Applications of Computer Modeling and Simulation in Cartilage Tissue Engineering

  • Daniel Pearce
  • Sarah Fischer
  • Fatama Huda
  • Ali VahdatiEmail author
Review Article



Advances in cartilage tissue engineering have demonstrated noteworthy potential for developing cartilage for implantation onto sites impacted by joint degeneration and injury. To supplement resource-intensive in vivo and in vitro studies required for cartilage tissue engineering, computational models and simulations can assist in enhancing experimental design.


Research articles pertinent to cartilage tissue engineering and computer modeling were identified, reviewed, and summarized. Various applications of computer modeling for cartilage tissue engineering are highlighted, limitations of in silico modeling are addressed, and suggestions for future work are enumerated.


Computational modeling can help better characterize shear stresses generated by bioreactor fluid flow, refine scaffold geometry, customize the mechanical properties of engineered cartilage tissue, and model rates of cell growth and dynamics. Thus, results from in silico studies can help resourcefully enhance in vitro and in vivo studies; however, the limitations of these studies, such as the underlying assumptions and simplifications applied in each model, should always be addressed and justified where applicable. In silico models should also seek validation and verification when possible.


Future studies may adopt similar approaches to supplement in vitro trials and further investigate effects of mechanical stimulation on chondrocyte and stem cell dynamics. Additionally, as precision medicine, machine learning, and powerful open-source software become more popular and accessible, applications of multi-scale and multiphysics computational models in cartilage tissue engineering are expected to increase.


Cartilage Tissue engineering Chondrogenesis Computer modeling In silico 



No funding was received.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical statement

There are no animal experiments carried out for this article.


