0
Research Papers

Sensitivity of Arterial Hyperelastic Models to Uncertainties in Stress-Free Measurements

[+] Author and Article Information
Nir Emuna

Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 32000, Israel
e-mail: emuna@campus.technion.ac.il

David Durban

Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 32000, Israel
e-mail: aer6903@technion.ac.il

Shmuel Osovski

Faculty of Mechanical Engineering,
Technion—Israel Institute of Technology,
Haifa 32000, Israel
e-mail: osovski.technion@gmail.com

Manuscript received November 9, 2017; final manuscript received May 4, 2018; published online July 2, 2018. Assoc. Editor: Seungik Baek.

J Biomech Eng 140(10), 101013 (Jul 02, 2018) (13 pages) Paper No: BIO-17-1516; doi: 10.1115/1.4040400 History: Received November 09, 2017; Revised May 04, 2018

Despite major advances made in modeling vascular tissue biomechanics, the predictive power of constitutive models is still limited by uncertainty of the input data. Specifically, key measurements, like the geometry of the stress-free (SF) state, involve a definite, sometimes non-negligible, degree of uncertainty. Here, we introduce a new approach for sensitivity analysis of vascular hyperelastic constitutive models to uncertainty in SF measurements. We have considered two vascular hyperelastic models: the phenomenological Fung model and the structure-motivated Holzapfel–Gasser–Ogden (HGO) model. Our results indicate up to 160% errors in the identified constitutive parameters for a 5% measurement uncertainty in the SF data. Relative margins of errors of up to 30% in the luminal pressure, 36% in the axial force, and over 200% in the stress predictions were recorded for 10% uncertainties. These findings are relevant to the large body of studies involving experimentally based modeling and analysis of vascular tissues. The impact of uncertainties on calibrated constitutive parameters is significant in context of studies that use constitutive parameters to draw conclusions about the underlying microstructure of vascular tissues, their growth and remodeling processes, and aging and disease states. The propagation of uncertainties into the predictions of biophysical parameters, e.g., force, luminal pressure, and wall stresses, is of practical importance in the design and execution of clinical devices and interventions. Furthermore, insights provided by the present findings may lead to more robust parameters identification techniques, and serve as selection criteria in the trade-off between model complexity and sensitivity.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Humphrey, J. D. , 2008, “ Vascular Adaptation and Mechanical Homeostasis at Tissue, Cellular, and Sub-Cellular Levels,” Cell Biochem. Biophys., 50(2), pp. 53–78. [CrossRef] [PubMed]
Wicker, B. , Hutchens, H. , Wu, Q. , Yeh, A. , and Humphrey, J. , 2008, “ Normal Basilar Artery Structure and Biaxial Mechanical Behaviour,” Comput. Methods Biomech. Biomed. Eng., 11(5), pp. 539–551. [CrossRef]
O'Rourke, M. , 1990, “ Arterial Stiffness, Systolic Blood Pressure, and Logical Treatment of Arterial Hypertension,” Hypertension, 15(4), pp. 339–347. [CrossRef] [PubMed]
