Viscoelastic properties of the passive mechanical behavior of the porcine carotid artery: influence of proximal and distal positions.

The viscoelastic properties of porcine carotid tissue are investigated in this work. Experimental uniaxial stress relaxation tests along the longitudinal and circumferential directions of the vessel were performed for carotid strips extracted from 10 vessels. Directional and local differences--distal versus proximal position--in the tissue behavior were investigated. The experimental tests reveal a highly anisotropic, non-linear viscoelastic response and local dependence of the samples. The carotid artery shows anisotropic relaxation behavior for both proximal and distal samples. The highest stress relaxation was found in the circumferential tensile test for the highest applied strain at the distal position. For the circumferential direction, the relaxation stress was higher than in the longitudinal being at its highest in the distal position. These facts show that the stress relaxation is higher in the distal than in the proximal position. However, there are no differences between both positions in the longitudinal direction. In addition, a constitutive law that takes into account the fundamental features, including non-linear viscoelasticity, of the arterial tissue is proposed. The present results are correlated with the purely elastic response and the microstructural analysis of the tissue by means of histological quantification presented in a previous study.

[1]  T Christian Gasser,et al.  Numerical simulation of the failure of ventricular tissue due to deep penetration: the impact of constitutive properties. , 2011, Journal of biomechanics.

[2]  R Armentano,et al.  Effects of hypertension on viscoelasticity of carotid and femoral arteries in humans. , 1995, Hypertension.

[3]  A. Ibrahimbegovic Nonlinear Solid Mechanics , 2009 .

[4]  D. Foran,et al.  Mechanical Behavior of Vessel Wall: A Comparative Study of Aorta, Vena Cava, and Carotid Artery , 2003, Annals of Biomedical Engineering.

[5]  M Doblaré,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. , 2011, Medical engineering & physics.

[6]  A Natali,et al.  Viscoelastic Response of the Periodontal Ligament: An Experimental–Numerical Analysis , 2004, Connective tissue research.

[7]  Johannes A. G. Rhodin,et al.  Architecture of the Vessel Wall , 1980 .

[8]  G. Guinea,et al.  Thermomechanical behavior of human carotid arteries in the passive state. , 2005, American journal of physiology. Heart and circulatory physiology.

[9]  Manuel Doblaré,et al.  Experimental study and constitutive modelling of the passive mechanical properties of the ovine infrarenal vena cava tissue. , 2008, Journal of biomechanics.

[10]  R. Ogden,et al.  Hyperelastic modelling of arterial layers with distributed collagen fibre orientations , 2006, Journal of The Royal Society Interface.

[11]  T. R. Hughes,et al.  Mathematical foundations of elasticity , 1982 .

[12]  G. Holzapfel,et al.  A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis , 2002 .

[13]  J. M. Goicolea,et al.  On thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic solids with application to biomechanics , 2007 .

[14]  G S Kassab,et al.  Shear modulus of porcine coronary artery: contributions of media and adventitia. , 2003, American journal of physiology. Heart and circulatory physiology.

[15]  M. Barber Symptoms and Outcome Measures of Pelvic Organ Prolapse , 2005, Clinical obstetrics and gynecology.

[16]  M. Puso,et al.  Finite element implementation of anisotropic quasilinear viscoelasticity , 1995 .

[17]  H. Haslach,et al.  The Influence of Medial Substructures on Rupture in Bovine Aortas , 2011 .

[18]  J. C. Simo,et al.  On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects , 1987 .

[19]  M. Doblaré,et al.  Computational Modelling of Diarthrodial Joints. Physiological, Pathological and Pos-Surgery Simulations , 2007 .

[20]  Yanina Zócalo Germán,et al.  An in vitro study of cryopreserved and fresh human arteries: a comparison with ePTFE prostheses and human arteries studied non-invasively in vivo. , 2006, Cryobiology.

[21]  B. S. Gow,et al.  Measurement of Viscoelastic Properties of Arteries in the Living Dog , 1968, Circulation research.

