Computational approaches in bioprinting processes

Computational approaches in bioprinting processes

  • Moroni, L. et al. Biofabrication strategies for 3D in vitro models and regenerative medicine. Nat. Rev. Mater. 3, 21–37 (2018).

    Article 

    Google Scholar
     

  • Zhang, Y. S. & Khademhosseini, A. Advances in engineering hydrogels. Science 356, eaaf3627 (2017).

    Article 

    Google Scholar
     

  • Murphy, S. V. & Atala, A. 3D bioprinting of tissues and organs. Nat. Biotechnol. 32, 773–785 (2014).

    Article 

    Google Scholar
     

  • Agarwal, T. et al. 3D bioprinting in tissue engineering: current state-of-the-art and challenges towards system standardization and clinical translation. Biofabrication 17, 042003 (2025).

    Article 

    Google Scholar
     

  • Zhang, Y. S., Dolatshahi-Pirouz, A. & Orive, G. Regenerative cell therapy with 3D bioprinting. Science 385, 604–606 (2024).

    Article 

    Google Scholar
     

  • Rahimi-Gorji, M. et al. Optimization of intraperitoneal aerosolized drug delivery using computational fluid dynamics (CFD) modeling. Sci. Rep. 12, 6305 (2022).

    Article 

    Google Scholar
     

  • Mishra, S., Kumar, V., Sarkar, J. & Rathore, A. S. CFD based mass transfer modeling of a single use bioreactor for production of monoclonal antibody biotherapeutics. Chem. Eng. J. 412, 128592 (2021).

    Article 

    Google Scholar
     

  • Ferreira, M. et al. Advances in microfluidic systems and numerical modeling in biomedical applications: a review. Micromachines 15, 873 (2024).

    Article 

    Google Scholar
     

  • Omar, A. M. et al. Geometry-based computational fluid dynamic model for predicting the biological behavior of bone tissue engineering scaffolds. J. Funct. Biomater. 13, 104 (2022).

    Article 

    Google Scholar
     

  • Cao, B. et al. Studying the influence of finite element mesh size on the accuracy of ventricular tachycardia simulation. Rev. Cardiovasc. Med. 24, 351 (2023).

    Article 

    Google Scholar
     

  • Fareez, U. N. M., Naqvi, S. A. A., Mahmud, M. & Temirel, M. Computational fluid dynamics (CFD) analysis of bioprinting. Adv. Healthc. Mater. 13, e2400643 (2024).

    Article 

    Google Scholar
     

  • Malekpour, A. & Chen, X. Printability and cell viability in extrusion-based bioprinting from experimental, computational, and machine learning views. J. Funct. Biomater. 13, 40 (2022).

    Article 

    Google Scholar
     

  • Shi, J. et al. Shear stress analysis and its effects on cell viability and cell proliferation in drop-on-demand bioprinting. Biomed. Phys. Eng. Express 4, 045028 (2018).

    Article 

    Google Scholar
     

  • Göhl, J. et al. Simulations of 3D bioprinting: predicting bioprintability of nanofibrillar inks. Biofabrication 10, 034105 (2018). A key study combining computational simulations and experimental measurements to establish quantitative metrics for predicting extrusion bioink printability.

    Article 

    Google Scholar
     

  • Shi, J., Song, J., Song, B. & Lu, W. F. Multi-objective optimization design through machine learning for drop-on-demand bioprinting. Engineering 5, 586–593 (2019).

    Article 

    Google Scholar
     

  • Gómez-Blanco, J. C. et al. Computational simulation-based comparative analysis of standard 3D printing and conical nozzles for pneumatic and piston-driven bioprinting. Int. J. Bioprinting 9, 730 (2023).

    Article 

    Google Scholar
     

  • Ates, G. & Bartolo, P. Computational fluid dynamics for the optimization of internal bioprinting parameters and mixing conditions. Int. J. Bioprinting 9, 0219 (2023).

    Article 

    Google Scholar
     

  • Ning, L., Betancourt, N., Schreyer, D. J. & Chen, X. Characterization of cell damage and proliferative ability during and after bioprinting. ACS Biomater. Sci. Eng. 4, 3906–3918 (2018). A key study integrating computational simulations and experimental measurements to quantify cell damages caused by shear and extensional stresses during extrusion bioprinting.

    Article 

    Google Scholar
     

  • Shi, J. et al. Learning-based cell injection control for precise drop-on-demand cell printing. Ann. Biomed. Eng. 46, 1267–1279 (2018). A key study combining computational fluid dynamics, machine learning and experimental validations to investigate droplet formation and jet stability in inkjet bioprinting.