Vorp, D. A. , and Geest, J. P. V. , 2005, “ Biomechanical Determinants of Abdominal Aortic Aneurysm Rupture,” Arterioscler., Thromb., Vasc. Biol., 25(8), pp. 1558–1566. [CrossRef]
Vande Geest, J. P. , Sacks, M. S. , and Vorp, D. A. , 2006, “ The Effects of Aneurysm on the Biaxial Mechanical Behavior of Human Abdominal Aorta,” J. Biomech., 39(7), pp. 1324–1334. [CrossRef] [PubMed]
Rodriguez, J. F. , Ruiz, C. , Doblare, M. , and Holzapfel, G. A. , 2008, “ Mechanical Stresses in Abdominal Aortic Aneurysms: Influence of Diameter, Asymmetry, and Material Anisotropy,” ASME J. Biomech. Eng., 130(2), p. 021023. [CrossRef]
Eberth, J. F. , Taucer, A. I. , Wilson, E. , and Humphrey, J. D. , 2009, “ Mechanics of Carotid Arteries in a Mouse Model of Marfan Syndrome,” Ann. Biomed. Eng., 37(6), pp. 1093–1104. [CrossRef] [PubMed]
Holzapfel, G. A. , 2009, “ Arterial Tissue in Health and Disease: Experimental Data, Collagen-Based Modeling and Simulation, Including Aortic Dissection,” Biomechanical Modelling at the Molecular, Cellular and Tissue Levels, Vol. 508, G. A. Holzapfel and R. W. Ogden , eds., Springer, Vienna, Austria, pp. 259–344. [CrossRef]
Ferruzzi, J. , Vorp, D. A. , and Humphrey, J. D. , 2010, “ On Constitutive Descriptors of the Biaxial Mechanical Behaviour of Human Abdominal Aorta and Aneurysms,” J. R. Soc. Interface, 8(56), pp. 435–450. [CrossRef] [PubMed]
Teng, Z. , Zhang, Y. , Huang, Y. , Feng, J. , Yuan, J. , Lu, Q. , Sutcliffe, M. P. F. , Brown, A. J. , Jing, Z. , and Gillard, J. H. , 2014, “ Material Properties of Components in Human Carotid Atherosclerotic Plaques: A Uniaxial Extension Study,” Acta Biomater., 10(12), pp. 5055–5063. [CrossRef] [PubMed]
Thondapu, V. , Bourantas, C. V. , Foin, N. , Jang, I.-K. , Serruys, P. W. , and Barlis, P. , 2016, “ Biomechanical Stress in Coronary Atherosclerosis: Emerging Insights From Computational Modelling,” Eur. Heart J., 38(2), pp. 81–92.
Rogers, C. , Tseng, D. Y. , Squire, J. C. , and Edelman, E. R. , 1999, “ Balloon-Artery Interactions During Stent Placement: A Finite Element Analysis Approach to Pressure, Compliance, and Stent Design as Contributors to Vascular Injury,” Circ. Res., 84(4), pp. 378–383. [CrossRef] [PubMed]
Holzapfel, G. A. , Stadler, M. , and Schulze-Bauer, C. A. J. , 2002, “ A Layer-Specific Three-Dimensional Model for the Simulation of Balloon Angioplasty Using Magnetic Resonance Imaging and Mechanical Testing,” Ann. Biomed. Eng., 30(6), pp. 753–767. [CrossRef] [PubMed]
Liang, D. K. , Yang, D. Z. , Qi, M. , and Wang, W. Q. , 2005, “ Finite Element Analysis of the Implantation of a Balloon-Expandable Stent in a Stenosed Artery,” Int. J. Cardiol., 104(3), pp. 314–318. [CrossRef] [PubMed]
Kiousis, D. E. , Wulff, A. R. , and Holzapfel, G. A. , 2009, “ Experimental Studies and Numerical Analysis of the Inflation and Interaction of Vascular Balloon Catheter-Stent Systems,” Ann. Biomed. Eng., 37(2), pp. 315–330. [CrossRef] [PubMed]
Prendergast, P. J. , Lally, C. , Daly, S. , Reid, A. J. , Lee, T. C. , Quinn, D. , and Dolan, F. , 2003, “ Analysis of Prolapse in Cardiovascular Stents: A Constitutive Equation for Vascular Tissue and Finite-Element Modelling,” ASME J. Biomech. Eng., 125(5), pp. 692–699. [CrossRef]
