Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations

Yuri Vassilevski, Alexey Liogky and Victoria Salamatova
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Yuri Vassilevski: Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, 119333 Moscow, Russia
Alexey Liogky: Moscow Institute of Physics and Technology, 141701 Dolgoprudny, Russia
Victoria Salamatova: Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, 119333 Moscow, Russia

Mathematics, 2021, vol. 9, issue 12, 1-15

Abstract: Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.

Keywords: aortic valve; coaptation; shell; membrane; mathematical modeling; hyperelastic nodal force; rotation-free element (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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