Breast hyperelastic models parameters comparison
S.A. Muslov
, P.Yu. Sukhochev
, S.A. Plaksin
, V.V. Shadrin
, A.N. Nikishenko
, S.S. Pertsov
, N.V. Zaitseva
Abstract: Objective. Unfortunately, knowledge about the mechanical properties of breast tissue is limited, although it has been proven that the stiffness of biological tissues can serve as a predictor of cancer. Despite the successes in the theoretical consideration of aspects of hyperelasticity and a wide range of formulated models, there are very few original works devoted to the practical definition of parameters of hyperelastic models, interpretation and discussion of their values. In addition to the potential for use in cancer diagnosis and classification, the data presented in this topic is quite important for applications such as surgery planning and virtual reality-based physician training systems, where accurate nonlinear modelling of tissue response is required. Goal: This report compares the literature data on the numerical values of the parameters for the most common hyperelastic models each other and with the new results of our own calculations. Materials and methods: Calculation of the material constants of hyperelastic models in our own research was performed in Mathcad 15.0 using the genfit and corr functions. Results: Numerical values of the parameters of the neohookean, Mooney-Rivlin, Ogden, polynomial, Yeoh, and Veronda-Westmann hyperelastic models of breast tissue were obtained. Conclusion: The results of calculating the parameters of the hyperelastic models of the mammary gland vary significantly, requiring further research.
Series on Biomechanics, Vol.40, No. 1 (2026), 14-20
DOI:10.7546/SB.01.02.2026
Keywords: biological tissues; Breast; hyperelastic models; mammary gland
| References: (click to open/close) | [1] Kim J, Harper A, McCormack V, Sung H, Houssami N, Morgan E, Mutebi M, Garvey G, Soerjomataram I, Fidler-Benaoudia MM, 2025. Global patterns and trends in breast cancer incidence and mortality across 185 countries. Nat Med. Apr 31, 4, 1154-1162. doi: 10.1038/s41591-025-03502-3.
[2] Teixeira AM, Martins P., 2023. A review of bioengineering techniques applied to breast tissue: Mechanical properties, tissue engineering and finite element analysis. Front Bioeng Biotechnol. Apr 3,11, 1161815. doi: 10.3389/fbioe.2023.1161815.
[3] S. A. Muslov, S. D. Arutyunov, 2021. Physical properties of tooth tissues. М.: Practical Medicine, ISBN 978-5-98811-642-4. – 176 С. DOI: 10.17513/np.597.
[4] Wellman PS, Howe RD, Dalton E, Kern KA, 1999. Breast tissue stiffness in compression is correlated to histological diagnosis. Harvard BioRobotics Laboratory Technical Report. 1-15 P.
[5] Krouskop TA, Wheeler TM, Kallel F, Garra BS, Hall T., 1998. Elastic moduli of breast and prostate tissues under compression. Ultrason Imaging. Oct;20, 4, 260-74. doi: 10.1177/016173469802000403.
[6] Azar F.S., Metaxas D.N., Schnall M.D., 2002. Methods for modeling and predicting mechanical deformations of the breast under external perturbations. Med Image Anal. Mar; 6, 1, 1-27. doi: 10.1016/s1361-8415(01)00053-6.
[7] Phipps S., Yang T.H., Habib F.K., Reuben R.L., McNeill S.A., 2005. Measurement of tissue mechanical characteristics to distinguish between benign and malignant prostatic disease. Urology 66, 447-450. https://doi.org/10.1016/j.urology.2005.03.017
[8] Liesbet Roose, Wim De Maerteleire, Wouter Mollemans, Paul Suetens, 2005. Validation of different soft tissue simulation methods for breast augmentation. May International Congress Series 1281, 4, 485-490. DOI: 10.1016/j.ics.2005.03.126.
[9] Tanner C, Schnabel JA, Hill DL, Hawkes DJ, Leach MO, Hose DR., 2006. Factors influencing the accuracy of biomechanical breast models. Med Phys. Jun;33, 6, 1758-69. doi: 10.1118/1.2198315.