Lally, C. , Dolan, F. , and Prendergast, P. J. , 2005, “ Cardiovascular Stent Design and Vessel Stresses: A Finite Element Analysis,” J. Biomech., 38(8), pp. 1574–1581. [CrossRef] [PubMed]
Zahedmanesh, H. , and Lally, C. , 2009, “ Determination of the Influence of Stent Strut Thickness Using the Finite Element Method: Implications for Vascular Injury and in-Stent Restenosis,” Med. Biol. Eng. Comput., 47(4), pp. 385–393. [CrossRef] [PubMed]
Zahedmanesh, H. , John Kelly, D. , and Lally, C. , 2010, “ Simulation of a Balloon Expandable Stent in a Realistic Coronary Artery-Determination of the Optimum Modelling Strategy,” J. Biomech., 43(11), pp. 2126–2132. [CrossRef] [PubMed]
Holzapfel, G. A. , Stadler, M. , and Gasser, T. C. , 2005, “ Changes in the Mechanical Environment of Stenotic Arteries During Interaction With Stents: Computational Assessment of Parametric Stent Designs,” ASME J. Biomech. Eng., 127(1), pp. 166–180. [CrossRef]
Wu, W. , Wang, W.-Q. , Yang, D.-Z. , and Qi, M. , 2007, “ Stent Expansion in Curved Vessel and Their Interactions: A Finite Element Analysis,” J. Biomech., 40(11), pp. 2580–2585. [CrossRef] [PubMed]
Mortier, P. , Holzapfel, G. A. , Beule, M. D. , Loo, D. V. , Taeymans, Y. , Segers, P. , Verdonck, P. , and Verhegghe, B. , 2010, “ A Novel Simulation Strategy for Stent Insertion and Deployment in Curved Coronary Bifurcations: Comparison of Three Drug-Eluting Stents,” Ann. Biomed. Eng., 38(1), pp. 88–99. [CrossRef] [PubMed]
Martin, D. M. , Murphy, E. A. , and Boyle, F. J. , 2014, “ Computational Fluid Dynamics Analysis of Balloon-Expandable Coronary Stents: Influence of Stent and Vessel Deformation,” Med. Eng. Phys., 36(8), pp. 1047–1056. [CrossRef] [PubMed]
Antoniadis, A. P. , Mortier, P. , Kassab, G. , Dubini, G. , Foin, N. , Murasato, Y. , Giannopoulos, A. A. , Tu, S. , Iwasaki, K. , Hikichi, Y. , Migliavacca, F. , Chiastra, C. , Wentzel, J. J. , Gijsen, F. , Reiber, J. H. C. , Barlis, P. , Serruys, P. W. , Bhatt, D. L. , Stankovic, G. , Edelman, E. R. , Giannoglou, G. D. , Louvard, Y. , and Chatzizisis, Y. S. , 2015, “ Biomechanical Modeling to Improve Coronary Artery Bifurcation Stenting: Expert Review Document on Techniques and Clinical Implementation,” JACC: Cardiovasc. Interventions, 8(10), pp. 1281–1296. [CrossRef]
Gupta, B. S. , and Kasyanov, V. A. , 1997, “ Biomechanics of Human Common Carotid Artery and Design of Novel Hybrid Textile Compliant Vascular Grafts,” J. Biomed. Mater. Res., 34(3), pp. 341–349. [CrossRef] [PubMed]
Greenwald, S. E. , and Berry, C. L. , 2000, “ Improving Vascular Grafts: The Importance of Mechanical and Haemodynamic Properties,” J. Pathology, 190(3), pp. 292–299. [CrossRef]
Konig, G. , McAllister, T. N. , Dusserre, N. , Garrido, S. A. , Iyican, C. , Marini, A. , Fiorillo, A. , Avila, H. , Wystrychowski, W. , Zagalski, K. , Maruszewski, M. , Jones, A. L. , Cierpka, L. , de la Fuente, L. M. , and L'Heureux, N. , 2009, “ Mechanical Properties of Completely Autologous Human Tissue Engineered Blood Vessels Compared to Human Saphenous Vein and Mammary Artery,” Biomaterials, 30(8), pp. 1542–1550. [CrossRef] [PubMed]
