Skip to main content
Log in

Finite element analysis of the influence of cyclic strain on cells anchored to substrates with varying properties

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

The response of cytoskeleton to mechanical cues plays a pivotal role in understanding several aspects of cellular growth, migration, and cell–cell and cell–matrix interactions under normal and diseased conditions. Finite element analysis (FEA) has become a powerful computational technique to study the response of cytoskeleton in the maintenance of overall cellular mechanics. With the revelation of role of external mechanical microenvironment on cell mechanics, FEA models have also been developed to simulate the effect of substrate stiffness on the mechanical properties of cancer cells. However, the models developed so far model cellular response under static mode, whereas in physiological condition, cells always experience dynamic loading conditions. To develop a more accurate model of cell-extracellular matrix (ECM) interactions, this paper models the cytoskeleton and other parts of the cell by beam and solid elements respectively, assuming spherical morphology of the cell. The stiffness and roughness of extracellular matrix were varied. Furthermore, static and dynamic sinusoidal loads were applied through a flat plate indenter on the cell along with providing sinusoidal strain at the substrate. It is observed that due to axial loading, cell reaches a plastic region, and when the sinusoidal loading is added to the axial load, the cell experiences permanent deformation. Degradation of the cytoskeleton elements and a physiologically more relevant spherical cap shape of the cell were also considered during the analysis. This study suggests that asperity topology of the substrate and indirect cyclic load can play a significant role in the shape alterations and motion of a cell.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data availability

NA.

Code availability

NA.

References

  1. Romani P, Valcarcel-Jimenez L, Frezza C, Dupont S (2021) Crosstalk between mechanotransduction and metabolism. Nat Rev Mol Cell Biol. Nature Research 22(1):22 38https://doi.org/10.1038/s41580-020-00306-w

  2. Ingber DE (2003) Mechanobiology and diseases of mechanotransduction. Ann Med 35(8):564–577. https://doi.org/10.1080/07853890310016333

    Article  PubMed  Google Scholar 

  3. Ayad NME, Kaushik S, Weaver VM (2019) Tissue mechanics, an important regulator of development and disease. Philos Trans R Soc B Biol Sci. Royal Society Publishing 374(1779). https://doi.org/10.1098/rstb.2018.0215

  4. Macri-Pellizzeri L, De-Juan-Pardo EM, Prosper F, Pelacho B (2018) Role of substrate biomechanics in controlling (stem) cell fate: implications in regenerative medicine. J Tissue Eng Regen Med. John Wiley and Sons Ltd 12(4):1012-1019.https://doi.org/10.1002/term.2586

  5. Deville SS, Cordes N (2019) The extracellular, cellular, and nuclear stiffness, a trinity in the cancer resistome—a review. Front Oncol. Frontiers Media S.A. 9:1376.https://doi.org/10.3389/fonc.2019.01376

  6. Tsimbouri PM, McNamara LE, Alakpa EV, Dalby MJ, Turner LA (2014) Cell-material interactions. In: Tissue Engineering: Second Edition, Elsevier Inc., pp 217–251

  7. Wells RG (2008) The role of matrix stiffness in regulating cell behavior Hepatology. John Wiley & Sons 47(4):1394-1400.https://doi.org/10.1002/hep.22193

  8. Wiche G (1998) Role of plectin in cytoskeleton organization and dynamics. J Cell Sci. Company of Biologists Ltd 111(9):2477–2486. https://doi.org/10.1242/jcs.111.17.2477

  9. Gerasymchuk D, Hubiernatorova A, Domanskyi A (2020) MicroRNAs regulating cytoskeleton dynamics, endocytosis, and cell motility—a link between neurodegeneration and cancer? Front Neurol. Frontiers Media S.A. 11:549006. https://doi.org/10.3389/fneur.2020.549006

  10. Kräter M, Sapudom J, Bilz N, Pompe T, Guck J, Claus C (2018) Alterations in cell mechanics by actin cytoskeletal changes correlate with strain-specific Rubella virus phenotypes for cell migration and induction of apoptosis. Cells 7(9):136. https://doi.org/10.3390/cells7090136

    Article  CAS  PubMed Central  Google Scholar 

  11. Liu L, Luo Q, Sun J, Song G (2019) Cytoskeletal control of nuclear morphology and stiffness are required for OPN-induced bone-marrow-derived mesenchymal stem cell migration. Biochem Cell Biol 97(4):463–470. https://doi.org/10.1139/bcb-2018-0263

    Article  CAS  PubMed  Google Scholar 

  12. Fletcher DA Mullins RD (2010) Cell mechanics and the cytoskeleton. Nature. Nature Publishing Group 463(7280):485–492. https://doi.org/10.1038/nature08908

