Study on methods measuring mechanical properties of arterial wall by macroscopic indentation_Journal of Biomedical Engineering

Authors：

CAO Yifan ¹ , GAO Zhipeng ¹ , SHI Yike ¹ , LI Fen ^2,3 , SONG Hui ^2,3 , ZHANG Qianqian ¹ , ZHAO Yawei ¹ ,  CHEN Lingfeng ¹ , LI Xiaona ¹ , CHEN Weiyi ¹

1. College of Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, P.R. China;
2. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, P.R. China;
3. Institute of Applied Mechanics, Taiyuan University of Technology, Taiyuan 030024, P.R. China;

Corresponding author：

CHEN Lingfeng, Email: chenlingfeng@tyut.edu.cn

Keywords：

Biomechanics; Arteries; Indentation tests

DOI：

10.7507/1001-5515.202310062

Video：

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Accurately evaluating the local biomechanics of arterial wall is crucial for diagnosing and treating arterial diseases. Indentation measurement can be used to evaluate the local mechanical properties of the artery. However, the effects of the indenter’s geometric structure and the analysis theory on measurement results remain uncertain. In this paper, four kinds of indenters were used to measure the pulmonary aorta, the proximal thoracic aorta and the distal thoracic aorta in pigs, and the arterial elastic modulus was calculated by Sneddon and Sirghi theory to explore the influence of the indenter geometry and analysis theory on the measured elastic modulus. The results showed that the arterial elastic modulus measured by cylindrical indenter was lower than that measured by spherical indenter. In addition, compared with the calculated results of Sirghi theory, the Sneddon theory, which does not take adhesion forces in account, resulted in slightly larger elastic modulus values. In conclusion, this study provides parametric support for effective measurement of arterial local mechanical properties by millimeter indentation technique.

Citation： CAO Yifan, GAO Zhipeng, SHI Yike, LI Fen, SONG Hui, ZHANG Qianqian, ZHAO Yawei, CHEN Lingfeng, LI Xiaona, CHEN Weiyi. Study on methods measuring mechanical properties of arterial wall by macroscopic indentation. Journal of Biomedical Engineering, 2024, 41(3): 469-475. doi: 10.7507/1001-5515.202310062 Copy

