New Multiscale Approach of Complex Modelling Chordae Tendineae Considering Strain-Dependent Modulus of Elasticity

Alicia Menéndez Hurtado, Sergejus Borodinas, Olga Chabarova, Jelena Selivonec () and Eugeniuš Stupak
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Alicia Menéndez Hurtado: Department of Applied Mechanics, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Sergejus Borodinas: Department of Applied Mechanics, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Olga Chabarova: Department of Applied Mechanics, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Jelena Selivonec: Department of Applied Mechanics, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Eugeniuš Stupak: Department of Applied Mechanics, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania

Mathematics, 2025, vol. 13, issue 20, 1-18

Abstract: Understanding the nonlinear mechanical behaviour of mitral valve chordae tendineae is critical for accurate biomechanical modelling in cardiac simulations. This study integrates high-resolution 3D finite element analysis with experimentally derived Cauchy stress–Green–Lagrange strain data to capture both material and geometric nonlinearities. A one-dimensional formulation incorporating strain-dependent elasticity and large deformation kinematics was developed and validated against 3D simulations in COMSOL Multiphysics. Calibrated using experimental stress–strain data and validated against high-fidelity 3D finite element simulations in COMSOL, it reveals that neglecting transverse deformation overestimates axial force by 7%. Cross-sectional area reduction during stretch remained consistently around 12%, underscoring the importance of Poisson effects. A polynomial fit to the strain-dependent modulus of elasticity enables efficient force prediction with excellent agreement to experimental data. These results advance the mathematical modelling of biological tissues with nonlinear hyperelastic behaviour, providing a foundation for patient-specific simulations and real-time predictive tools in cardiovascular engineering.

Keywords: chordae tendineae; combined modelling; strain-dependent modulus of elasticity; finite element method; physical and geometrical nonlinearities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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