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REVIEW

Extrusion bioprinting from a fluid mechanics perspective

Reza Gharraei1 ,  Donald J. Bergstrom2 ,  Xiongbiao Chen1,2*
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1 Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
2 Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada
IJB 2024, 10(6), 3973 https://doi.org/10.36922/ijb.3973
Submitted: 18 June 2024 | Accepted: 9 August 2024 | Published: 30 August 2024
© 2024 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
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Abstract

Bioprinting is an emerging technology for fabricating intricate and diverse structures that closely mimic natural tissues and organs for applications, such as tissue engineering, drug delivery, and cancer research. Among the various bioprinting techniques, extrusion-based bioprinting stands out due to its capability to apply a wide range of biomaterials and living cells and its controllability over printed structures. In bioprinting, bioink stored in a syringe is extruded through a nozzle connected to the syringe and deposited onto the printing stage to form 3D structures. The bioprinting process involves the flow of bioink through the syringe and nozzle, then spreading on a printing stage. As a result, fluid mechanics plays a crucial role in extrusion bioprinting. Notably, the biomaterials used in bioprinting are typically non-Newtonian fluids, which have complex viscoelastic and thixotropic behaviors; the influence of these behaviors on the bioprinting process has garnered considerable attention, with various methods employed, including numerical simulations via computational fluid dynamics (CFD). This paper reviews the latest developments in the fluid mechanics of extrusion-based bioprinting to shed light on the challenges and key considerations involved. This review covers the topics of extrusion bioprinting (including driving mechanisms, printability, and cell viability), biomaterial rheology and its effect on bioprinting, multi-material bioprinting, and numerical simulations of bioprinting. Key issues and challenges are also discussed along with recommendations for future research.

Graphical abstract
Keywords
3D bioprinting
Fluid Mechanics
Viscoelasticity
Tissue engineering
Funding
This research was financially supported by the University of Saskatchewan Dean’s Scholarship and the Devolved Scholarship from the Department of Mechanical Engineering for the first author, and by the Natural Sciences and Engineering Research Council (NSERC) funds for the co-authors. Grant numbers: RGPIN 06396- 2019, RGPIN 04981-2022
Conflict of interest
Xiongbiao Chen serves as the Editorial Board Member of the journal, but did not in any way involve in the editorial and peer-review process conducted for this paper, directly or indirectly. Other authors declare they have no competing interests.
References
  1. Derakhshanfar S, Mbeleck R, Xu K, Zhang X, Zhong W, Xing M. 3D bioprinting for biomedical devices and tissue engineering: a review of recent trends and advances. Bioact Mater. 2018;3(2):144-156. doi: 10.1016/j.bioactmat.2017.11.008
  2. DeSimone E, Schacht K, Jungst T, Groll J, Scheibel T. Biofabrication of 3D constructs: fabrication technologies and spider silk proteins as bioinks. Pure Appl Chem. 2015;87(8):737-749. doi: 10.1515/pac-2015-0106
  3. Gao W, Zhang Y, Ramanujan D, et al. The status, challenges, and future of additive manufacturing in engineering. Computer-Aided Design. 2015;69:65-89. doi: 10.1016/j.cad.2015.04.001
  4. Ozbolat IT, Yin Yu. Bioprinting toward organ fabrication: challenges and future trends. IEEE Trans Biomed Eng. 2013;60(3):691-699. doi: 10.1109/TBME.2013.2243912
  5. Farzin A, Miri AK, Sharifi F, et al. 3D-printed sugar-based stents facilitating vascular anastomosis. Adv Healthc Mater. 2018;7(24):1800702. doi: 10.1002/adhm.201800702
  6. Do AV, Khorsand B, Geary SM, Salem AK. 3D printing of scaffolds for tissue regeneration applications. Adv Healthc Mater. 2015;4(12):1742-1762. doi: 10.1002/adhm.201500168
  7. Faramarzi N, Yazdi IK, Nabavinia M, et al. Patient-specific bioinks for 3D bioprinting of tissue engineering scaffolds. Adv Healthc Mater. 2018;7(11):1701347. doi: 10.1002/adhm.201701347
  8. Ozbolat IT, Hospodiuk M. Current advances and future perspectives in extrusion-based bioprinting. Biomaterials. 2016;76:321-343. doi: 10.1016/j.biomaterials.2015.10.076
  9. Bakarich SE, Gorkin R, Gately R, Naficy S, in het Panhuis M, Spinks GM. 3D printing of tough hydrogel composites with spatially varying materials properties. Addit Manuf. 2017;14:24-30. doi: 10.1016/j.addma.2016.12.003
  10. Kirchmajer DM, Gorkin R, In Het Panhuis M. An overview of the suitability of hydrogel-forming polymers for extrusion-based 3D-printing. J Mater Chem B. 2015;3: 4105-4117. doi: 10.1039/c5tb00393h
  11. Tavafoghi M, Darabi MA, Mahmoodi M, et al. Multimaterial bioprinting and combination of processing techniques towards the fabrication of biomimetic tissues and organs. Biofabrication. 2021;13(4):042002. doi: 10.1088/1758-5090/ac0b9a
