Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations
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 nu...
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| Format: | Article |
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MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1450 |
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| author | Yuri Vassilevski Alexey Liogky Victoria Salamatova |
| author_facet | Yuri Vassilevski Alexey Liogky Victoria Salamatova |
| author_sort | Yuri Vassilevski |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T10:13:17Z |
| format | Article |
| id | doaj.art-0c1d77e99a2a4a249178fc13ad0e6537 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:13:17Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0c1d77e99a2a4a249178fc13ad0e65372023-11-22T01:01:50ZengMDPI AGMathematics2227-73902021-06-01912145010.3390/math9121450Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane FormulationsYuri Vassilevski0Alexey Liogky1Victoria Salamatova2Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, 119333 Moscow, RussiaMoscow Institute of Physics and Technology, 141701 Dolgoprudny, RussiaMarchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, 119333 Moscow, RussiaCoaptation 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.https://www.mdpi.com/2227-7390/9/12/1450aortic valvecoaptationshellmembranemathematical modelinghyperelastic nodal force |
| spellingShingle | Yuri Vassilevski Alexey Liogky Victoria Salamatova Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations Mathematics aortic valve coaptation shell membrane mathematical modeling hyperelastic nodal force |
| title | Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations |
| title_full | Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations |
| title_fullStr | Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations |
| title_full_unstemmed | Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations |
| title_short | Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations |
| title_sort | application of hyperelastic nodal force method to evaluation of aortic valve cusps coaptation thin shell vs membrane formulations |
| topic | aortic valve coaptation shell membrane mathematical modeling hyperelastic nodal force |
| url | https://www.mdpi.com/2227-7390/9/12/1450 |
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