1.	Roth G A, Mensah G A, Johnson C O, et al. The global burden of cardiovascular diseases and risk factors, 1990–2019: update from the GBD 2019 study. Journal of the American College of Cardiology, 2020, 76(25): 2982-3021.
2.	Bunton T E, Biery N J, Myers L, et al. Phenotypic alteration of vascular smooth muscle cells precedes elastolysis in a mouse model of Marfan syndrome. Circulation Research, 2001, 88(1): 37-43.
3.	Pearson G D, Devereux R, Loeys B, et al. Report of the national heart, lung, and blood institute and national marfan foundation working group on research in Marfan syndrome and related disorders. Circulation, 2008, 118(7): 785-791.
4.	Pereira L, Lee S Y, Gayraud B, et al. Pathogenetic sequence for aneurysm revealed in mice underexpressing fibrillin-1. Proc Natl Acad Sci U S A, 1999, 96(7): 3819-3823.
5.	刘明, 张亚星, 高祖婕, 等. 腹主动脉瘤性别差异性的生物力学研究进展. 生物医学工程学杂志, 2018, 35(6): 959-963.
6.	刘梦辰, 潘霁超, 蔡彦, 等. 动脉粥样硬化斑块的生物力学模型和数值模拟研究. 生物医学工程学杂志, 2020, 37(6): 948-955.
7.	Pillalamarri N R, Patnaik S, Piskin S, et al. Ex vivo regional mechanical characterization of porcine pulmonary arteries. Experimental Mechanics, 2021, 61(1): 285-303.
8.	Pena J A, Martínez M A, Peña E. Failure damage mechanical properties of thoracic and abdominal porcine aorta layers and related constitutive modeling: phenomenological and microstructural approach. Biomechanics and Modeling in Mechanobiology, 2019, 18(6): 1709-1730.
9.	van Disseldorp E M J, van den Hoven M H M H, van de Vosse F N, et al. Reproducibility assessment of ultrasound-based aortic stiffness quantification and verification using bi-axial tensile testing. Journal of the Mechanical Behavior of Biomedical Materials, 2020, 103: 103571.
10.	Kim J, Baek S. Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test. Journal of Biomechanics, 2011, 44(10): 1941-1947.
11.	Pesen D, Hoh J H. Micromechanical architecture of the endothelial cell cortex. Biophysical Journal, 2005, 88(1): 670-679.
12.	Viswanathan P, Ephstein Y, Garcia J G, et al. Differential elastic responses to barrier-altering agonists in two types of human lung endothelium. Biochemical and Biophysical Research Communications, 2016, 478(2): 599-605.
13.	Wang X, Bleher R, Brown M E, et al. Nano-biomechanical study of spatio-temporal cytoskeleton rearrangements that determine subcellular mechanical properties and endothelial permeability. Scientific Reports, 2015, 5: 11097.
14.	Rothermel T M, Franczek I A, Alford P W. Anisotropic mechanics of vascular smooth muscle cells exposed to dynamic loads. Journal of Biomechanical Engineering, 2021, 143(12): 121007.
15.	Pailler-Mattéi C, Zahouani H. Analysis of adhesive behaviour of human skin in vivo by an indentation test. Tribology International, 2006, 39(1): 12-21.
16.	Barrett S R, Sutcliffe M P, Howarth S, et al. Experimental measurement of the mechanical properties of carotid atherothrombotic plaque fibrous cap. Journal of Biomechanics, 2009, 42(11): 1650-1655.
17.	Chai C K, Akyildiz A C, Speelman L, et al. Local axial compressive mechanical properties of human carotid atherosclerotic plaques-characterisation by indentation test and inverse finite element analysis. Journal of Biomechanics, 2013, 46(10): 1759-1766.
18.	Walraevens J, Willaert B, De Win G, et al. Correlation between compression, tensile and tearing tests on healthy and calcified aortic tissues. Medical Engineering & Physics, 2008, 30(9): 1098-1104.
19.	Sicard D, Fredenburgh L E, Tschumperlin D J. Measured pulmonary arterial tissue stiffness is highly sensitive to AFM indenter dimensions. Journal of the Mechanical Behavior of Biomedical Materials, 2017, 74: 118-127.
20.	Stolz M, Raiteri R, Daniels A U, et al. Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy. Biophysical Journal, 2004, 86(5): 3269-3283.
21.	Sirghi L, Rossi F. Adhesion and elasticity in nanoscale indentation. Applied Physics Letters, 2006, 89(24): 243118.
22.	Sneddon I N. The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. International Journal of Engineering Science, 1965, 3(1): 47-57.
23.	Czerner M, Fellay L S, Suárez M P, et al. Determination of elastic modulus of gelatin gels by indentation experiments. Procedia Materials Science, 2015, 8: 287-296.
24.	Zhang C Y, Zhang Y W. Computational analysis of adhesion force in the indentation of cells using atomic force microscopy. Phys Rev E Stat Nonlin Soft Matter Phys, 2008, 77(2 Pt 1): 021912.
25.	Liu K, Vanlandingham M R, Ovaert T C. Mechanical characterization of soft viscoelastic gels via indentation and optimization-based inverse finite element analysis. Journal of the Mechanical Behavior of Biomedical Materials, 2009, 2(4): 355-362.
26.	Tong K J, Ebenstein D M. Comparison of spherical and flat tips for indentation of hydrogels. The Journal of The Minerals, 2015, 67(4): 713-719.
27.	Zhang M, Zheng Y P, Mak A F. Estimating the effective Young’s modulus of soft tissues from indentation tests-nonlinear finite element analysis of effects of friction and large deformation. Medical Engineering & Physics, 1997, 19(6): 512-517.
28.	Azinfar L, Ravanfar M, Wang Y, et al. High resolution imaging of the fibrous microstructure in bovine common carotid artery using optical polarization tractography. Journal of Biophotonics, 2017, 10(2): 231-241.
29.	O'Connell M K, Murthy S, Phan S, et al. The three-dimensional micro- and nanostructure of the aortic medial lamellar unit measured using 3D confocal and electron microscopy imaging. Matrix Biology, 2008, 27(3): 171-181.
30.	McKee C T, Last J A, Russell P, et al. Indentation versus tensile measurements of Young’s modulus for soft biological tissues. Tissue Engineering Part B: Reviews, 2011, 17(3): 155-164.
31.	陈凌峰. 基于多种测量方法的动脉系统区域性力学性能研究. 太原: 太原理工大学, 2019.