  1. 1.
    Litwic A, Edwards MH, Dennison EM, Cooper C. Epidemiology and burden of osteoarthritis. Br Med Bull. 2013;105:185–99.CrossRefGoogle Scholar
  2. 2.
    Plotnikoff R, Karunamuni N, Lytvyak E, Penfold C, Schopflocher D, Imayama I, et al. Osteoarthritis prevalence and modifiable factors: a population study. BMC Public Health. 2015;15:1195.CrossRefGoogle Scholar
  3. 3.
    Nelson AE, Allen KD, Golightly YM, Goode AP, Jordan JM. A systematic review of recommendations and guidelines for the management of osteoarthritis: the chronic osteoarthritis management initiative of the U.S. bone and joint initiative. Semin Arthritis Rheum. 2014;43:701–12.CrossRefGoogle Scholar
  4. 4.
    Xu M, Stattin EL, Shaw G, Heinegård D, Sullivan G, Wilmut I, et al. Chondrocytes derived from mesenchymal stromal cells and induced pluripotent cells of patients with familial osteochondritis dissecans exhibit an endoplasmic reticulum stress response and defective matrix assembly. Stem Cells Transl Med. 2016;5:1171–81.CrossRefGoogle Scholar
  5. 5.
    Vahdati A, Zhao Y, Ovaert TC, Wagner DR. Computational investigation of fibrin mechanical and damage properties at the interface between native cartilage and implant. J Biomech Eng. 2012;134:111004.CrossRefGoogle Scholar
  6. 6.
    Grässel S. Collagens in hyaline cartilage. In: Grässel S, Aszódi A, editors. Cartilage. Cham: Springer; 2016. p. 23–53.CrossRefGoogle Scholar
  7. 7.
    Cortez S, Freitas FL, Completo A, Alves JL. A 3D finite element model to predict the arcade-like collagen structure in a layered PCL scaffold for cartilage tissue engineering. Comput Methods Biomech Biomed Engin. 2017;20:47–8.CrossRefGoogle Scholar
  8. 8.
    Wilson W, Driessen NJ, van Donkelaar CC, Ito K. Prediction of collagen orientation in articular cartilage by a collagen remodeling algorithm. Osteoarthritis Cartilage. 2006;14:1196–202.CrossRefGoogle Scholar
  9. 9.
    Koh YG, Lee JA, Kim YS, Lee HY, Kim HJ, Kang KT. Optimal mechanical properties of a scaffold for cartilage regeneration using finite element analysis. J Tissue Eng. 2019;10:2041731419832133.CrossRefGoogle Scholar
  10. 10.
    Olivares AL, Marsal E, Planell JA, Lacroix D. Finite element study of scaffold architecture design and culture conditions for tissue engineering. Biomaterials. 2009;30:6142–9.CrossRefGoogle Scholar
  11. 11.
    Chung CA, Chen CW, Chen CP, Tseng CS. Enhancement of cell growth in tissue-engineering constructs under direct perfusion: modeling and simulation. Biotechnol Bioeng. 2007;97:1603–16.CrossRefGoogle Scholar
  12. 12.
    Chung CA, Yang CW, Chen CW. Analysis of cell growth and diffusion in a scaffold for cartilage tissue engineering. Biotechnol Bioeng. 2006;94:1138–46.CrossRefGoogle Scholar
  13. 13.
    Kelly DJ, Prendergast PJ. Effect of a degraded core on the mechanical behaviour of tissueengineered cartilage constructs: a poro-elastic finite element analysis. Med Biol Eng Comput. 2004;42:9–13.CrossRefGoogle Scholar
  14. 14.
    Stoffel M, Yi JH, Weichert D, Zhou B, Nebelung S, Müller-Rath R, et al. Bioreactor cultivation and remodelling simulation for cartilage replacement material. Med Eng Phys. 2012;34:56–63.CrossRefGoogle Scholar
  15. 15.
    Smith DW, Gardiner BS, Davidson JB, Grodzinsky AJ. Computational model for the analysis of cartilage and cartilage tissue constructs. J Tissue Eng Regen Med. 2016;10:334–47.CrossRefGoogle Scholar
  16. 16.
    Tajsoleiman T, Abdekhodaie MJ, Gernaey KV, Krühne U. Geometry optimization of a fibrous scaffold based on mathematical modelling and CFD simulation of a dynamic cell culture. In: Computer Aided Chemical Engineering. Elsevier, 2016. Vol. 38, p. 1413–8.Google Scholar
  17. 17.
    Tajsoleiman T, Abdekhodaie MJ, Gernaey KV, Krühne U. Efficient computational design of a scaffold for cartilage cell regeneration. Bioengineering (Basel). 2018;5:E33.CrossRefGoogle Scholar
  18. 18.