[22]  P. Dobrin,et al.  Elastase, collagenase, and the biaxial elastic properties of dog carotid artery. , 1984, The American journal of physiology.

[23]  R. Ogden,et al.  A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models , 2000 .

[24]  D. Letourneur,et al.  Mechanical properties of rat thoracic and abdominal aortas. , 2008, Journal of biomechanics.

[25]  Ghassan S Kassab,et al.  A rate-insensitive linear viscoelastic model for soft tissues. , 2007, Biomaterials.

[26]  H. Haslach,et al.  Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue , 2005, Biomechanics and modeling in mechanobiology.

[27]  Yanhang Zhang,et al.  The orthotropic viscoelastic behavior of aortic elastin , 2011, Biomechanics and modeling in mechanobiology.

[28]  Boumediene Nedjar,et al.  An anisotropic viscoelastic fibre–matrix model at finite strains: Continuum formulation and computational aspects , 2007 .

[29]  Gerhard A. Holzapfel,et al.  A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications , 2001 .

[30]  J D Humphrey,et al.  Heat-induced changes in the mechanical behavior of passive coronary arteries. , 1995, Journal of biomechanical engineering.

[31]  G. Kassab,et al.  Variation of mechanical properties along the length of the aorta in C57bl/6 mice. , 2003, American journal of physiology. Heart and circulatory physiology.

[32]  Thibault P. Prevost,et al.  Biomechanics of brain tissue. , 2011, Acta biomaterialia.

[33]  Gerhard Sommer,et al.  Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling. , 2005, American journal of physiology. Heart and circulatory physiology.

[34]  Damian Craiem,et al.  Fractional-order viscoelasticity applied to describe uniaxial stress relaxation of human arteries , 2008, Physics in medicine and biology.

[35]  M Doblaré,et al.  On modelling nonlinear viscoelastic effects in ligaments. , 2008, Journal of biomechanics.

[36]  Estefanía Peña,et al.  A formulation to model the nonlinear viscoelastic properties of the vascular tissue , 2011 .

[37]  Y. Fung,et al.  Biomechanics: Mechanical Properties of Living Tissues , 1981 .

[38]  Manuel Doblaré,et al.  Numerical framework for patient‐specific computational modelling of vascular tissue , 2010 .

[39]  V. Barocas,et al.  Effects of Freezing and Cryopreservation on the Mechanical Properties of Arteries , 2006, Annals of Biomedical Engineering.

[40]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[41]  E Peña,et al.  Influence of geometrical parameters on radial force during self-expanding stent deployment. Application for a variable radial stiffness stent. , 2012, Journal of the mechanical behavior of biomedical materials.

[42]  M Doblaré,et al.  A constitutive formulation of vascular tissue mechanics including viscoelasticity and softening behaviour. , 2010, Journal of biomechanics.

[43]  F H Silver,et al.  Viscoelasticity of the vessel wall: the role of collagen and elastic fibers. , 2001, Critical reviews in biomedical engineering.

[44]  J. Merodio,et al.  On Constitutive Equations For Anisotropic Nonlinearly Viscoelastic Solids , 2006 .

[45]  A.J.M. Spencer,et al.  Theory of invariants , 1971 .

[46]  Manuel Doblaré,et al.  An anisotropic visco-hyperelastic model for ligaments at finite strains. Formulation and computational aspects , 2007 .

[47]  D. Pioletti,et al.  Non-linear viscoelastic laws for soft biological tissues , 2000 .

[48]  S. Hatzikiriakos,et al.  Effect of deformation rate on the mechanical properties of arteries , 2010 .

[49]  Ray Vanderby,et al.  Viscoelastic Relaxation and Recovery of Tendon , 2009, Annals of Biomedical Engineering.

[50]  L. Kasakov,et al.  Age dependent changes of arterial wall viscoelasticity. , 2008, Clinical hemorheology and microcirculation.