title: Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery.
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.
  
  
  METHODS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain; Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA.
authors.forename: P
authors.initials: P
authors.lastname: Sáez
authors.affiliation: Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain; Department of Chemistry, Materials and Chemical Engineering "Giulio Natta", Politecnico di Milano, Italy.
authors.forename: A
authors.initials: A
authors.lastname: García
authors.affiliation: Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain; CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain.
authors.forename: E
authors.initials: E
authors.lastname: Peña
authors.affiliation: Department of Solid Mechanics, Royal Institute of Technology, Stockholm, Sweden.
authors.forename: T C
authors.initials: TC
authors.lastname: Gasser
authors.affiliation: Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain; CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Zaragoza, Spain. Electronic address: miguelam@unizar.es.
authors.forename: M A
authors.initials: MA
authors.lastname: Martínez
mesh_terms: D000818:Animals; D002339:Carotid Arteries / Q000033:anatomy & histology / Q000502:physiology*; D003094:Collagen / Q000737:chemistry*; D005260:Female; D008954:Models, Biological; D008955:Models, Cardiovascular; D013314:Stress, Mechanical; D034421:Sus scrofa; D013718:Tensile Strength
chemical_list: D003094:Collagen
keywords: Carotid artery; Collagen distribution; Micro-sphere; Polarized light