An Analytical Study on Mechanical Behavior of Human Arteries – A Nonlinear Elastic Double Layer Model

Document Type : Article

Authors

1 Department of Mechanical Engineering, Shahid Bahonar University, Kerman, Iran.; Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran.

2 Department of Mechanical Engineering, Shahid Bahonar University, Kerman, Iran.

Abstract

The focus of this article is on analytical solution for stress and deformation of human arteries. The artery is considered as a long homogeneous isotropic cylinder. Hyperelastic, incompressible stress-strain behavior is used by adopting a classical Mooney-Rivlin material model. The elastic constants of the arteries are calculated by using the reported results of biaxial test. The analysis is based on both single and double layer arterial wall models and. Radial and circumferential stress distribution on the minimum and maximum blood pressure is calculated. Variation of radii due to internal pressure within the arteries is found which is in a good accordance with the experimental results. The results containing the changes in diameter and thickness together with the stress distribution for both single and double layer models have been plotted. It is shown that the major difference between the single and double layer models is in their stress distributions. The circumferential stress distribution for different human’s ages is plotted which shows that the stress increases by increasing the age due to decreasing the flexibility of the artery. It is also shown that despite the artery’s inner layer is softer than the outer layer, the maximum stresses occur at the inner layer.

Keywords

Main Subjects

References

Refrences:
1.Lakatta, E.G. Central arterial aging and the epidemic of systolic hypertension and atherosclerosis", Journal of the American Society of Hypertension, 1(5), pp. 302- 340 (2007).
2. Sta_, B.C. Medical gallery of Blausen medical 2014", WikiJournal of Medicine, 1(2), pp. 1-79 (2014).
3. Meyers, M.A., Chen, P.Y., Lin, A.Y.M., and Seki, Y. Biological materials: structure and mechanical properties", Progress in Materials Science, 53(1), pp. 1-206 (2008). 4. Ja_e, E.A. Cell biology of endothelial cells", Human Pathology, 18(3), pp. 234-239 (1987). 5. Cox, R.H. Regional variation of series elasticity in canine arterial smooth muscles", American Journal of Physiology-Heart and Circulatory Physiology, 234(5), pp. 542-551 (1978). 6. Kar_saj, I. and Humphrey, J.D. A multilayered wall model of arterial growth and remodeling", Mechanics of Materials, 44, pp. 110-119 (2012). 7. Hudetz, A.G. Continuum mechanical methods and models in arterial biomechanics", Cardiovascular Physiology-Heart, Peripheral Circulation and Methodology, Advances in Physiological Science, 8, pp. 223- 232 (2014). 8. Taber, L. A model for aortic growth based on uid shear and _ber stresses", Journal of Biomechanical Engineering, 120(3), pp. 348-354 (1998). 9. Rachev, A. A model of arterial adaptation to alterations in blood ow", Journal of Elasticity and the Physical Science of Solids, 61(1-3), pp. 83-111 (2000). 10. Gleason, R., Taber, L., and Humphrey, J. A 2-D model of ow-induced alterations in the geometry, structure, and properties of carotid arteries", Journal of Biomechanical Engineering, 126(3), pp. 371-381 (2004). 11. Garc__a-Herrera, C.M., Celentano, D.J., Cruchaga, M.A., and Guinea, G.V. Mechanical characterization of the human aorta: Experiments, modeling and simulation", in Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials, Ed., 4th Edn., Springer, pp. 151-202 (2016). 12. Carew, T.E., Vaishnav, R.N., and Patel, D.J. Compressibility of the arterial wall", Circulation Research, 23(1), pp. 61-68 (1968). 13. Karimi, A., Navidbakhsh, M., Alizadeh, M., and Shojaei, A. A comparative study on the mechanical properties of the umbilical vein and umbilical artery under uniaxial loading", Artery Research, 8(2), pp. 51- 56 (2014). 14. Akhtar R. In vitro characterisation of arterial sti_- ening: From the macro-to the nano-scale", Artery Research, 8(1), pp. 1-8 (2014). 15. Vaishnav, R.N., Young, J.T., Janicki, J.S., and Patel, D.J. Nonlinear anisotropic elastic properties of the canine aorta", Biophysical Journal, 12(8), p. 1008 (1972). 16. Chuong, C. and Fung, Y. Compressibility and constitutive equation of arterial wall in radial compression experiments", Journal of Biomechanics, 17(1), pp. 35- 40 (1984). 