  12. Schwab A, Levato R, D’Este M, Piluso S, Eglin D, Malda J. Printability and shape fidelity of bioinks in 3D bioprinting. Chem Rev. 2020;120(19):11028-11055. doi: 10.1021/acs.chemrev.0c00084
  13. Richard C, Neild A, Cadarso VJ. The emerging role of microfluidics in multi-material 3D bioprinting. Lab Chip. 2020;20(12):2044-2056. doi: 10.1039/c9lc01184f
  14. Askari M, Afzali Naniz M, Kouhi M, Saberi A, Zolfagharian A, Bodaghi M. Recent progress in extrusion 3D bioprinting of hydrogel biomaterials for tissue regeneration: a comprehensive review with focus on advanced fabrication techniques. Biomater Sci. 2021;9(3):535-573. doi: 10.1039/d0bm00973c
  15. Zhang J, Allardyce BJ, Rajkhowa R, et al. 3D printing of silk particle-reinforced chitosan hydrogel structures and their properties. ACS Biomater Sci Eng. 2018;4(8):3036-3046. doi: 10.1021/acsbiomaterials.8b00804
  16. Aydogdu MO, Oner ET, Ekren N, et al. Comparative characterization of the hydrogel added PLA/β-TCP scaffolds produced by 3D bioprinting. Bioprinting. 2019; 13:e00046. doi: 10.1016/j.bprint.2019.e00046
  17. Yan J, Wang Y, Zhang X, et al. Snakegourd root/Astragalus polysaccharide hydrogel preparation and application in 3D printing. Int J Biol Macromol. 2019;121:309-316. doi: 10.1016/j.ijbiomac.2018.10.008
  18. Yazdanpanah Z, Johnston JD, Cooper DML, Chen X. 3D bioprinted scaffolds for bone tissue engineering: state-of-the-art and emerging technologies. Front Bioeng Biotechnol. 2022;10(April):824156. doi: 10.3389/fbioe.2022.824156
  19. Ratner BD, Bryant SJ. Biomaterials: where we have been and where we are going. Annu Rev Biomed Eng. 2004;6:41-75. doi: 10.1146/annurev.bioeng.6.040803.140027
  20. Caló E, Khutoryanskiy VV. Biomedical applications of hydrogels: a review of patents and commercial products. Eur Polym J. 2015;65:252-267. doi: 10.1016/j.eurpolymj.2014.11.024
  21. Roehm KD, Madihally SV. Bioprinted chitosan-gelatin thermosensitive hydrogels using an inexpensive 3D printer. Biofabrication. 2018;10(1):015002. doi: 10.1088/1758-5090/aa96dd
  22. Mora-Boza A, Włodarczyk-Biegun MK, Del Campo A, Vázquez-Lasa B, Román JS. Glycerylphytate as an ionic crosslinker for 3D printing of multi-layered scaffolds with improved shape fidelity and biological features. Biomater Sci. 2019;8(1):506-516. doi: 10.1039/c9bm01271k
  23. Chen XB, Fazel Anvari-Yazdi A, Duan X, et al. Biomaterials / bioinks and extrusion bioprinting. Bioact Mater. 2023;28:511-536. doi: 10.1016/j.bioactmat.2023.06.006
  24. Akkineni AR, Ahlfeld T, Lode A, Gelinsky M. A versatile method for combining different biopolymers in a core/ shell fashion by 3D plotting to achieve mechanically robust constructs. Biofabrication. 2016;8(4):045001. doi: 10.1088/1758-5090/8/4/045001
  25. Liu X, Zhao K, Gong T, et al. Delivery of growth factors using a smart porous nanocomposite scaffold to repair a mandibular bone defect. Biomacromolecules. 2014;15(3):1019-1030. doi: 10.1021/bm401911p
  26. Augst AD, Kong HJ, Mooney DJ. Alginate hydrogels as biomaterials. Macromol Biosci. 2006;6(8):623-633. doi: 10.1002/mabi.200600069
  27. Izadifar Z, Chang T, Kulyk W, Chen X, Eames BF. Analyzing biological performance of 3D-printed, cell-impregnated hybrid constructs for cartilage tissue engineering. Tissue Eng Part C Methods. 2016;22:173-188. doi: 10.1089/ten.tec.2015.0307
  28. Naghieh S, Sarker M, Izadifar M, Chen X. Dispensing-based bioprinting of mechanically-functional hybrid scaffolds with vessel-like channels for tissue engineering applications – a brief review. J Mech Behav Biomed Mater. 2018;78:298-314. doi: 10.1016/j.jmbbm.2017.11.037
  29. Kiyotake EA, Douglas AW, Thomas EE, Nimmo SL, Detamore MS. Development and quantitative characterization of the precursor rheology of hyaluronic acid hydrogels for bioprinting. Acta Biomater. 2019;95:176-187. doi: 10.1016/j.actbio.2019.01.041
  30. Hölzl K, Lin S, Tytgat L, Van Vlierberghe S, Gu L, Ovsianikov A. Bioink properties before, during and after 3D bioprinting. Biofabrication. 2016;8(3):032002. doi: 10.1088/1758-5090/8/3/032002
  31. Monika Hospodiuk KKMMDITO. Extrusion-Based Biofabrication in Tissue Engineering and Regenerative Medicine. 1st ed. Springer; 2018.
  32. Khalil S, Nam J, Sun W. Multi-nozzle deposition for construction of 3D biopolymer tissue scaffolds. Rapid Prototyp J. 2005;11(1):9-17. doi: 10.1108/13552540510573347
  33. Boularaoui S, Al Hussein G, Khan KA, Christoforou N, Stefanini C. An overview of extrusion-based bioprinting with a focus on induced shear stress and its effect on cell viability. Bioprinting. 2020;20(August):e00093. doi: 10.1016/j.bprint.2020.e00093
  34. Ning L, Yang B, Mohabatpour F, et al. Process-induced cell damage: pneumatic versus screw-driven bioprinting. Biofabrication. 2020;12(2):025011. doi: 10.1088/1758-5090/ab5f53
  35. Murphy SV, Atala A. 3D bioprinting of tissues and organs. Nat Biotechnol. 2014;32(8):773-785. doi: 10.1038/nbt.2958
  36. Daniel X. B. Chen. Extrusion Bioprinting of Scaffolds for Tissue Engineering Applications. 1st ed. Springer Nature; 2019.
