The interplay between tissue growth and scaffold degradation in engineered tissue constructs

Journal of Mathematical Biology

Volumn 67, Issue 5, 2013, Pages 1199-1225

  O'Dea, R D ^a   Osborne, J M ^b   El Haj, A J ^c   Byrne, H M ^b   Waters, S L ^b  

^a NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c KEELE UNIVERSITY   (United Kingdom)

Author keywords

Multiphase; Perfusion bioreactor; Scaffold heterogeneity

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; BIOREACTOR; CELL PROLIFERATION; COMPUTER SIMULATION; EXTRACELLULAR MATRIX; HUMAN; MECHANOTRANSDUCTION; METHODOLOGY; PHYSIOLOGY; TISSUE ENGINEERING;

BIOREACTORS; CELL PROLIFERATION; COMPUTER SIMULATION; EXTRACELLULAR MATRIX; HUMANS; MECHANOTRANSDUCTION, CELLULAR; MODELS, BIOLOGICAL; TISSUE ENGINEERING;

EID: 84885373180     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-012-0587-9     Document Type: Article

References (52)

1. Adachi T, Osako Y, Tanaka M, Hojo M, Hollister SJ (2006) Framework for optimal design of porous scaffold microstructure by compututational simulation of bone regeneration. Biomaterials 27: 3964-3972.
2. Ahearne M, Wilson SL, Liu K-K, Rauz S, El Haj AJ, Yang Y (2010) Influence of cell and collagen concentration on the cell-matrix mechanical relationship in a corneal stroma wound healing model. Exp Eye Res 91: 584-591.
3. Araujo RP, McElwain DLS (2005) A mixture theory for the genesis of residual stresses in growing tissues i: a general formulation. SIAM J Appl Math 65(4): 1261-1284.
4. Bakker A, Klein-Nulend J, Burger E (2004a) Shear stress inhibits while disuse promotes osteocyte apoptosis. Biochem Biophys Res Commun 320(4): 1163-1168.
5. Bakker A, Klein-Nulend J, Burger E (2004b) Shear stress inhibits while disuse promotes osteocyte apoptosis. Biochem Biophys Res Comm 320: 1163-1168.
6. Breward CJW, Byrne HM, Lewis CE (2002) The role of cell-cell interactions in a two-phase model for avascular tumour growth. J Math Biol 45: 125-152.
7. Burdick JA, Mauck RL (eds) (2010) Biomaterials for tissue engineering applications: a review of the past and future trends. Springer, Wien.
8. Byrne DP, Lacroix D, Planell JA, Kelly DJ, Prendergast PJ (2007) Simulation of tissue differentiation in a scaffold as a function of porosity, Young's modulus and dissolution rate: application of mechanobiological models in tissue engineering. Biomaterials 28(36): 5544-5554.
9. Byrne HM, Preziosi L (2003) Modelling solid tumour growth using the theory of mixtures. Math Med Biol 20(4): 341-366.
10. Cartmell SH, El Haj AJ (2005) Mechanical bioreactors for tissue engineering. In: Chaudhuri J, Al-Rubeai M (eds) Bioreactors for tissue engineering: principles, design and operation, chapt. 8. Springer, Dordrecht, pp 193-209.
11. Chaplain MAJ, Graziano L, Preziosi L (2006) Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Math Med Biol 23(3): 197.
12. Cowin SC (2000) How is a tissue built? J Biomech Eng 122: 553.
13. Cowin SC (2004) Tissue growth and remodeling. Ann Rev Biomed Eng 6(1): 77-107.
14. Curtis A, Riehle M (2001) Tissue engineering: the biophysical background. Phys Med Biol 46: 47-65.
15. Drew DA, Segel LA (1971) Averaged equations for two-phase flows. Studies Appl Math 50: 205-231.
16. El Haj AJ, Minter SL, Rawlinson SC, Suswillo R, Lanyon LE (1990) Cellular responses to mechanical loading in vitro. J Bone Min Res 5(9): 923-932.
17. Franks SJ, King JR (2003) Interactions between a uniformly proliferating tumour and its surroundings: uniform material properties. Math Med Biol 20: 47-89.
18. Freed LE, Vunjak-Novakovic G (1998) Culture of organized cell communities. Adv Drug Deliv Rev 33: 15-30.
19. Freed LE, Vunjak-Novakovic G, Biron RJ, Eagles DB, Lesnoy DC, Barlow SK, Langer R (1994) Biodegradable polymer scaffolds for tissue engineering. Nat Biotech 12(7): 689-693.
20. Fung YC (1991) What are residual stresses doing in our blood vesels? Ann Biomed Eng 19: 237-249.
21. Haider MA, Olander JE, Arnold RF, Marous DR, McLamb AJ, Thompson KC, Woodruff WR, Haugh JM (2010) A phenomenological mixture model for biosynthesis and linking of cartilage extracellular matrix in scaffolds seeded with chondrocytes. Biomech Model Mechanobiol 1-10. ISSN 1617-7959.
22. Han Y, Cowin SC, Schaffler MB, Weinbaaum S (2004) Mechanotransduction and strain amplification in osteocyte cell processes. Proc Natl Acad Sci 101(47): 16689-16694.
23. Holzapfel GA, Ogden RW (2006) Mechanics of biological tissue. Springer, Berlin.
24. Kelly DJ, Prendergast PJ (2003) Effect of a degraded core on the mechanical behaviour of tissue-engineered cartilage constructs: a poro-elastic finite element analysis. Med Biol Eng Comp 42: 9-13.