    Malvè M, Bergstrom DJ, Chen XB. Modeling the flow and mass transport in a mechanically stimulated parametric porous scaffold under fluid-structure interaction approach. Int J Heat Mass Transf. 2018;96:53–60.CrossRefGoogle Scholar
  19. 19.
    Ramin E, Harris RA. Advanced computer-aided design for bone tissue-engineering scaffolds. Proc Inst Mech Eng H. 2009;223:289–301.CrossRefGoogle Scholar
  20. 20.
    Reiffel A, Zhou S, Chan S, Kafka C, Popa S, Spector J, et al. CAD-CAM tissue engineering of auricular cartilage scaffolds for reconstruction of pediatric microtia. In: Northeastern Society Plastic Surgeons. 2011.
  21. 21.
    Armstrong JPK, Stevens MM. Emerging technologies for tissue engineering: from gene editing to personalized medicine. Tissue Eng Part A. 2019;25:688–92.CrossRefGoogle Scholar
  22. 22.
    Boschetti F, Raimondi MT, Migliavacca F, Dubini G. Prediction of the micro-fluid dynamic environment imposed to three-dimensional engineered cell systems in bioreactors. J Biomech. 2006;39:418–25.CrossRefGoogle Scholar
  23. 23.
    Gemmiti CV, Guldberg RE. Shear stress magnitude and duration modulates matrix composition and tensile mechanical properties in engineered cartilaginous tissue. Biotechnol Bioeng. 2009;104:809–20.PubMedPubMedCentralGoogle Scholar
  24. 24.
    Pazzano D, Mercier KA, Moran JM, Fong SS, DiBiasio DD, Rulfs JX, et al. Comparison of chondrogensis in static and perfused bioreactor culture. Biotechnol Prog. 2000;16:893–6.CrossRefGoogle Scholar
  25. 25.
    Hu JC, Athanasiou KA. The effects of intermittent hydrostatic pressure on self-assembled articular cartilage constructs. Tissue Eng. 2006;12:1337–44.CrossRefGoogle Scholar
  26. 26.
    Shakeel M, Raza S. Nonlinear computational model of biological cell proliferation and nutrient delivery in a bioreactor. Appl Math (Irvine). 2014;5:2284–98.CrossRefGoogle Scholar
  27. 27.
    Bilgen B, Barabino GA. Location of scaffolds in bioreactors modulates the hydrodynamic environment experienced by engineered tissues. Biotechnol Bioeng. 2007;98:282–94.CrossRefGoogle Scholar
  28. 28.
    Sucosky P, Osorio DF, Brown JB, Neitzel GP. Fluid mechanics of a spinner-flask bioreactor. Biotechnol Bioeng. 2004;85:34–46.CrossRefGoogle Scholar
  29. 29.
    Cinbiz MN, Tığlı RS, Beşkardeş IG, Gümüşderelioğlu M, Colak U. Computational fluid dynamics modeling of momentum transport in rotating wall perfused bioreactor for cartilage tissue engineering. J Biotechnol. 2010;150:389–95.CrossRefGoogle Scholar
  30. 30.
    Sacco R, Causin P, Zunino P, Raimondi MT. A multiphysics/multiscale 2D numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor. Biomech Model Mechanobiol. 2011;10:577–89.CrossRefGoogle Scholar
  31. 31.
    Pisu M, Lai N, Cincotti A, Concas A, Cao G. Modeling of engineered cartilage growth in rotating bioreactors. Chem Eng Sci. 2004;59:5035–40.CrossRefGoogle Scholar
  32. 32.
    Williams KA, Saini S, Wick TM. Computational fluid dynamics modeling of steady-state momentum and mass transport in a bioreactor for cartilage tissue engineering. Biotechnol Prog. 2002;18:951–63.CrossRefGoogle Scholar
  33. 33.
    Gharravi AM, Orazizadeh M, Hashemitabar M, Ansari-Asl K, Banoni S, Alifard A, et al. Design and validation of perfusion bioreactor with low shear stress for tissue engineering. J Med Biol Eng. 2013;33:185–92.CrossRefGoogle Scholar
  34. 34.
    Laganà K, Moretti M, Dubini G, Raimondi MT. A new bioreactor for the controlled application of complex mechanical stimuli for cartilage tissue engineering. Proc Inst Mech Eng H. 2008;222:705–15.CrossRefGoogle Scholar
  35. 35.
    Raimondi MT, Causin P, Mara A, Nava M, Laganà M, Sacco R. Breakthroughs in computational modeling of cartilage regeneration in perfused bioreactors. IEEE Trans Biomed Eng. 2011;58:3496–9.CrossRefGoogle Scholar
  36. 36.
    Klein TJ, Sah RL. Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion: a continuum model of matrix metabolism and transport. Biomech Model Mechanobiol. 2007;6:21–32.CrossRefGoogle Scholar
  37. 37.