  13. Ispanixtlahuatl-Meráz O, Schins RPF, Chirino YI (2018) Cell type specific cytoskeleton disruption induced by engineered nanoparticles. Environ Sci Nano. Royal Society of Chemistry 5(2):228–245. https://doi.org/10.1039/c7en00704c

  14. Liu Y, Mollaeian K, Shamim MH, Ren J (2020) Effect of F-actin and microtubules on cellular mechanical behavior studied using atomic force microscope and an image recognition-based cytoskeleton quantification approach. Int J Mol Sci 21(2):392. https://doi.org/10.3390/ijms21020392

    Article  CAS  PubMed Central  Google Scholar 

  15. Jean RP, Gray DS, Spector AA, Chen CS (2004) Characterization of the nuclear deformation caused by changes in endothelial cell shape. J Biomech Eng 126(5):552–558. https://doi.org/10.1115/1.1800559

    Article  PubMed  Google Scholar 

  16. Jean RP, Chen CS, Spector AA (2005) Finite-element analysis of the adhesion-cytoskeleton-nucleus mechanotransduction pathway during endothelial cell rounding: axisymmetric model. J Biomech Eng 127(4):594–600. https://doi.org/10.1115/1.1933997

    Article  PubMed  Google Scholar 

  17. Fallqvist B, Fielden ML, Pettersson T, Nordgren N, Kroon M, Gad AKB (2016) Experimental and computational assessment of F-actin influence in regulating cellular stiffness and relaxation behaviour of fibroblasts. J Mech Behav Biomed Mater 59:168–184. https://doi.org/10.1016/j.jmbbm.2015.11.039

    Article  CAS  PubMed  Google Scholar 

  18. Khan MI, Ferdous SF, Adnan A (2021) Mechanical behavior of actin and spectrin subjected to high strain rate: a molecular dynamics simulation study. Comput Struct Biotechnol J 19:1738–1749. https://doi.org/10.1016/j.csbj.2021.03.026

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Rotsch C, Radmacher M (2000) Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: an atomic force microscopy study. Biophys J 78(1):520–535. https://doi.org/10.1016/S0006-3495(00)76614-8

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Mohammed D et al (2019) Innovative tools for mechanobiology: unraveling outside-in and inside-out mechanotransduction. Front Bioeng Biotechnol. Frontiers Media S.A. 7(JUL.):162. https://doi.org/10.3389/fbioe.2019.00162

  21. Vining KH Mooney DJ (2017) Mechanical forces direct stem cell behaviour in development and regeneration. Nat Rev Mol Cell Biol. Nature Publishing Group 18. https://doi.org/10.1038/nrm.2017.108

  22. Langrand B, Casadei F, Marcadon V, Portemont G, Kruch S (2017) Experimental and finite element analysis of cellular materials under large compaction levels. Int J Solids Struct 128:99–116. https://doi.org/10.1016/j.ijsolstr.2017.08.019

    Article  Google Scholar 

  23. Bansod YD, Matsumoto T, Nagayama K, Bursa J (2018) A finite element bendo-tensegrity model of eukaryotic cell. J Biomech Eng 140(10). https://doi.org/10.1115/1.4040246

  24. Xue F, Lennon AB, McKayed KK, Campbell VA, Prendergast PJ (2015) Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells. Comput Methods Biomech Biomed Engin 18(5):468–476. https://doi.org/10.1080/10255842.2013.811234

    Article  PubMed  Google Scholar 

  25. Zhao J, Manuchehrfar F, Liang J (2020) Cell–substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model. Biomech Model Mechanobiol 19(5):1781–1796. https://doi.org/10.1007/s10237-020-01308-5

    Article  PubMed  PubMed Central  Google Scholar 

  26. Cross SE, Jin YS, Rao J, Gimzewski JK (2007) Nanomechanical analysis of cells from cancer patients. Nat Nanotechnol 2(12):780–783. https://doi.org/10.1038/nnano.2007.388

    Article  CAS  PubMed  Google Scholar 

  27. Barreto S, Perrault CM, Lacroix D (2014) Structural finite element analysis to explain cell mechanics variability. J Mech Behav Biomed Mater 38:219–231. https://doi.org/10.1016/j.jmbbm.2013.11.022

    Article  CAS  PubMed  Google Scholar 

  28. Katti DR, Katti KS (2017) Cancer cell mechanics with altered cytoskeletal behavior and substrate effects: A 3D finite element modeling study. J Mech Behav Biomed Mater 76:125–134. https://doi.org/10.1016/j.jmbbm.2017.05.030