  37. Malekpour A, Chen X. Printability and cell viability in extrusion-based bioprinting from experimental, computational, and machine learning views. J Funct Biomater. 2022;13(2):40. doi: 10.3390/jfb13020040
  38. Fu Z, Naghieh S, Xu C, Wang C, Sun W, Chen X. Printability in extrusion bioprinting. Biofabrication. 2021;13(3):033001. doi: 10.1088/1758-5090/abe7ab
  39. Gillispie G, Prim P, Copus J, et al. Assessment methodologies for extrusion-based bioink printability. Biofabrication. 2020;12(2):22003. doi: 10.1088/1758-5090/ab6f0d
  40. Xu X, Jagota A, Peng S, Luo D, Wu M, Hui CY. Gravity and surface tension effects on the shape change of soft materials. Langmuir. 2013;29(27):8665-8674. doi: 10.1021/la400921h
  41. Hospodiuk M, Dey M, Sosnoski D, Ozbolat IT. The bioink: a comprehensive review on bioprintable materials. Biotechnol Adv. 2017;35(2):217-239. doi: 10.1016/j.biotechadv.2016.12.006
  42. Petta D, Grijpma DW, Alini M, Eglin D, D’Este M. Three-dimensional printing of a tyramine hyaluronan derivative with double gelation mechanism for independent tuning of shear thinning and postprinting curing. ACS Biomater Sci Eng. 2018;4(8):3088-3098. doi: 10.1021/acsbiomaterials.8b00416
  43. Gao T, Gillispie GJ, Copus JS, et al. Optimization of gelatin– alginate composite bioink printability using rheological parameters: a systematic approach. Biofabrication. 2018;10(3):034106. doi: 10.1088/1758-5090/aacdc7
  44. Saha D, Bhattacharya S. Hydrocolloids as thickening and gelling agents in food: a critical review. J Food Sci Technol. 2010;47(6):587-597. doi: 10.1007/s13197-010-0162-6
  45. He Y, Yang F, Zhao H, Gao Q, Xia B, Fu J. Research on the printability of hydrogels in 3D bioprinting. Sci Rep. 2016;6(1):29977. doi: 10.1038/srep29977
  46. Soltan N, Ning L, Mohabatpour F, Papagerakis P, Chen X. Printability and cell viability in bioprinting alginate dialdehyde-gelatin scaffolds. ACS Biomater Sci Eng. 2019;5(6):2976-2987. doi: 10.1021/acsbiomaterials.9b00167
  47. Lee JM, Ng WL, Yeong WY. Resolution and shape in bioprinting: strategizing towards complex tissue and organ printing. Appl Phys Rev. 2019;6(1):011307. doi: 10.1063/1.5053909
  48. Ribeiro A, Blokzijl MM, Levato R, et al. Assessing bioink shape fidelity to aid material development in 3D bioprinting. Biofabrication. 2017;10(1):014102. doi: 10.1088/1758-5090/aa90e2
  49. Ouyang L, Yao R, Zhao Y, Sun W. Effect of bioink properties on printability and cell viability for 3D bioplotting of embryonic stem cells. Biofabrication. 2016;8(3):035020. doi: 10.1088/1758-5090/8/3/035020
  50. Herrada-Manchón H, Fernández MA, Aguilar E. Essential guide to hydrogel rheology in extrusion 3D printing: how to measure it and why it matters? Gels. 2023;9(7):517. doi: 10.3390/gels9070517
  51. Cooke ME, Rosenzweig DH. The rheology of direct and suspended extrusion bioprinting. APL Bioeng. 2021;5(1):011502. doi: 10.1063/5.0031475
  52. Clasen C, Entov V, Bico J, McKinley GH. `Gobbling Drops´ : the jetting / dripping transition in flows of polymeric liquids. J Fluid Mech. 2009;636:5-40. doi: 10.1017/S0022112009008143
  53. Clanet C, Lasheras JC. Transition from dripping to jetting. J Fluid Mech. 1999;383:307-326. doi: 10.1017/S0022112098004066
  54. Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein. Fundamentals of Fluid Mechanics. 8th ed. Wiley; 2018.
  55. Liliang Ouyang. 3D bioprinting of thermal-sensitive bioink. In: Study on Microextrusion-Based 3D Bioprinting and Bioink Crosslinking Mechanisms. Springer; 2019.
  56. Savart F. M’emoire sur la constitution des veines liquides lanc’ees par des ori ces circulaires en mince paroi. Ann Chim (Paris). 1833;53:337-386.
  57. Plateau J. Statique Expe’rimentale et The’orique des Liquides. In: Gauthier-Villars et Cie; 1873.
  58. Lord R. Investigations in capillarity: the size of drops. - The liberation of gas from supersaturated solutions. - Colliding jets. - The tension of contaminated water-surfaces. Curious observation. Philos Magaz J Sci. 1899;48(293):321-337.
  59. Chen XB, Ke H. Effects of fluid properties on dispensing processes for electronics packaging. IEEE Trans Electron Pack Manuf. 2006;29(2):75-82. doi: 10.1109/TEPM.2006.874964
  60. De Maria C, Vozzi G, Moroni L. Multimaterial, heterogeneous, and multicellular three-dimensional bioprinting. MRS Bull. 2017;42(8):578-584. doi: 10.1557/mrs.2017.165
  61. You F, Wu X, Zhu N, Lei M, Eames BF, Chen X. 3D printing of porous cell-laden hydrogel constructs for potential applications in cartilage tissue engineering. ACS Biomater Sci Eng. 2016;2(7). doi: 10.1021/acsbiomaterials.6b00258
  62. Ning L, Sun H, Lelong T, et al. 3D bioprinting of scaffolds with living Schwann cells for potential nerve tissue engineering applications. Biofabrication. 2018;10(3):035014. doi: 10.1088/1758-5090/aacd30
  63. Ning L, Betancourt N, Schreyer DJ, Chen X. Characterization of cell damage and proliferative ability during and after bioprinting. ACS Biomater Sci Eng. 2018;4(11):3906-3918. doi: 10.1021/acsbiomaterials.8b00714
  64. Xu HQ, Liu JC, Zhang ZY, Xu CX. A review on cell damage, viability, and functionality during 3D bioprinting. Mil Med Res. 2022;9(1):1-15. doi: 10.1186/s40779-022-00429-5
  65. Fakhruddin K, Hamzah MSA, Razak SIA. Effects of extrusion pressure and printing speed of 3D bioprinted construct on the fibroblast cells viability. IOP Conf Ser Mater Sci Eng. 2018;440(1):012042. doi: 10.1088/1757-899X/440/1/012042
  66. Ning L, Chen X. A brief review of extrusion-based tissue scaffold bio-printing. Biotechnol J. 2017;12(8):1200-1210. doi: 10.1002/biot.201600671
  67. Bae YB, Jang HK, Shin TH, et al. Microfluidic assessment of mechanical cell damage by extensional stress. Lab Chip. 2016;16(1):96-103. doi: 10.1039/C5LC01006C
  68. Aguado BA, Mulyasasmita W, Su J, Lampe KJ, Heilshorn SC. Improving viability of stem cells during syringe needle flow through the design of hydrogel cell carriers. Tissue Eng Part A. 2012;18(7-8):806-815. doi: 10.1089/ten.tea.2011.0391
  69. Down LA, Papavassiliou DV, O’Rear EA. Significance of extensional stresses to red blood cell lysis in a shearing flow. Ann Biomed Eng. 2011;39(6):1632-1642. doi: 10.1007/s10439-011-0262-0