McClure, M. J. , Sell, S. A. , Simpson, D. G. , Walpoth, B. H. , and Bowlin, G. L. , 2010, “ A Three-Layered Electrospun Matrix to Mimic Native Arterial Architecture Using Polycaprolactone, Elastin, and Collagen: A Preliminary Study,” Acta Biomater., 6(7), pp. 2422–2433. [CrossRef] [PubMed]
McClure, M. J. , Simpson, D. G. , and Bowlin, G. L. , 2012, “ Tri-Layered Vascular Grafts Composed of Polycaprolactone, Elastin, Collagen, and Silk: Optimization of Graft Properties,” J. Mech. Behav. Biomed. Mater., 10, pp. 48–61. [CrossRef] [PubMed]
Singh, C. , Wong, C. S. , and Wang, X. , 2015, “ Medical Textiles as Vascular Implants and Their Success to Mimic Natural Arteries,” J. Funct. Biomater., 6(3), pp. 500–525. [CrossRef] [PubMed]
Harrison, S. , Tamimi, E. , Uhlorn, J. , Leach, T. , and Geest, J. P. V. , 2016, “ Computationally Optimizing the Compliance of a Biopolymer Based Tissue Engineered Vascular Graft,” ASME J. Biomech. Eng., 138(1), p. 014505. [CrossRef]
Jia, Y. , Qiao, Y. , Ricardo Argueta-Morales, I. , Maung, A. , Norfleet, J. , Bai, Y. , Divo, E. , Kassab, A. J. , and DeCampli, W. M. , 2017, “ Experimental Study of Anisotropic Stress/Strain Relationships of Aortic and Pulmonary Artery Homografts and Synthetic Vascular Grafts,” ASME J. Biomech. Eng., 139(10), p. 101003. [CrossRef]
Keyes, J. T. , Lockwood, D. R. , Utzinger, U. , Montilla, L. G. , Witte, R. S. , and Geest, J. P. V. , 2013, “ Comparisons of Planar and Tubular Biaxial Tensile Testing Protocols of the Same Porcine Coronary Arteries,” Ann. Biomed. Eng., 41(7), pp. 1579–1591. [CrossRef] [PubMed]
Fung, Y. C. , 1991, “ What Are the Residual Stresses Doing in Our Blood Vessels?,” Ann. Biomed. Eng., 19(3), pp. 237–249. [CrossRef] [PubMed]
Holzapfel, G. A. , Gasser, T. C. , and Ogden, R. W. , 2000, “ A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models,” J. Elasticity Phys. Sci. Solids, 61, pp. 1–48. [CrossRef]
Humphrey, J. D. , 2002, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Springer, New York. [CrossRef]
Volokh, K. Y. , 2006, “ Stresses in Growing Soft Tissues,” Acta Biomater., 2(5), pp. 493–504. [CrossRef] [PubMed]
Holzapfel, G. A. , Sommer, G. , Auer, M. , Regitnig, P. , and Ogden, R. W. , 2007, “ Layer-Specific 3D Residual Deformations of Human Aortas With Non-Atherosclerotic Intimal Thickening,” Ann. Biomed. Eng., 35(4), pp. 530–545. [CrossRef] [PubMed]
Holzapfel, G. A. , and Ogden, R. W. , 2009, “ Modelling the Layer-Specific Three-Dimensional Residual Stresses in Arteries, With an Application to the Human Aorta,” J. R. Soc. Interface, 46, pp. 787–799.
Vaishnav, R. N. , and Vossoughi, J. , 1987, “ Residual Stress and Strain in Aortic Segments,” J. Biomech., 20(3), p. 239. [CrossRef]
Matsumoto, T. , and Hayashi, K. , 1996, “ Stress and Strain Distribution in Hypertensive and Normotensive Rat Aorta Considering Residual Strain,” ASME J. Biomech. Eng., 118(1), pp. 62–73. [CrossRef]
Bellini, C. , Ferruzzi, J. , Roccabianca, S. , DiMartino, E. , and Humphrey, J. , 2014, “ A Microstructurally Motivated Model of Arterial Wall Mechanics With Mechanobiological Implications,” Ann. Biomed. Eng., 42(3), pp. 488–502. [CrossRef] [PubMed]
