Advertisement

A computational reaction–diffusion model for biosynthesis and linking of cartilage extracellular matrix in cell-seeded scaffolds with varying porosity

  • Sarah D. OlsonEmail author
  • Mansoor A. Haider
Original Paper
  • 40 Downloads

Abstract

Cartilage tissue engineering is commonly initiated by seeding cells in porous materials such as hydrogels or scaffolds. Under optimal conditions, the resulting engineered construct has the potential to fill regions where native cartilage has degraded or eroded. Within a cell-seeded scaffold supplied by nutrients and growth factors, extracellular matrix accumulation should occur concurrently with scaffold degradation. At present, the interplay between cell-mediated synthesis and linking of matrix constituents and the evolving scaffold properties is not well understood. We develop a computational model of extracellular matrix accumulation in a cell-seeded scaffold based on a continuum reaction–diffusion system with inhomogeneous inclusions representing individual cells. The effects of porosity on engineered tissue outcomes is accounted for via the use of mixture variables capturing the spatiotemporal dynamics of both bound and unbound system constituents. The unbound constituents are the nutrients and unlinked extracellular matrix, while the bound constituents are the scaffold and the linked extracellular matrix. The linking model delineates binding of matrix constituents to either existing bound extracellular matrix or to scaffold. Results on a representative domain exhibit bound matrix trapping (vs spreading) around cells in scaffolds with lower (vs higher) initial porosity, similar to experimental results obtained by Erickson et al. (Osteoarthr Cartil 17:1639–1648, 2009). Significant alterations in the spatiotemporal accumulation of bound matrix are observed when, among the set of all model parameters, only the initial scaffold porosity is varied. The model presented herein proposes a methodology to investigate coupling between cell-mediated biosynthesis and linking of extracellular matrix in porous, cell-seeded scaffolds that has the potential to aid in the design of optimal tissue-engineered cartilage constructs.

Keywords

Scaffold porosity Tissue-engineered cartilage Extracellular matrix linking Reaction–diffusion Computational model 