25. Klein-Nulend J, Roelofsen J, Sterck JG, Semeins CM, Burger EH (1995) Mechanical loading stimulates the release of transforming growth factor-beta activity by cultured mouse calvariae and periosteal cells. J Cell Physiol 163(1): 115-119.
26. Wu L, Ding J (2004) In vitro degradation of three-dimensional porous poly(d, l-lactide-co-glycolide) scaffolds for tissue engineering. Biomaterials 25(27): 5821-5830.
27. Landman KA, Please CP (2001) Tumour dynamics and necrosis: surface tension and stability. IMA J Math Appl Med Biol 18(2): 131-158.
28. Lemon G, King JR (2007) Multiphase modelling of cell behaviour on artificial scaffolds: effects of nutrient depletion and spatially nonuniform porosity. Math Med Biol 24(1): 57.
29. Lemon G, King JR, Byrne HM, Jensen OE, Shakesheff K (2006) Multiphase modelling of tissue growth using the theory of mixtures. J Math Biol 52(2): 571-594.
30. Lewis MC, Macarthur BD, Malda J, Pettet G, Please CP (2005) Heterogeneous proliferation within engineered cartilaginous tissue: the role of oxygen tension. Biotech Bioeng 91(5): 607-615.
31. Lubkin SR, Jackson T (2002) Multiphase mechanics of capsule formation in tumors. J Biomech Eng 124: 237.
32. Martin I, Wendt D, Heberer M (2004) The role of bioreactors in tissue engineering. Trends Biotechnol 22(2): 80-86.
33. Nikolovski J, Mooney DJ (2000) Smooth muscle cell adhesion to tissue engineering scaffolds. Biomaterials 21(20): 2025-2032.
34. O'Dea RD, Waters SL, Byrne HM (2008) A two-fluid model for tissue growth within a dynamic flow environment. Eur J Appl Math 19(641): 607-634.
35. O'Dea RD, Waters SL, Byrne HM (2010) A three phase model for tissue construct growth in a perfusion bioreactor. J Math Med Biol 27(2): 95-127.
36. O'Dea RD, Waters SL, Byrne HM (2012) Modelling tissue growth in bioreactors: a review. In: Geris L (ed) Computational modeling in tissue engineering. Springer, Berlin.
37. Osborne JM, O'Dea RD, Whiteley JP, Byrne HM, Waters SL (2010) The influence of bioreactor geometry and the mechanical environment on engineered tissues. J Biomech Eng 132(5), doi: 10. 1115/1. 4001160.
38. Osborne JM, Whiteley JP (2010) A numerical method for the multiphase viscous flow equations. Comput Methods Appl Mech Engrg 199: 3402-3417. doi: 10. 1016/j. cma. 2010. 07. 011.
39. Preziosi L, Tosin A (2009) Multiphase and multiscale trends in cancer modelling. Math Model Nat Phenom 4(3): 1-11, ISSN 0973-5348.
40. Roelofsen J, Klein-Nulend J, Burger EH (1995) Mechanical stimulation by intermittent hydrostatic compression promotes bone-specific gene expression in vitro. J Biomech 28(12): 1493-1503.
41. Roose T, Neti PA, Munn LL, Boucher Y, Jain RK (2003) Solid stress generated by spheroid growth estimated using a poroelasticity model. Microvasc Res 66: 204-212.
42. Sanz-Herrera JA, García-Aznar JM, Doblaré M (2008) On scaffold designing for bone regeneration: a computational multiscale approach. Acta Biomat (online preprint).
43. Sipe JD (2002) Tissue engineering and reparative medicine. Ann N Y Acad Sci 961: 1-9.
44. Skalak R, Zargaryan S, Jain RK, Netti PA, Hoger A (1996) Compatibility and the genesis of residual stress by volumetric growth. J Math Biol 34: 889-914.
45. Urban JPG (1994) The chondrocyte: a cell under pressure. Rheumatology 33(10): 901-908.
46. VonNeumann J, Richtmyer RD (1950) A method for the numerical calculation of hydrodynamic shocks. J Appl Phys 21: 232.
47. Wang QG, Nguyen B, Thomas CR, Zhang Z, El Haj AJ, Kuiper NJ (2010) Molecular profiling of single cells in response to mechanical force: comparison of chondrocytes, chondrons and encapsulated chondrocytes. Biomaterials 31(7): 1619-1625.
48. Wilson DJ, King JR, Byrne HM (2007) Modelling scaffold occupation by a growing, nutrient-rich tissue. Math Models Methods Appl Sci 17: 1721.
49. Yang Y, El Haj AJ (2006) Biodegradable scaffolds-delivery systems for cell therapies. Expert Opin Biol Ther 6(5): 485-498.
50. You J, Yellowley CE, Donahue HJ, Zhang Y, Chen Q, Jacobs CR (2000) Substrate deformation levels associated with routine physical activity are less stimulatory to bone cells relative to loading-induced oscillatory fluid flow. J Biomech Eng 122: 377-393.
51. You L, Cowin SC, Schaffler MB, Weinbaum S (2001) A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. J Biomech 34(11): 1375-1386.
52. Yourek G, Al-Hadlaq A, Patel R, McCormick S, Reilly GC, Mao JJ (2004) Nanophysical properties of living cells. In: Stroscio Michael A, Dutta Mitra, He Bin (eds) Biological nanostructures and applications of nanostructures in biology, bioelectric engineering. Springer, US, pp 69-97.