Han, H. C. , and Fung, Y. C. , 1996, “ Direct Measurement of Transverse Residual Strains in Aorta,” Am. J. Physiol.-Heart Circ. Physiol., 270(2), pp. H750–H759. [CrossRef]
Takamizawa, K. , and Hayashi, K. , 1987, “ Strain Energy Density Function and Uniform Strain Hypothesis for Arterial Mechanics,” J. Biomech., 20(1), pp. 7–17. [CrossRef] [PubMed]
Kang, T. , and Humphrey, J. , 1991, “ Finite Deformation of an Inverted Artery,” Advances in Bioengineering, American Society of Mechanical Engineers, New York.
Sokolis, D. P. , 2015, “ Effects of Aneurysm on the Directional, Regional, and Layer Distribution of Residual Strains in Ascending Thoracic Aorta,” J. Mech. Behav. Biomed. Mater., 46, pp. 229–243. [CrossRef] [PubMed]
Sassani, S. G. , Kakisis, J. , Tsangaris, S. , and Sokolis, D. P. , 2015, “ Layer-Dependent Wall Properties of Abdominal Aortic Aneurysms: Experimental Study and Material Characterization,” J. Mech. Behav. Biomed. Mater., 49, pp. 141–161. [CrossRef] [PubMed]
Saini, A. , Berry, C. , and Greenwald, S. , 1995, “ Effect of Age and Sex on Residual Stress in the Aorta,” J. Vasc. Res., 32(6), pp. 398–405. [CrossRef] [PubMed]
Yuan, J. , Teng, Z. , Feng, J. , Zhang, Y. , Brown, A. J. , Gillard, J. H. , Jing, Z. , and Lu, Q. , 2015, “ Influence of Material Property Variability on the Mechanical Behaviour of Carotid Atherosclerotic Plaques: A 3D Fluid-Structure Interaction Analysis,” Int. J. Numer. Methods Biomed. Eng., 31(8), p. e02722.
Eck, V. G. , Feinberg, J. , Langtangen, H. P. , and Hellevik, L. R. , 2015, “ Stochastic Sensitivity Analysis for Timing and Amplitude of Pressure Waves in the Arterial System,” Int. J. Numer. Methods Biomed. Eng., 31(4), p. e02711.
Eck, V. G. , Donders, W. P. , Sturdy, J. , Feinberg, J. , Delhaas, T. , Hellevik, L. R. , and Huberts, W. , 2016, “ A Guide to Uncertainty Quantification and Sensitivity Analysis for Cardiovascular Applications,” Int. J. Numer. Methods Biomed. Eng., 32(8), p. e02755.
Biehler, J. , Kehl, S. , Gee, M. W. , Schmies, F. , Pelisek, J. , Maier, A. , Reeps, C. , Eckstein, H.-H. , and Wall, W. A. , 2016, “ Probabilistic Noninvasive Prediction of Wall Properties of Abdominal Aortic Aneurysms Using Bayesian Regression,” Biomech. Model. Mechanobiol., 16(1), pp. 1–17.
Eck, V. G. , Sturdy, J. , and Hellevik, L. R. , 2017, “ Effects of Arterial Wall Models and Measurement Uncertainties on Cardiovascular Model Predictions,” J. Biomech., 50, pp. 188–194. [CrossRef] [PubMed]
Chen, P. , Quarteroni, A. , and Rozza, G. , 2013, “ Simulation-Based Uncertainty Quantification of Human Arterial Network Hemodynamics,” Int. J. Numer. Methods Biomed. Eng., 29(6), pp. 698–721. [CrossRef]
Sankaran, S. , Kim, H. J. , Choi, G. , and Taylor, C. A. , 2016, “ Uncertainty Quantification in Coronary Blood Flow Simulations: Impact of Geometry, Boundary Conditions and Blood Viscosity,” J. Biomech., 49(12), pp. 2540–2547. [CrossRef] [PubMed]
