Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 5, pp 1331–1341 | Cite as

Model of dissolution in the framework of tissue engineering and drug delivery

  • J. A. Sanz-HerreraEmail author
  • L. Soria
  • E. Reina-Romo
  • Y. Torres
  • A. R. Boccaccini
Original Paper


Dissolution phenomena are ubiquitously present in biomaterials in many different fields. Despite the advantages of simulation-based design of biomaterials in medical applications, additional efforts are needed to derive reliable models which describe the process of dissolution. A phenomenologically based model, available for simulation of dissolution in biomaterials, is introduced in this paper. The model turns into a set of reaction–diffusion equations implemented in a finite element numerical framework. First, a parametric analysis is conducted in order to explore the role of model parameters on the overall dissolution process. Then, the model is calibrated and validated versus a straightforward but rigorous experimental setup. Results show that the mathematical model macroscopically reproduces the main physicochemical phenomena that take place in the tests, corroborating its usefulness for design of biomaterials in the tissue engineering and drug delivery research areas.


Dissolution Reaction–diffusion equations Computational simulation Tissue engineering Drug delivery 



This work was supported by the Ministry of Economy and Competitiveness of the State General Administration of Spain under the Grant MAT2015-71284-P. The authors would like to thank technician M. Sánchez for assistance in the manufacture and dissolution of the green pellets.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Abdullah R, Adzali NM, Daud ZC (2016) Bioactivity of a bio-composite fabricated from CoCrMo/bioactive glass by powder metallurgy method for biomedical application. Procedia Chem 19:566–570CrossRefGoogle Scholar
  2. Adachi T, Tsubota KI, Tomita Y, Hollister SJ (2001) Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models. J Biomech Eng-T ASME 123:403–409CrossRefGoogle Scholar
  3. Aguilar-Reyes EA, Leon-Patino CA, Villicana-Molina E, Macias-Andres VI, Lefebvre L-P (2017) Processing and in vitro bioactivity of high-strength 45S5 glass-ceramic scaffolds for bone regeneration. Ceram Int 43(9):6868–6875CrossRefGoogle Scholar
  4. Akalp U, Bryant SJ, Vernerey FJ (2016) Tuning tissue growth with scaffold degradation in enzyme-sensitive hydrogels: a mathematical model. Soft Matter 12(36):7505–7520CrossRefGoogle Scholar
  5. Bajger P, Ashbourn JMA, Manhas V, Guyot Y, Lietaert K, Geris L (2017) Mathematical modelling of the degradation behaviour of biodegradable metals. Biomech Model Mechanobiol 16:227–238CrossRefGoogle Scholar
  6. Bathe KJ (1996) Finite element procedures. Prentice-Hall, Upper Saddle River, NJzbMATHGoogle Scholar
  7. Carman PC (1937) Fluid flow through granular beds. Trans Inst Chem Eng 15:150–166Google Scholar
  8. Carrier RL, Rupnick M, Langer R, Schoen FJ, Freed LE, Vunjak-Novakovic G (2002a) Perfusion improves tissue architecture of engineered cardiac muscle. Tissue Eng 8:175–188CrossRefGoogle Scholar
  9. Carrier RL, Rupnick M, Langer R, Schoen FJ, Freed LE, Vunjak-Novakovic G (2002b) Effects of oxygen on engineered cardiac muscle. Biotechnol Bioeng 78:617–625CrossRefGoogle Scholar
  10. Chen QZ, Thompson ID, Boccaccini AR (2006a) 45S5 Bioglass-derived glass-ceramic scaffolds for bone tissue engineering. Biomaterials 27:2414–2425CrossRefGoogle Scholar
  11. Demirkiran H, Hu Y, Zuin L, Appathurai N, Aswath PB (2011) XANES analysis of calcium and sodium phosphates and silicates and hydroxyapatite-bioglass45S5 co-sintered bioceramics. Mater Sci Eng C 31:134–143CrossRefGoogle Scholar
  12. Dhote V, Vernerey FJ (2014) Mathematical model of the role of degradation on matrix development in hydrogel scaffold. Biomech Model Mechanobiol 13(1):167–183CrossRefGoogle Scholar
