Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

Ruslan Yanbarisov, Yuri Efremov, Nastasia Kosheleva, Peter Timashev and Yuri Vassilevski
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Ruslan Yanbarisov: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia
Yuri Efremov: Institute for Regenerative Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, Russia
Nastasia Kosheleva: Institute for Regenerative Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, Russia
Peter Timashev: Institute for Regenerative Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, Russia
Yuri Vassilevski: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia

Mathematics, 2021, vol. 9, issue 18, 1-12

Abstract: 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.

Keywords: multicellular spheroid; viscoelastic solid; viscoelastic fluid (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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