Abstract
The design of bone tissue engineering materials and scaffold structures made thereof is a delicate task, owing to the various, sometimes contradicting requirements that must be fulfilled. The traditional approach is based on a trial-and-error strategy, which may result in a lengthy and inefficient process. Aiming at improvement of this unsatisfactory situation, computer simulations, based on sound mathematical modeling of the involved processes, have been identified as promising complement to experimental testing. After giving a brief overview of available modeling and simulation concepts, the core of this chapter is presented, namely recent examples of multiscale, continuum micromechanics-based homogenization approaches developed in relation to bone tissue engineering. First, the fundamentals of continuum micromechanics are introduced, in order to lay the groundwork for the subsequently elaborated stiffness and strength homogenization approach related to a hydroxyapatite-based granular bone tissue engineering material. For the latter, the derivation of an upscaling scheme allowing for estimating the macroscopic stiffness and the macroscopic strength is demonstrated. Finally, avenues to utilization of this method in the design process of such materials are pointed out.
Similar content being viewed by others
References
Adachi T, Osako Y, Tanaka M, Hojo M, Hollister SJ (2006) Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration. Biomaterials 27(21):3964–3972
Akao M, Aoki H, Kato K (1981) Mechanical properties of sintered hydroxyapatite for prosthetic applications. J Mater Sci 16(3):809–812
Amini AR, Laurencin CT, Nukavarapu SP (2012) Bone tissue engineering: recent advances and challenges. Crit Rev Biomed Eng 40(5):363–408
Bertrand E, Hellmich C (2009) Multiscale elasticity of tissue engineering scaffolds with tissue-engineered bone: a continuum micromechanics approach. J Eng Mech (ASCE) 135(5):395–412
Bose S, Roy M, Bandyopadhyay A (2012) Recent advances in bone tissue engineering scaffolds. Trends Biotechnol 30(10):546–554
Bose S, Vahabzadeh S, Bandyopadhyay A (2013) Bone tissue engineering using 3D printing. Mater Today 16(12):496–504
Botchwey EA, Pollack SR, Levine EM, Johnston ED, Laurencin CT (2004) Quantitative analysis of three-dimensional fluid flow in rotating bioreactors for tissue engineering. J Biomed Mater Res A 69A(2):205–215
Budianksy B, O’Connell RJ (1976) Elastic moduli of a cracked solid. Int J Solids Struct 12(2):81–97
Chung CA, Chen CW, Chen CP, Tseng CS (2007) Enhancement of cell growth in tissue-engineering constructs under direct perfusion: modeling and simulation. Biotechnol Bioeng 97(6):1603–1616
Czenek A, Blanchard R, Dejaco A, Sigurjónsson ÓE, Örlygsson G, Gargiulo P, Hellmich C (2014) Quantitative intravoxel analysis of microct-scanned resorbing ceramic biomaterials – perspectives for computer-aided biomaterial design. J Mater Res 29(23):2757–2772
Dejaco A, Komlev VS, Jaroszewicz J, Swieszkowski W, Hellmich C (2012) Micro CT-based multiscale elasticity of double-porous (pre-cracked) hydroxyapatite granules for regenerative medicine. J Biomech 45(6):1068–1075
Deudé V, Dormieux L, Kondo D, Maghous S (2002) Micromechanical approach to nonlinear poroelasticity: application to cracked rocks. J Eng Mech (ASCE) 128(8):848–855
Dias MR, Fernandes PR, Guedes JM, Hollister SJ (2012) Permeability analysis of scaffolds for bone tissue engineering. J Biomech 45(6):938–944
Dormieux L, Lemarchand E, Kondo D, Fairbairn E (2004) Elements of poromicromechanics applied to concrete. Mater Struct/Concr Sci Eng 37(265):31–42
Dormieux L, Kondo D, Ulm F-J (2006) Microporomechanics. Wiley, Chichester