    Article 

    Google Scholar
     

  • Kang, R. et al. 3D bioprinting technology and equipment based on microvalve control. Biotechnol. Bioeng. 121, 3768–3781 (2024).

    Article 

    Google Scholar
     

  • Jiang, L., Yu, L., Premaratne, P., Zhang, Z. & Qin, H. CFD-based numerical modeling to predict the dimensions of printed droplets in electrohydrodynamic inkjet printing. J. Manuf. Process. 66, 125–132 (2021).

    Article 

    Google Scholar
     

  • Moghadasi, H., Mollah, M. T., Marla, D., Saffari, H. & Spangenberg, J. Computational fluid dynamics modeling of top-down digital light processing additive manufacturing. Polymers 15, 2459 (2023).

    Article 

    Google Scholar
     

  • Zhang, Q. et al. Design for the reduction of volume shrinkage-induced distortion in digital light processing 3D printing. Extreme Mech. Lett. 48, 101403 (2021). A foundational study on photopolymerization simulations and evolution of material properties in DLP-fabricated constructs.

    Article 

    Google Scholar
     

  • Zhang, S., Vijayavenkataraman, S., Lu, W. F. & Fuh, J. Y. A review on the use of computational methods to characterize, design and optimize tissue engineering scaffolds, with a potential in 3D printing fabrication. J. Biomed. Mater. Res. Part B Appl. Biomater. 107, 1329–1351 (2019).

    Article 

    Google Scholar
     

  • Ahmadi Soufivand, A., Lee, S. J., Jüngst, T. & Budday, S. Challenges and perspectives in using finite element modeling to advance 3D bioprinting. Prog. Biomed. Eng. 7, 032004 (2025). A key review of modelling extrusion bioprinting highlighting computational simulation strategies across pre-printing, printing and post-printing stages while outlining the challenges that remain.

    Article 

    Google Scholar
     

  • Carracciuolo, L. & D’Amora, U. Mathematical tools for simulation of 3D bioprinting processes on high-performance computing resources: the state of the art. Appl. Sci. 14, 6110 (2024).

    Article 

    Google Scholar
     

  • Gupta, D. & Negi, N. P. 3D bioprinting: printing the future and recent advances. Bioprinting 27, e00211 (2022).

    Article 

    Google Scholar
     

  • Schwab, A. et al. Printability and shape fidelity of bioinks in 3D bioprinting. Chem. Rev. 120, 11028–11055 (2020).

    Article 

    Google Scholar
     

  • Li, X. et al. Inkjet bioprinting of biomaterials. Chem. Rev. 120, 10793–10833 (2020).

    Article 

    Google Scholar
     

  • Amorim, P. A. et al. Insights on shear rheology of inks for extrusion-based 3D bioprinting. Bioprinting 22, e00129 (2021).

    Article 

    Google Scholar
     

  • Bird, R. B., Armstrong, R. C. & Hassager, O. Dynamics of Polymeric Liquids 2nd edn, Vol. 1 (Wiley, 1987).

  • Bird, R. B., Armstrong, R. C. & Hassager, O. Dynamics of Polymeric Liquids 2nd edn, Vol. 2 (Wiley, 1987).

  • Bercea, M. Rheology as a tool for fine-tuning the properties of printable bioinspired gels. Molecules 28, 2766 (2023).

    Article 

    Google Scholar
     

  • Yu, S., Luo, Y., Chen, S., Fan, J. & Zhang, H. Quantitative assessment of hydrogel printability in extrusion bioprinting. Gels 12, 189 (2026).

    Article 

    Google Scholar
     

  • Gao, T. et al. Optimization of gelatin–alginate composite bioink printability using rheological parameters: a systematic approach. Biofabrication 10, 034106 (2018).

    Article 

    Google Scholar
     

  • Sánchez-Sánchez, R., Rodríguez-Rego, J. M., Macías-García, A., Mendoza-Cerezo, L. & Díaz-Parralejo, A. Relationship between shear-thinning rheological properties of bioinks and bioprinting parameters. Int. J. Bioprinting 9, 687 (2023).

    Article 

    Google Scholar
     

  • Herschel, W. H. & Bulkley, R. Konsistenzmessungen von gummi-benzollösungen. Kolloid-Zeitschrift 39, 291–300 (1926).

    Article 

    Google Scholar
     

  • Sahu, K., Valluri, P., Spelt, P. & Matar, O. Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid. Phys. Fluids 19, 122101 (2007).

    Article 

    Google Scholar
     

  • Kim, E. & Baek, J. Numerical study on the effects of non-dimensional parameters on drop-on-demand droplet formation dynamics and printability range in the up-scaled model. Phys. Fluids 24, 082103 (2012).