  70. Byron Bird R, Stewart WE, Lightfoot EN. Transport Phenomena. 2nd ed. Wiley; 2009.
  71. Cogswell FN. Measuring the extensional rheology of polymer melts. Trans Soc Rheol. 1972;16(3):383-403. doi: 10.1122/1.549257
  72. Mitsoulis E, Hatzikiriakos SG, Christodoulou K, Vlassopoulos D. Sensitivity analysis of the Bagley correction to shear and extensional rheology. Rheol Acta. 1998;37(5):438-448. doi: 10.1007/s003970050131
  73. Han S, Kim CM, Jin S, Kim TY. Study of the process-induced cell damage in forced extrusion bioprinting. Biofabrication. 2021;13(3):035048. doi: 10.1088/1758-5090/ac0415
  74. Chirianni F, Vairo G, Marino M. Development of process design tools for extrusion-based bioprinting: From numerical simulations to nomograms through reduced-order modeling. Comput Methods Appl Mech Eng. 2024;419:116685. doi: 10.1016/j.cma.2023.116685
  75. Li M, Tian X, Zhu N, Schreyer DJ, Chen X. Modeling process-induced cell damage in the biodispensing process. Tissue Eng Part C Methods. 2010;16(3):533-542. doi: 10.1089/ten.tec.2009.0178
  76. Li M, Tian X, Schreyer DJ, Chen X. Effect of needle geometry on flow rate and cell damage in the dispensing-based biofabrication process. Biotechnol Prog. 2011;27(6):1777-1784. doi: 10.1002/btpr.679
  77. Chhabra RP, Richardson JF. Non-Newtonian Dlow and Applied Rheology. Oxford, UK: Butterworth-Heinemann 2nd ed.; 2008. doi: 10.1016/B978-0-7506-8532-0.X0001-7
  78. Byron Bird R, Robert C, Armstrong OH. Dynamics of Polymeric Liquids. 2nd ed. John Wiley & Sons; 1987. doi: 10.1002/aic.690340623
  79. Cooke ME, Rosenzweig DH. The rheology of direct and suspended extrusion bioprinting. APL Bioeng. 2021;5(1):011502. doi: 10.1063/5.0031475
  80. Ostwald W. Ueber die rechnerische Darstellung des Strukturgebietes der Viskosität. Kolloid-Zeitschrift. 1929;47(2):176-187. doi: 10.1007/BF01496959
  81. de Waele A. Viscometry and plastometry. J Oil and Colour Chemists’ Assoc. 1923;6(38):33-88.
  82. Carreau PiJ. Rheological equations from molecular network theories. Trans Soc Rheol. 1972;16(1):99-127. doi: 10.1122/1.549276.
  83. Yasuda K. Investigation of the Analogies Berween Viscometric and Linear Viscoelastic Properties of Polystyrene Fluids. Massachusetts Institute of Technology; 1979. http://hdl.handle.net/1721.1/16043
  84. Cross MM. Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic systems. J Colloid Sci. 1965;20(5):417-437. doi: 10.1016/0095-8522(65)90022-X
  85. Herschel VWH, Bulkley R. Ronsistenzmessungen yon ( ummi-BenzollGsungen). Colloid Polym Sci. 1926;39:291-300. doi: 10.1007/BF01432034
  86. Nelson AZ, Schweizer KS, Rauzan BM, Nuzzo RG, Vermant J, Ewoldt RH. Designing and transforming yield-stress fluids. Curr Opin Solid State Mater Sci. 2019;23(5):100758. doi: 10.1016/j.cossms.2019.06.002
  87. Pereira RF, Sousa A, Barrias CC, Bártolo PJ, Granja PL. A single-component hydrogel bioink for bioprinting of bioengineered 3D constructs for dermal tissue engineering. Mater Horiz. 2018;5(6):1100-1111. doi: 10.1039/C8MH00525G
  88. Ramesh S, Harrysson OLA, Rao PK, et al. Extrusion bioprinting: Recent progress, challenges, and future opportunities. Bioprinting. 2021;21(November 2020): e00116. doi: 10.1016/j.bprint.2020.e00116
  89. Nair K, Gandhi M, Khalil S, et al. Characterization of cell viability during bioprinting processes. Biotechnol J. 2009;4(8):1168-1177. doi: 10.1002/biot.200900004
  90. Jiang Y, Zhou J, Feng C, Shi H, Zhao G, Bian Y. Rheological behavior, 3D printability and the formation of scaffolds with cellulose nanocrystals/gelatin hydrogels. J Mater Sci. 2020;55(33):15709-15725. doi: 10.1007/s10853-020-05128-x
  91. Ouyang L, Armstrong JPK, Lin Y, et al. Expanding and optimizing 3D bioprinting capabilities using complementary network bioinks. Sci Adv. 2020;6(38):eabc5529. doi: 10.1126/sciadv.abc5529
  92. Paxton N, Smolan W, Böck T, Melchels F, Groll J, Jungst T. Proposal to assess printability of bioinks for extrusion-based bioprinting and evaluation of rheological properties governing bioprintability. Biofabrication. 2017;9(4):044107. doi: 10.1088/1758-5090/aa8dd8
  93. Tuladhar S, Nelson C, Habib A. Rheological study of highly thixotropic hydrogels for 3D bio-printing processes. In: Ghate A, Krishnaiyer K, Paynabar K, eds. Proceedings of the 2021 IISE Annual Conference; 2021.
  94. Diañez I, Gallegos C, Brito-de la Fuente E, et al. 3D printing in situ gelification of κ-carrageenan solutions: effect of printing variables on the rheological response. Food Hydrocoll. 2019;87:321-330. doi: 10.1016/j.foodhyd.2018.08.010
  95. Herrada-Manchón H, Celada L, Rodríguez-González D, Alejandro Fernández M, Aguilar E, Chiara MD. Three-dimensional bioprinted cancer models: A powerful platform for investigating tunneling nanotube-like cell structures in complex microenvironments. Mater Sci Eng: C. 2021;128:112357. doi: 10.1016/j.msec.2021.112357
  96. Chen Y, Wang Y, Yang Q, et al. A novel thixotropic magnesium phosphate-based bioink with excellent printability for application in 3D printing. J Mater Chem B. 2018;6(27):4502-4513. doi: 10.1039/C8TB01196F
  97. Jungst T, Smolan W, Schacht K, Scheibel T, Groll J. Strategies and molecular design criteria for 3D printable hydrogels. Chem Rev. 2016;116(3):1496-1539. doi: 10.1021/acs.chemrev.5b00303
  98. Ma J, Lin Y, Chen X, Zhao B, Zhang J. Flow behavior, thixotropy and dynamical viscoelasticity of sodium alginate aqueous solutions. Food Hydrocoll. 2014;38:119-128. doi: 10.1016/j.foodhyd.2013.11.016
  99. Cheng Y, Qin H, Acevedo NC, Jiang X, Shi X. 3D printing of extended-release tablets of theophylline using hydroxypropyl methylcellulose (HPMC) hydrogels. Int J Pharm. 2020;591:119983. doi: 10.1016/j.ijpharm.2020.119983
  100. Sombatsompop N, Sergsiri S. Die swell ratio of polystyrene melt from an electro-magnetized capillary die in an extrusion rheometer: effects of barrel diameter, shear rate and die temperature. Polym Adv Technol. 2004;15(8):472-480. doi: 10.1002/pat.490
  101. Michal Bathory. Modelling and analysis of flows of viscoelastic fluids Beyond the Navier–Stokes equations. Res Outreach. 2022;(132). doi: 10.32907/RO-132-3331282634
  102. Boger DV, Binnington RJ. Experimental removal of the re‐entrant corner singularity in tubular entry flows. J Rheol. 1994;38(2):333-349. doi: 10.1122/1.550517
  103. Maklad O, Poole RJ. A review of the second normal-stress difference; its importance in various flows, measurement techniques, results for various complex fluids and theoretical predictions. J Nonnewton Fluid Mech. 2021;292:104522. doi: 10.1016/j.jnnfm.2021.104522