Drugan WR, Willis JR (1996) A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J Mech Phys Solids 44(4):497–524
Engh CA, Bobyn JD, Glassman AH (1987) Porous-coated hip replacement. The factors governing bone ingrowth, stress shielding, and clinical results. Bone Joint J 69-B(1):45–55
Fritsch A, Hellmich C (2007) ‘Universal’ microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity. J Theor Biol 244(4):597–620
Fritsch A, Dormieux L, Hellmich C (2006) Porous polycrystals built up by uniformly and axisymmetrically oriented needles: homogenization of elastic properties. C R Méc 334(3):151–157
Fritsch A, Dormieux L, Hellmich C, Sanahuja J (2007) Micromechanics of crystal interfaces in polycrystalline solid phases of porous media: fundamentals and application to strength of hydroxyapatite biomaterials. J Mater Sci 42(21):8824–8837
Fritsch A, Dormieux L, Hellmich C, Sanahuja J (2009a) Mechanical behavior of hydroxyapatite biomaterials: an experimentally validated micromechanical model for elasticity and strength. J Biomed Mater Res – Part A 88A(1):149–161
Fritsch A, Hellmich C, Dormieux L (2009b) Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: experimentally supported micromechanical explanation of bone strength. J Theor Biol 260(2):230–252
Fritsch A, Hellmich C, Dormieux L (2010) The role of disc-type crystal shape for micromechanical predictions of elasticity and strength of hydroxyapatite biomaterials. Philos Trans R Soc Lond A 368:1913–1935
Fritsch A, Hellmich C, Young P (2013) Micromechanics-derived scaling relations for poroelasticity and strength of brittle porous polycrystals. J Appl Mech (ASME) 80(2):020905
Geris L (2013) Computational modeling in tissue engineering, Studies in mechanobiology, tissue engineering and biomaterials, vol 10. Springer, Berlin/Heidelberg
Gilmore RS, Katz JL (1982) Elastic properties of apatites. J Mater Sci 17(4):1131–1141
Hellmich C, Ulm F-J (2002) Micromechanical model for ultra-structural stiffness of mineralized tissues. J Eng Mech (ASCE) 128(8):898–908
Hellmich C, Ulm F-J, Dormieux L (2004) Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? - arguments from a multiscale approach. Biomech Model Mechanobiol 2(4):219–238
Hervé E, Zaoui A (1993) n-Layered inclusion-based micromechanical modelling. Int J Eng Sci 31(1):1–10
Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11(5):357–372
Hollister SJ (2005) Porous scaffold design for tissue engineering. Nat Mater 4(7):518–524
Hutmacher DW (2000) Scaffolds in tissue engineering bone and cartilage. Biomaterials 21(24):2529–2543
Hutmacher DW, Singh H (2008) Computational fluid dynamics for improved bioreactor design and 3D culture. Trends Biotechnol 26(4):166–172
Jacobs CR, Temiyasathit S, Castillo AB (2010) Osteocyte mechanobiology and pericellular mechanics. Annu Rev Biomed Eng 12:369–400
Jaecques SVN, Van Oosterwyck H, Muraru L, Van Cleynenbreugel T, De Smet E, Wevers M, Naert I, Vander Sloten J (2004) Individualised, micro CT-based finite element modelling as a tool for biomechanical analysis related to tissue engineering of bone. Biomaterials 25(9):1683–1696
Katz JL, Ukraincik K (1971) On the anisotropic elastic properties of bone. Calcif Tissue Int 4(3):221–227
Kohlhauser C, Hellmich C (2013) Ultrasonic contact pulse transmission for elastic wave velocity and stiffness determination: influence of specimen geometry and porosity. Eng Struct 47:115–133
Komlev VS, Barinov SM, Koplik EV (2002) A method to fabricate porous spherical hydroxyapatite granules intended for time-controlled drug release. Biomaterials 23(16):3449–3454
Komlev VS, Barinov SM, Girardin E, Oscarsson S, Rosengren A, Rustichelli F, Orlovskii VP (2003) Porous spherical hydroxyapatite and fluorhydroxyapatite granules: processing and characterization. Sci Technol Adv Mater 4(6):503–508