    Article  CAS  PubMed  Google Scholar 

  29. Prauzner-Bechcicki S et al (2018) Adaptability of single melanoma cells to surfaces with distinct hydrophobicity and roughness. Appl Surf Sci 457:881–890. https://doi.org/10.1016/j.apsusc.2018.06.251

    Article  CAS  Google Scholar 

  30. Amani H et al (2019) Controlling cell behavior through the design of biomaterial surfaces: a focus on surface modification techniques. Adv Mater Interfaces. Wiley-VCH Verlag 6(13):1900572. https://doi.org/10.1002/admi.201900572

  31. Zhou J et al (2018) The effects of surface topography of nanostructure arrays on cell adhesion. Phys Chem Chem Phys 20(35):22946–22951. https://doi.org/10.1039/C8CP03538E

    Article  CAS  PubMed  Google Scholar 

  32. Miller MA, Zachary JF (2017) Mechanisms and Morphology of Cellular Injury, Adaptation, and Death. Pathologic Basis of Veterinary Disease:2–43.e19. https://doi.org/10.1016/B978-0-323-35775-3.00001-1

  33. Livne A, Bouchbinder E, Geiger B (2014) Cell reorientation under cyclic stretching. Nat Commun 5(1):1–8. https://doi.org/10.1038/ncomms4938

    Article  CAS  Google Scholar 

  34. Belaadi N, Aureille J, Guilluy C (2016) Under pressure: mechanical stress management in the nucleus. Cells 5(2):27. https://doi.org/10.3390/cells5020027

    Article  CAS  PubMed Central  Google Scholar 

  35. Weber A, Iturri J, Benitez R, Zemljic-Jokhadar S, Toca-Herrera JL (2019) Microtubule disruption changes endothelial cell mechanics and adhesion. Sci Rep 9(1):1–12. https://doi.org/10.1038/s41598-019-51024-z

    Article  CAS  Google Scholar 

  36. Ingber DE, Heidemann SR, Lamoureux P, Buxbaum RE (2000) Opposing views on tensegrity as a structural framework for understanding cell mechanics. J Appl Physiol. https://doi.org/10.1152/jappl.2000.89.4.1663

    Article  PubMed  Google Scholar 

  37. Suresh S (2007) Biomechanics and biophysics of cancer cells. Acta Mater. https://doi.org/10.1016/j.actamat.2007.04.022

    Article  Google Scholar 

  38. Barreto S, Clausen CH, Perrault CM, Fletcher DA, Lacroix D (2013) A multi-structural single cell model of force-induced interactions of cytoskeletal components. Biomaterials. https://doi.org/10.1016/j.biomaterials.2013.04.022

    Article  PubMed  PubMed Central  Google Scholar 

  39. Jiang H, Sun SX (2013) Cellular pressure and volume regulation and implications for cell mechanics. Biophys J. https://doi.org/10.1016/j.bpj.2013.06.021

    Article  PubMed  PubMed Central  Google Scholar 

  40. Wang L, Hsu HY, Li X, Xian CJ (2016) Effects of frequency and acceleration amplitude on opsteoblast mechanical vibration responses: a finite element study. Biomed Res Int. https://doi.org/10.1155/2016/2735091

    Article  PubMed  PubMed Central  Google Scholar 

  41. Høilund-Carlsen PF, Hess S, Werner TJ, Alavi A (2018) Cancer metastasizes to the bone marrow and not to the bone: time for a paradigm shift! Eur J Nucl Med Mol Imaging. Springer Berlin Heidelberg 45(6):893–897. https://doi.org/10.1007/s00259-018-3959-6

  42. Khanna R, Katti KS, Katti DR (2011) Experiments in nanomechanical properties of live osteoblast cells and cell-biomaterial interface. J Nanotechnol Eng Med. https://doi.org/10.1115/1.4005666

    Article  Google Scholar 

  43. Ambre AH, Katti DR, Katti KS (2015) Biomineralized hydroxyapatite nanoclay composite scaffolds with polycaprolactone for stem cell-based bone tissue engineering. J Biomed Mater Res A. https://doi.org/10.1002/jbm.a.35342

    Article  PubMed  Google Scholar 

  44. Khanna R, Katti KS, Katti DR (2010) In situ swelling behavior of chitosan-polygalacturonic acid/hydroxyapatite nanocomposites in cell culture media. Int J Polym Sci. https://doi.org/10.1155/2010/175264

    Article  Google Scholar 

  45. Nikpour MR, Rabiee SM, Jahanshahi M (2012) Synthesis and characterization of hydroxyapatite/chitosan nanocomposite materials for medical engineering applications. Compos B Eng. https://doi.org/10.1016/j.compositesb.2012.01.056

    Article  Google Scholar 

  46. Khanna R, Katti KS, Katti DR (2009) Nanomechanics of surface modified nanohydroxyapatite particulates used in biomaterials. J Eng Mech. https://doi.org/10.1061/(asce)em.1943-7889.0000002

    Article  Google Scholar 

  47. Sommerhage F, Helpenstein R, Rauf A, Wrobel G, Offenhäusser A, Ingebrandt S (2008) Membrane allocation profiling: a method to characterize three-dimensional cell shape and attachment based on surface reconstruction. Biomaterials 29(29):3927–3935. https://doi.org/10.1016/j.biomaterials.2008.06.020

    Article  CAS  PubMed  Google Scholar 

  48. Frisch T, Thoumine O (2002) Predicting the kinetics of cell spreading. J Biomech. https://doi.org/10.1016/S0021-9290(02)00075-1

    Article  PubMed  Google Scholar 

  49. Thoumine O, Cardoso O, Meister JJ (1999) Changes in the mechanical properties of fibroblasts during spreading: a micromanipulation study. Eur Biophys J 28(3):222–234. https://doi.org/10.1007/s002490050203

    Article  CAS  PubMed  Google Scholar 

  50. Thompson MK, Thompson JM (2010) Methods for Generating Probabilistic Rough Surfaces in ANSYS. In Proceedings of the 20th KOREA ANSYS User’s Conference

  51. Anguiano M et al (2020) The use of mixed collagen-Matrigel matrices of increasing complexity recapitulates the biphasic role of cell adhesion in cancer cell migration: ECM sensing, remodeling and forces at the leading edge of cancer invasion. PLoS One 15(1):e0220019. https://doi.org/10.1371/journal.pone.0220019

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Li Z et al (2017) Cellular traction forces: a useful parameter in cancer research. Nanoscale 9(48):19039–19044. https://doi.org/10.1039/c7nr06284b

    Article  CAS  PubMed  Google Scholar 

  53. Malandrino A, Mak M, Kamm RD, Moeendarbary E (2018) Complex mechanics of the heterogeneous extracellular matrix in cancer. Extreme Mech Lett. Elsevier Ltd 21:5–34. https://doi.org/10.1016/j.eml.2018.02.003

  54. Fu S, Yin L, Lin X, Lu J, Wang X (2018) Effects of cyclic mechanical stretch on the proliferation of L6 myoblasts and its mechanisms: PI3K/Akt and MAPK signal pathways regulated by IGF-1 receptor. Int J Mol Sci 19(6):1649. https://doi.org/10.3390/ijms19061649

    Article  CAS  PubMed Central  Google Scholar 

  55. Gershon ND, Porter KR, Trus BL (1985) The cytoplasmic matrix: its volume and surface area and the diffusion of molecules through it. Proc Natl Acad Sci U S A. https://doi.org/10.1073/pnas.82.15.5030

    Article  PubMed  PubMed Central  Google Scholar 

  56. Freitas RA Jr (1999) Nanomedicine VolumeI: Basic capabilities. Landes Bioscience, Georgetown

    Google Scholar 

  57. Vakifahmetoglu-Norberg H et al (2013) Caspase-2 promotes cytoskeleton protein degradation during apoptotic cell death. Cell Death Dis. https://doi.org/10.1038/cddis.2013.463

    Article  PubMed  PubMed Central  Google Scholar 

  58. Povea-Cabello S et al (2017) Dynamic reorganization of the cytoskeleton during apoptosis: the two coffins hypothesis. Int J Mol Sci. https://doi.org/10.3390/ijms18112393

    Article  PubMed  PubMed Central  Google Scholar 

  59. Chaudhuri O et al (2014) Extracellular matrix stiffness and composition jointly regulate the induction of malignant phenotypes in mammary epithelium. Nat Mater. https://doi.org/10.1038/nmat4009

    Article  PubMed  Google Scholar 

  60. Han YL et al (2020) Cell swelling, softening and invasion in a three-dimensional breast cancer model. Nat Phys 16(1):101–108. https://doi.org/10.1038/s41567-019-0680-8

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amit Roy Chowdhury.

Ethics declarations

Conflicts of interest

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Banerjee, A., Khan, M.P., Barui, A. et al. Finite element analysis of the influence of cyclic strain on cells anchored to substrates with varying properties. Med Biol Eng Comput 60, 171–187 (2022). https://doi.org/10.1007/s11517-021-02453-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-021-02453-4

Keywords

Navigation