Computers in Biology and Medicine
Volume 42, Issue 2 , Pages 147-155 , February 2012

Modeling porous scaffold microstructure by a reaction–diffusion system and its degradation by hydrolysis

  • Diego A. Garzón-Alvarado

      Affiliations

    • Engineering Modeling and Numerical Methods Group, Universidad Nacional de Colombia, Cra 30 No. 45-03, Bogotá, Colombia
    • Corresponding Author InformationCorresponding author.
  • ,
  • Marco A. Velasco

      Affiliations

    • Mechanical Engineering Applications and Research Group, Universidad Santo Tomás, Cra 9 No. 51-11, Bogotá, Colombia
  • ,
  • Carlos A. Narváez-Tovar

      Affiliations

    • Mechanical Engineering Applications and Research Group, Universidad Santo Tomás, Cra 9 No. 51-11, Bogotá, Colombia
    • Engineering Modeling and Numerical Methods Group, Universidad Nacional de Colombia, Cra 30 No. 45-03, Bogotá, Colombia

Received 12 November 2010 ,Accepted 14 November 2011.

References 

  1. Pettway GJ, et al. Anabolic actions of PTH (1–34): use of a novel tissue engineering model to investigate temporal effects on bone. Bone. 2005;36:959–970
  2. Mckenna MJ, Frame B. Hormonal influences on osteoporosis. Am. J. Med. 1987;82:61–67
  3. Heaney RP. Osteoporosis. In:  Marcus R,  Feldman D,  Kelsey J editor. Osteoporosis. Academic Press; 2001;p. 669–700
  4. Domingues ZR, et al. Bioactive glass as a drug delivery system of tetracycline and tetracycline associated with β-cyclodextrin. Biomaterials. 2004;25:327–333
  5. Fuchs B, Ossendorf C, Leerapun T, Sim FH. Intercalary segmental reconstruction after bone tumor resection. Eur. J. Surg. Oncol. 2008;34:1271–1276
  6. Knowledge Enterprises, The worldwide orthopedic market—2005–2006, no. December. Chagrin Falls, Knowledge Enterprises, 2006, p. 119.
  7. Lanza R, Langer R, Vacanti J. Principles of Tissue Engineering. 3rd ed. Elsevier, Inc.; 2007;
  8. Van Gaalen S, Kruyt M, Meijer G, Mistry A, Mikos A, van den Beucken J, et al. Tissue Engineering. In:  van Blitterswijk C,  Thomsen P,  Lindahl A,  Hubbell J,  Williams DF,  Cancedda R,  de Bruijn JD,  Sohier J editor. Tissue Engineering. Elsevier Academic Press; 2008;p. 559–610
  9. Burg KJ, Porter S, Kellam JF. Biomaterial developments for bone tissue engineering. Biomaterials. 2000;21(23):2347–2359
  10. Cook EA, Cook JJ. Bone graft substitutes and allografts for reconstruction of the foot and ankle. Clin. Podiat. Med. Surg. 2000;26:589–605
  11. Blom A. Which scaffold for which application?. Curr. Orthop. 2007;21:280–287
  12. Hutmacher DW. Scaffolds in tissue engineering bone and cartilage. Biomaterials. 2000;21(24):2529–2543
  13. Rezwan K, Chen QZ, Blaker JJ, Boccaccini AR. Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering. Biomaterials. 2006;27(18):3413–3431
  14. Dorozhkin SV. Amorphous calcium (ortho)phosphates. Acta Biomater. 2010;6(12):4457–4475
  15. Chow LC. Solubility of calcium phosphates. Monogr. Oral Sci. 2001;18:94–111
  16. Nair LS, Laurencin CT. Biodegradable polymers as biomaterials. Prog. Polym. Sci. 2007;32(8–9):762–798
  17. Madhavan Nampoothiri K, Nair NR, John RP. An overview of the recent developments in polylactide (PLA) research. Bioresource Technol. 2010;101(22):8493–8501
  18. Adachi T, Osako Y, Tanaka M, Hojo M, Hollister SJ. Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration. Biomaterials. 2006;27(21):3964–3972
  19. Göpferich A. Mechanisms of polymer degradation and erosion. Biomaterials. 1996;17(2):103–114
  20. Wang Y, Pan J, Han X, Sinka C, Ding L. A phenomenological model for the degradation of biodegradable polymers. Biomaterials. 2008;29(23):3393–3401
  21. Chen Y, Zhou S, Li Q. Mathematical modeling of degradation for bulk-erosive polymers: applications in tissue engineering scaffolds and drug delivery systems. Acta Biomater. 2011;7(3):1140–1149
  22. Kang Y, et al. A comparative study of the in vitro degradation of poly(l-lactic asid)/β-tricalcium phosphate scaffold in static and dynamic simulated body fluid. Eur. Polym. J. 2007;43(5):1768–1778
  23. Kim S-S, Sun Park M, Jeon O, Yong Choi C, Kim B-S. Poly(lactide-co-glycolide)/hydroxyapatite composite scaffolds for bone tissue engineering. Biomaterials. 2006;27(8):1399–1409
  24. Karageorgiou V, àDK. Porosity of 3D biomaterial scaffolds and osteogenesis. Biomaterials. 2005;26:5474–5491