Notes

Funding

This study was funded in part by the National Science Foundation (Olson—1455270, Haider—1615820).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Ateshian GA (2007) On the theory of reactive mixtures for modeling biological growth. Biomech Model Mechanobiol 6:423–445CrossRefGoogle Scholar
  2. Ateshian GA, Costa KD, Azeloglu EU, Morrison B, Hung CT (2009) Continuum modeling of biological tissue growth by cell division, and alteration of intracellular osmolytes and extracellular fixed charge density. J Biomech Eng 131:10101Google Scholar
  3. Ateshian GA, Nims RJ, Maas S, Weiss JA (2014) Computational modeling of chemical reactions and interstitial growth and remodeling involving charged solutes and solid-bound molecules. Biomech Model Mechanobiol 13:1105–1120CrossRefGoogle Scholar
  4. Bandeiras C, Completo A, Ramos A (2015) Influence of the scaffold geometry on the spatial and temporal evolution of the mechanical properties of tissue-engineered cartilage: insights from a mathematical model. Biomech Model Mechanobiol 14:1057–1070CrossRefGoogle Scholar
  5. Buschmann MD, Gluzband Y, Grodzinsky AJ, Kimura JH, Hunziker EB (1992) Chondrocytes in agarose culture synthesize a mechanically functional extracellular matrix. J Orthop Res 10:745–758CrossRefGoogle Scholar
  6. Buxton AN, Zhu J, Marchant R, West JL, Yoo JU, Johnston B (2007) Design and characterization of poly(ethylene glycol) photopolymerizable semi-interpenetrating networks for chondrogenesis of human mesenchymal stem cells. Tissue Eng 13:2549–2560CrossRefGoogle Scholar
  7. Chomchalao P, Pongcharoen S, Sutheerawattananonda M, Tiyaboonchai W (2013) Fibroin and fibroin blended three-dimensional scaffolds for rat chondrocyte culture. Biomech Eng Online 12:28CrossRefGoogle Scholar
  8. Chung CA, Chen CW, Chen CP, Tseng CS (2007) Enhancement of cell growth in tissue-engineering constructs under direct perfusion: modeling and simulation. Biotechnol Bioeng 97:1603–1616CrossRefGoogle Scholar
  9. Chung CA, Lin TH, Chen SD, Huang HI (2010) Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs. J Theor Biol 262:267–278CrossRefzbMATHGoogle Scholar
  10. Cigan AD, Roach BL, Nims RJ, Tan AR, Albro MB, Stoker AM, Cook JL, Vunjak-Novakovic G, Hung CT, Ateshian GA (2016) High seeding density of human chondrocytes in agarose produces tissue-engineered cartilage approaching native mechanical and biochemical properties. J Biomech 49:1909–1917CrossRefGoogle Scholar
  11. Comper WD, Williams RPW (1987) Hydrodynamics of concentrated proteoglycan solutions. J Biol Chem 262:13464–13471Google Scholar
  12. Dado D, Levenberg S (2009) Cell-scaffold mechanical interplay within engineered tissue. Semin Cell Dev Biol 20:656–664CrossRefGoogle Scholar
  13. Dimicco MA, Sah RL (2003) Dependence of cartilage matrix composition on biosynthesis, diffusion and reaction. Transp Porous Media 50:57–73CrossRefGoogle Scholar
  14. Erickson E, Huang AH, Sengupta S, Kestle S, Burdick JA, Mauck RL (2009) Macromer density influences mesenchymal stem cell chondrogenesis and maturation in photocrosslinked hyaluronic acid hydrogels. Osteoarthr Cartil 17:1639–1648CrossRefGoogle Scholar
  15. Fernandes H, Moroni L, van Bitterswijk C, de Boer J (2009) Extracellular matrix and tissue engineering applications. J Mater Chem 19:5474–5484CrossRefGoogle Scholar
  16. Freed LE, Marquis JC, Vunjak-Novakovic G, Emmanual J, Langer R (1994a) Composition of cell-polymer cartilage implants. Biotechnol Bioeng 43:605–614CrossRefGoogle Scholar
  17. Freed LE, Vunjak-Novakovic G, Marquis JC, Langer R (1994b) Kinetics of chondrocyte growth in cell-polymer implants. Biotechnol Bioeng 43:597–604CrossRefGoogle Scholar
  18. Freyria AM, Mallein-Gerin F (2012) Chondrocytes or adult stem cells for cartilage repair: the indisputable role of growth factors. Injury 43:259–265CrossRefGoogle Scholar
  19. Goldring MB, Goldring SR (2007) Osteoarthritis. J Cell Physiol 213:626–634CrossRefGoogle Scholar
  20. Gribbon P, Hardingham TE (1998) Macromolecular diffusion of biological polymers measured by confocal fluorescence recovery after photobleaching. Biophys J 75:1032–1039CrossRefGoogle Scholar
  21. Gu WY, Yao H, Vega AL, Flagler D (2004) Diffusivity of ions in agarose gels and intervertebral disc: effect of porosity. Ann Biomed Eng 32(12):1710–1717CrossRefGoogle Scholar