Laz, P. J. , Stowe, J. Q. , Baldwin, M. A. , Petrella, A. J. , and Rullkoetter, P. J. , 2007, “ Incorporating Uncertainty in Mechanical Properties for Finite Element-Based Evaluation of Bone Mechanics,” J. Biomech., 40(13), pp. 2831–2836. [CrossRef] [PubMed]
Wille, H. , Rank, E. , and Yosibash, Z. , 2012, “ Prediction of the Mechanical Response of the Femur With Uncertain Elastic Properties,” J. Biomech., 45(7), pp. 1140–1148. [CrossRef] [PubMed]
Campoli, G. , Bolsterlee, B. , Helm, F. V. D. , Weinans, H. , and Zadpoor, A. A. , 2014, “ Effects of Densitometry, Material Mapping and Load Estimation Uncertainties on the Accuracy of Patient-Specific Finite-Element Models of the Scapula,” J. R. Soc. Interface, 11(93), p. 20131146. [CrossRef] [PubMed]
Gasser, T. C. , and Grytsan, A. , 2017, “ Biomechanical Modeling the Adaptation of Soft Biological Tissue,” Curr. Opin. Biomed. Eng., 1, pp. 71–77. [CrossRef]
Biehler, J. , Gee, M. W. , and Wall, W. A. , 2015, “ Towards Efficient Uncertainty Quantification in Complex and Large-Scale Biomechanical Problems Based on a Bayesian Multi-Fidelity Scheme,” Biomech. Model. Mechanobiol., 14(3), pp. 489–513. [CrossRef] [PubMed]
Heusinkveld, M. H. G. , Quicken, S. , Holtackers, R. J. , Huberts, W. , Reesink, K. D. , Delhaas, T. , and Spronck, B. , 2017, “ Uncertainty Quantification and Sensitivity Analysis of an Arterial Wall Mechanics Model for Evaluation of Vascular Drug Therapies,” Biomech. Model. Mechanobiol., 17(1), pp. 1–15.
Eddhahak-Ouni, A. , Masson, I. , Mohand-Kaci, F. , and Zidi, M. , 2013, “ Influence of Random Uncertainties of Anisotropic Fibrous Model Parameters on Arterial Pressure Estimation,” Appl. Math. Mech., 34(5), pp. 529–540. [CrossRef]
Zeinali-Davarani, S. , Choi, J. , and Baek, S. , 2009, “ On Parameter Estimation for Biaxial Mechanical Behavior of Arteries,” J. Biomech., 42(4), pp. 524–530. [CrossRef] [PubMed]
Kamenskiy, A. V. , Dzenis, Y. A. , Kazmi, S. A. J. , Pemberton, M. A. , Pipinos, I. I. , Phillips, N. Y. , Herber, K. , Woodford, T. , Bowen, R. E. , Lomneth, C. S. , and MacTaggart, J. N. , 2014, “ Biaxial Mechanical Properties of the Human Thoracic and Abdominal Aorta, Common Carotid, Subclavian, Renal and Common Iliac Arteries,” Biomech. Model. Mechanobiol., 13(6), pp. 1341–1359. [CrossRef] [PubMed]
Chuong, C. J. , and Fung, Y. C. , 1983, “ Three-Dimensional Stress Distribution in Arteries,” ASME J. Biomech. Eng., 105(3), pp. 268–274. [CrossRef]
Fung, Y.-C. , 1993, Biomechanics, Springer, New York. [CrossRef]
Garcia, J. R. , Lamm, S. D. , and Han, H.-C. , 2013, “ Twist Buckling Behavior of Arteries,” Biomech. Model. Mechanobiol., 12(5), pp. 915–927. [CrossRef] [PubMed]
Wang, C. , Garcia, M. , Lu, X. , Lanir, Y. , and Kassab, G. S. , 2006, “ Three-Dimensional Mechanical Properties of Porcine Coronary Arteries: A Validated Two-Layer Model,” Am. J. Physiol.—Heart Circ. Physiol., 291(3), pp. H1200–H1209. [CrossRef] [PubMed]
Baek, S. , Gleason, R. L. , Rajagopal, K. R. , and Humphrey, J. D. , 2007, “ Theory of Small on Large: Potential Utility in Computations of Fluid-Solid Interactions in Arteries,” Comput. Methods Appl. Mech. Eng., 196(31–32), pp. 3070–3078. [CrossRef]