  25. Dunn JCY, et al. Analysis of cell growth in three-dimensional scaffolds. Tissue Eng. 2006;12(4):705–716
  26. Montjovent M-O, et al. Human fetal bone cells associated with ceramic reinforced PLA scaffolds for tissue engineering. Bone. 2008;42(3):554–564
  27. Meneghello G, et al. Fabrication and characterization of poly(lactic-co-glycolic acid)/polyvinyl alcohol blended hollow fibre membranes for tissue engineering applications. J. Membr. Sci. 2009;344(1–2):55–61
  28. Meyer U, Meyer T, Handschel J, Wiesmann HP. Fundamentals of Tissue Engineering and Regenerative Medicine. Springer; 2009;
  29. Bagaria V, Deshpande S, Rasalkar DD, Kuthe A, Paunipagar BK. Use of rapid prototyping and three-dimensional reconstruction modeling in the management of complex fractures. Eur. J. Radiol. 2011;80(3):814–820
  30. Winder J, Bibb R. Medical rapid prototyping technologies: state of the art and current limitations for application in oral and maxillofacial surgery. J. Oral Maxillofac. Surg. 2005;63(7):1006–1015
  31. Zhang S, et al. Application of rapid prototyping for temporomandibular joint reconstruction. J. Oral Maxillofac. Surg. 2011;69(2):432–438
  32. Chua CK, Leong KF, Cheah CM, Chua SW. Development of a tissue engineering scaffold structure library for rapid prototyping. Part 1□: investigation and classification. Tissue Eng. 2003;291–301
  33. Ciocca L, De Crescenzio F, Fantini M, Scotti R. CAD/CAM and rapid prototyped scaffold construction for bone regenerative medicine and surgical transfer of virtual planning: a pilot study. Comput. Med. Imaging Graph. 2009;33(1):58–62
  34. Armillotta A, Pelzer R. Modeling of porous structures for rapid prototyping of tissue engineering scaffolds. Int. J. Adv. Manuf. Technol. 2007;39(5–6):501–511
  35. Feng B, Guolin M, Yuan Y, Changshen L, Zhen W, Jian L. Role of macropore size in the mechanical properties and in vitro degradation of porous calcium phosphate cements. Mater. Lett. 2010;64(18):2028–2031
  36. Kenny SM, Buggy M. Bone cements and fillers: a review. J. Mater. Sci. 2003;14:923–938
  37. Turing AM. The chemical basis of morphogenesis. Philos. Trans. R. Soc. London Ser. B Biol. Sci. 1952;237(641):37
  38. Volpert V, Petrovskii S. Reaction–diffusion waves in biology. Phys. Life Rev. 2009;6:267–310
  39. Li Q, Zheng C, Wang N. Spiral waves in LIMA model and its LBGK simulation. Commun. Nonlinear Sci. Numer. Simulat. 2001;6:68–73
  40. Kapral R. Pattern formation in chemical systems. Science. 1995;86:149–157
  41. Ristori S, Rossi F, Biosa G, Marchettini N, Rustici M, Tiezzi E. Interplay between the Belousov–Zhabotinsky reaction–diffusion system and biomimetic matrices. Chem. Phys. Lett. 2007;436:175–178
  42. Grzybowski B. Chemistry in Motion: Reaction–diffusion Systems for Micro-and Nanotechnology. Wiley Online Library; 2009;p. 288
  43. Suetsugu Y, Walsh D, Tanaka J, Mann S. Hydroxyapatite pattern formation in PVA gels. J. Mater. Sci. 2009;44(21):5806–5814
  44. Furuichi K, Oaki Y, Ichimiya H, Komotori J, Imai H. Preparation of hierarchically organized calcium phosphate—organic polymer composites by calcification of hydrogel. Sci. Technol. Adv. Mater. 2006;219:
  45. Callahan TK, Knobloch E. Pattern formation in three-dimensional reaction–diffusion systems. Physica D. 1999;132:339–362
  46. Page KM, Maini PK, Monk NAM. Complex pattern formation in reaction–diffusion systems with spatially varying parameters. Physica D: Nonlinear Phenom. 2005;202:95–115
  47. Murray JD. Mathematical Biology II: Spatial Models and Biomedical Applications. Springer-Verlag; 1993;pp. 75–97
  48. A. Madzvamuse, A Numerical Approach to the Study of Spatial Pattern Formation, D.Phil. Thesis, Oxford University, UK, 2000.
  49. Rekow D, John ÆPVTÆ. Influence of scaffold meso-scale features on bone tissue response. Med. Instrum. 2006;(July):5113–5121
  50. T. Leppanen, M. Karttunen, K. Kaski, R.A. Barrio, Dimensionality effects in Turing pattern formation, Arxiv preprint cond-mat/0306121, 2003, pp. 1–16.
  51. Nagorcka BN. Evidence for a reaction–diffusion system as a mechanism controlling mammalian hair growth. Biosystems. 1983;16:323–332
  52. Shoji H, Yamada K, Ueyama D, Ohta T. Turing patterns in three dimensions. Phys. Rev. E. 2007;1–13

PII: S0010-4825(11)00221-6

doi: 10.1016/j.compbiomed.2011.11.002

Computers in Biology and Medicine
Volume 42, Issue 2 , Pages 147-155 , February 2012