    Article 

    Google Scholar
     

  • Wijshoff, H. The dynamics of the piezo inkjet printhead operation. Phys. Rep. 491, 77–177 (2010).

    Article 

    Google Scholar
     

  • Levato, R. et al. Light-based vat-polymerization bioprinting. Nat. Rev. Methods Primers 3, 47 (2023).

    Article 

    Google Scholar
     

  • Na, K. et al. Effect of solution viscosity on retardation of cell sedimentation in DLP 3D printing of gelatin methacrylate/silk fibroin bioink. J. Ind. Eng. Chem. 61, 340–347 (2018).

    Article 

    Google Scholar
     

  • Lapique, F. & Redford, K. Curing effects on viscosity and mechanical properties of a commercial epoxy resin adhesive. Int. J. Adhes. Adhes. 22, 337–346 (2002).

    Article 

    Google Scholar
     

  • Alparslan, C. & Bayraktar, Ş. Advances in digital light processing (DLP) bioprinting: a review of biomaterials and its applications, innovations, challenges, and future perspectives. Polymers 17, 1287 (2025).

    Article 

    Google Scholar
     

  • Zhao, Z. et al. Origami by frontal photopolymerization. Sci. Adv. 3, e1602326 (2017).

    Article 

    Google Scholar
     

  • Thalhamer, A., Fuchs, P., Strohmeier, L., Hasil, S. & Wolfberger, A. A simulation-based assessment of print accuracy for microelectronic parts manufactured with DLP 3D printing process. In Proc. 2022 23rd International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (IEEE, 2022).

  • White, S. R. & Hahn, H. T. Process modeling of composite materials: residual stress development during cure. Part I. Model formulation. J. Compos. Mater. 26, 2402–2422 (1992).

    Article 

    Google Scholar
     

  • Wu, X., Xu, C., Zhang, Z. & Guo, C. Modeling and visualization of layered curing conversion profile in ceramic mask projection stereolithography process. Ceram. Int. 46, 25750–25757 (2020).

    Article 

    Google Scholar
     

  • Zawawi, M. H. et al. A review: fundamentals of computational fluid dynamics (CFD). AIP Conf. Proc. 2030, 020252 (2018).

    Article 

    Google Scholar
     

  • Mao, J., Li, F., Wang, S., Zhao, L. & Di, Y. A CFD-FEM-IBM simulation scheme for the strong coupling between the fluid and the structure with large deformations and movements. Comput. Struct. 310, 107673 (2025).

    Article 

    Google Scholar
     

  • Jeong, W. & Seong, J. Comparison of effects on technical variances of computational fluid dynamics (CFD) software based on finite element and finite volume methods. Int. J. Mech. Sci. 78, 19–26 (2014).

    Article 

    Google Scholar
     

  • Sourov, M. A. et al. A general simulation-based study on printability of inks in direct ink writing. Sci. Rep. 15, 1–16 (2025).

    Article 

    Google Scholar
     

  • Majeed, R. et al. Parallel implementation of FEM solver for shared memory using OpenMP. Math. Probl. Eng. 2022, 2375102 (2022).

    Article 

    Google Scholar
     

  • Galloway, M. et al. Implementation of nozzle motion for material extrusion additive manufacturing in Ansys Fluent. Virtual Phys. Prototyp. 19, e2397816 (2024).

    Article 

    Google Scholar
     

  • Nooranidoost, M., Izbassarov, D., Tasoglu, S. & Muradoglu, M. A computational study of droplet-based bioprinting: effects of viscoelasticity. Phys. Fluids 31, 081901 (2019).

    Article 

    Google Scholar
     

  • Mézel, C., Souquet, A., Hallo, L. & Guillemot, F. Bioprinting by laser-induced forward transfer for tissue engineering applications: jet formation modeling. Biofabrication 2, 014103 (2010).

    Article 

    Google Scholar
     

  • Jarauta, A., Ryzhakov, P., Secanell, M., Waghmare, P. R. & Pons-Prats, J. Numerical study of droplet dynamics in a polymer electrolyte fuel cell gas channel using an embedded Eulerian-Lagrangian approach. J. Power Sources 323, 201–212 (2016).

    Article 

    Google Scholar
     

  • Biswas, R. & Strawn, R. C. Tetrahedral and hexahedral mesh adaptation for CFD problems. Appl. Numer. Math. 26, 135–151 (1998).

    Article 
    MathSciNet 

    Google Scholar
     

  • Xie, Z. et al. Adaptive unstructured mesh modelling of multiphase flows. Int. J. Multiph. Flow 67, 104–110 (2014).

