Proposal and validation of polyconvex strain-energy function for biological soft tissues

Article type: Research Article

Authors: Funai, Takashi^{a; b; c;} | Kataoka, Hiroyuki^d | Yokota, Hideo^{b; e} | Suzuki, Taka-aki^a

Affiliations: [a] Industrial Research Institute of Shizuoka Prefecture, 2078 Makigaya, Aoi-ku, Shizuoka City, Shizuoka, Japan | [b] Image Processing Research Team, Center for Advanced Photonics, RIKEN, 2-1 Hirosawa, Wako City, Saitama, Japan | [c] Division of Human Mechanical Systems and Design, Graduate School of Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo, Hokkaido, Japan | [d] Computational Biomechanics Unit, RIKEN, 2-1 Hirosawa, Wako City, Saitama, Japan | [e] Division of Human Mechanical Systems and Design, Faculty of Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo, Hokkaido, Japan

Correspondence: [*] Corresponding author: Takashi Funai, Industrial Research Institute of Shizuoka Prefecture, 2078 Makigaya, Aoi-ku, Shizuoka City, Shizuoka, 421-1298, Japan. Tel.: +81 54 278 3027; Fax: +81 54 278 3027; E-mail: [email protected]

Abstract: BACKGROUND:Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE:Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD:Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS:A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS:The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

Keywords: Biological tissue, biomechanical simulation, finite element method, hyperelasticity, tissue modelling

DOI: 10.3233/BME-196015

Journal: Bio-Medical Materials and Engineering, vol. 32, no. 3, pp. 131-144, 2021