  22. Haider MA, Olander JE, Arnold RF, Marous DR, McLamb AJ, Thompson KC, Woodruff WR, Haugh JM (2011) A phenomenological mixture model for biosynthesis and linking of cartilage extracellular matrix in scaffolds seeded with chondrocytes. Biomech Model Mechanobiol 10:915–924CrossRefGoogle Scholar
  23. Handley S, Lowther DA (1977) Extracellular matrix metabolism by chondrocytes III. Modulation of proteoglycan synthesis by extracellular levels of proteoglycan in cartilage cells in culture. Biochim Biophys Acta 500:132–139CrossRefGoogle Scholar
  24. Haugh MG, Murphy CM, O’Brien FJ (2010) Novel freeze-drying methods to produce a range of collagen-glycosaminoglycan scaffolds with tailored mean pore sizes. Tissue Eng C 16:887–894CrossRefGoogle Scholar
  25. Hauselmann HJ, Aydelotte MB, Schumacher BL, Kuettner KE, Gitelis SH, Thonar E (1992) Synthesis and turnover of proteoglycans by human and bovine adult articular chondrocytes cultured in alginate beads. Matrix 12:116–129CrossRefGoogle Scholar
  26. Hossain MS, Bergstrom DJ, Chen XB (2015) Modelling and simulation of the chondrocyte cell growth, glucose consumption and lactate production within a porous tissue scaffold inside a perfusion bioreactor. Biotech Rep 5:55–62CrossRefGoogle Scholar
  27. Ingber DE (2006) Cellular mechanotransduction: putting all the pieces together again. FASEB J 20:811–827CrossRefGoogle Scholar
  28. Jutila AA, Zignego DL, Hwang BK, Hilmer JK, Hamerly T, Minor CA, Walk ST, June RK (2014) Candidate mediators of chondrocyte mechanotransduction via targeted and untargeted metabolomic measurements. Arch Biochem Biophys 545:116–123CrossRefGoogle Scholar
  29. Keeney M, Lai JH, Yang F (2011) Recent progress in cartilage tissue engineering. Curr Opin Biotech 22:734–740CrossRefGoogle Scholar
  30. Kipper MJ, Almodovar JL (2010) Engineering soft nano structures for guided cell response. In: Popat K (ed) Nanotechnology in tissue engineering and regenerative medicine. CRC Press, Boca RatonGoogle Scholar
  31. Kock L, van Donkelaar CC, Ito K (2012) Tissue engineering of functional articular cartilage: the current status. Cell Tissue Res 347:613–627CrossRefGoogle Scholar
  32. Kretlow JD, Mikos AG (2008) From material to tissue: biomaterial development, scaffold fabrication, and tissue engineering. AIChE J 54:3048–3067CrossRefGoogle Scholar
  33. Kuberka M, von Heimburg D, Schoof H, Heschel I, Rau G (2002) Magnification of the pore size in biodegradable collagen sponges. Int J Artif Organs 25:67–73CrossRefGoogle Scholar
  34. Lemon G, King JR, Byrne HM, Jensen OE, Shakesheff KM (2006) Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory. J Math Biol 52:571–594MathSciNetCrossRefzbMATHGoogle Scholar
  35. Mak AF (1986) The apparent viscoelastic behavior of articular cartilage—the contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. J Biomech Eng 108:123–130CrossRefGoogle Scholar
  36. Maroudas A (1970) Distribution and diffusion of solutes in articular cartilage. Biophys J 10(5):365–379CrossRefGoogle Scholar
  37. Masaro L, Zhu XX (1999) Physical models of diffusion for polymer solutions, gels, and solids. Prog Polym Sci 24:731–755CrossRefGoogle Scholar
  38. Matsiko A, Gleeson JP, O’Brien FJ (2015) Scaffold mean pore size influences mesenchymal stem cell chondrogenic differentiation and matrix deposition. Tissue Eng A 21:486–497CrossRefGoogle Scholar
  39. Mohan R, Mohan N, Vaiikath D (2018) Hyaluronic acid dictates chondrocyte morphology and migration in composite gels. Tiss Eng A 24:1481–1491CrossRefGoogle Scholar
  40. Mollenhauer JA (2008) Perspectives on articular cartilage biology and osteoarthritis. Injury 39:S5–S12CrossRefGoogle Scholar
  41. Mourao PAS, Michelacci YM, Toledo OMS (1979) Glycosaminoglycans and proteoglycans of normal and tumoral cartilages of humans and rats. Cancer Res 39:2802–2806Google Scholar
  42. Mow VC, Ratcliffe A, Poole AR (1992) Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures. Biomaterials 13:67–97CrossRefGoogle Scholar
  43. Musielak MM, Karp-Boss L, Jumars PA, Fauci LJ (2009) Nutrient transport and acquisition by diatom chains in a moving fluid. J Fluid Mech 638:401–421MathSciNetCrossRefzbMATHGoogle Scholar
  44. Narayanan J, Xiong JY, Liu XY (2006) Determination of agarose gel pore size: absorbance measurements vis a vis other techniques. J Phys Conf Ser 28:83–86CrossRefGoogle Scholar
  45. Nava MM, Raimondi MT, Pietrabissa R (2013) A multiphysics 3D model of tissue growth under interstitial perfusion in a tissue engineering bioreactor. Biomech Model Mechanobiol 12:1169–79CrossRefGoogle Scholar