    Article 

    Google Scholar
     

  • Panton, R. L. Incompressible Flow (Wiley, 2024).

  • Gharraei, R., Bergstrom, D. J. & Chen, X. Extrusion bioprinting from a fluid mechanics perspective. Int. J. Bioprinting 10, 3973 (2024).

    Article 

    Google Scholar
     

  • Gerhart, A. L., Hochstein, J. I. & Gerhart, P. M. Munson, Young and Okiishi’s Fundamentals of Fluid Mechanics (Wiley, 2020).

  • Blanco, J. C. G. et al. Optimising bioprinting nozzles through computational modelling and design of experiments. Biomimetics 9, 460 (2024).

    Article 

    Google Scholar
     

  • Wei, Q., An, Y., Li, M. & Zhao, X. Research on the flow behavior of bio-ink inside the extrusion nozzle during printing. J. Appl. Phys. 136, 174701 (2024).

    Article 

    Google Scholar
     

  • Landau, L. D. & Lifshitz, E. M. Fluid Mechanics (Elsevier, 1987).

  • Müller, M., Öztürk, E., Arlov, Ø, Gatenholm, P. & Zenobi-Wong, M. Alginate sulfate–nanocellulose bioinks for cartilage bioprinting applications. Ann. Biomed. Eng. 45, 210–223 (2016).

    Article 

    Google Scholar
     

  • Liu, W. et al. Extrusion bioprinting of shear-thinning gelatin methacryloyl bioinks. Adv. Healthc. Mater. 6, 1601451 (2017).

    Article 

    Google Scholar
     

  • Chan, K., Pericleous, K. & Cross, M. Numerical simulation of flows encountered during mold-filling. Appl. Math. Model. 15, 624–631 (1991).

    Article 

    Google Scholar
     

  • Tryggvason, G., Scardovelli, R. & Zaleski, S. Direct Numerical Simulations of Gas–Liquid Multiphase Flows (Cambridge Univ. Press, 2011).

  • Albadawi, A., Donoghue, D., Robinson, A., Murray, D. & Delauré, Y. On the assessment of a VOF based compressive interface capturing scheme for the analysis of bubble impact on and bounce from a flat horizontal surface. Int. J. Multiph. Flow 65, 82–97 (2014).

    Article 

    Google Scholar
     

  • Bilger, C., Aboukhedr, M., Vogiatzaki, K. & Cant, R. S. Evaluation of two-phase flow solvers using level set and volume of fluid methods. J. Comput. Phys. 345, 665–686 (2017).

    Article 
    MathSciNet 

    Google Scholar
     

  • Hartmann, D., Meinke, M. & Schröder, W. The constrained reinitialization equation for level set methods. J. Comput. Phys. 229, 1514–1535 (2010).

    Article 
    MathSciNet 

    Google Scholar
     

  • Hartmann, D., Meinke, M. & Schröder, W. On accuracy and efficiency of constrained reinitialization. Int. J. Numer. Methods Fluids 63, 1347–1358 (2010).

    Article 
    MathSciNet 

    Google Scholar
     

  • Osher, S. & Fedkiw, R. P. Level set methods: an overview and some recent results. J. Comput. Phys. 169, 463–502 (2001).

    Article 
    MathSciNet 

    Google Scholar
     

  • Sussman, M., Smereka, P. & Osher, S. A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146–159 (1994).

    Article 

    Google Scholar
     

  • Kim, H. & Park, S. Coupled level-set and volume of fluid (CLSVOF) solver for air lubrication method of a flat plate. J. Mar. Sci. Eng. 9, 231 (2021).

    Article 

    Google Scholar
     

  • Kasmaiee, S., Tadjfar, M., Kasmaiee, S. & Ahmadi, G. Linear stability analysis of surface waves of liquid jet injected in transverse gas flow with different angles. Theor. Comput. Fluid Dyn. 38, 107–138 (2024).

    Article 
    MathSciNet 

    Google Scholar
     

  • Ouyang, L. Study on Microextrusion-Based 3D Bioprinting and Bioink Crosslinking Mechanisms (Springer, 2019).

  • Brackbill, J. U., Kothe, D. B. & Zemach, C. A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992).

    Article 
    MathSciNet 

    Google Scholar
     

  • Gueyffier, D., Li, J., Nadim, A., Scardovelli, R. & Zaleski, S. Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J. Comput. Phys. 152, 423–456 (1999).

    Article 

    Google Scholar
     

  • Loghman, F., Kami, A., Azami, M. & Abedini, V. Numerical study on the influence of process parameters in direct ink writing of high viscosity bio-inks. Proc. Inst. Mech. Eng. L 237, 274–282 (2022).