  104. R J Poole. The Deborah and Weissenberg numbers. Rheol Bull. 2012;52(2):32-39.
  105. Wu Q, Therriault D, Heuzey MC. Processing and properties of chitosan inks for 3D printing of hydrogel microstructures. ACS Biomater Sci Eng. 2018;4(7):2643-2652. doi: 10.1021/acsbiomaterials.8b00415
  106. Vlachopoulos J, Polychronopoulos N. Basic concepts in polymer melt rheology and their importance in processing. In: Kontopoulou M, eds. Applied Polymer Rheology. John Wiley & Sons, Inc.; 2011:1-27. doi: 10.1002/9781118140611.ch1
  107. Koopmans RJ. Die swell or extrudate swell. In: Karger-Kocsis J, ed. Polypropylene: An A-Z Reference. Kluwer Publishers; 1999.
  108. Sodupe-Ortega E, Sanz-Garcia A, Pernia-Espinoza A, Escobedo-Lucea C. Accurate calibration in multi-material 3D bioprinting for tissue engineering. Materials (Basel). 2018;11(8):1402. doi: 10.3390/ma11081402
  109. Anna SL, Rogers C, McKinley GH. On controlling the kinematics of a filament stretching rheometer using a real-time active control mechanism. J Nonnewton Fluid Mech. 1999;87(2-3):307-335. doi: 10.1016/S0377-0257(99)00072-5
  110. Ooi YW, Sridhar T. Extensional rheometry of fluid S1. J Nonnewton Fluid Mech. 1994;52(2):153-162. doi: 10.1016/0377-0257(94)80047-2
  111. McKinley GH, Tripathi A, Yao M. Extensional rheometry of polymeric fluids and the uniaxial elongation of viscoelastic filaments. In: Kruijt PGM, Meijer HEH, van de Vosse FN, eds. 15th Annual Meeting of the International Polymer Processing Society; 1999.
  112. Göhl J, Markstedt K, Mark A, Håkansson K, Gatenholm P, Edelvik F. Simulations of 3D bioprinting: Predicting bioprintability of nanofibrillar inks. Biofabrication. 2018;10(3):34105. doi: 10.1088/1758-5090/aac872
  113. Zaeri A, Zgeib R, Cao K, Zhang F, Chang RC. Numerical analysis on the effects of microfluidic-based bioprinting parameters on the microfiber geometrical outcomes. Sci Rep. 2022;12(1):3364. doi: 10.1038/s41598-022-07392-0
  114. Hemasian Etefagh A, Razfar MR. Numerical study of the process parameters affecting the feature size of a microfiber fabricated by microfluidic-based bioprinting. Proc Instit Mech Eng E: J Process Mech Eng. 2024. doi: 10.1177/09544089241236265
  115. Ma J, Lin Y, Chen X, Zhao B, Zhang J. Flow behavior, thixotropy and dynamical viscoelasticity of sodium alginate aqueous solutions. Food Hydrocoll. 2014;38:119-128. doi: 10.1016/j.foodhyd.2013.11.016
  116. Talluri DJS, Nguyen HT, Avazmohammadi R, Miri AK. Ink rheology regulates stability of bioprinted strands. J Biomech Eng. 2022;144(7) 074503. doi: 10.1115/1.4053404
  117. Gregory T, Benhal P, Scutte A, et al. Rheological characterization of cell-laden alginate-gelatin hydrogels for 3D biofabrication. J Mech Behav Biomed Mater. 2022;136:105474. doi: 10.1016/j.jmbbm.2022.105474
  118. López-Marcial GR, Zeng AY, Osuna C, Dennis J, García JM, O’Connell GD. Agarose-based hydrogels as suitable bioprinting materials for tissue engineering. ACS Biomater Sci Eng. 2018;4(10):3610-3616. doi: 10.1021/acsbiomaterials.8b00903
  119. Benchabane A, Bekkour K. Rheological properties of carboxymethyl cellulose (CMC) solutions. Colloid Polym Sci. 2008;286(10):1173-1180. doi: 10.1007/s00396-008-1882-2
  120. Ramezani H, Mohammad Mirjamali S, He Y. Simulations of extrusion 3d printing of chitosan hydrogels. Appl Sci. 2022;12(15):7530. doi: 10.3390/app12157530
  121. Rahimnejad M, Labonté-Dupuis T, Demarquette NR, Lerouge S. A rheological approach to assess the printability of thermosensitive chitosan-based biomaterial inks. Biomed Mater. 2021;16(1):015003. doi: 10.1088/1748-605X/abb2d8
  122. Lan X, Adesida A, Boluk Y. Rheological and viscoelastic properties of collagens and their role in bioprinting by micro-extrusion. Biomed Mater. 2022;17(6):062005. doi: 10.1088/1748-605X/ac9b06
  123. Andrade RD, Skurtys O, Osorio F, Zuluaga R, Gañán P, Castro C. Rheological and physical properties of gelatin suspensions containing cellulose nanofibers for potential coatings. Food Sci Technol Int. 2015;21(5):332-341. doi: 10.1177/1082013214535944
  124. Kokol V, Pottathara YB, Mihelčič M, Perše LS. Rheological properties of gelatine hydrogels affected by flow- and horizontally-induced cooling rates during 3D cryo-printing. Colloids Surf A Physicochem Eng Asp. 2021;616:126356. doi: 10.1016/j.colsurfa.2021.126356
