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

Author

Listed:
  • Ruslan Yanbarisov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia
    Institute for Computer Science and Mathematical Modelling, Sechenov First Moscow State Medical University, 119991 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
    Institute for Computer Science and Mathematical Modelling, Sechenov First Moscow State Medical University, 119991 Moscow, Russia
    Moscow Institute of Physics and Technology, 141701 Dolgoprudny, Russia)

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.

Suggested Citation

  • Ruslan Yanbarisov & Yuri Efremov & Nastasia Kosheleva & Peter Timashev & Yuri Vassilevski, 2021. "Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid," Mathematics, MDPI, vol. 9(18), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2333-:d:639530
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