Lacroix D, Chateau A, Ginebra M-P, Planell JA (2006) Micro-finite element models of bone tissue-engineering scaffolds. Biomaterials 27(30):5326–5334
Lacroix D, Planell JA, Prendergast PJ (2009) Computer-aided design and finiteelement modelling of biomaterial scaffolds for bone tissue engineering. Philos Trans R Soc London, Ser A 367(1895):1993–2009
Langer R, Tirrell DA (2004) Designing materials for biology and medicine. Nature 428(6982):487–492
Li X, Wang L, Fan Y, Feng Q, Cui F-Z, Watari F (2013) Nanostructured scaffolds for bone tissue engineering. J Biomed Mater Res A 101A(8):2424–2435
Luczynski K, Dejaco A, Lahayne O, Jaroszewicz J, Swieszkowski W, Hellmich C (2012) MicroCT/micromechanics-based finite element models and quasi-static unloading tests deliver consistent values for Young’s modulus of rapid-prototyped polymer-ceramic tissue engineering scaffold. CMES – Comput Model Eng Sci 87(6):505–529
Melchels FPW, Bertoldi K, Gabbrielli R, Velders AH, Feijen J, Grijpma DW (2010) Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials 31(27):6909–6916
Milan J-L, Planell JA, Lacroix D (2009) Computational modelling of the mechanical environment of osteogenesis within a polylactic acid–calcium phosphate glass scaffold. Biomaterials 30(25):4219–4226
Morin C, Vass V, Hellmich C (2017) Micromechanics of elastoplastic porous polycrystals: theory, algorithm, and application to osteonal bone. Int J Plast 91:238–267
Olivares AL, Marsal È, Planell JA, Lacroix D (2009) Finite element study of scaffold architecture design and culture conditions for tissue engineering. Biomaterials 30(30):6142–6149
Pastrama MI, Scheiner S, Pivonka P, Hellmich C (2018) A mathematical multiscale model of bone remodeling, accounting for pore space-specific mechanosensation. Bone 107: 208–221
Porter B, Zauel R, Stockman H, Guldberg R, Fyhrie D (2005) 3-D computational modeling of media flow through scaffolds in a perfusion bioreactor. J Biomech 38(3):543–549
Porter JR, Ruckh TT, Popat KC (2009) Bone tissue engineering: a review in bone biomimetics and drug delivery strategies. Biotechnol Prog 25(6):1539–1560
Rezwan K, Chen QZ, Blaker JJ, Boccaccini AR (2006) Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering. Biomaterials 27(18):3413–3431
Robling AG, Castillo A, Turner CH (2006) Biomechanical and molecular regulation of bone remodeling. Annu Rev Biomed Eng 8:455–498
Sandino C, Lacroix D (2011) A dynamical study of the mechanical stimuli and tissue differentiation within a cap scaffold based on micro-ct finite element models. Biomech Model Mechanobiol 10(4):565–576
Sandino C, Planell JA, Lacroix D (2008) A finite element study of mechanical stimuli in scaffolds for bone tissue engineering. J Biomech 41(5):1005–1014
Sanz-Herrera JA, García-Aznar JM, Doblaré M, Micro-macro M (2008) Numerical modelling of bone regeneration in tissue engineering. Comput Methods Appl Mech Eng 197(33–40):3092–3107
Sanz-Herrera JA, García-Aznar JM, Doblaré M (2009a) On scaffold designing for bone regeneration: a computational multiscale approach. Acta Biomater 5(1):219–229
Sanz-Herrera JA, García-Aznar JM, Doblaré M (2009b) A mathematical approach to bone tissue engineering. Philos Trans R Soc London, Ser A 367(1895):2055–2078
Scheiner S, Sinibaldi R, Pichler B, Komlev V, Renghini C, Vitale-Brovarone C, Rustichelli F, Hellmich C (2009) Micromechanics of bone tissue-engineering scaffolds, based on resolution error-cleared computer tomography. Biomaterials 30(12):2411–2419
Scheiner S, Pivonka P, Hellmich C (2013) Coupling systems biology with multi-scale mechanics, for computer simulations of bone remodeling. Comput Methods Appl Mech Eng 254:181–196
