Skip to main content

2018 | OriginalPaper | Buchkapitel

Mathematical Modeling of 3D Tissue Engineering Constructs

verfasst von : Henrique Amorim Almeida, Paulo Jorge da Silva Bártolo

Erschienen in: 3D Printing and Biofabrication

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Tissue engineering represents a new field aiming at developing biological substitutes to restore, maintain, or improve tissue functions. In this approach, scaffolds provide a temporary mechanical and vascular support for tissue regeneration while tissue ingrowth is being formed. The design of optimized scaffolds for tissue engineering applications is a key topic of research, as the complex macro- and micro-architectures required for a scaffold depends on the mechanical and vascular properties and physical and molecular queues of the surrounding tissue at the defect site. One way to achieve such hierarchical designs is to create a library of unit cells, which can be assembled through a computational tool.
Besides presenting an overview scaffold designs based hyperbolic surfaces, this chapter investigates the use of two different types of triply periodic minimal surfaces, Schwarz and Schoen, in order to design better biomimetic scaffolds with high surface-to-volume ratio, high porosity, and good mechanical properties. The effect of two parametric parameters (thickness and surface radius) is also evaluated regarding its porosity and mechanical behavior.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Almeida, H.A. and Bártolo, P.J. (2008) computer simulation and optimisation of tissue engineering scaffolds: mechanical and vascular behaviour”, 9th biennial ASME conference on engineering systems design and analysis (ESDA2008), Y. Halevi and A. Fischer (Eds.), ASME conference proceedings, Haifa Isreal. Almeida, H.A. and Bártolo, P.J. (2008) computer simulation and optimisation of tissue engineering scaffolds: mechanical and vascular behaviour”, 9th biennial ASME conference on engineering systems design and analysis (ESDA2008), Y. Halevi and A. Fischer (Eds.), ASME conference proceedings, Haifa Isreal.
Zurück zum Zitat Almeida HA, Bártolo PJ (2012a) Chapter 12: Structural and vascular analysis of tissue engineering scaffolds: part 1 – numerical fluid analysis. In: Liebschner M, Kim D (eds) Computer-aided tissue engineering. Springer, LondonCrossRef Almeida HA, Bártolo PJ (2012a) Chapter 12: Structural and vascular analysis of tissue engineering scaffolds: part 1 – numerical fluid analysis. In: Liebschner M, Kim D (eds) Computer-aided tissue engineering. Springer, LondonCrossRef
Zurück zum Zitat Almeida HA, Bártolo PJ (2012b) Chapter 13: Structural and vascular analysis of tissue engineering scaffolds: part 2 – topology optimization. In: Liebschner M, Kim D (eds) computer-aided tissue engineering. Springer, LondonCrossRef Almeida HA, Bártolo PJ (2012b) Chapter 13: Structural and vascular analysis of tissue engineering scaffolds: part 2 – topology optimization. In: Liebschner M, Kim D (eds) computer-aided tissue engineering. Springer, LondonCrossRef
Zurück zum Zitat Almeida HA, Bártolo PJ (2013) Numerical simulations of BioExtruded polymer scaffolds for tissue engineering applications. Polym Int 62(11):1544–1552 Almeida HA, Bártolo PJ (2013) Numerical simulations of BioExtruded polymer scaffolds for tissue engineering applications. Polym Int 62(11):1544–1552
Zurück zum Zitat Almeida HA, Bártolo PJ, Ferreira J (2007a) Mechanical behaviour and vascularisation analysis of tissue engineering scaffolds. In: Bártolo PJ et al (eds) Virtual and rapid manufacturing – Advanced research in virtual and rapid prototyping. Taylor & Francis, London, pp 73–80 Almeida HA, Bártolo PJ, Ferreira J (2007a) Mechanical behaviour and vascularisation analysis of tissue engineering scaffolds. In: Bártolo PJ et al (eds) Virtual and rapid manufacturing – Advanced research in virtual and rapid prototyping. Taylor & Francis, London, pp 73–80
Zurück zum Zitat Almeida HA, Bártolo PJ, Ferreira J (2007b) Design of scaffolds assisted by computer. In: Brebbia CA (ed) Modelling in medicine and biology VII. Wit Press, pp 157–166 Almeida HA, Bártolo PJ, Ferreira J (2007b) Design of scaffolds assisted by computer. In: Brebbia CA (ed) Modelling in medicine and biology VII. Wit Press, pp 157–166
Zurück zum Zitat Andersson S (1983) On the description of complex inorganic crystal structures. Angew Chem Int Ed 22(2):69–81CrossRef Andersson S (1983) On the description of complex inorganic crystal structures. Angew Chem Int Ed 22(2):69–81CrossRef
Zurück zum Zitat Andersson S, Hyde ST, Larsson K, Lidin S (1988) Minimal surfaces and structures: from inorganic and metal crystals to cell membranes and biopolymers. Chem Rev 88:221–242CrossRef Andersson S, Hyde ST, Larsson K, Lidin S (1988) Minimal surfaces and structures: from inorganic and metal crystals to cell membranes and biopolymers. Chem Rev 88:221–242CrossRef
Zurück zum Zitat Bao G, Suresh S (2003) Cell and molecular mechanics of biological materials. Nature Materials 2:715–725CrossRefPubMed Bao G, Suresh S (2003) Cell and molecular mechanics of biological materials. Nature Materials 2:715–725CrossRefPubMed
Zurück zum Zitat Bártolo PJ, Almeida HA, Rezende RA, Laoui T, Bidanda B (2008) Advanced processes to fabricate scaffolds for tissue engineering. In: Bidanda B, Bártolo PJ (eds) Virtual Prototyping & bio-Manufacturing in medical applications. Springer, New York, pp 151–174CrossRef Bártolo PJ, Almeida HA, Rezende RA, Laoui T, Bidanda B (2008) Advanced processes to fabricate scaffolds for tissue engineering. In: Bidanda B, Bártolo PJ (eds) Virtual Prototyping & bio-Manufacturing in medical applications. Springer, New York, pp 151–174CrossRef
Zurück zum Zitat Bártolo PJ, Almeida H, Laoui T (2009a) Rapid prototyping & manufacturing for tissue engineering scaffolds. Int J Comput Appl Technol 36(1):1–9CrossRef Bártolo PJ, Almeida H, Laoui T (2009a) Rapid prototyping & manufacturing for tissue engineering scaffolds. Int J Comput Appl Technol 36(1):1–9CrossRef
Zurück zum Zitat Bártolo PJ, Chua CK, Almeida HA, Chou SM, Lim ASC (2009b) Biomanufacturing for tissue engineering: present and future trends. Virtual Phys Prototyping 4(4):203–216CrossRef Bártolo PJ, Chua CK, Almeida HA, Chou SM, Lim ASC (2009b) Biomanufacturing for tissue engineering: present and future trends. Virtual Phys Prototyping 4(4):203–216CrossRef
Zurück zum Zitat Bártolo PJ, Kruth JP, Silva J, Levy G, Malshe A, Rajurkar K, Mitsuishi M, Ciurana J, Leu M (2012) Biomedical production of implants by additive electro-chemical and physical processes. CIRP Ann Manuf Technol 61(2):635–655CrossRef Bártolo PJ, Kruth JP, Silva J, Levy G, Malshe A, Rajurkar K, Mitsuishi M, Ciurana J, Leu M (2012) Biomedical production of implants by additive electro-chemical and physical processes. CIRP Ann Manuf Technol 61(2):635–655CrossRef
Zurück zum Zitat Brunello G, Sivolella S, Meneghello R, Ferroni L, Gardin C, Piattelli A, Zavan B, Bressan E (2016) Powder-based 3D printing for bone tissue engineering. Biotechnol Adv 34:740–753CrossRefPubMed Brunello G, Sivolella S, Meneghello R, Ferroni L, Gardin C, Piattelli A, Zavan B, Bressan E (2016) Powder-based 3D printing for bone tissue engineering. Biotechnol Adv 34:740–753CrossRefPubMed
Zurück zum Zitat Dinis JC, Morais TF, Amorin PHJ, Ruben RB, Almeida HA, Inforçati PN, Bártolo PJ, Silva JVL (2014) Open source software for the automatic Design of Scaffold Structures for tissue engineering applications. Procedia Technol 16:1542–1547CrossRef Dinis JC, Morais TF, Amorin PHJ, Ruben RB, Almeida HA, Inforçati PN, Bártolo PJ, Silva JVL (2014) Open source software for the automatic Design of Scaffold Structures for tissue engineering applications. Procedia Technol 16:1542–1547CrossRef
Zurück zum Zitat Eshraghi S, Das S (2010) Mechanical and microstructuralproperties of polycaprolactonescaffolds with one-dimensional, two-dimensional, and three-dimensional orthogonally oriented porous architectures produced by selective laser sintering. Acta Biomater 6(7):2467–2476CrossRefPubMedPubMedCentral Eshraghi S, Das S (2010) Mechanical and microstructuralproperties of polycaprolactonescaffolds with one-dimensional, two-dimensional, and three-dimensional orthogonally oriented porous architectures produced by selective laser sintering. Acta Biomater 6(7):2467–2476CrossRefPubMedPubMedCentral
Zurück zum Zitat Fallahiarezoudar E, Ahmadipourroudposht M, Idris A, Yusof NM (2015) A review of: application of synthetic scaffold in tissue engineering heart valves. Mater Sci Eng C 48:556–565CrossRef Fallahiarezoudar E, Ahmadipourroudposht M, Idris A, Yusof NM (2015) A review of: application of synthetic scaffold in tissue engineering heart valves. Mater Sci Eng C 48:556–565CrossRef
Zurück zum Zitat Gandy PJF, Bardhan S, Mackay AL, Klinowski J (2001) Nodal surface approximations to the P, G, D and I-WP triply periodic minimal surfaces. Chem Phys Lett 336(3):187–195CrossRef Gandy PJF, Bardhan S, Mackay AL, Klinowski J (2001) Nodal surface approximations to the P, G, D and I-WP triply periodic minimal surfaces. Chem Phys Lett 336(3):187–195CrossRef
Zurück zum Zitat Giannitelli SM, Mozetic P, Trombetta M, Rainer A (2015) Combined additive manufacturing approaches in tissue engineering. Acta Biomater 24:1–11CrossRef Giannitelli SM, Mozetic P, Trombetta M, Rainer A (2015) Combined additive manufacturing approaches in tissue engineering. Acta Biomater 24:1–11CrossRef
Zurück zum Zitat Hyde S (1996) Bicontinuous structures in lyotropic liquid crystals and crystalline hyperbolic surfaces. Curr Opin Solid State Mater Sci 1:653–662CrossRef Hyde S (1996) Bicontinuous structures in lyotropic liquid crystals and crystalline hyperbolic surfaces. Curr Opin Solid State Mater Sci 1:653–662CrossRef
Zurück zum Zitat Hyde ST, Oguey C (2000) From 2D hyperbolic forests to 3D Euclidean entangled thickets. Eur Phys J B 16(4):613–630CrossRef Hyde ST, Oguey C (2000) From 2D hyperbolic forests to 3D Euclidean entangled thickets. Eur Phys J B 16(4):613–630CrossRef
Zurück zum Zitat Jana S, Lerman A (2015) Bioprinting a cardiac valve. Biotechnol Adv 33:1503–1521CrossRef Jana S, Lerman A (2015) Bioprinting a cardiac valve. Biotechnol Adv 33:1503–1521CrossRef
Zurück zum Zitat Janik H, Marzec M (2015) A review: fabrication of porous polyurethane scaffolds. Mater Sci Eng C 48:586–591CrossRef Janik H, Marzec M (2015) A review: fabrication of porous polyurethane scaffolds. Mater Sci Eng C 48:586–591CrossRef
Zurück zum Zitat Jazayeri HE, Tahriri M, Razavi M, Khoshroo K, Fahimipour F, Dashtimoghadam E, Almeida L, Tayebi L (2017) A current overview of materials and strategies for potential use in maxillofacial tissue regeneration. Mater Sci Eng C 70:913–929CrossRef Jazayeri HE, Tahriri M, Razavi M, Khoshroo K, Fahimipour F, Dashtimoghadam E, Almeida L, Tayebi L (2017) A current overview of materials and strategies for potential use in maxillofacial tissue regeneration. Mater Sci Eng C 70:913–929CrossRef
Zurück zum Zitat Jiang T, Carbone EJ, Lo KWH, Laurencin CT (2015) Electrospinning of polymer nanofibers for tissue regeneration. Prog Polym Sci 46:1–24CrossRef Jiang T, Carbone EJ, Lo KWH, Laurencin CT (2015) Electrospinning of polymer nanofibers for tissue regeneration. Prog Polym Sci 46:1–24CrossRef
Zurück zum Zitat Jung Y, Chu KT, Torquato S (2007) A variational level set approach for surface area minimization of triply-periodic surfaces. J Comput Phys 223(2):711–730CrossRef Jung Y, Chu KT, Torquato S (2007) A variational level set approach for surface area minimization of triply-periodic surfaces. J Comput Phys 223(2):711–730CrossRef
Zurück zum Zitat Kapfer SC, Hyde ST, Mecke K, Arns CH, Schroder-Turk GE (2011) Minimal surface scaffold designs for tissue engineering. Biomaterials 32(29):6875–6882CrossRefPubMed Kapfer SC, Hyde ST, Mecke K, Arns CH, Schroder-Turk GE (2011) Minimal surface scaffold designs for tissue engineering. Biomaterials 32(29):6875–6882CrossRefPubMed
Zurück zum Zitat Karcher H, Polthier K (2014) Construction of triply periodic minimal surfaces. Philos Trans R Soc Lond A 354(1715):2077–2104CrossRef Karcher H, Polthier K (2014) Construction of triply periodic minimal surfaces. Philos Trans R Soc Lond A 354(1715):2077–2104CrossRef
Zurück zum Zitat Langer R, Vacanti JP (1993) Tissue engineering. Science 260:920–926CrossRef Langer R, Vacanti JP (1993) Tissue engineering. Science 260:920–926CrossRef
Zurück zum Zitat Larsson M, Terasaki O, Larsson K (2003) A solid state transition in the tetragonal lipid bilayer structure at the lung alveolar surface. Solid State Sci 5(1):109–114CrossRef Larsson M, Terasaki O, Larsson K (2003) A solid state transition in the tetragonal lipid bilayer structure at the lung alveolar surface. Solid State Sci 5(1):109–114CrossRef
Zurück zum Zitat Law JX, Liau LL, Aminuddin BS, Ruszymah BHI (2016) Tissue-engineered trachea: a review. Int J Pediatr Otorhinolaryngol 91:55–63CrossRefPubMed Law JX, Liau LL, Aminuddin BS, Ruszymah BHI (2016) Tissue-engineered trachea: a review. Int J Pediatr Otorhinolaryngol 91:55–63CrossRefPubMed
Zurück zum Zitat Lord EA, Mackay AL (2003) Periodic minimal surfaces of cubic symmetry. Curr Sci 85(3):346–362 Lord EA, Mackay AL (2003) Periodic minimal surfaces of cubic symmetry. Curr Sci 85(3):346–362
Zurück zum Zitat Melchels FPW, Barradas AMC, Blitterswijk CA, Boer J, Feijen J (2010a) Effects of the architecture of tissue engineering scaffolds on cell seeding and culturing. Acta Biomater 6(11):4208–4217CrossRef Melchels FPW, Barradas AMC, Blitterswijk CA, Boer J, Feijen J (2010a) Effects of the architecture of tissue engineering scaffolds on cell seeding and culturing. Acta Biomater 6(11):4208–4217CrossRef
Zurück zum Zitat Melchels FPW, Bertoldi K, Gabbielli R, Velders AH, Feijen J (2010b) Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials 31(27):6909–6916CrossRefPubMed Melchels FPW, Bertoldi K, Gabbielli R, Velders AH, Feijen J (2010b) Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials 31(27):6909–6916CrossRefPubMed
Zurück zum Zitat Melek LN (2015) Tissue engineering in oral and maxillofacial reconstruction. Tanta Dent J 12:211–223CrossRef Melek LN (2015) Tissue engineering in oral and maxillofacial reconstruction. Tanta Dent J 12:211–223CrossRef
Zurück zum Zitat Nesper R, Leoni S (2001) On tilings and patterns on hyperbolic surfaces and their relation to structural chemistry. ChemPhysChem 2(7):413–422CrossRefPubMed Nesper R, Leoni S (2001) On tilings and patterns on hyperbolic surfaces and their relation to structural chemistry. ChemPhysChem 2(7):413–422CrossRefPubMed
Zurück zum Zitat Osman NI, Hillary C, Bullock AJ, MacNeil S, Chapple CR (2015) Tissue engineered buccal mucosa for urethroplasty: progress and future directions. Adv Drug Deliv Rev 82–83:69–76CrossRefPubMed Osman NI, Hillary C, Bullock AJ, MacNeil S, Chapple CR (2015) Tissue engineered buccal mucosa for urethroplasty: progress and future directions. Adv Drug Deliv Rev 82–83:69–76CrossRefPubMed
Zurück zum Zitat Qi C, Wang Y (2009) Feature-based crystal construction in computer-aided nano-design. Comput Aided Des 41(11):792–800CrossRef Qi C, Wang Y (2009) Feature-based crystal construction in computer-aided nano-design. Comput Aided Des 41(11):792–800CrossRef
Zurück zum Zitat Rajagopalan S, Robb RA (2006) Schwarz meets Schwann: design and fabrication of biomorphic and durataxic tissue engineering scaffolds. Med Image Anal 10(5):693–712CrossRefPubMed Rajagopalan S, Robb RA (2006) Schwarz meets Schwann: design and fabrication of biomorphic and durataxic tissue engineering scaffolds. Med Image Anal 10(5):693–712CrossRefPubMed
Zurück zum Zitat Risbud M (2001) Tissue engineering: implications in the treatment of organ and tissue defects. Biogerontology 2:117–125CrossRefPubMed Risbud M (2001) Tissue engineering: implications in the treatment of organ and tissue defects. Biogerontology 2:117–125CrossRefPubMed
Zurück zum Zitat Scriven LE (1976) Equilibrium bicontinuous structure. Nature 263(5573):123–125CrossRef Scriven LE (1976) Equilibrium bicontinuous structure. Nature 263(5573):123–125CrossRef
Zurück zum Zitat Selimis A, Mironov V, Farsari M (2015) Direct laser writing: principles and materials for scaffold 3D printing. Microelectron Eng 132:83–89CrossRef Selimis A, Mironov V, Farsari M (2015) Direct laser writing: principles and materials for scaffold 3D printing. Microelectron Eng 132:83–89CrossRef
Zurück zum Zitat Skalak R, Fox CF (1988) Tissue Engineering. Alan R. Liss, New York Skalak R, Fox CF (1988) Tissue Engineering. Alan R. Liss, New York
Zurück zum Zitat Stratton, S., Shelke, N.B,. Hoshino, K., Rudraiah, S. and Kumbar S.G. (2016) “Bioactive polymeric scaffolds for tissue engineering”, Bioact Mater, 1:93–108.CrossRefPubMedPubMedCentral Stratton, S., Shelke, N.B,. Hoshino, K., Rudraiah, S. and Kumbar S.G. (2016) “Bioactive polymeric scaffolds for tissue engineering”, Bioact Mater, 1:93–108.CrossRefPubMedPubMedCentral
Zurück zum Zitat Sun W, Lal P (2002) Recent development on computer aided tissue engineering - a review. Comput Methods Prog Biomed 67:85–103CrossRef Sun W, Lal P (2002) Recent development on computer aided tissue engineering - a review. Comput Methods Prog Biomed 67:85–103CrossRef
Zurück zum Zitat Tajbakhsh S, Hajiali F (2017) A comprehensive study on the fabrication and properties of biocomposites of poly(lactic acid)/ceramics for bone tissue engineering. Mater Sci Eng C 70:897–912CrossRef Tajbakhsh S, Hajiali F (2017) A comprehensive study on the fabrication and properties of biocomposites of poly(lactic acid)/ceramics for bone tissue engineering. Mater Sci Eng C 70:897–912CrossRef
Zurück zum Zitat Tan KH, Chua CK, Leong KF, Cheah CM, Gui WS, Tan WS, Wiria FE (2005) Selective laser sintering of biocompatible polymers for applications in tissue engineering. Biomed Mater Eng 15:113–124PubMed Tan KH, Chua CK, Leong KF, Cheah CM, Gui WS, Tan WS, Wiria FE (2005) Selective laser sintering of biocompatible polymers for applications in tissue engineering. Biomed Mater Eng 15:113–124PubMed