1. Roth G A, Mensah G A, Johnson C O, et al. The global burden of cardiovascular diseases and risk factors, 1990–2019: update from the GBD 2019 study. Journal of the American College of Cardiology, 2020, 76(25): 2982-3021.
2. Bunton T E, Biery N J, Myers L, et al. Phenotypic alteration of vascular smooth muscle cells precedes elastolysis in a mouse model of Marfan syndrome. Circulation Research, 2001, 88(1): 37-43.
3. Pearson G D, Devereux R, Loeys B, et al. Report of the national heart, lung, and blood institute and national marfan foundation working group on research in Marfan syndrome and related disorders. Circulation, 2008, 118(7): 785-791.
4. Pereira L, Lee S Y, Gayraud B, et al. Pathogenetic sequence for aneurysm revealed in mice underexpressing fibrillin-1. Proc Natl Acad Sci U S A, 1999, 96(7): 3819-3823.
5. 刘明, 张亚星, 高祖婕, 等. 腹主动脉瘤性别差异性的生物力学研究进展. 生物医学工程学杂志, 2018, 35(6): 959-963.
6. 刘梦辰, 潘霁超, 蔡彦, 等. 动脉粥样硬化斑块的生物力学模型和数值模拟研究. 生物医学工程学杂志, 2020, 37(6): 948-955.
7. Pillalamarri N R, Patnaik S, Piskin S, et al. Ex vivo regional mechanical characterization of porcine pulmonary arteries. Experimental Mechanics, 2021, 61(1): 285-303.
8. Pena J A, Martínez M A, Peña E. Failure damage mechanical properties of thoracic and abdominal porcine aorta layers and related constitutive modeling: phenomenological and microstructural approach. Biomechanics and Modeling in Mechanobiology, 2019, 18(6): 1709-1730.
9. van Disseldorp E M J, van den Hoven M H M H, van de Vosse F N, et al. Reproducibility assessment of ultrasound-based aortic stiffness quantification and verification using bi-axial tensile testing. Journal of the Mechanical Behavior of Biomedical Materials, 2020, 103: 103571.
10. Kim J, Baek S. Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test. Journal of Biomechanics, 2011, 44(10): 1941-1947.
11. Pesen D, Hoh J H. Micromechanical architecture of the endothelial cell cortex. Biophysical Journal, 2005, 88(1): 670-679.
12. Viswanathan P, Ephstein Y, Garcia J G, et al. Differential elastic responses to barrier-altering agonists in two types of human lung endothelium. Biochemical and Biophysical Research Communications, 2016, 478(2): 599-605.
13. Wang X, Bleher R, Brown M E, et al. Nano-biomechanical study of spatio-temporal cytoskeleton rearrangements that determine subcellular mechanical properties and endothelial permeability. Scientific Reports, 2015, 5: 11097.
14. Rothermel T M, Franczek I A, Alford P W. Anisotropic mechanics of vascular smooth muscle cells exposed to dynamic loads. Journal of Biomechanical Engineering, 2021, 143(12): 121007.
15. Pailler-Mattéi C, Zahouani H. Analysis of adhesive behaviour of human skin in vivo by an indentation test. Tribology International, 2006, 39(1): 12-21.
16. Barrett S R, Sutcliffe M P, Howarth S, et al. Experimental measurement of the mechanical properties of carotid atherothrombotic plaque fibrous cap. Journal of Biomechanics, 2009, 42(11): 1650-1655.
17. Chai C K, Akyildiz A C, Speelman L, et al. Local axial compressive mechanical properties of human carotid atherosclerotic plaques-characterisation by indentation test and inverse finite element analysis. Journal of Biomechanics, 2013, 46(10): 1759-1766.
18. Walraevens J, Willaert B, De Win G, et al. Correlation between compression, tensile and tearing tests on healthy and calcified aortic tissues. Medical Engineering & Physics, 2008, 30(9): 1098-1104.
19. Sicard D, Fredenburgh L E, Tschumperlin D J. Measured pulmonary arterial tissue stiffness is highly sensitive to AFM indenter dimensions. Journal of the Mechanical Behavior of Biomedical Materials, 2017, 74: 118-127.
20. Stolz M, Raiteri R, Daniels A U, et al. Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy. Biophysical Journal, 2004, 86(5): 3269-3283.
21. Sirghi L, Rossi F. Adhesion and elasticity in nanoscale indentation. Applied Physics Letters, 2006, 89(24): 243118.
22. Sneddon I N. The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. International Journal of Engineering Science, 1965, 3(1): 47-57.
23. Czerner M, Fellay L S, Suárez M P, et al. Determination of elastic modulus of gelatin gels by indentation experiments. Procedia Materials Science, 2015, 8: 287-296.
24. Zhang C Y, Zhang Y W. Computational analysis of adhesion force in the indentation of cells using atomic force microscopy. Phys Rev E Stat Nonlin Soft Matter Phys, 2008, 77(2 Pt 1): 021912.
25. Liu K, Vanlandingham M R, Ovaert T C. Mechanical characterization of soft viscoelastic gels via indentation and optimization-based inverse finite element analysis. Journal of the Mechanical Behavior of Biomedical Materials, 2009, 2(4): 355-362.
26. Tong K J, Ebenstein D M. Comparison of spherical and flat tips for indentation of hydrogels. The Journal of The Minerals, 2015, 67(4): 713-719.
27. Zhang M, Zheng Y P, Mak A F. Estimating the effective Young’s modulus of soft tissues from indentation tests-nonlinear finite element analysis of effects of friction and large deformation. Medical Engineering & Physics, 1997, 19(6): 512-517.
28. Azinfar L, Ravanfar M, Wang Y, et al. High resolution imaging of the fibrous microstructure in bovine common carotid artery using optical polarization tractography. Journal of Biophotonics, 2017, 10(2): 231-241.
29. O'Connell M K, Murthy S, Phan S, et al. The three-dimensional micro- and nanostructure of the aortic medial lamellar unit measured using 3D confocal and electron microscopy imaging. Matrix Biology, 2008, 27(3): 171-181.
30. McKee C T, Last J A, Russell P, et al. Indentation versus tensile measurements of Young’s modulus for soft biological tissues. Tissue Engineering Part B: Reviews, 2011, 17(3): 155-164.
31. 陈凌峰. 基于多种测量方法的动脉系统区域性力学性能研究. 太原: 太原理工大学, 2019.

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Study on methods measuring mechanical properties of arterial wall by macroscopic indentation

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