# Estimation of Young's modulus and Poisson's ratio of soft tissue from indentation using two different-sized indentors: Finite element analysis of the finite deformation effect

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## Abstract

Young's modulus and Poisson's ratio of a tissue can be simultaneously obtained using two indentation tests with two different sized indentors in two indentations. Owing to the assumption of infinitesimal deformation of the indentation, the finite deformation effect of indentation on the calculated material parameters was not fully understood in the double indentation approach. However, indentation tests with infinitesimal deformation are not practical for the measurement of real tissues. Accordingly, finite element models were developed to simulate the indentation with different indentor diameters and different deformation ratios to investigate the finite deformation effect of indentation. The results indicated that Young's modulus E increased with the increase in the indentation deformation w, if the finite deformation effect of indentation was not considered. This phenomenon became obvious when Poisson's ratio v approached 0.5 and/or the ratio of indentor radius and tissue thickness a/h increased. The calculated Young's modulus could be different by 23% at 10% deformation in comparison with its real value. The results also demonstrated that the finite deformation effect to indentation on the calculation of Poisson's ratio v was much smaller. After the finite deformation effect of indentation was considered, the error of the calculated Young's modulus could be controlled within 5% (a/h=1) and 2% (a/h=2) for deformation up to 10%.

## Keywords

Indentation Finite element analysis Soft tissue Young's modulus Poisson's ratio## Preview

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## References

- Athanasiou, K. A., Agarwal, A., andDzida, F. J. (1994): ‘Comparative study if the intrinsic mechanical properties of the human acetabular and femoral head cartilage’,
*J. Orthop. Res.*,**12**, pp. 340–349CrossRefGoogle Scholar - Barker, M. K., andSeedhom, B. B. (1997): ‘Articular cartilage deformation under physiological cyclic loading—apparatus and measurement technique’,
*J. Biomech.*,**30**, pp. 377–381CrossRefGoogle Scholar - Hayes, W. C., Keer, L. M., Herrmann, G., andMockros, L. F. (1972): ‘A mathematical analysis for indentation tests of articular cartilage’,
*J. Biomech.*,**5**, pp. 541–551CrossRefGoogle Scholar - Jin, H., andLewis, J. L. (2004): ‘Determination of Poisson's ratio of articular cartilage by indentation using different-sized indenters’,
*J. Biomech. Eng.*,**126**, pp. 138–145CrossRefGoogle Scholar - Jurvelin, J. S., Buschmann, M. D., andHunziker, E. B. (1997): ‘Optical and mechanical determination of Poisson's ratio of adult bovine humeral articular cartilage’,
*J. Biomech.*,**30**, pp. 235–241CrossRefGoogle Scholar - Kempson, G. E., Freeman, M. A. R., andSwanson, S. A. V. (1971): ‘The determination of a creep modulus for articular cartilage from indentation tests on the human femoral head’,
*J. Biomech.*,**4**, pp. 239–250Google Scholar - Klaesner, J. W., Commean, P. K., Hastings, M. K., Zou, D. Q., andMueller, M. J. (2001): ‘Accuracy and reliability testing of a portable soft tissue indentor’,
*IEEE. Trans. Neural Syst. Rehabil. Eng.*,**9**, pp. 232–240CrossRefGoogle Scholar - Mak, A. F. T., Liu, G. H. W., andLee, S. Y. (1994): ‘Biomechanical assessment of below-knee residual limb tissue’,
*J. Rehabil. Res. Dev.*,**31**, pp. 188–198Google Scholar - Mow, V. C., Gibbs, M. C., Lai, W. M., Zhu, W. B., andAthanasiou, K. A. (1989): ‘Biphasic indentation of articular cartilage. Part II: a numerical algorithm and an experimental study’,
*J. Biomech.*,**22**, pp. 853–861CrossRefGoogle Scholar - Pierard, G. E. (1984): ‘Evaluation of mechanical properties of skin by indentation and compression methods’,
*Dermatology*,**168**, pp. 61–66Google Scholar - Spilker, R. L., Suh, J. K., andMow, V. C. (1992): ‘A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage’,
*J. Biomech. Eng.*,**114**, pp. 191–201Google Scholar - Suh, J. K. F., Youn, I., andFu, F. H. (2001): ‘An
*in situ*calibration of an ultrasound transducer: a potential application for an ultrasonic indentation test of articular cartilage’,*J. Biomech.*,**34**, pp. 1347–1353CrossRefGoogle Scholar - Toyras, J., Lyyra, L. T., Niinimaki, M., Lindgren, R., Nieminen, M. T., Kiviranta, I., andJurvelin, J. S. (2001): ‘Estimation of the Young's modulus of articular cartilage using an arthroscopic indentation instrument and ultrasonic measurement of tissue thickness’,
*J. Biomech.*,**34**, pp. 251–256Google Scholar - Zhang, M., Zheng, Y. P., andMak, A. F. T. (1997): ‘Estimating the effective Young's modulus of soft tissues from indentation tests-nonlinear finite element analysis of effects of frication and large deformation’,
*Med. Eng. Phys.*,**19**, pp. 512–517Google Scholar - Zheng, Y. P., andMak, A. F. T. (1996): ‘An ultrasound indentation system for biomechanical properties assessment of soft tissue
*in-vivo*’,*IEEE. Trans. Biomed. Eng.*,**43**, pp. 912–918Google Scholar - Zheng, Y. P., Mak, A. F. T., andLue, B. (1999): ‘Objective assessment of limb tissue elasticity: Development of a manual indentation procedure’,
*J. Rehabil. Res. Dev.*,**36**, pp. 71–85Google Scholar - Zheng, Y. P., Choi, Y. K. C., Wong, K., Chan, S., andMak, A. F. T. (2000): ‘Biomechanical assessment of plantar foot tissue in diabetic patients using an ultrasound indentation system’,
*Ultrasound Med. Biol.*,**26**, pp. 451–456CrossRefGoogle Scholar - Zheng, Y. P., Mak, A. F. T., andLeung, A. K. L. (2001): ‘State of the art methods for geometric and biomechanical assessments of residual limbs: A review’,
*J. Rehabil. Res. Dev.*,**38**, pp. 487–504Google Scholar