[10] Samani A, Plewes D., 2004. A method to measure the hyperelastic parameters of ex vivo breast tissue samples. Phys Med Biol. Sep 21, 49, 18, 4395-405. doi: 10.1088/0031-9155/49/18/014.
[11] O'Hagan JJ, Samani A., 2009. Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples. Phys Med Biol. Apr 21;54, 8, 2557-69. doi: 10.1088/0031-9155/54/8/020.
[12] Semakane L., Pandurangan M., Ngwangwa H., Pandelani T., A.G. Kuchumov, Nemavhola F., 2025. Mechanical behaviour of breast tissue: an in-depth systematic review. Russian Journal of Biomechanics Т. 29, 1, 29-53.DOI: 10.15593/RZhBiomeh/2025.1.02.
[13] Mehrabian H, Campbell G, Samani A., 2010. A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment. Phys Med Biol. Dec 21; 55, 24, 7489-508. doi: 10.1088/0031-9155/55/24/007.
[14] Shmurak M.I., Kuchumov A.G., Voronova N.O., 2017. Analysis of hyperelastic models for describing the behavior of soft tissues of the human body. Master's Journal, 1, 230-243.
[15] Ivanov D.V., Fomkina O.A., 2008. Determination of constants for the neo-Hooke and Mooney-Rivlin models based on the results of experiments on uniaxial stretching. Bulletin of the Saratov University. Mathematics. Mechanics 10 114-117.
[16] Ogden R.W., Saccomandi G., Sgura I., 2004. Fitting hyperelastic models to experimental data. Comput. Mech. 34, 6, 484-502. doi:10.1007/s00466-004-0593-y.
[17] Michael Rackl, 2015. Material testing and hyperelastic material model curve fitting for Ogden, Polynomial and Yeoh models. Conference: ScilabTEC, 7th International Scilab Users ConferenceAt: Paris, France. DOI: 10.13140/RG.2.2.29552.25600/1
[18] Yeoh O.H., 1993. Some forms of the strain energy function for rubber // Rubber Chemistry and Technology 66, 5, 754-771. https://doi.org/10.5254/1.3538343.
[19] Veronda D. and Westmann R., 1970. Mechanical characterizations of skin-finite deformations. J. Biomech. 3, 3, 111-124. https://doi.org/10.1016/0021-9290(70)90055-2.
[20] S.A. Muslov, P.Yu. Sukhochev, 2025. On the question of the physical interpretation of material constants of hyperelastic models. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 25, 3,380–390. DOI: https://doi.org/10.18500/1816-9791-2025-25-3-380-390.
[21] S. Muslov, S. Pertsov, P. Sukhochev, A. Minasyan, 2025. Elastic moduli of hyperelastic models of biological tissues. Series on Biomechanics, 2, 24-33. DOI:10.7546/SB.02.02.2025.
[22] Lopez JI, Kang I, You W-K, McDonald DM, Weaver VM, 2011. In situ force mapping of mammary gland transformation. Integr Biol 3: 910–921. doi:10.1039/c1ib00043h.
[23] V.V. Shadrin, S.A. Plaksin, V.A. Platunova, 2024. Mechanical properties of silicone breast implants. Russian Journal of Biomechanics, 28, 4. 200–207. DOI: 10.15593/RZhBiomeh/2024.4.17.
[24] Bone, A., Liman Kaoye, M.B.-A., Baidi, B.B. and Samon, J.-B., 2025. Comparison of Hyperelastic Models for Analysis of Human and Pig Skins Behavior. Journal of Applied Mathematics and Physics, 13, 2045-2062. https://doi.org/10.4236/jamp.2025.136114.
[25] Hill R., 1958. General theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, 6, 236–249. https://doi.org/10.1016/0022-5096(58)90029-2.
[26] Drucker D.C., 1959. A definition of a stable inelastic material, Journal of Applied Mechanics, 26, 101–195. https://doi.org/10.1115/1.4011929.
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| Date published: 2026-03-23
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