Scheiner S, Komlev VS, Gurin AN, Hellmich C (2016a) Multiscale mathematical modeling in dental tissue engineering: towards computer-aided design of a regenerative system based on hydroxyapatite granules, focusing on early and mid-term stiffness recovery. Front Physiol 7(383):1–18
Scheiner S, Komlev VS, Hellmich C (2016b) Strength increase during ceramic biomaterial-induced bone regeneration: a micromechanical study. Int J Fract 202(2):217–235
Shareef MY, Messer PF, van Noort R (1993) Fabrication, characterization and fracture study of a machinable hydroxyapatite ceramic. Biomaterials 14(1):69–75
Simmons CA, Meguid SA, Pilliar RM (2001) Differences in osseointegration rate due to implant surface geometry can be explained by local tissue strains. J Orthop Res 19(2):187–194
Sturm S, Zhou S, Mai Y-W, Li Q (2010) On stiffness of scaffolds for bone tissue engineering – a numerical study. J Biomech 43(9):1738–1744
Thompson M, Willis JR (1991) A reformation of the equations anisotropic elasticity. J Appl Mech 58(3):612–616
Truscello S, Kerckhofs G, Van Bael S, Pyka G, Schrooten J, Van Oosterwyck H (2012) Prediction of permeability of regular scaffolds for skeletal tissue engineering: a combined computational and experimental study. Acta Biomater 8(4):1648–1658
van Gaalen S, Kruyt M, Meijer G, Mistry A, Mikos A, van den Beucken J, Jansen J, de Groot K, Cancedda R, Olivo C, Yaszemski M, Dhert W (2008) Chapter 19. Tissue engineering of bone. In: Van Blitterswijk C, Thomsen P, Lindahl A, Hubbell J, Williams DF, Cancedda R, de Bruijn JD, Sohier J (eds) Tissue Engineering. Academic, Burlington, pp 559–610
Voronov R, VanGordon S, Sikavitsas VI, Papavassiliou DV (2010) Computational modeling of flow-induced shear stresses within 3D salt-leached porous scaffolds imaged via micro-ct. J Biomech 43(7):1279–1286
Williams DF (2008) On the mechanisms of biocompatibility. Biomaterials 29(20):2941–2953
Williams JM, Adewunmi A, Schek RM, Flanagan CL, Krebsbach PH, Feinberg SE, Hollister SJ, Das S (2005) Bone tissue engineering using polycaprolactone scaffolds fabricated via selective laser sintering. Biomaterials 26(23):4817–4827
Zaoui A (1997) Chapter 6. Structural morphology and constitutive behavior of microheterogeneous materials. In: Suquet PM (ed) Continuum micromechanics, CISM courses and lectures, vol 377. Springer, Wien/New York, pp 291–347
Zaoui A (2002) Continuum micromechanics: survey. J Eng Mech (ASCE) 128(8):808–816
Acknowledgments
In the context of the research presented in Sect. 3.3 of this chapter, the partial financial support by the European Research Council (ERC), in the framework of the project Multiscale poromicromechanics of bone materials, with links to biology and medicine (project number FP7-257023), as well as the partial financial support by the Russian Science Foundation (grant number 15-13-00108), are gratefully acknowledged. Furthermore, COST-action MP1005, NAMABIO – From nano to macro biomaterials (design, processing, characterization, modeling) and applications to stem cells regenerative orthopedic and dental medicine has provided means for a sustainable collaboration over several years.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this entry
Cite this entry
Scheiner, S., Komlev, V.S., Hellmich, C. (2018). Computational Methods for the Predictive Design of Bone Tissue Engineering Scaffolds. In: Ovsianikov, A., Yoo, J., Mironov, V. (eds) 3D Printing and Biofabrication. Reference Series in Biomedical Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-40498-1_21-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-40498-1_21-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40498-1
Online ISBN: 978-3-319-40498-1
eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences