Advertisement

Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 1, pp 159–168 | Cite as

The potential for intercellular mechanical interaction: simulations of single chondrocyte versus anatomically based distribution

  • Jason P. Halloran
  • Scott C. Sibole
  • Ahmet Erdemir
Original Paper
  • 203 Downloads

Abstract

Computational studies of chondrocyte mechanics, and cell mechanics in general, have typically been performed using single cell models embedded in an extracellular matrix construct. The assumption of a single cell microstructural model may not capture intercellular interactions or accurately reflect the macroscale mechanics of cartilage when higher cell concentrations are considered, as may be the case in many instances. Hence, the goal of this study was to compare cell-level response of single and eleven cell biphasic finite element models, where the latter provided an anatomically based cellular distribution representative of the actual number of cells for a commonly used \(100 \, \upmu \hbox {m}\) edge cubic representative volume in the middle zone of cartilage. Single cell representations incorporated a centered single cell model and eleven location-corrected single cell models, the latter to delineate the role of cell placement in the representative volume element. A stress relaxation test at 10% compressive strain was adopted for all simulations. During transient response, volume- averaged chondrocyte mechanics demonstrated marked differences (up to 60% and typically greater than 10%) for the centered single versus the eleven cell models, yet steady-state loading was similar. Cell location played a marked role, due to inhomogeneity of the displacement and fluid pressure fields at the macroscopic scale. When the single cell representation was corrected for cell location, the transient response was consistent, while steady-state differences on the order of 1–4% were realized, which may be attributed to intercellular mechanical interactions. Anatomical representations of the superficial and deep zones, where cells reside in close proximity, may exhibit greater intercellular interactions, but these have yet to be explored.

Keywords

Multi-scale Computational modeling Finite element Cartilage Chondrocyte Poroelastic Biphasic Tissue mechanics Cell mechanics Homogenization 

Notes

Acknowledgements

This study was funded by the National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health (R01EB009643: Erdemir, Principal Investigator). Computing resources from Ohio Supercomputer Center are greatly appreciated.

Funding Funding was provided by the National Institute of Biomedical Imaging and Bioengineering, National Institutes of Health (R01EB009643: Erdemir, Principal Investigator)

Compliance with ethical standards

Conflict of interest

Author Halloran has received research grants from Active Implants Inc, Orthosensor Inc. and Stryker Orthopaedics. Author Erdemir has received research grants from the National Aeronautics and Space Administration (NASA). Author Erdemir is a lead member of the Committee on Credible Practice of Modeling & Simulation in Healthcare.