17. Papageorgiou, G. and Jones, N. Physical modelling of the arterial wall. Part 2: Simulation of the non-linear elasticity of the arterial wall", Journal of Biomedical Engineering, 9(3), pp. 216-221 (1987). 18. Rastgar-Agah, M., Laksari, K., Assari, S., and Darvish, K. Mechanical Instability of Aorta due to Intraluminal Pressure", International Journal of Applied Mechanics, 8(1), p. 1650002 (2016). 19. Taghizadeh, D., Bagheri, A., and Darijani, H. On the hyperelastic pressurized thick-walled spherical shells and cylindrical tubes using the analytical closed-form solutions", International Journal of Applied Mechanics, 7(2), pp. 115-127 (2015). 20. Von Maltzahn, W.W., Besdo, D., and Wiemer, W. Elastic properties of arteries: a nonlinear two-layer cylindrical model", Journal of Biomechanics, 14(6), pp. 389-397 (1981). 2440 A. Sa_ Jahanshahi and A.R. Saidi/Scientia Iranica, Transactions B: Mechanical Engineering 26 (2019) ??{?? 21. Von Maltzahn, W.W. Stresses and strains in the coneshaped carotid sinus and their e_ects on baroreceptor functions", Journal of Biomechanics, 15(10), pp. 757- 765 (1982). 22. Von Maltzahn, W.W., Warriyar, R.G., and Keitzer, W.F. Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries", Journal of Biomechanics, 17(11), pp. 839-847 (1984). 23. Holzapfel, G.A. and Ogden, R.W., Biomechanical Modelling at the Molecular, Cellular and Tissue Levels, 508, Springer Science & Business Media (2009). 24. Holzapfel, G.A. and Weizsacker, H.W. Biomechanical behavior of the arterial wall and its numerical characterization", Computers in Biology and Medicine, 28(4), pp. 377-392 (1998). 25. Kroon, M. and Holzapfel, G.A. A theoretical model for _broblast-controlled growth of saccular cerebral aneurysms", Journal of Theoretical Biology, 257(1), pp. 73-83 (2009). 26. Watton, P., Hill, N., and Heil, M. A mathematical model for the growth of the abdominal aortic aneurysm", Biomechanics and Modeling in Mechanobiology, 3(2), pp. 98-113 (2004). 27. Wulandana, R. and Robertson, A. An inelastic multimechanism constitutive equation for cerebral arterial tissue", Biomechanics and Modeling in Mechanobiology, 4(4), pp. 235-248 (2005). 28. Zasadzinski, J., Wong, A.B., Forbes, N., Braun, G., and Wu, G. Novel methods of enhanced retention in and rapid, targeted release from liposomes", Current Opinion in Colloid & Interface Science, 16(3), pp. 203- 214 (2011). 29. Sa_ Jahanshahi, A. and Saidi, A. Mechanical behavior of human arteries in large deformation using non-linear elasticity theory", Modares Mechanical Engineering, 15(12), pp. 153-158 (2015). 30. Tsamis, A., Stergiopulos, N., and Rachev, A. A structure-based model of arterial remodeling in response to sustained hypertension", Journal of Biomechanical Engineering, 131(10), p. 101004 (2009). 31. Valent _n, A., Cardamone, L., Baek, S., and Humphrey, J. Complementary vasoactivity and matrix remodelling in arterial adaptations to altered ow and pressure", Journal of The Royal Society Interface, 6(32), pp. 293-306 (2009). 32. Wan, W., Hansen, L., and Gleason Jr, R.L. A 3-D constrained mixture model for mechanically mediated vascular growth and remodeling", Biomechanics and Modeling in Mechanobiology, 9(4), pp. 403-419 (2010). 33. Holzapfel, G.A. and Ogden, R.W. Modelling the layer-speci_c three-dimensional residual stresses in arteries, with an application to the human aorta", Journal of the Royal Society Interface, pp. 290-357 (2009). 34. Zem_anek, M., Bur_sa, J., and D_et_ak, M. Biaxial tension tests with soft tissues of arterial wall", Engineering Mechanics, 16(1), pp. 3-11 (2009). 35. Mohan, D. and Melvin, J.W. Failure properties of passive human aortic tissue. II Biaxial tension tests", Journal of Biomechanics, 16(1), pp. 31-44 (1983). 36. Batra, R. and Bahrami, A. Ination and eversion of functionally graded non-linear elastic incompressible circular cylinders", International Journal of Non- Linear Mechanics, 44(3), pp. 311-323 (2009). 37. Rubin, D., Krempl, E., and Lai, W.M. Introduction to Continuum Mechanics, 3th Edn., pp. 314-347, Butterworth Heinemann, Woburn (1993).
Scientia Iranica
Volume 26, Issue 4
Transactions on Mechanical Engineering (B)
July and August 2019
Pages 2431-2440

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History

  • Receive Date: 05 December 2017
  • Revise Date: 03 March 2018
  • Accept Date: 15 September 2018

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