Zurück zum Zitat Tollemar V, Collier ZJ, Mohammed MK, Lee MJ, Ameer GA, Reid RR (2016) Stem cells, growth factors and scaffolds in craniofacial regenerative medicine. Genes Dis 3:56–71CrossRefPubMed Tollemar V, Collier ZJ, Mohammed MK, Lee MJ, Ameer GA, Reid RR (2016) Stem cells, growth factors and scaffolds in craniofacial regenerative medicine. Genes Dis 3:56–71CrossRefPubMed
Zurück zum Zitat Vozzi G, Flaim C, Ahluwalia A, Bhatia S (2003) Fabrication of PLGA scaffolds using soft lithography and microsyringe deposition. Biomaterials 24:2533–2540CrossRef Vozzi G, Flaim C, Ahluwalia A, Bhatia S (2003) Fabrication of PLGA scaffolds using soft lithography and microsyringe deposition. Biomaterials 24:2533–2540CrossRef
Zurück zum Zitat Wang Y (2007) Periodic surface modeling for computer aided nano design. Comput Aided Des 39(3):179–189CrossRef Wang Y (2007) Periodic surface modeling for computer aided nano design. Comput Aided Des 39(3):179–189CrossRef
Zurück zum Zitat Xue Y, Sant V, Phillippi J, Sant S (2017) Biodegradable and biomimetic elastomeric scaffolds for tissue engineered heart valves. Acta Biomater 48:2–19CrossRefPubMed Xue Y, Sant V, Phillippi J, Sant S (2017) Biodegradable and biomimetic elastomeric scaffolds for tissue engineered heart valves. Acta Biomater 48:2–19CrossRefPubMed
Zurück zum Zitat Yoo DJ (2011a) Computer-aided porous scaffold design for tissue engineering using triply periodic minimal surfaces. Int J Precis Eng Manuf 12(1):61–71CrossRef Yoo DJ (2011a) Computer-aided porous scaffold design for tissue engineering using triply periodic minimal surfaces. Int J Precis Eng Manuf 12(1):61–71CrossRef
Zurück zum Zitat Yoo DJ (2011b) Porous scaffold design using the distance field and triply periodic minimal surface models. Biomaterials 32(31):7741–7754CrossRefPubMed Yoo DJ (2011b) Porous scaffold design using the distance field and triply periodic minimal surface models. Biomaterials 32(31):7741–7754CrossRefPubMed
Zurück zum Zitat Yoo DJ (2012a) Heterogeneous porous scaffold design for tissue engineering using triply periodic minimal surfaces. Int J Precis Eng Manuf 13(4):527–537CrossRef Yoo DJ (2012a) Heterogeneous porous scaffold design for tissue engineering using triply periodic minimal surfaces. Int J Precis Eng Manuf 13(4):527–537CrossRef
Zurück zum Zitat Yoo, D.J. (2012b) Heterogeneous minimal surface porous scaffold design using the distance field and radial basis functions, Med Eng Phys 34(5):625–639CrossRef Yoo, D.J. (2012b) Heterogeneous minimal surface porous scaffold design using the distance field and radial basis functions, Med Eng Phys 34(5):625–639CrossRef
Zurück zum Zitat Yoo DJ (2013) Heterogeneous porous scaffold design using the continuous transformations of triply periodic minimal surface models. Int J Precis Eng Manuf 14(10):1743–1753CrossRef Yoo DJ (2013) Heterogeneous porous scaffold design using the continuous transformations of triply periodic minimal surface models. Int J Precis Eng Manuf 14(10):1743–1753CrossRef
Zurück zum Zitat Yoo DJ (2014) Advanced porous scaffold design using multi-void triply periodic minimal surface models with high surface area to volume ratios. Int J Precis Eng Manuf 15(8):1657–1666CrossRef Yoo DJ (2014) Advanced porous scaffold design using multi-void triply periodic minimal surface models with high surface area to volume ratios. Int J Precis Eng Manuf 15(8):1657–1666CrossRef
Metadaten
Titel
Mathematical Modeling of 3D Tissue Engineering Constructs
verfasst von
Henrique Amorim Almeida
Paulo Jorge da Silva Bártolo
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-45444-3_5

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.