A Discrete Element Method for Modelling Cell Mechanics: Application to the Simulation of Chondrocyte Behavior in the Growth Plate

  • Grand R. JoldesEmail author
  • George C. Bourantas
  • Adam Wittek
  • Karol Miller
  • David W. Smith
  • Bruce S. Gardiner
Conference paper


In this paper we describe a discrete element method (DEM) framework we have developed for modelling the mechanical behavior of cells and tissues. By using a particle method we are able to simulate mechanical phenomena involved in tissue cell biomechanics (such as extracellular matrix degradation, secretion, growth) which would be very difficult to simulate using a continuum approach.

We use the DEM framework to study chondrocyte behavior in the growth plate. Chondrocytes have an important role in the growth of long bones. They produce cartilage on one side of the growth plate, which is gradually replaced by bone. We will model some mechanical aspects of the chondrocyte behavior during two stages of this process.

The DEM framework can be extended by including other mechanical and chemical processes (such as cell division or chemical regulation). This will help us gain more insight into the complex phenomena governing bone growth.


Discrete element method Chondrocyte Extracellular matrix Bone growth Growth plate 



This research was supported partially by the Australian Government through the Australian Research Council’s Discovery Projects funding scheme (project DP160100714). The views expressed herein are those of the authors and are not necessarily those of the Australian Government or Australian Research Council. We wish to acknowledge the Raine Medical Research Foundation for funding G. R. Joldes through a Raine Priming Grant, and the Department of Health, Western Australia, for funding G. R. Joldes through a Merit Award.


  1. 1.
    Hunziker EB (1994) Mechanism of longitudinal bone growth and its regulation by growth plate chondrocytes. Microsc Res Tech 28(6):505–519CrossRefGoogle Scholar
  2. 2.
    Gardiner BS et al (2015) Discrete element framework for modelling extracellular matrix, deformable cells and subcellular components. PLoS Comput Biol. CrossRefGoogle Scholar
  3. 3.
    Alman BA (2015) The role of hedgehog signalling in skeletal health and disease. Nat Rev Rheumatol 11(9):552–560CrossRefGoogle Scholar
  4. 4.
    Gentili C, Cancedda R (2009) Cartilage and bone extracellular matrix. Curr Pharm Des 15(12):1334–1348CrossRefGoogle Scholar
  5. 5.
    Prein C et al (2016) Structural and mechanical properties of the proliferative zone of the developing murine growth plate cartilage assessed by atomic force microscopy. Matrix Biol 50:1–15CrossRefGoogle Scholar
  6. 6.
    Luding S (2008) Introduction to discrete element methods. Eur J Environ Civ Eng 12(7-8):785–826CrossRefGoogle Scholar
  7. 7.
    Joldes GR, Wittek A, Miller K (2009) Computation of intra-operative brain shift using dynamic relaxation. Comput Methods Appl Mech Eng 198(41-44):3313–3320MathSciNetCrossRefGoogle Scholar
  8. 8.
    Joldes GR, Wittek A, Miller K (2011) An adaptive dynamic relaxation method for solving nonlinear finite element problems. Application to brain shift estimation. Int J Numer Methods Biomed Eng 27(2):173–185MathSciNetCrossRefGoogle Scholar
  9. 9.
    Horton A et al (2010) A meshless Total Lagrangian explicit dynamics algorithm for surgical simulation. Int J Numer Methods Biomed Eng 26(8):977–998CrossRefGoogle Scholar
  10. 10.
    Joldes GR, Wittek A, Miller K (2012) Stable time step estimates for mesh-free particle methods. Int J Numer Methods Eng 91(4):450–456MathSciNetCrossRefGoogle Scholar
  11. 11.
    Williams JR, Perkins E, Cook B (2004) A contact algorithm for partitioning N arbitrary sized objects. Eng Comput 21(2/3/4):235–248CrossRefGoogle Scholar
  12. 12.
    Gardiner BS et al (2016) Controlling seepage in discrete particle simulations of biological systems. Comput Methods Biomech Biomed Engin 19(10):1160–1170CrossRefGoogle Scholar
  13. 13.
    Blair HC, Zaidi M, Schlesinger PH (2002) Mechanisms balancing skeletal matrix synthesis and degradation. Biochem J 364(Pt 2):329–341CrossRefGoogle Scholar
  14. 14.
    Miller K, Lu J (2013) On the prospect of patient-specific biomechanics without patient-specific properties of tissues. J Mech Behav Biomed Mater 27:154–166CrossRefGoogle Scholar
  15. 15.
    Poole CA, Ayad S, Gilbert RT (1992) Chondrons from articular cartilage. V. Immunohistochemical evaluation of type VI collagen organisation in isolated chondrons by light, confocal and electron microscopy. J Cell Sci 103(4):1101–1110Google Scholar
  16. 16.
    Joldes GR, Wittek A, Miller K (2010) Real-time nonlinear finite element computations on GPU - application to neurosurgical simulation. Comput Methods Appl Mech Eng 199(49-52):3305–3314CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Grand R. Joldes
    • 1
    • 2
    Email author
  • George C. Bourantas
    • 2
  • Adam Wittek
    • 2
  • Karol Miller
    • 2
    • 3
  • David W. Smith
    • 4
  • Bruce S. Gardiner
    • 1
  1. 1.School of Engineering and Information TechnologyMurdoch UniversityMurdochAustralia
  2. 2.Intelligent Systems for Medicine LaboratoryThe University of Western AustraliaPerthAustralia
  3. 3.School of EngineeringCardiff UniversityCardiffUK
  4. 4.Engineering Computational Biology, School of Computer Science and Software EngineeringThe University of Western AustraliaPerthAustralia

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