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

Abstract

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.

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References

  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 19:566–570

    Article  Google 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 123:403–409

    Article  Google 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):6868–6875

    Article  Google 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):7505–7520

    Article  Google 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 16:227–238

    Article  Google Scholar 

  6. Bathe KJ (1996) Finite element procedures. Prentice-Hall, Upper Saddle River, NJ

    Google Scholar 

  7. Carman PC (1937) Fluid flow through granular beds. Trans Inst Chem Eng 15:150–166

    Google 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 8:175–188

    Article  Google 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 78:617–625

    Article  Google Scholar 

  10. Chen QZ, Thompson ID, Boccaccini AR (2006a) 45S5 Bioglass-derived glass-ceramic scaffolds for bone tissue engineering. Biomaterials 27:2414–2425

    Article  Google 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 31:134–143

    Article  Google 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):167–183

    Article  Google Scholar 

  13. Frenning G (2003) Theoretical investigation of drug release from planar matrix systems: effects of a finite dissolution rate. J Control Release 92:331–339

    Article  Google 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 107:320–329

    Article  Google Scholar 

  15. Gopferich A (1997) Polymer bulk erosion. Macromolecules 30:2598–2604

    Article  Google 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. https://doi.org/10.1088/1758-5090/aa6370

    Article  Google Scholar 

  17. Han X, Pan J (2009) A model for simultaneous crystallisation and biodegradation of biodegradable polymers. Biomaterials 30:423–430

    Article  Google Scholar 

  18. Hench LL, Paschall HA (1973) Direct chemical bond of bioactive glass-ceramic materials to bone and muscle. J Biomed Mater Res Symp 4:25–42

    Article  Google 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 232–238

    Google Scholar 

  20. Hench LL, West JK (1996) Biological applications of bioactive glasses. Life Chem Rep 13:187–241

    Google Scholar 

  21. Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis, 2nd edn. McGraw-Hill, Dover

    Google Scholar 

  22. Hutmacher DW (2000) Scaffolds in tissue engineering bone and cartilage. Biomaterials 21:2529–2543

    Article  Google 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 130:1358–1363

    Article  Google Scholar 

  24. Jog R, Burgess DJ (2017) Pharmaceutical amorphous nanoparticles. J Pharm Sci 106:39–65

    Article  Google Scholar 

  25. Knowles JC, Talal S, Santos JD (1996) Sintering effects in a glass reinforced hydroxyapatite. Biomaterials 17:1437–1442

    Article  Google 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 8:1230–1238

    Article  Google Scholar 

  27. Lefebvre L, Gremillard L, Chevalier J, Zenati R, Bernache-Assolant D (2008) Sintering behaviour of 45S5 bioactive glass. Acta Biomater 4:1894–1903

    Article  Google 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 16:425–438

    Article  Google 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 62:1019–1026

    Article  Google 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 50:161–177

    Article  Google 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 9:981–994

    Article  Google 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 190:75–81

    Article  Google Scholar 

  33. Reddy JN (1993) An introductory course to the finite element method, 2nd edn. McGraw-Hill, Boston

    Google 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 23:3871–3878

    Article  Google Scholar 

  35. Rezwan K, Chen QZ, Blaker JJ, Boccaccini AR (2006) Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering. Biomaterials 27:3413–3431

    Article  Google 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 197:3092–3107

    Article  Google Scholar 

  37. Sanz-Herrera JA, García-Aznar JM, Doblaré M (2009a) On scaffold designing for bone regeneration: a computational multiscale approach. Acta Biomater 5:219–229

    Article  Google Scholar 

  38. Sanz-Herrera JA, García-Aznar JM, Doblaré M (2009b) A mathematical approach to bone tissue engineering. Proc R Soc A 367:2055–2078

    MathSciNet  MATH  Google Scholar 

  39. Sanz-Herrera JA, Boccaccini AR (2011) Modelling bioactivity and degradation of bioactive glass based tissue engineering scaffolds. Int J Solids Struct 48:257–268

    Article  Google Scholar 

  40. Shin M, Ishii O, Sueda T, Vacanti JP (2004) Contractile cardiac grafts using a novel nanofibrous mesh. Biomaterials 25:3717–3723

    Article  Google 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 274:1–33

    Article  Google Scholar 

  42. Staiger MP, Pietak AM, Huadmai J, Dias G (2006) Magnesium and its alloys as orthopedic biomaterials: a review. Biomaterials 27:1728–1734

    Article  Google Scholar 

  43. Tilocca A (2014) Current challenges in atomistic simulations of glasses for biomedical applications. Phys Chem Chem Phys 16:3874–3880

    Article  Google Scholar 

  44. Trecant M, Daculsi G, Leroy M (1995) Dynamic compaction of calcium phosphate biomaterials. J Mater Sci Mater Med 6:545–551

    Article  Google Scholar 

  45. Uhrich KE, Cannizzaro SM, Langer RS, Shakesheff KM (1999) Polymeric systems for controlled drug release. Chem Rev 99:3181–3198

    Article  Google Scholar 

  46. Vallet-Regi M, Balas F, Arcos D (2007) Mesoporous materials for drug delivery. Angew Chem Int Ed Engl 46:7548–7558

    Article  Google 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):29–37

    Article  Google Scholar 

  48. Wang Y, Pan J, Han X, Sinka C, Ding L (2009) A phenomenological model for the degradation of biodegradable polymers. Biomaterials 29:3393–3401

    Article  Google Scholar 

  49. Wilson J, Low SB (1992) Bioactive ceramics for periodontal treatment: comparative studies in the Patus monkey. J Appl Biomater 3:123–169

    Article  Google 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 63–74

    Google 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 335–342

    Google Scholar 

  52. Zienkiewicz OC, Taylor RL (2000) The finite element method, 5th edn. Butterworth-Heinemann, Oxford

    Google 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 26:5330–5338

    Article  Google Scholar 

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Acknowledgements

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.

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Correspondence to J. A. Sanz-Herrera.

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Sanz-Herrera, J.A., Soria, L., Reina-Romo, E. et al. Model of dissolution in the framework of tissue engineering and drug delivery. Biomech Model Mechanobiol 17, 1331–1341 (2018). https://doi.org/10.1007/s10237-018-1029-4

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Keywords

  • Dissolution
  • Reaction–diffusion equations
  • Computational simulation
  • Tissue engineering
  • Drug delivery