Kamenskiy, A. V. , Pipinos, I. I. , Dzenis, Y. A. , Lomneth, C. S. , Kazmi, S. A. J. , Phillips, N. Y. , and MacTaggart, J. N. , 2014, “ Passive Biaxial Mechanical Properties and In Vivo Axial Pre-Stretch of the Diseased Human Femoropopliteal and Tibial Arteries,” Acta Biomater., 10(3), pp. 1301–1313. [CrossRef] [PubMed]
Sommer, G. , and Holzapfel, G. A. , 2012, “ 3D Constitutive Modeling of the Biaxial Mechanical Response of Intact and Layer-Dissected Human Carotid Arteries,” J. Mech. Behav. Biomed. Mater., 5(1), pp. 116–128. [CrossRef] [PubMed]
Hayashi, K. , Handa, H. , Nagasawa, S. , Okumura, A. , and Moritake, K. , 1980, “ Stiffness and Elastic Behavior of Human Intracranial and Extracranial Arteries,” J. Biomech., 13(2), pp. 175–184. [CrossRef] [PubMed]
Kasyanov, V. , Ozolanta, I. , Purinya, B. , Ozols, A. , and Kancevich, V. , 2003, “ Compliance of a Biocomposite Vascular Tissue in Longitudinal and Circumferential Directions as a Basis for Creating Artificial Substitutes,” Mech. Compos. Mater., 39(4), pp. 347–358. [CrossRef]
Holzapfel, G. A. , and Ogden, R. W. , 2009, “ On Planar Biaxial Tests for Anisotropic Nonlinearly Elastic Solids. A Continuum Mechanical Framework,” Math. Mech. Solids, 14(5), pp. 474–489. [CrossRef]
Sokolis, D. P. , 2013, “ Experimental Investigation and Constitutive Modeling of the 3D Histomechanical Properties of Vein Tissue,” Biomech. Model. Mechanobiol., 12(3), pp. 431–451. [CrossRef] [PubMed]
Sokolis, D. P. , Savva, G. D. , Papadodima, S. A. , and Kourkoulis, S. K. , 2017, “ Regional Distribution of Circumferential Residual Strains in the Human Aorta According to Age and Gender,” J. Mech. Behav. Biomed. Mater., 67, pp. 87–100. [CrossRef] [PubMed]
Han, H. C. , and Fung, Y. C. , 1991, “ Species Dependence of the Zero-Stress State of Aorta: Pig Versus Rat,” ASME J. Biomech. Eng., 113(4), pp. 446–451. [CrossRef]
Holzapfel, G. A. , Gasser, T. C. , and Ogden, R. W. , 2004, “ Comparison of a Multi-Layer Structural Model for Arterial Walls With a Fung-Type Model, and Issues of Material Stability,” ASME J. Biomech. Eng., 126(2), pp. 264–275. [CrossRef]
Desyatova, A. , MacTaggart, J. , and Kamenskiy, A. , 2017, “ Constitutive Modeling of Human Femoropopliteal Artery Biaxial Stiffening Due to Aging and Diabetes,” Acta Biomater., 64, pp. 50–58. [CrossRef] [PubMed]
Spronck, B. , Heusinkveld, M. H. G. , Donders, W. P. , Lepper, A. G. W. D. , Roodt, J. O. , Kroon, A. A. , Delhaas, T. , and Reesink, K. D. , 2015, “ A Constitutive Modeling Interpretation of the Relationship Among Carotid Artery Stiffness, Blood Pressure, and Age in Hypertensive Subjects,” Am. J. Physiol.–Heart Circ. Physiol., 308(6), pp. H568–H582. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Fit (solid lines) to data (dots) from multiple biaxial testing protocols of a human common carotid for (a) the phenomenological seven-parameter Fung model and (b) the structure motivated eight-parameter, four-fiber family HGO model. The arrows indicate the force ratio Pz: Pθ applied in the longitudinal and circumferential directions, respectively. The fit quality (overall, axial, and circumferential) of each model is displayed by the error measures e2D, ez, and eθ, respectively.

