Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid
Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models....
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/18/2333 |
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| author | Ruslan Yanbarisov Yuri Efremov Nastasia Kosheleva Peter Timashev Yuri Vassilevski |
| author_facet | Ruslan Yanbarisov Yuri Efremov Nastasia Kosheleva Peter Timashev Yuri Vassilevski |
| author_sort | Ruslan Yanbarisov |
| collection | DOAJ |
| description | Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting. |
| first_indexed | 2024-03-10T07:27:56Z |
| format | Article |
| id | doaj.art-54347f7256034e169a92b018b2037c85 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T07:27:56Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-54347f7256034e169a92b018b2037c852023-11-22T14:06:50ZengMDPI AGMathematics2227-73902021-09-01918233310.3390/math9182333Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic SolidRuslan Yanbarisov0Yuri Efremov1Nastasia Kosheleva2Peter Timashev3Yuri Vassilevski4Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, RussiaInstitute for Regenerative Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, RussiaInstitute for Regenerative Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, RussiaInstitute for Regenerative Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, RussiaMarchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, RussiaParallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting.https://www.mdpi.com/2227-7390/9/18/2333multicellular spheroidviscoelastic solidviscoelastic fluid |
| spellingShingle | Ruslan Yanbarisov Yuri Efremov Nastasia Kosheleva Peter Timashev Yuri Vassilevski Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid Mathematics multicellular spheroid viscoelastic solid viscoelastic fluid |
| title | Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid |
| title_full | Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid |
| title_fullStr | Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid |
| title_full_unstemmed | Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid |
| title_short | Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid |
| title_sort | numerical modelling of multicellular spheroid compression viscoelastic fluid vs viscoelastic solid |
| topic | multicellular spheroid viscoelastic solid viscoelastic fluid |
| url | https://www.mdpi.com/2227-7390/9/18/2333 |
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