    Google Scholar
     

  • 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. 13, 113–123 (2017).


    Google Scholar
     

  • Gómez-Blanco, J. C. et al. Bioink temperature influence on shear stress, pressure and velocity using computational simulation. Processes 8, 865 (2020).

    Article 

    Google Scholar
     

  • Song, K., Zhang, D., Yin, J. & Huang, Y. Computational study of extrusion bioprinting with jammed gelatin microgel-based composite ink. Addit. Manuf. 41, 101963 (2021).


    Google Scholar
     

  • Emmermacher, J. et al. Engineering considerations on extrusion-based bioprinting: interactions of material behavior, mechanical forces and cells in the printing needle. Biofabrication https://doi.org/10.1088/1758-5090/ab7553 (2020).

  • Zaeri, A., Zgeib, R., Cao, K., Zhang, F. & Chang, R. C. Numerical analysis on the effects of microfluidic-based bioprinting parameters on the microfiber geometrical outcomes. Sci. Rep. https://doi.org/10.1038/s41598-022-07392-0 (2022). A key study presenting computational modelling of coaxial bioprinting to investigate flow behaviours and the formation of core–shell hydrogel filaments.

  • Chand, R., Muhire, B. S. & Vijayavenkataraman, S. Computational fluid dynamics assessment of the effect of bioprinting parameters in extrusion bioprinting. Int. J. Bioprinting 8, 545 (2022).

    Article 

    Google Scholar
     

  • Reid, J. A. et al. Accessible bioprinting: adaptation of a low-cost 3D-printer for precise cell placement and stem cell differentiation. Biofabrication https://doi.org/10.1088/1758-5090/8/2/025017 (2016).

  • Guo, C.-F., Zhang, M. & Bhandari, B. A comparative study between syringe-based and screw-based 3D food printers by computational simulation. Comput. Electron. Agric. 162, 397–404 (2019).

    Article 

    Google Scholar
     

  • Magalhães, I. P., Oliveira, P. M. D., Dernowsek, J., Casas, E. B. L. & Casas, M. S. L. Investigation of the effect of nozzle design on rheological bioprinting properties using computational fluid dynamics. Matéria https://doi.org/10.1590/s1517-707620190003.0714 (2019).

  • Ramezani, H., Mohammad Mirjamali, S. & He, Y. Simulations of extrusion 3D printing of chitosan hydrogels. Appl. Sci. https://doi.org/10.3390/app12157530 (2022).

  • Barton, I. E. Comparison of SIMPLE- and PISO-type algorithms for transient flows. Int. J. Numer. Methods Fluids 26, 459–483 (1998).

    Article 

    Google Scholar
     

  • Chen, D. X. & Chen, D. X. Extrusion Bioprinting of Scaffolds (Springer, 2019).

  • Prendergast, M. E. & Burdick, J. A. Computational modeling and experimental characterization of extrusion printing into suspension baths. Adv. Healthc. Mater. 11, 2101679 (2022). A foundational study demonstrating computational simulations of embedded bioprinting processes.

    Article 

    Google Scholar
     

  • Narei, H. et al. Numerical simulation of a core–shell polymer strand in material extrusion additive manufacturing. Polymers 13, 476 (2021).

    Article 

    Google Scholar
     

  • Ahmad, A. et al. Coaxial bioprinting of a stentable and endothelialized human coronary artery-sized in vitro model. J. Mater. Chem. B https://doi.org/10.1039/d4tb00601a (2024).

  • Shin, S. et al. Gelation of uniform interfacial diffusant in embedded 3D printing. Adv. Funct. Mater. 33, 2307435 (2023).

    Article 

    Google Scholar
     

  • Friedrich, L. M. & Seppala, J. E. Simulated filament shapes in embedded 3D printing. Soft Matter 17, 8027–8046 (2021).

    Article 

    Google Scholar
     

  • McCormack, A., Highley, C. B., Leslie, N. R. & Melchels, F. P. 3D printing in suspension baths: keeping the promises of bioprinting afloat. Trends Biotechnol. 38, 584–593 (2020).

    Article 

    Google Scholar
     

  • Mirdamadi, E., Muselimyan, N., Koti, P., Asfour, H. & Sarvazyan, N. Agarose slurry as a support medium for bioprinting and culturing freestanding cell-laden hydrogel constructs. 3D Print. Addit. Manuf. 6, 158–164 (2019).

    Article 

    Google Scholar
     

  • Huang, W., Ren, Y. & Russell, R. D. Moving mesh methods based on moving mesh partial differential equations. J. Comput. Phys. 113, 279–290 (1994).

