The influence of the Hill-Drucker Criterion on the Parameters of the hyperelastic Mooney-Rivlin model of the breast
S.A. Muslov
, P.Yu. Sukhochev
, A.N. Nikishenko
, A.A. Korneev
, M.V. Chistyakov
, M.V. Fedotova
Резюме: Introduction: Various methods exist for detecting cancerous tissues, one of which is measuring the stiffness of the breast. Thus, parameters characterizing the deformation properties of gland tissues can serve as biomarkers for early cancer detection. Hyperelastic models have gained considerable popularity over recent decades for describing these properties. It is a well-known fact that hyperelastic models describe the behavior of materials exhibiting a nonlinear stress-strain relations and several studies have demonstrated that changes in these hyperelastic parameters can indicate various diseases. Besides, some studies have found that the changes in parameters of hyperelastic properties of tissues are predictors of different diseases. Objective: This report analyzes the two-parameter hyperelastic Mooney-Rivlin model both in its standard form and taking the Hill-Drucker stability criterion into account. Materials and methods: As an example, the deformation dependence σ-λ of the mammary gland is considered. The calculations were performed in the computer mathematics system Mathcad 15.0 using the genfit functionality. The predictive ability of the models was assessed based on descriptive statistics. Results: Taking into account the criterion, significant differences were found in the parameters of the C10, C01 model, as well as in the initial Young's modulus E0 and the hyperelastic stress-strain curves σ(λ). Conclusion: The Mooney-Rivlin model remains an acceptable option for describing the deformation properties of the soft biological tissues, the one with the application of the stability criterion or without it is the matter of choice.
Series on Biomechanics, Vol.40, No. 1 (2026), 21-25
DOI: 10.7546/SB.01.03.2026
Ключови думи: breast; Hill-Drucker criterion; Hyperelastic models; Mooney-Rivlin; stability
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| Дата на публикуване: 2026-03-23
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