Full length articleMicrostructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery
Graphical abstract
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 denoting an arbitrary vector in the 3D space, the Bingham ODF readswhere Z is a diagonal matrix with eigenvalues
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 () and inner diameter () are higher in the proximal region than in the distal one ( [mm] and [mm] & [mm] and [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 (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).
References (45)
- et al.
Anisotropic micro-sphere-based finite elasticity applied to blood vessel modelling
J. Mech. Phys. Solids
(2009) - et al.
On the use of bingham statistical distribution in microsphere-based constitutive models of arterial tissue
Mech. Res. Commun.
(2010) - et al.
Experimental study and constitutive modelling of the passive mechanical properties of the porcine carotid artery and its relation to histological analysis. Implications in animal cardiovascular device trials
Med. Eng. Phys.
(2011) - et al.
Spatial orientation of collagen fibers in the abdominal aortic aneurysm’s wall and its relation to wall mechanics
Acta Biomater.
(2012) A structural theory for the homogeneous biaxial stress-strain relationship in flat collageneous tissues
J. Biomech.
(1979)- et al.
Two-dimensional mechanical properties of rabbit skin-I. Experimental system
J. Biomech.
(1974) - et al.
Regional differences in mechanical properties between major arteries: an experimental study in sheep
Eur. J. Vasc. Endovasc. Surg.
(1996) - et al.
A constitutive model for vascular tissue that integrates fibril, fiber and continuum levels
J. Biomech.
(2011) - et al.
The three-dimensional micro- and nanostructure of the aortic medial lamellar unit measured using 3D confocal and electron microscopy imaging
Matrix Biol.
(2008) - et al.
Structure-based constitutive model can accurately predict planar biaxial properties of aortic wall tissue
Acta Biomater.
(2015)
A strain energy function for arteries accounting for wall composition and structure
Biophys. J.
Analysis of the passive mechanical properties of rat carotid arteries
J. Biomech.
Review. biomechanical factors in the biology of aortic wall and aortic valve diseases
Cardiovasc. Res.
An antipodally symmetric distribution on the sphere
Ann. Stat.
Measurements from light and polarised light microscopy of human coronary arteries fixed at distending pressure
Cardiovasc. Res.
Regional structural and biomechanical alternations of the ovine main pulmonary artery during postnatal growth
J. Biomech. Eng.
Three-dimensional collagen organization of human brain arteries at different transmural pressures
J. Vasc. Res.
Biomechanics. Mechanical Properties of Living Tissues
Elasticity of soft tissues in simple elongation
Am. J. Physiol.
Hyperelastic modelling of arterial layers with distributed collagen fibre orientations
J. R. Soc. Interface
Constructing fully symmetric cubature formulae for the sphere
Math. Comput.
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These two authors contributed equally to this work.