Grahic Jump Location
Fig. 2

Simulated inflation–extension biaxial test data in four axial stretch protocols (Λz = 1.20, 1.25, 1.30, 1.35) using (a) the seven-parameter phenomenological Fung model and (b) the structure motivated eight-parameter, four-fiber family model. The data were generated based on (1) constitutive parameters identified from a real planar biaxial data and (2) measurements of the UL and SF configurations geometry (ρo, Ri, Ro, α, and Λ0) from Table 4 of Ref. [64] for specimen #9R.

Grahic Jump Location
Fig. 3

Constitutive sensitivity versus measurement uncertainty in the opening-angle ((a) and (b)) and axial prestretch ((c) and (d)) of the phenomenological seven-parameter Fung model ((a) and (c)) and the structure motivated eight-parameter, four-fiber family HGO model ((b) and (d)). The left panel of each subfigure shows the value of the error measures ePi, eFz, and eIE (in the luminal pressure, axial force, and overall response, respectively) versus ϵα ((a) and (b)) and ϵΛ0 ((c) and (d)), the relative errors in the true values of α and ϵΛ0, respectively. The right panels show the relative errors in the fitted constitutive parameters ϵc of Eq. (14) as a function of ϵα and ϵΛ0.

Grahic Jump Location
Fig. 4

Summary of maximal and average relative absolute constitutive sensitivities for SF measurements uncertainties in opening angle (α) and axial prestretch (Λ0): (a) The phenomenological seven-parameter Fung model and (b) the structure motivated eight-parameter, four-fiber family HGO model

Grahic Jump Location
Fig. 5

Propagation of measurement uncertainty of ±10% in the opening-angle ((a) and (b)) and axial prestretch ((c) and (d)) to errors in the inflation–extension response of the phenomenological seven-parameter Fung model ((a) and (c)) and the structure motivated eight-parameter, four-fiber family HGO model ((b) and (d)). Solid lines represent the simulated experimental curves, and dots and dashes indicate positive (ϵα=+0.1, ϵΛ0=+0.1) and negative (ϵα=−0.1, ϵΛ0=−0.1) deviations, respectively. The level of axial stretch (Λz = 1.20, 1.25, 1.30, and 1.35) is indicated above each curve.

Grahic Jump Location
Fig. 6

Summary of the predictive sensitivity of the phenomenological seven-parameter Fung model ((a) and (c)) and the structure motivated eight-parameter, four-fiber family HGO model ((b) and (d)) to ±10% errors in the opening-angle ((a) and (b)) and axial prestretch ((c) and (d)). The average (circle), maximal (upper bar), and minimal (lower bar) relative margins in the internal pressure ΔPi¯ (left panels) and axial force ΔFz¯ (right panels) are displayed in different axial stretch protocols (Λz = 1.20, 1.25, 1.30, and 1.35). The value of the circumferential stretch λo for which the maximal margin was obtained is indicated next to its associated upper bar.

Grahic Jump Location
Fig. 7

Propagation of measurement uncertainties of ±10% in the opening-angle ((a) and (b)) and axial prestretch ((c) and (d)) to errors in the stresses predicted by the phenomenological seven-parameter Fung model ((a) and (c)) and the structure motivated eight-parameter, four-fiber family HGO model ((b) and (d)). Solid lines represent the “real” stresses, dots and dashes indicate the positive (ϵα=+0.1, ϵΛ0=+0.1) and negative (ϵα=−0.1, ϵΛ0=−0.1) deviations, respectively. The left (right) panel display the stresses and the associated errors under low (high) deformation, indicated by values of the circumferential (λo) and axial (Λz) stretches.

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In