    Article 
    MathSciNet 

    Google Scholar
     

  • Paul, A. et al. Thermodynamics, Diffusion and the Kirkendall Effect in Solids (Springer, 2014).

  • Brunel, L. G., Hull, S. M. & Heilshorn, S. C. Engineered assistive materials for 3D bioprinting: support baths and sacrificial inks. Biofabrication 14, 032001 (2022).

    Article 

    Google Scholar
     

  • Chiesa, I. et al. Modeling the three-dimensional bioprinting process of β-sheet self-assembling peptide hydrogel scaffolds. Front. Med. Technol. 2, 571626 (2020).

    Article 

    Google Scholar
     

  • Akkineni, A. R., 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 8, 045001 (2016).

    Article 

    Google Scholar
     

  • Jung, J. & Hassanein, A. Three-phase CFD analytical modeling of blood flow. Med. Eng. Phys. 30, 91–103 (2008).

    Article 

    Google Scholar
     

  • Mirani, B., Stefanek, E., Godau, B., Hossein Dabiri, S. M. & Akbari, M. Microfluidic 3D printing of a photo-cross-linkable bioink using insights from computational modeling. ACS Biomater. Sci. Eng. 7, 3269–3280 (2021).

    Article 

    Google Scholar
     

  • Guazzelli, N., Cacopardo, L., Corti, A. & Ahluwalia, A. An integrated in silico–in vitro approach for bioprinting core–shell bioarchitectures. Int. J. Bioprinting 9, 771 (2023).

    Article 

    Google Scholar
     

  • Dong, H., Carr, W. W. & Morris, J. F. An experimental study of drop-on-demand drop formation. Phys. Fluids 18, 072102 (2006).

    Article 

    Google Scholar
     

  • Visser, C. W. et al. Dynamics of high-speed micro-drop impact: numerical simulations and experiments at frame-to-frame times below 100 ns. Soft Matter 11, 1708–1722 (2015).

    Article 

    Google Scholar
     

  • Shah, R. & Mohan, R. V. Computational modeling of droplet-based printing using multiphase volume of fluid (VOF) method: prediction of flow, spread behavior, and printability. Fluids 10, 123 (2025).

    Article 

    Google Scholar
     

  • Suh, Y. & Son, G. A sharp-interface level-set method for simulation of a piezoelectric inkjet process. Numer. Heat Transf. B: Fundam. 55, 295–312 (2009).

    Article 

    Google Scholar
     

  • Liu, N., Sheng, X., Zhang, M., Han, W. & Wang, K. Squeeze-type piezoelectric inkjet printhead actuating waveform design method based on numerical simulation and experiment. Micromachines https://doi.org/10.3390/mi13101695 (2022).

  • Tofan, T., Borodinas, S. & Jasevičius, R. Droplet trajectory movement modeling using a drop-on-demand inkjet printhead simulations. Mathematics 13, 280 (2025).

    Article 

    Google Scholar
     

  • Lohse, D. Fundamental fluid dynamics challenges in inkjet printing. Annu. Rev. Fluid Mech. 54, 349–382 (2022). A key study outlining the fundamental fluid dynamics challenges governing droplet formation and jet stability in inkjet printing.

    Article 

    Google Scholar
     

  • Kalaitzis, A. et al. Jetting dynamics of Newtonian and non-Newtonian fluids via laser-induced forward transfer: experimental and simulation studies. Appl. Surf. Sci. 465, 136–142 (2019).

    Article 

    Google Scholar
     

  • Hu, Q. et al. Longitudinal and transverse piezoelectric effects of ferroelectret metamaterials with positive and negative Poisson’s ratios. Appl. Phys. Lett. 124, 142902 (2024).

    Article 

    Google Scholar
     

  • Kim, S., Sohn, D. K. & Ko, H. S. Numerical study on piezoelectric inkjet with liquid compressibility. Phys. Fluids https://doi.org/10.1063/5.0213865 (2024).

  • Kim, S., Choi, J. H., Sohn, D. K. & Ko, H. S. The effect of ink supply pressure on piezoelectric inkjet. Micromachines https://doi.org/10.3390/mi13040615 (2022).

  • Cui, X., Boland, T., D’Lima, D. D. & Lotz, M. K. Thermal inkjet printing in tissue engineering and regenerative medicine. Recent Pat. Drug Deliv. Formul. 6, 149–155 (2012).

    Article 

    Google Scholar
     

  • Sohrabi, S. & Liu, Y. Modeling thermal inkjet and cell printing process using modified pseudopotential and thermal lattice Boltzmann methods. Phys. Rev. E 97, 033105 (2018).