    Spitters TW, Leijten JC, Deus FD, Costa IB, van Apeldoorn AA, van Blitterswijk CA, et al. A dual flow bioreactor with controlled mechanical stimulation for cartilage tissue engineering. Tissue Eng Part C Methods. 2013;19:774–83.CrossRefGoogle Scholar
  38. 38.
    Santoro R, Olivares AL, Brans G, Wirz D, Longinotti C, Lacroix D, et al. Bioreactor based engineering of large-scale human cartilage grafts for joint resurfacing. Biomaterials. 2010;31:8946–52.CrossRefGoogle Scholar
  39. 39.
    Vaca-González JJ, Gutiérrez ML, Guevara JM, Garzón-Alvarado DA. Cellular automata model for human articular chondrocytes migration, proliferation and cell death: an in vitro validation. Silico Biol. 2017;12:83–93.CrossRefGoogle Scholar
  40. 40.
    Lutianov M, Naire S, Roberts S, Kuiper JH. A mathematical model of cartilage regeneration after cell therapy. J Theor Biol. 2011;289:136–50.CrossRefGoogle Scholar
  41. 41.
    Shakhawath Hossain M, Bergstrom DJ, Chen XB. A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor. Biotechnol Bioeng. 2015;112:2601–10.CrossRefGoogle Scholar
  42. 42.
    Vahdati A, Wagner DR. Implant size and mechanical properties influence the failure of the adhesive bond between cartilage implants and native tissue in a finite element analysis. J Biomech. 2013;46:1554–60.CrossRefGoogle Scholar
  43. 43.
    Vahdati A, Wagner DR. Finite element study of a tissue-engineered cartilage transplant in human tibiofemoral joint. Comput Methods Biomech Biomed Engin. 2012;15:1211–21.CrossRefGoogle Scholar
  44. 44.
    Hossain MS, Bergstrom DJ, Chen XB. Modelling and simulation of the chondrocyte cell growth, glucose consumption and lactate production within a porous tissue scaffold inside a perfusion bioreactor. Biotechnol Rep (Amst). 2015;5:55–62.CrossRefGoogle Scholar
  45. 45.
    Sengers BG, van Donkelaar CC, Oomens CW, Baaijens FP. Computational study of culture conditions and nutrient supply in cartilage tissue engineering. Biotechnol Prog. 2005;21:1252–61.CrossRefGoogle Scholar
  46. 46.
    Cassani S, Olson SD. A hybrid cellular automaton model of cartilage regeneration capturing the interactions between cellular dynamics and scaffold porosity. arXiv. 2018.
  47. 47.
    Freed LE, Marquis JC, Langer R, Vunjak-Novakovic G. Kinetics of chondrocyte growth in cell-polymer implants. Biotechnol Bioeng. 1994;43:597–604.CrossRefGoogle Scholar
  48. 48.
    Catt CJ, Schuurman W, Sengers BG, van Weeren PR, Dhert WJ, Please CP, et al. Mathematical modelling of tissue formation in chondrocyte filter cultures. Eur Cell Mater. 2011;22:377–92.CrossRefGoogle Scholar
  49. 49.
    Hossain MS, Bergstrom DJ, Chen XB. Computational modelling of the scaffold-free chondrocyte regeneration: a two-way coupling between the cell growth and local fluid flow and nutrient concentration. Biomech Model Mechanobiol. 2015;14:1217–25.CrossRefGoogle Scholar
  50. 50.
    Raimondi MT, Bonacina E, Candiani G, Laganà M, Rolando E, Talò G, et al. Comparative chondrogenesis of human cells in a 3D integrated experimental-computational mechanobiology model. Biomech Model Mechanobiol. 2011;10:259–68.CrossRefGoogle Scholar
  51. 51.
    Nava MM, Raimondi MT, Pietrabissa R. A multiphysics 3D model of tissue growth under interstitial perfusion in a tissue-engineering bioreactor. Biomech Model Mechanobiol. 2013;12:1169–79.CrossRefGoogle Scholar
  52. 52.
    Guyot Y, Papantoniou I, Luyten FP, Geris L. Coupling curvature-dependent and shear stress-stimulated neotissue growth in dynamic bioreactor cultures: a 3D computational model of a complete scaffold. Biomech Model Mechanobiol. 2016;15:169–80.CrossRefGoogle Scholar
  53. 53.
    Guyot Y, Papantoniou I, Chai YC, Van Bael S, Schrooten J, Geris L. A computational model for cell/ECM growth on 3D surfaces using the level set method: a bone tissue engineering case study. Biomech Model Mechanobiol. 2014;13:1361–71.CrossRefGoogle Scholar
  54. 54.
    Guyot Y, Luyten FP, Schrooten J, Papantoniou I, Geris L. A three-dimensional computational fluid dynamics model of shear stress distribution during neotissue growth in a perfusion bioreactor. Biotechnol Bioeng. 2015;112:2591–600.CrossRefGoogle Scholar