  46. Nikolaev NI, Obradovic B, Versteeg HK, Lemon G, Williams DJ (2010) A validated model of GAG deposition, cell distribution, and growth of tissue engineered cartilage cultured in a rotating bioreactor. Biotechnol Bioeng 105:842–853Google Scholar
  47. Obradovic B, Meldon JH, Freed LE (2000) Glycosaminoglycan (GAG) deposition in engineered cartilage: experiments and mathematical model. AIChE J 46:1860–1871CrossRefGoogle Scholar
  48. O’Dea RD, Osborne JM, El Haj AJ, Byrne HM, Waters L (2013) The interplay between tissue growth and scaffold degradation in engineered tissue constructs. J Math Biol 67:1199–1225MathSciNetCrossRefzbMATHGoogle Scholar
  49. Pernodet N, Maaloum M, Tinland B (1997) Pore size of agarose gels by atomic force microscopy. Eletrophoresis 18:55–58CrossRefGoogle Scholar
  50. Podrazky V, Sedmerova V (1966) Densities of collagen dehydrated by some organic solvents. Cell Mol Life Sci 32:871–879Google Scholar
  51. Rai V, Dillisio MF, Dietz NE, Agrawal DK (2017) Recent strategies in cartilage repair: a systematic review of the scaffold development and tissue engineering. J Biomed Mater Res 105:2343–2354CrossRefGoogle Scholar
  52. Reddi AH, Becerra J, Andrades JA (2011) Nanomaterials and hydrogel scaffolds for articular cartilage regeneration. Tissue Eng B 17:301–305CrossRefGoogle Scholar
  53. Sacco R, Causin P, Zunino P, Raimondi MT (2011) A multiphysics/multiscale 2D numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor. Biomech Model Mechanobiol 10:577–589CrossRefGoogle Scholar
  54. Saha AK, Mazumdar J, Kohles SS (2004) Prediction of growth factor effects on engineered cartilage composition using deterministic and stochastic modeling. Ann Biomed Eng 32:871–879CrossRefGoogle Scholar
  55. Salinas EY, Hu JC, Athanasiou K (2018) A guide for using mechanical stimulation to enhance tissue-engineered articular cartilage properties. Tissue Eng Part B Rev.  https://doi.org/10.1089/ten.teb.2018.0006
  56. Sanchez-Adams J, Athanasiou KA (2010) Biomechanical characterization of single chondrocytes. In: Gefen A (ed) Cellular and biomolecular mechanisms and mechanobiology. Studies in mechanobiology, tissue engineering, and biomaterials, vol 4. Springer, BerlinGoogle Scholar
  57. Sengers BG, van Donkelaar CC, Oomens CWJ, Baaijens FPT (2004) The local matrix distribution and the functional development of tissue engineered cartilage, a finite element study. Ann Biomed Eng 32:1718–1727CrossRefGoogle Scholar
  58. Sengers BG, van Donkelaar CC, Oomens CWJ, Baaijens FPT (2005a) Computational study of culture conditions and nutrient supply in cartilage tissue engineering. Biotechnol Prog 21:1252–1261CrossRefGoogle Scholar
  59. Sengers BG, Heywood HK, Lee DA, Oomens CWJ, Bader DL (2005b) Nutrient utilization by bovine articular chondrocytes: a combined experimental and theoretical approach. J Biomech Eng 127:758–766CrossRefGoogle Scholar
  60. Sengers BG, Taylor M, Please CP, Oreffo OC (2007) Computational modelling of cell spreading and tissue regeneration in porous scaffolds. Biomaterials 28:1926–1940CrossRefGoogle Scholar
  61. Song X, Zhu C, Fan D, Mi Y, Li X, Fu RZ, Duan Z, Wang Y, Feng RR (2017) A novel human-like collagen hydrogel scaffold with porous structures and sponge-like properties. Polymers 9:638CrossRefGoogle Scholar
  62. Trewenack AJ, Please CP, Landman KA (2009) A continuum model for the development of tissue-engineered cartilage around a chondrocyte. Math Med Biol 26:241–262CrossRefzbMATHGoogle Scholar
  63. Vunjak-Novakic G, Obradovic B, Martin I, Bursac PM, Langer R, Freed LE (1998) Dynamic cell seeding of polymer scaffolds for cartilage tissue engineering. Biotechnol Prog 14:193–202CrossRefGoogle Scholar
  64. Waggoner GR (2013) Effects of glucose levels on glucose consumption and viability of chondrocytes and intervertebral disc cells. Open Access Theses, vol 429. Retrieved from Scholarly RepositoryGoogle Scholar
  65. Wilson CG, Bonassar LJ, Kohles SS (2002) Modeling the dynamic composition of engineered cartilage. Arch Biochem Biophys 408:246–254CrossRefGoogle Scholar
  66. Wong M, Carter DR (2003) Articular cartilage functional histomorphology and mechanobiology: a research perspective. Bone 33:1–13CrossRefGoogle Scholar
  67. Zhang J, Yang S, Yang X, Zhenhao X, Zhao L, Cen L, Lu E, Yang Y (2018) Novel fabricating process for porous polyglycolic acid scaffolds by melt-foaming using supercritical carbon dioxide. ACS Biomater Sci Eng 4:694–706CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

Personalised recommendations