  13. Frenning G (2003) Theoretical investigation of drug release from planar matrix systems: effects of a finite dissolution rate. J Control Release 92:331–339CrossRefGoogle Scholar
  14. Frenning G, Brohede U, Stromme M (2005) Finite element analysis of the release of slowly dissolving drugs from cylindrical matrix systems. J Control Release 107:320–329CrossRefGoogle Scholar
  15. Gopferich A (1997) Polymer bulk erosion. Macromolecules 30:2598–2604CrossRefGoogle Scholar
  16. Guo T, Holzberg T, Lim C, Gao F, Gargava A, Trachtenberg J, Mikos A, Fisher J (2017) 3D printing PLGA: a quantitative examination of the effects of polymer composition and printing parameters on print resolution. Biofabrication. CrossRefGoogle Scholar
  17. Han X, Pan J (2009) A model for simultaneous crystallisation and biodegradation of biodegradable polymers. Biomaterials 30:423–430CrossRefGoogle Scholar
  18. Hench LL, Paschall HA (1973) Direct chemical bond of bioactive glass-ceramic materials to bone and muscle. J Biomed Mater Res Symp 4:25–42CrossRefGoogle Scholar
  19. Hench LL, Stanley HR, Clark AE, Hall M, Wilson J (1991) Dental application of bioglass implant. In: Bonfield E, Hastings GW, Tanner KE (eds) Bioceramics, vol 4. Butterworth Heinemann, Oxford, pp 232–238Google Scholar
  20. Hench LL, West JK (1996) Biological applications of bioactive glasses. Life Chem Rep 13:187–241Google Scholar
  21. Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis, 2nd edn. McGraw-Hill, DoverzbMATHGoogle Scholar
  22. Hutmacher DW (2000) Scaffolds in tissue engineering bone and cartilage. Biomaterials 21:2529–2543CrossRefGoogle Scholar
  23. Ishii O, Shin M, Sueda T, Vacanti JP (2005) In vitro tissue engineering of a cardiac graft using a degradable scaffold with an extracellular matrix-like topography. J Thorac Cardiovasc Surg 130:1358–1363CrossRefGoogle Scholar
  24. Jog R, Burgess DJ (2017) Pharmaceutical amorphous nanoparticles. J Pharm Sci 106:39–65CrossRefGoogle Scholar
  25. Knowles JC, Talal S, Santos JD (1996) Sintering effects in a glass reinforced hydroxyapatite. Biomaterials 17:1437–1442CrossRefGoogle Scholar
  26. Kraus T, Fischerauer SF, Hänzi AC, Uggowitzer PJ, Löffler JF, Weinberg AM (2012) Magnesium alloys for temporary implants in osteosynthesis: in vivo studies of their degradation and interaction with bone. Acta Biomater 8:1230–1238CrossRefGoogle Scholar
  27. Lefebvre L, Gremillard L, Chevalier J, Zenati R, Bernache-Assolant D (2008) Sintering behaviour of 45S5 bioactive glass. Acta Biomater 4:1894–1903CrossRefGoogle Scholar
  28. Manhas V, Guyot Y, Kerckhofs G, Chai YC, Geris L (2017) Computational modelling of local calcium ions release from calcium phosphate-based scaffolds. Biomech Model Mechanobiol 16:425–438CrossRefGoogle Scholar
  29. Mills GA, Urey HC (1940) The kinetics of isotopic exchange between carbon dioxide, bicarbonate ion, carbonate ion and water. J Am Chem Soc—ACS Pubs 62:1019–1026CrossRefGoogle Scholar
  30. Muller RH, Mader K, Gohla S (2000) Solid lipid nanoparticles (SLN) for controlled drug delivery—a review of the state of the art. Eur J Pharm Biopharm 50:161–177CrossRefGoogle Scholar
  31. Pego AP, Siebum B, Van Luyn MJ, Gallego y Van Seijen XJ, Poot AA, Grijpma DW, Feijen J (2003) Preparation of degradable porous structures based on 1,3-trimethylene carbonate and D, L-lactide (co)polymers for heart tissue engineering. Tissue Eng 9:981–994CrossRefGoogle Scholar
  32. Peppas NA, Narasimhan B (2014) Mathematical models in drug delivery: how modeling has shaped the way we design new drug delivery systems. J Control Release 190:75–81CrossRefGoogle Scholar
  33. Reddy JN (1993) An introductory course to the finite element method, 2nd edn. McGraw-Hill, BostonGoogle Scholar