    Article 

    Google Scholar
     

  • Suh, Y. & Son, G. A level-set method for simulation of a thermal inkjet process. Numer. Heat Transf. B: Fundam. 54, 138–156 (2008).

    Article 

    Google Scholar
     

  • Sen, A. & Darabi, J. Droplet ejection performance of a monolithic thermal inkjet print head. J. Micromech. Microeng. 17, 1420 (2007).

    Article 

    Google Scholar
     

  • Lindemann, T. et al. Three-dimensional CFD-simulation of a thermal bubble jet printhead. In NSTI Nanotechnology Conference and Trade Show, 227–230 (NSTI-Nanotech, 2004).

  • Chang, J. & Sun, X. Laser-induced forward transfer based laser bioprinting in biomedical applications. Front. Bioeng. Biotechnol. https://doi.org/10.3389/fbioe.2023.1255782 (2023).

  • Qu, J. et al. Printing quality improvement for laser-induced forward transfer bioprinting: numerical modeling and experimental validation. Phys. Fluids https://doi.org/10.1063/5.0054675 (2021).

  • Brown, M. S., Brasz, C. F., Ventikos, Y. & Arnold, C. B. Impulsively actuated jets from thin liquid films for high-resolution printing applications. J. Fluid Mech. 709, 341–370 (2012).

    Article 
    MathSciNet 

    Google Scholar
     

  • Sotrop, J., Kersch, A., Domke, M., Heise, G. & Huber, H. P. Numerical simulation of ultrafast expansion as the driving mechanism for confined laser ablation with ultra-short laser pulses. Appl. Phys. A 113, 397–411 (2013).

    Article 

    Google Scholar
     

  • He, B., Yang, S., Qin, Z., Wen, B. & Zhang, C. The roles of wettability and surface tension in droplet formation during inkjet printing. Sci. Rep. 7, 11841 (2017).

    Article 

    Google Scholar
     

  • Jing, S. et al. Advances in volumetric bioprinting. Biofabrication https://doi.org/10.1088/1758-5090/ad0978 (2023).

  • Reid, A., Jackson, J. C. & Windmill, J. Voxel based method for predictive modelling of solidification and stress in digital light processing based additive manufacture. Soft Matter 17, 1881–1887 (2021).

    Article 

    Google Scholar
     

  • Myrick, M. L. et al. The Kubelka-Munk diffuse reflectance formula revisited. Appl. Spectrosc. Rev. 46, 140–165 (2011).

    Article 

    Google Scholar
     

  • Bernal, P. N. et al. The road ahead in materials and technologies for volumetric 3D printing. Nat. Rev. Mater. 10.1038/s41578-025-00785-3 (2025).

  • Shusteff, M. et al. One-step volumetric additive manufacturing of complex polymer structures. Sci. Adv. 3, eaao5496 (2017). A seminal study introducing volumetric additive manufacturing and combining optical modelling with reaction–diffusion simulations of photopolymerization to predict 3D curing.

    Article 

    Google Scholar
     

  • Salajeghe, R. et al. Numerical modeling of tomographic volumetric additive manufacturing based on energy threshold method. Addit. Manuf. 96, 104552 (2024).


    Google Scholar
     

  • Álvarez-Castaño, M. I. et al. Holographic tomographic volumetric additive manufacturing. Nat. Commun. 16, 1551 (2025).

    Article 

    Google Scholar
     

  • Jacobs, P. F. Fundamentals of Stereolithography (SME, 1992).

  • Salajeghe, R., Meile, D. H., Kruse, C. S., Marla, D. & Spangenberg, J. Numerical modeling of part sedimentation during volumetric additive manufacturing. Addit. Manuf. 66, 103459 (2023).


    Google Scholar
     

  • Long, K. N., Scott, T. F., Qi, H. J., Bowman, C. N. & Dunn, M. L. Photomechanics of light-activated polymers. J. Mech. Phys. Solids 57, 1103–1121 (2009).

    Article 

    Google Scholar
     

  • Hosseinabadi, H. G. et al. Ink material selection and optical design considerations in DLP 3D printing. Appl. Mater. Today 30, 101721 (2023).

    Article 

    Google Scholar
     

  • Lim, K. S. et al. New visible-light photoinitiating system for improved print fidelity in gelatin-based bioinks. ACS Biomater. Sci. Eng. 2, 1752–1762 (2016).

    Article 

    Google Scholar
     

  • Buback, M., Huckestein, B. & Russell, G. T. Modeling of termination in intermediate and high conversion free radical polymerizations. Macromol. Chem. Phys. 195, 539–554 (1994).

