Skip to main content

Advertisement

SpringerLink
Log in

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

  • Original Paper
  • Published:
Biomechanics and Modeling in Mechanobiology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

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

    MATH  Google Scholar 

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

    Google Scholar 

  • 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 

  • 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 

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

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

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

    Article  Google Scholar 

  • 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 

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

    Article  Google Scholar 

  • 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 

  • 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 

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

    Google Scholar 

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

    MATH  Google Scholar 

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

    Article  Google Scholar 

  • 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

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

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

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

    Article  Google Scholar 

  • 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 

  • 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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

    Chapter  Google Scholar 

  • 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 

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

    MATH  Google Scholar 

  • 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 

Download references

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.

Author information

Authors and Affiliations

  1. School of Engineering, University of Seville, Camino de los descubrimientos s/n, 41092, Seville, Spain

    J. A. Sanz-Herrera, L. Soria, E. Reina-Romo & Y. Torres

  2. Institute of Biomaterials, Department of Materials Science and Engineering, University of Erlangen-Nuremberg, Erlangen, Germany

    A. R. Boccaccini

Authors
  1. J. A. Sanz-Herrera
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Soria
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Reina-Romo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. Torres
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. R. Boccaccini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. A. Sanz-Herrera.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10237-018-1029-4

Keywords

Search

Navigation