References

  1. Abusara Z, Seerattan R, Leumann A, Thompson R, Herzog W (2011) A novel method for determining articular cartilage chondrocyte mechanics in vivo. J Biomech 44(5):930–934CrossRefGoogle Scholar
  2. Alexopoulos LG, Setton LA, Guilak F (2005) The biomechanical role of the chondrocyte pericellular matrix in articular cartilage. Acta Biomater 1(3):317–325CrossRefGoogle Scholar
  3. Bennetts CJ, Sibole S, Erdemir A (2015) Automated generation of tissue-specific three-dimensional finite element meshes containing ellipsoidal cellular inclusions. Comput Methods Biomech Biomed Eng 18(12):1293–1304CrossRefGoogle Scholar
  4. Breuls RGM, Sengers BG, Oomens CWJ, Bouten CVC, Baaijens FPT (2002) Predicting local cell deformations in engineered tissue constructs: a multilevel finite element approach. J Biomech Eng 124(2):198–207CrossRefGoogle Scholar
  5. Chen AC, Bae WC, Schinagl RM, Sah RL (2001) Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression. J Biomech 34(1):1–12CrossRefGoogle Scholar
  6. Choi JB et al (2007) Zonal changes in the three-dimensional morphology of the chondron under compression: the relationship among cellular, pericellular, and extracellular deformation in articular cartilage. J Biomech 40(12):2596–2603MathSciNetCrossRefGoogle Scholar
  7. Clark AL, Votta BJ, Kumar S, Liedtke W, Guilak F (2010) Chondroprotective role of the osmotically sensitive ion channel transient receptor potential vanilloid 4: age- and sex-dependent progression of osteoarthritis in Trpv4-deficient mice. Arthritis Rheum 62(10):2973–2983CrossRefGoogle Scholar
  8. Erdemir A, Bennetts C, Davis S, Reddy A, Sibole S (2015) Multiscale cartilage biomechanics: technical challenges in realizing a high-throughput modelling and simulation workflow. Interface Focus 5(2):20140081CrossRefGoogle Scholar
  9. Federico S, Grillo A, La Rosa G, Giaquinta G, Herzog W (2005) A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage. J Biomech 38(10):2008–2018CrossRefGoogle Scholar
  10. Grodzinsky AJ, Levenston ME, Jin M, Frank EH (2000) Cartilage tissue remodeling in response to mechanical forces. Annu Rev Biomed Eng 2:691–713CrossRefGoogle Scholar
  11. Guilak F (1994) Volume and surface area measurement of viable chondrocytes in situ using geometric modelling of serial confocal sections. J Microsc 173(Pt 3):245–256CrossRefGoogle Scholar
  12. Guilak F, Hung CT (2005) Physical regulation of cartilage metabolism. In: Mow VC, Huiskes R (eds) Basic orthopaedic biomechanics and mechanobiology. Lippincott Williams & Wilkins, Philadelphia, pp 259–300Google Scholar
  13. Guilak F, Mow VC (2000) The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage. J Biomech 33(12):1663–1673CrossRefGoogle Scholar
  14. Haldar A, Mahadevan S (2000) Probability, reliability, and statistical methods in engineering design. Wiley, New YorkGoogle Scholar
  15. Halloran JP et al (2012) Multiscale mechanics of articular cartilage: potentials and challenges of coupling musculoskeletal, joint, and microscale computational models. Ann Biomed Eng 40(11):2456–2474Google Scholar
  16. Han S-K, Federico S, Herzog W (2011) A depth-dependent model of the pericellular microenvironment of chondrocytes in articular cartilage. Comput Methods Biomech Biomed Eng 14(7):657–664CrossRefGoogle Scholar
  17. Han S-K, Madden R, Abusara Z, Herzog W (2012) In situ chondrocyte viscoelasticity. J Biomech 45(14):2450–2456CrossRefGoogle Scholar
  18. Helminen HJ et al (2000) Regular joint loading in youth assists in the establishment and strengthening of the collagen network of articular cartilage and contributes to the prevention of osteoarthrosis later in life: a hypothesis. J Bone Miner Metab 18(5):245–257CrossRefGoogle Scholar
  19. Kim Y, Bonassar L, Grodzinsky A (1995) The role of cartilage streaming potential, fluid-flow and pressure in the stimulatin of chondrocyte biosynthesis during dynamic compression. J Biomech 28(9):1055–1066CrossRefGoogle Scholar
  20. Kim E, Guilak F, Haider MA (2008) The dynamic mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions under cyclic compressive loading. J Biomech Eng 130(6):061009CrossRefGoogle Scholar
  21. Korhonen RK, Herzog W (2008) Depth-dependent analysis of the role of collagen fibrils, fixed charges and fluid in the pericellular matrix of articular cartilage on chondrocyte mechanics. J Biomech 41(2):480–485CrossRefGoogle Scholar
  22. Korhonen RK, Julkunen P, Rieppo J, Lappalainen R, Konttinen YT, Jurvelin JS (2006) Collagen network of articular cartilage modulates fluid flow and mechanical stresses in chondrocyte. Biomech Model Mechanobiol 5(2–3):150–159CrossRefGoogle Scholar
  23. Korhonen RK, Han S-K, Herzog W (2010) Osmotic loading of articular cartilage modulates cell deformations along primary collagen fibril directions. J Biomech 43(4):783–787CrossRefGoogle Scholar
  24. Laz PJ, Pal S, Halloran JP, Petrella AJ, Rullkoetter PJ (2006) Probabilistic finite element prediction of knee wear simulator mechanics. J Biomech 39(12):2303–2310CrossRefGoogle Scholar
  25. Maas SA, Ellis BJ, Ateshian GA, Weiss JA (2012) FEBio: finite elements for biomechanics. J Biomech Eng 134(1):011005CrossRefGoogle Scholar
  26. Madden RMJ, Han S-K, Herzog W (2015) The effect of compressive loading magnitude on in situ chondrocyte calcium signaling. Biomech Model Mechanobiol 14(1):135–142CrossRefGoogle Scholar
  27. Moo EK et al (2014) Extracellular matrix integrity affects the mechanical behaviour of in-situ chondrocytes under compression. J Biomech 47(5):1004–1013CrossRefGoogle Scholar
  28. Mow VC, Kuei SC, Lai WM, Armstrong CG (1980) Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J Biomech Eng 102(1):73–84CrossRefGoogle Scholar
  29. Ofek G, Dowling EP, Raphael RM, McGarry JP, Athanasiou KA (2010) Biomechanics of single chondrocytes under direct shear. Biomech Model Mechanobiol 9(2):153–162CrossRefGoogle Scholar
  30. Quinn TM, Hunziker EB, Häuselmann H-J (2005) Variation of cell and matrix morphologies in articular cartilage among locations in the adult human knee. Osteoarthr Cartil 13(8):672–678CrossRefGoogle Scholar
  31. Sibole SC, Erdemir A (2012) Chondrocyte deformations as a function of tibiofemoral joint loading predicted by a generalized high-throughput pipeline of multi-scale simulations. PLoS ONE 7(5):e37538CrossRefGoogle Scholar
  32. Sibole SC, Maas S, Halloran JP, Weiss JA, Erdemir A (2013) Evaluation of a post-processing approach for multiscale analysis of biphasic mechanics of chondrocytes. Comput Methods Biomech Biomed Eng 16(10):1112–1126CrossRefGoogle Scholar
  33. Stolz M, Raiteri R, Daniels AU, VanLandingham MR, Baschong W, Aebi U (2004) Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy. Biophys J 86(5):3269–3283CrossRefGoogle Scholar
  34. Urban JP (2000) Present perspectives on cartilage and chondrocyte mechanobiology. Biorheology 37(1–2):185–190Google Scholar
  35. Zelenski NA et al (2015) Type VI collagen regulates pericellular matrix properties, chondrocyte swelling, and mechanotransduction in mouse articular cartilage. Arthritis Rheumatol (Hoboken, NJ) 67(5):1286–1294CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and the Mechanics and Control of Living Systems LabCleveland State UniversityClevelandUSA
  2. 2.Human Performance Lab, Department of Biomedical EngineeringUniversity of CalgaryCalgaryCanada
  3. 3.Computational Biomodeling (CoBi) Core and the Department of Biomedical EngineeringLerner Research InstituteClevelandUSA

Personalised recommendations