  55. 55.
    Guyot Y, Smeets B, Odenthal T, Subramani R, Luyten FP, Ramon H, et al. Immersed boundary models for quantifying flow-induced mechanical stimuli on stem cells seeded on 3D scaffolds in perfusion bioreactors. PLoS Comput Biol. 2016;12:e1005108.CrossRefGoogle Scholar
  56. 56.
    Bandeiras C, Completo A. A mathematical model of tissue-engineered cartilage development under cyclic compressive loading. Biomech Model Mechanobiol. 2017;16:651–66.CrossRefGoogle Scholar
  57. 57.
    Mizuno S, Tateishi T, Ushida T, Glowacki J. Hydrostatic fluid pressure enhances matrix synthesis and accumulation by bovine chondrocytes in three-dimensional culture. J Cell Physiol. 2002;193:319–27.CrossRefGoogle Scholar
  58. 58.
    DiMicco MA, Sah RL. Dependence of cartilage matrix composition on biosynthesis, diffusion, and reaction. Transp Porous Media. 2003;50:57–73.CrossRefGoogle Scholar
  59. 59.
    Hossain MS, Bergstrom DJ, Chen XB. Prediction of cell growth rate over scaffold strands inside a perfusion bioreactor. Biomech Model Mechanobiol. 2015;14:333–44.CrossRefGoogle Scholar
  60. 60.
    Hauge Ø, Ayala C, Conradi R. Adoption of open source software in software-intensive organizations—a systematic literature review. Inf Softw Technol. 2010;52:1133–54.CrossRefGoogle Scholar
  61. 61.
    Abar S, Theodoropoulos GK, Lemarinier P, O’Hare GMP. Agent Based Modelling and Simulation tools: a review of the state-of-art software. Comput Sci Rev. 2017;24:13–33.CrossRefGoogle Scholar
  62. 62.
    Solovyev A, Mikheev M, Zhou L, Dutta-Moscato J, Ziraldo C, An G, et al. SPARK: a framework for multi-scale agent-based biomedical modeling. Int J Agent Technol Syst. 2010;2:18–30.CrossRefGoogle Scholar
  63. 63.
    Swat MH, Thomas GL, Belmonte JM, Shirinifard A, Hmeljak D, Glazier JA. Multi-scale modeling of tissues using CompuCell 3D. Methods Cell Biol. 2012;110:325–66.CrossRefGoogle Scholar
  64. 64.
    UConn Health. VCell Modeling and Analysis Software. Accessed May 10 2019.
  65. 65.
    Ghaffarizadeh A, Heiland R, Friedman SH, Mumenthaler SM, Macklin P. PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput Biol. 2018;14:e1005991.CrossRefGoogle Scholar
  66. 66.
    Hockings C, Brett P, Terentjevs M. Making a difference—inclusive learning and teaching in higher education through open educational resources. Distance Education. 2012;33:237–52.CrossRefGoogle Scholar
  67. 67.
    Knox J. The limitations of access alone: moving towards open processes in education technology. Open Praxis. 2003;5:21–9.Google Scholar
  68. 68.
    Metzcar J, Wang Y, Heiland R, Macklin P. A review of cell-based computational modeling in cancer biology. JCO Clin Cancer Inform. 2019;3:1–13.CrossRefGoogle Scholar
  69. 69.
    Fischer DS, Fiedler AK, Kernfeld EM, Genga RMJ, Bastidas-Ponce A, Bakhti M, et al. Inferring population dynamics from single-cell RNA-sequencing time series data. Nat Biotechnol. 2019;37:461–8.CrossRefGoogle Scholar
  70. 70.
    Saelens W, Cannoodt R, Todorov H, Saeys Y. A comparison of single-cell trajectory inference methods. Nat Biotechnol. 2019;37:547–54.CrossRefGoogle Scholar
  71. 71.
    Sommer C, Gerlich DW. Machine learning in cell biology—teaching computers to recognize phenotypes. J Cell Sci. 2013;126:5529–39.CrossRefGoogle Scholar
  72. 72.
    Reiter DA, Irrechukwu O, Lin PC, Moghadam S, Von Thaer S, Pleshko N, et al. Improved MR-based characterization of engineered cartilage using multiexponential T2 relaxation and multivariate analysis. NMR Biomed. 2012;25:476–88.CrossRefGoogle Scholar

Copyright information

© The Korean Tissue Engineering and Regenerative Medicine Society 2019

Authors and Affiliations

  1. 1.Department of EngineeringEast Carolina UniversityGreenvilleUSA
  2. 2.Department of Biomedical EngineeringUniversity of StuttgartStuttgartGermany

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