model provides a good approximation to the experimental data.

Introduction

Although health care systems have made great strides in reducing death rates associated with cardiovascular diseases, vascular events are still ranked amongst the main mortality causes in the western world. It is known that onset and progression of cardiovascular diseases are associated with the alteration of the biomechanical properties of cardiovascular tissues [3]. Consequently, some of the variables describing this mechanical behavior such as stress and strain may play a role in different arterial pathologies or some evolutive processes as tissue growth and remodeling [9], [18].

Mechanical characteristics of vascular tissue may play a role in different arterial pathologies. Besides vascular smooth muscle cells (VSMC), the extracellular matrix proteins collagen and elastin play a central role in the biomechanics of vascular tissue, i.e. their spatial organization and their interaction dominate the macroscopic non-linear vessel properties. While elastin provides elasticity and determines low-strain vessel properties, collagen protects the wall from overtretching and contributes mainly to the walls properties at higher strains [29]. However, the collagen fibers are not individually placed along the arteries, they are connected each other, therefore it is important modeling the contribution of both collagen fibrils and the linkers between them. Most importantly, by a continuous turn over of VSMC and collagen, the tissue microstructure adapts to its mechanical environment/needs (see for example [17]), which naturally has significant implications on the physiological vessel performance. Vessel wall adaptation to mechanical needs also explains the reported intraspecies and interspecies variabilities of structural and mechanical properties [11], [21], [34].

Finite strains constitutive descriptions are needed that reliably capture the vessel wall’s anisotropic and non-linear properties. Many constitutive models are based on a strain energy function (SEF), i.e. a mathematical description of vessel wall properties, which in turn is calibrated to data from experimental vessel wall characterization. While phenomenological SEFs are purely based on mechanical input information, structural SEFs integrate also microstructural histological data. Most importantly, structural SEFs allocate macroscopic stress to different micro-structural components, and are able to link the macroscopic loading to potential cellular responses. Structural SEFs for the vessel wall are based on fiber-reinforced composite concepts, which assume straight and parallel-aligned [16], [33], [40], straight and orientation-dispersed [1], [13], undulated and parallel-aligned [39], [40], or undulated and orientation-dispersed [19], [23] (families of) fibers. Despite the fact that considerable work has been dedicated to develop and numerically implement structural SEFs, only very few studies consistently validated structural SEFs, i.e. by treating histological and mechanical input information strictly separately [12], [15], [26], [37]. In contrast, most studies estimated both histological and mechanical model parameters from mechanical experimental data, i.e. they did not consider appropriate microstructural information.

The ability to get detailed fiber orientation [6], [8], [27] and recruitment [7] data makes structural SEFs all the more relevant, such that structural and mechanical model parameters can be separately identified by histological and mechanical experiments, respectively. Specifically, inflation [35], [38], planar biaxial [20], [24] and uniaxial [11], [32] testing are preferable in vitro mechanical test protocols for vascular tissue. Here, animal models remain popular in clinical hypothesis testing, where specifically the pig carotid artery has a central role. In the case of stenting techniques, common carotid or coronary swine arteries are broadly employed to test the features of these devices. Additionally, the use of animal tissue allow us to collect a sufficient number of coherent wall specimens, i.e. a sample size large enough for sound statistical data analysis.

The aim of this study is to collect quantitative information of the collagen fiber organization in the wall of the porcine carotid artery. Subsequently, this information is incorporated in a structural SEF, and mechanical model parameters were calibrated by leased-square optimization of model prediction and in vitro vessel inflation experiments. Due to the applied structural constitutive modeling approach we hypothesize that the estimated material parameters reflect the properties of the microstructural components elastin and collagen. The structural information obtained through this study will not only improve our biomechanical understanding of the carotid artery, but also be helpful input information for continuum biomechanics-based simulations.

Section snippets

Tissue harvesting

Left and right common carotid arteries (see Fig. 1) were dissected from 10 female pigs (mean age: 3.5 months, SD 0.4 months). Animals did not present any pathology and were not used in any other experimental study. The animals were euthanized under general anesthesia through an intravenous injection of potassium chloride and sodium thiopental, and the carotid arteries were harvested by skilled veterinarians. Mechanical and histological samples preparation started within 24 h, and until then, the

Orientation distribution function of the collagen

Besides the Lambert equal area projection [5] also the Bingham orientation distribution function (ODF) [4] was used to analyze the collagen orientation distribution. The Bingham ODF allows to represent a wide range of orientation distributions with the von Mises distribution (for example used in [13]) being a particular case.

With r denoting an arbitrary vector in the 3D space, the Bingham ODF readsρ(r;Z,Q)dA4π=[F000(Z)]-1exp(tr(Z·QT·r·rT·Q))dA4π,where Z is a diagonal matrix with eigenvalues κ1,2

Artery dimensions

Wall thickness (range: 0.47–0.89 [mm]) and inner diameter (range: 3.46–5.12 [mm]) of the unloaded carotid artery samples are shown in Table 1. In all cases, wall thickness (p=0.022) and inner diameter (p=0.016) are higher in the proximal region than in the distal one (0.70±0.13 [mm] and 4.52±0.57 [mm] & 0.52±0.04 [mm] and 3.77±1.26 [mm]).

Collagen fibers orientation

Lambert equal area projections of the measured collagen fiber orientations are shown in Fig. 4. Lambert equal area projection is stereographic mapping that projects

Discussion

In this study, polarized light microscopy and in vitro inflation experiments were used for histological and mechanical characterizations of the common carotid artery. To this end the measured collagen fiber orientation distribution was integrated in a structural constitutive model of the artery wall, and mechanical model parameters were estimated through least square fitting the recordings from the inflation experiment. Note that type I and densely packed type III collagen fibers show similar

Conclusions

The present study found that thick collagen fibers in the porcine common carotid artery are dispersed around the circumferential direction. Integrating this information in a structural constitutive model allowed it to reflect the inflation characteristics of individual carotid artery samples. Specifically, only four mechanical parameters were required to cover the experimental data reasonable over a wide range of axial and circumferential stretches. Noticeably, the coupling parameter α (one out

Acknowledgements

Financial support for this research was provided by the Spanish Ministry of Economy and Competitiveness through research project DPI2013-44391-P and the Instituto de Salud Carlos III (ISCIII) through the CIBER initiative. Finally, we also thank the Spanish Ministry of Science and Technology for the financial support to A. García (BES-2008-002951) and to P. Sáez (BES-2009-028593).

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