  34. Roether JA, Boccaccini AR, Hench LL, Maquet V, Gautier S, Jerome R (2002a) Development and in vitro characterisation of novel bioresorbable and bioactive composite materials based on polylactide foams and bioglasss for tissue engineering applications. Biomaterials 23:3871–3878CrossRefGoogle Scholar
  35. Rezwan K, Chen QZ, Blaker JJ, Boccaccini AR (2006) Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering. Biomaterials 27:3413–3431CrossRefGoogle Scholar
  36. Sanz-Herrera JA, García-Aznar JM, Doblaré M (2008c) Micro-macro numerical modelling of bone regeneration in tissue engineering. Comput Methods Appl Mech Eng 197:3092–3107CrossRefGoogle Scholar
  37. Sanz-Herrera JA, García-Aznar JM, Doblaré M (2009a) On scaffold designing for bone regeneration: a computational multiscale approach. Acta Biomater 5:219–229CrossRefGoogle Scholar
  38. Sanz-Herrera JA, García-Aznar JM, Doblaré M (2009b) A mathematical approach to bone tissue engineering. Proc R Soc A 367:2055–2078MathSciNetzbMATHGoogle Scholar
  39. Sanz-Herrera JA, Boccaccini AR (2011) Modelling bioactivity and degradation of bioactive glass based tissue engineering scaffolds. Int J Solids Struct 48:257–268CrossRefGoogle Scholar
  40. Shin M, Ishii O, Sueda T, Vacanti JP (2004) Contractile cardiac grafts using a novel nanofibrous mesh. Biomaterials 25:3717–3723CrossRefGoogle Scholar
  41. Sinha VR, Singla AK, Wadhawan S, Kaushik R, Kumria R, Bansal K, Dhawan S (2004) Chitosan microspheres as a potential carrier for drugs. Int J Pharm 274:1–33CrossRefGoogle Scholar
  42. Staiger MP, Pietak AM, Huadmai J, Dias G (2006) Magnesium and its alloys as orthopedic biomaterials: a review. Biomaterials 27:1728–1734CrossRefGoogle Scholar
  43. Tilocca A (2014) Current challenges in atomistic simulations of glasses for biomedical applications. Phys Chem Chem Phys 16:3874–3880CrossRefGoogle Scholar
  44. Trecant M, Daculsi G, Leroy M (1995) Dynamic compaction of calcium phosphate biomaterials. J Mater Sci Mater Med 6:545–551CrossRefGoogle Scholar
  45. Uhrich KE, Cannizzaro SM, Langer RS, Shakesheff KM (1999) Polymeric systems for controlled drug release. Chem Rev 99:3181–3198CrossRefGoogle Scholar
  46. Vallet-Regi M, Balas F, Arcos D (2007) Mesoporous materials for drug delivery. Angew Chem Int Ed Engl 46:7548–7558CrossRefGoogle Scholar
  47. Versypt ANF, Pack DW, Braatz RD (2013) Mathematical modeling of drug delivery from autocatalytically degradable PLGA microspheres—a review. J Control Release 165(1):29–37CrossRefGoogle Scholar
  48. Wang Y, Pan J, Han X, Sinka C, Ding L (2009) A phenomenological model for the degradation of biodegradable polymers. Biomaterials 29:3393–3401CrossRefGoogle Scholar
  49. Wilson J, Low SB (1992) Bioactive ceramics for periodontal treatment: comparative studies in the Patus monkey. J Appl Biomater 3:123–169CrossRefGoogle Scholar
  50. Wilson J, Yli-Urpo A, Risto-Pekka H (1993) Bioactive glasses: clinical applications. In: Hench LL, Wilson J (eds) An introduction to bioceramics. World Scientific, Singapore, pp 63–74CrossRefGoogle Scholar
  51. Yamamuro T (1990) Reconstruction of the iliac crest with bioactive glass-ceramic prostheses. In: Yamamuro T, Hench LL, Wilson J (eds) Handbook of bioactive ceramics: 1. Bioactive glasses and glass-ceramics. CRC Press, Boca Raton, pp 335–342Google Scholar
  52. Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Butterworth-Heinemann, OxfordzbMATHGoogle Scholar
  53. Zong X, Bien H, Chung CY, Yin L, Fang D, Hsiao BS, Chu B, Entcheva E (2005) Electrospun fine-textured scaffolds for heart tissue constructs. Biomaterials 26:5330–5338CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • J. A. Sanz-Herrera
    • 1
    Email author
  • L. Soria
    • 1
  • E. Reina-Romo
    • 1
  • Y. Torres
    • 1
  • A. R. Boccaccini
    • 2
  1. 1.School of Engineering, University of SevilleSevilleSpain
  2. 2.Institute of Biomaterials, Department of Materials Science and EngineeringUniversity of Erlangen-NurembergErlangenGermany

Personalised recommendations