  125. Tirella A, De Maria C, Criscenti G, Vozzi G, Ahluwalia A. The PAM 2 system: a multilevel approach for fabrication of complex three-dimensional microstructures. Rapid Prototyp J. 2012;18(4):299-307. doi: 10.1108/13552541211231725
  126. Naghieh S, Karamooz-Ravari MR, Sarker M, Karki E, Chen X. Influence of crosslinking on the mechanical behavior of 3D printed alginate scaffolds: experimental and numerical approaches. J Mech Behav Biomed Mater. 2018;80:111-118. doi: 10.1016/j.jmbbm.2018.01.034
  127. Sarker Md, Izadifar M, Schreyer D, Chen X. Influence of ionic crosslinkers (Ca 2+ /Ba 2+ /Zn 2+ ) on the mechanical and biological properties of 3D Bioplotted Hydrogel Scaffolds. J Biomater Sci Polym Ed. 2018;29(10):1126-1154. doi: 10.1080/09205063.2018.1433420
  128. Pati F, Jang J, Ha DH, et al. Printing three-dimensional tissue analogues with decellularized extracellular matrix bioink. Nat Commun. 2014;5(1):3935. doi: 10.1038/ncomms4935
  129. Chang R, Nam J, Sun W. Effects of dispensing pressure and nozzle diameter on cell survival from solid freeform fabrication-based direct cell writing. Tissue Eng Part A. 2008;14(1):41-48. doi: 10.1089/ten.a.2007.0004
  130. Ashammakhi N, Ahadian S, Xu C, et al. Bioinks and bioprinting technologies to make heterogeneous and biomimetic tissue constructs. Mater Today Bio. 2019;1:100008. doi: 10.1016/j.mtbio.2019.100008
  131. Ozbolat IT, Chen H, Yu Y. Development of “Multi-arm Bioprinter” for hybrid biofabrication of tissue engineering constructs. Robot Comput Integr Manuf. 2014;30(3):295-304. doi: 10.1016/j.rcim.2013.10.005
  132. Hong S, Kim JS, Jung B, Won C, Hwang C. Coaxial bioprinting of cell-laden vascular constructs using a gelatin-tyramine bioink. Biomater Sci. 2019;7(11):4578-4587. doi: 10.1039/c8bm00618k
  133. Gao G, Lee JH, Jang J, et al. Tissue Engineered Bio-Blood- Vessels Constructed Using a Tissue-Specific Bioink and 3D Coaxial Cell Printing Technique: A Novel Therapy for Ischemic Disease. Adv Funct Mater. 2017;27(33):1700798. doi: 10.1002/adfm.201700798
  134. Shao L, Gao Q, Xie C, Fu J, Xiang M, He Y. Directly coaxial 3D bioprinting of large-scale vascularized tissue constructs. Biofabrication. 2020;12(3):035014. doi: 10.1088/1758-5090/ab7e76
  135. Millik SC, Dostie AM, Karis DG, et al. 3D printed coaxial nozzles for the extrusion of hydrogel tubes toward modeling vascular endothelium. Biofabrication. 2019;11(4):45009. doi: 10.1088/1758-5090/ab2b4d
  136. Gao Q, He Y, Fu JZ, Liu A, Ma L. Coaxial nozzle-assisted 3D bioprinting with built-in microchannels for nutrients delivery. Biomaterials. 2015;61:203-215. doi: 10.1016/j.biomaterials.2015.05.031
  137. Mistry P, Aied A, Alexander M, Shakesheff K, Bennett A, Yang J. Bioprinting using mechanically robust core– shell cell-laden hydrogel strands. Macromol Biosci. 2017;17(6)1600472. doi: 10.1002/mabi.201600472
  138. Tomasina C, Bodet T, Mota C, Moroni L, Camarero- Espinosa S. Bioprinting vasculature: materials, cells and emergent techniques. Materials (Basel). 2019;12(17):2701. doi: 10.3390/ma12172701
  139. Cameron T, Naseri E, MacCallum B, Ahmadi A. Development of a disposable single-nozzle printhead for 3D bioprinting of continuous multi-material constructs. Micromachines (Basel). 2020;11(5):459. doi: 10.3390/mi11050459
  140. Nelson C, Tuladhar S, Habib A. Designing an interchangeable multi-material nozzle system for the three-dimensional bioprinting process. J Med Device. 2023;17(2):1-8. doi: 10.1115/1.4055249
  141. Puertas-Bartolomé M, Włodarczyk-Biegun MK, Del Campo A, Vázquez-Lasa B, Román JS. 3D printing of a reactive hydrogel bio-ink using a static mixing tool. Polymers (Basel). 2020;12(9):1-17. doi: 10.3390/polym12091986
  142. Rocca M, Fragasso A, Liu W, Heinrich MA, Zhang YS. Embedded multimaterial extrusion bioprinting. SLAS Technol. 2018;23(2):154-163. doi: 10.1177/2472630317742071
  143. Liu W, Zhang YS, Heinrich MA, et al. Rapid continuous multimaterial extrusion bioprinting. Adv Mater. 2017;29(3):10.1002/adma.201604630. doi: 10.1002/adma.201604630
  144. Puryear III JR, Yoon JK, Kim Y. Advanced fabrication techniques of microengineered physiological systems. Micromachines (Basel). 2020;11(8):730. doi: 10.3390/mi11080730
  145. Kantak C, Beyer S, Trau D. A novel microfluidic droplet manipulation method for fabrication of reverse-phase two layer layer-by-layer protein microcapsules. In: Zengerle R, eds. 17th Int. Conf. on Miniaturized Systems for Chemistry and Life Sciences (MicroTAS 2013) ; 2013.
  146. Shin SR, Kilic T, Zhang YS, et al. Label‐free and regenerative electrochemical microfluidic biosensors for continual monitoring of cell secretomes. Adv Sci. 2017;4(5):1600522. doi: 10.1002/advs.201600522
  147. Bsoul A, Pan S, Cretu E, Stoeber B, Walus K. Design, microfabrication, and characterization of a moulded PDMS/ SU-8 inkjet dispenser for a Lab-on-a-Printer platform technology with disposable microfluidic chip. Lab Chip. 2016;16(17):3351-3361. doi: 10.1039/C6LC00636A
  148. Davoodi E, Sarikhani E, Montazerian H, et al. Extrusion and microfluidic-based bioprinting to fabricate biomimetic tissues and organs. Adv Mater Technol. 2020;5(8):1901044. doi: 10.1002/admt.201901044
  149. Hakimi N, Cheng R, Leng L, et al. Handheld skin printer: in situ formation of planar biomaterials and tissues. Lab Chip. 2018;18(10):1440-1451. doi: 10.1039/c7lc01236e
  150. Onoe H, Okitsu T, Itou A, et al. Metre-long cell-laden microfibres exhibit tissue morphologies and functions. Nat Mater. 2013;12(6):584-590. doi: 10.1038/nmat3606
  151. Raja N, Yun H suk. A simultaneous 3D printing process for the fabrication of bioceramic and cell-laden hydrogel core/shell scaffolds with potential application in bone tissue regeneration. J Mater Chem B. 2016;4(27):4707-4716. doi: 10.1039/C6TB00849F
  152. Angelozzi M, Miotto M, Penolazzi L, et al. Composite ECM-alginate microfibers produced by microfluidics as scaffolds with biomineralization potential. Mater Sci Eng C. 2015;56:141-153. doi: 10.1016/j.msec.2015.06.004
  153. Lee C, Abelseth E, de la Vega L, Willerth SM. Bioprinting a novel glioblastoma tumor model using a fibrin-based bioink for drug screening. Mater Today Chem. 2019; 12:78-84. doi: 10.1016/j.mtchem.2018.12.005
  154. Pati F, Jang J, Lee JW, and D.-W. Cho C. Extrusion Bioprinting. In: Atala A, Yoo JJ, eds. Extrusion Bioprinting, in Essentials of 3D Biofabrication and Translation. 1st ed. Academic Press; 2015.
  155. Hardin JO, Ober TJ, Valentine AD, Lewis JA. Microfluidic printheads for multimaterial 3d printing of viscoelastic inks. Adv Mater. 2015;27(21):3279-3284. doi: 10.1002/adma.201500222
  156. du Chatinier DN, Figler KP, Agrawal P, Liu W, Zhang YS. The potential of microfluidics-enhanced extrusion bioprinting. Biomicrofluidics. 2021;15(4):041304. doi: 10.1063/5.0033280
  157. Utada AS, Fernandez-Nieves A, Stone HA, Weitz DA. Dripping to jetting transitions in coflowing liquid streams. Phys Rev Lett. 2007;99(9):094502. doi: 10.1103/PhysRevLett.99.094502
  158. Derzsi L, Kasprzyk M, Plog JP, Garstecki P. Flow focusing with viscoelastic liquids. Phys Fluids. 2013;25(9):092001. doi: 10.1063/1.4817995
  159. Ober TJ, Foresti D, Lewis JA. Active mixing of complex fluids at the microscale. Proc Natl Acad Sci USA. 2015;112(40):12293-12298. doi: 10.1073/pnas.1509224112
  160. Hessel V, Löwe H, Schönfeld F. Micromixers—a review on passive and active mixing principles. Chem Eng Sci. 2005;60(8-9):2479-2501. doi: 10.1016/j.ces.2004.11.033
  161. Grace HP. Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chem Eng Commun. 1982;14(3-6):225-277. doi: 10.1080/00986448208911047
  162. Chávez-Madero C, De León-Derby MD, Samandari M, et al. Using chaotic advection for facile high-throughput fabrication of ordered multilayer micro-and nanostructures: continuous chaotic printing. Biofabrication. 2020;12(3): 035023. doi: 10.1088/1758-5090/ab84cc
  163. Ober TJ, Foresti D, Lewis JA. Active mixing of complex fluids at the microscale. Proc Natl Acad Sci USA. 2015;112(40):12293-12298. doi: 10.1073/pnas.1509224112
  164. Kuzucu M, Vera G, Beaumont M, et al. Extrusion-based 3D bioprinting of gradients of stiffness, cell density, and immobilized peptide using thermogelling hydrogels. ACS Biomater Sci Eng. 2021;7(6):2192-2197. doi: 10.1021/acsbiomaterials.1c00183
  165. Giachini PAGS, Gupta SS, Wang W, et al. Additive manufacturing of cellulose-based materials with continuous, multidirectional stiffness gradients. Sci Adv. 2020;6(8):1-12. doi: 10.1126/sciadv.aay0929
  166. Bracaglia LG, Smith BT, Watson E, Arumugasaamy N, Mikos AG, Fisher JP. 3D printing for the design and fabrication of polymer-based gradient scaffolds. Acta Biomater. 2017;56:3-13. doi: 10.1016/j.actbio.2017.03.030
  167. Nadernezhad A, Khani N, Skvortsov GA, et al. Multifunctional 3D printing of heterogeneous hydrogel structures. Sci Rep. 2016;6(September):1-12. doi: 10.1038/srep33178
  168. Samandari M, Alipanah F, Majidzadeh-A K, Alvarez MM, Trujillo-De Santiago G, Tamayol A. Controlling cellular organization in bioprinting through designed 3D microcompartmentalization. Appl Phys Rev. 2021;8(2): 021404. doi: 10.1063/5.0040732
  169. Ceballos‐González CF, Bolívar‐Monsalve EJ, Quevedo‐ Moreno DA, et al. Plug‐and‐play multimaterial chaotic printing/bioprinting to produce radial and axial micropatterns in hydrogel filaments. Adv Mater Technol. 2023;8(17):2202208. doi: 10.1002/admt.202202208
  170. Snyder J, Son AR, Hamid Q, Wu H, Sun W. Hetero-cellular prototyping by synchronized multi-material bioprinting for rotary cell culture system. Biofabrication. 2016;8(1):015002. doi: 10.1088/1758-5090/8/1/015002
  171. Colosi C, Shin SR, Manoharan V, et al. Microfluidic bioprinting of heterogeneous 3D tissue constructs using low-viscosity bioink. Adv Mater. 2016;28(4):677-684. doi: 10.1002/adma.201503310
  172. Stroock AD, Dertinger SKW, Ajdari A, Mezić I, Stone HA, Whitesides GM. Chaotic mixer for microchannels. Science (1979). 2002;295(5555):647-651. doi: 10.1126/science.1066238
  173. Idaszek J, Costantini M, Karlsen TA, et al. 3D bioprinting of hydrogel constructs with cell and material gradients for the regeneration of full-thickness chondral defect using a microfluidic printing head. Biofabrication. 2019;11(4):044101. doi: 10.1088/1758-5090/ab2622
  174. Li M, Tian X, Zhu N, Schreyer DJ, Chen X. Modeling process-induced cell damage in the biodispensing process. Tissue Eng Part C Methods. 2010;16(3):533-542. doi: 10.1089/ten.TEC.2009.0178
  175. Metzner YC and AB. An analysis of apparent slip flow of polymer solutions. Rheol Acta. 1986;25:28-35.
  176. Reid JA, Mollica PA, Johnson GD, Ogle RC, Bruno RD, Sachs PC. Accessible bioprinting: Adaptation of a low-cost 3D-printer for precise cell placement and stem cell differentiation. Biofabrication. 2016;8(2):025017. doi: 10.1088/1758-5090/8/2/025017
  177. Li M, Tian X, Kozinski JA, Chen X, Hwang DK. Modeling mechanical cell damage in the bioprinting process employing a conical needle. J Mech Med Biol. 2015;15(05):1550073. doi: 10.1142/S0219519415500736
  178. Martanto W, Baisch SM, Costner EA, Prausnitz MR, Smith MK. Fluid dynamics in conically tapered microneedles. AIChE J. 2005;51(6):1599-1607. doi: 10.1002/aic.10424
  179. Leppiniemi J, Lahtinen P, Paajanen A, et al. 3D-printable bioactivated nanocellulose-alginate hydrogels. ACS Appl Mater Interfaces. 2017;9(26):21959-21970. doi: 10.1021/acsami.7b02756
  180. Liravi F, Darleux R, Toyserkani E. Additive manufacturing of 3D structures with non-Newtonian highly viscous fluids: finite element modeling and experimental validation. Addit Manuf. 2017;13:113-123. doi: 10.1016/j.addma.2016.10.008
  181. Billiet T, Gevaert E, De Schryver T, Cornelissen M, Dubruel P. The 3D printing of gelatin methacrylamide cell-laden tissue-engineered constructs with high cell viability. Biomaterials. 2014;35(1):49-62. doi: 10.1016/j.biomaterials.2013.09.078
  182. Lee KY, Kong HJ, Larson RG, Mooney DJ. Hydrogel formation via cell crosslinking. Adv Mater. 2003;15(21):1828-1832. doi: 10.1002/adma.200305406
  183. Park H, Kang SW, Kim BS, Mooney DJ, Lee KY. Shear-reversibly crosslinked alginate hydrogels for tissue engineering. Macromol Biosci. 2009;9(9):895-901. doi: 10.1002/mabi.200800376
  184. Das S, Chowdhury AR, Datta P. Modelling cell deformations in bioprinting process using a multicompartment-smooth particle hydrodynamics approach. Proc Inst Mech Eng H. 2022;236(6):867-881. doi: 10.1177/09544119221089720
  185. Müller M, Öztürk E, Arlov Ø, Gatenholm P, Zenobi- Wong M. Alginate sulfate–nanocellulose bioinks for cartilage bioprinting applications. Ann Biomed Eng. 2017;45(1):210-223. doi: 10.1007/s10439-016-1704-5
  186. Ates G, Bartolo P. Computational fluid dynamics for the optimization of internal bioprinting parameters and mixing conditions. Int J Bioprint. 2023;9(6):0219. doi: 10.36922/ijb.0219
  187. Chand R, Muhire BS, Vijayavenkataraman S. Computational fluid dynamics assessment of the effect of bioprinting parameters in extrusion bioprinting. Int J Bioprint. 2022;8(2):45-60. doi: 10.18063/ijb.v8i2.545
  188. Magalhães IP, de Oliveira PM, Dernowsek J, Casas EB Las, Casas MS Las. Investigation of the effect of nozzle design on rheological bioprinting properties using computational fluid dynamics. Revista Materia. 2019;24(3):12401. doi: 10.1590/s1517-707620190003.0714
  189. Li Y, Liu Y, Jiang C, Li S, Liang G, Hu Q. A reactor-like spinneret used in 3D printing alginate hollow fiber: a numerical study of morphological evolution. Soft Matter. 2016;12(8):2392-2399. doi: 10.1039/c5sm02733k
  190. Li S, Liu Y, Li Y, Zhang Y, Hu Q. Computational and experimental investigations of the mechanisms used by coaxial fluids to fabricate hollow hydrogel fibers. Chem Eng Process. Process Intensif. 2015;95:98-104. doi: 10.1016/j.cep.2015.05.018
  191. Nyande BW, Thomas MK, Lakerveld R. CFD analysis of a kenics static mixer with a low pressure drop under laminar flow conditions. Ind Eng Chem Res. 2021;60(14):5264-5277. doi: 10.1021/acs.iecr.1c00135
  192. Ates G, Bartolo P. Numerical simulation of multimaterial polymer mixing for bioprinting applications. J Addit Manuf Technol. 2021;1:12–14. doi: 10.18416/JAMTECH.2111606
  193. Blaeser A, Duarte Campos DF, Puster U, Richtering W, Stevens MM, Fischer H. Controlling shear stress in 3D bioprinting is a key factor to balance printing resolution and stem cell integrity. Adv Healthc Mater. 2016;5(3): 326-333. doi: 10.1002/adhm.201500677
  194. Mammoli AA, Brebbia CA, eds. Computational Methods in Multiphase Flow. Vol III. WIT; 2005.
  195. Ramezani H, Mohammad Mirjamali S, He Y. Simulations of extrusion 3D printing of chitosan hydrogels. Appl Sci. 2022;12(15):7530. doi: 10.3390/app12157530
  196. Emmermacher J, Spura D, Cziommer J, et al. Engineering considerations on extrusion-based bioprinting: interactions of material behavior, mechanical forces and cells in the printing needle. Biofabrication. 2020;12(2):025022. doi: 10.1088/1758-5090/ab7553
  197. Phan‐Thien N. A nonlinear network viscoelastic model. J Rheol. 1978;22(3):259-283. doi: 10.1122/1.549481
  198. Thien NP, Tanner RI. A new constitutive equation derived from network theory. J Nonnewton Fluid Mech. 1977;2(4):353-365. doi: 10.1016/0377-0257(77)80021-9
  199. Brackbill JU, Kothe DB, Zemach C. A continuum method for modeling surface tension. J Comput Phys. 1992;100(2):335-354. doi: 10.1016/0021-9991(92)90240-Y
  200. On the formulation of rheological equations of state. Proc R Soc Lond A Math Phys Sci. 1950;200(1063):523-541. doi: 10.1098/rspa.1950.0035
  201. Phan-Thien N, Mai-Duy N. Understanding Viscoelasticity. Springer International Publishing; 2017. doi: 10.1007/978-3-319-62000-8
  202. Mustapha SMFDS, Phillips TN. A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum. J Phys D Appl Phys. 2000;33(10):1219-1229. doi: 10.1088/0022-3727/33/10/313

 

 



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International Journal of Bioprinting, Electronic ISSN: 2424-8002 Print ISSN: 2424-7723, Published by AccScience Publishing
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