    Article 

    Google Scholar
     

  • Achilias, D. S. A review of modeling of diffusion controlled polymerization reactions. Macromol. Theory Simul. 16, 319–347 (2007).

    Article 

    Google Scholar
     

  • Zennifer, A., Manivannan, S., Sethuraman, S., Kumbar, S. G. & Sundaramurthi, D. 3D bioprinting and photocrosslinking: emerging strategies & future perspectives. Biomater. Adv. 134, 112576 (2022).

    Article 

    Google Scholar
     

  • Nieto, D., Marchal Corrales, J. A., Jorge de Mora, A. & Moroni, L. Fundamentals of light-cell–polymer interactions in photo-cross-linking based bioprinting. APL Bioeng. 4, 041502 (2020).

    Article 

    Google Scholar
     

  • Madrid-Wolff, J., Boniface, A., Loterie, D., Delrot, P. & Moser, C. Controlling light in scattering materials for volumetric additive manufacturing. Adv. Sci. 9, 2105144 (2022).

    Article 

    Google Scholar
     

  • Yazdian Kashani, S., Keshavarz Moraveji, M. & Bonakdar, S. Computational and experimental studies of a cell-imprinted-based integrated microfluidic device for biomedical applications. Sci. Rep. 11, 12130 (2021).

    Article 

    Google Scholar
     

  • Boularaoui, S., Al Hussein, G., Khan, K. A., Christoforou, N. & Stefanini, C. An overview of extrusion-based bioprinting with a focus on induced shear stress and its effect on cell viability. Bioprinting https://doi.org/10.1016/j.bprint.2020.e00093 (2020).

  • Li, M., Tian, X., Schreyer, D. J. & Chen, X. Effect of needle geometry on flow rate and cell damage in the dispensing-based biofabrication process. Biotechnol. Prog. 27, 1777–1784 (2011).

    Article 

    Google Scholar
     

  • Li, M., Tian, X., Kozinski, J. A., Chen, X. & Hwang, D. K. Modeling mechanical cell damage in the bioprinting process employing a conical needle. J. Mech. Med. Biol. https://doi.org/10.1142/s0219519415500736 (2015).

  • Ding, Y., Xu, G.-K. & Wang, G.-F. On the determination of elastic moduli of cells by AFM based indentation. Sci. Rep. 7, 45575 (2017).

    Article 

    Google Scholar
     

  • Müller, S. J. et al. A hyperelastic model for simulating cells in flow. Biomech. Model. Mechanobiol. 20, 509–520 (2021).

    Article 

    Google Scholar
     

  • Müller, S. J., Fabry, B. & Gekle, S. Predicting cell stress and strain during extrusion bioprinting. Phys. Rev. Appl. 19, 064061 (2023).

    Article 

    Google Scholar
     

  • Tirella, A., Vozzi, F., Vozzi, G. & Ahluwalia, A. PAM2 (piston assisted microsyringe): a new rapid prototyping technique for biofabrication of cell incorporated scaffolds. Tissue Eng. Part C Methods 17, 229–237 (2011).

    Article 

    Google Scholar
     

  • Xiang, Y. et al. Iohexol as a refractive index tuning agent for bioinks in high cell density bioprinting. Biomater. Sci. 13, 3958–3971 (2025).

    Article 

    Google Scholar
     

  • Bernal, P. N. et al. Volumetric bioprinting of organoids and optically tuned hydrogels to build liver-like metabolic biofactories. Adv. Mater. 34, 2110054 (2022).

    Article 

    Google Scholar
     

  • Cooke, M. E. & Rosenzweig, D. H. The rheology of direct and suspended extrusion bioprinting. APL Bioeng. https://doi.org/10.1063/5.0031475 (2021).

  • Wang, P., Sun, Y., Diao, L. & Liu, H. Considering cell viability in 3D printing of structured inks: a comparative and equivalent analysis of fluid forces. Int. J. Bioprinting https://doi.org/10.36922/ijb.2362 (2024).

  • Zhang, Y. S. et al. 3D extrusion bioprinting. Nat. Rev. Methods Primers 1, 75 (2021).

    Article 

    Google Scholar
     

  • Bernasconi, R. et al. Piezoelectric drop-on-demand inkjet printing of high-viscosity inks. Adv. Eng. Mater. 24, 2100733 (2022).

    Article 

    Google Scholar
     

  • Reis, N. & Derby, B. Ink jet deposition of ceramic suspensions: modeling and experiments of droplet formation. MRS Online Proc. Libr. 625, 117 (2000).

    Article 

    Google Scholar
     

  • Jang, D., Kim, D. & Moon, J. Influence of fluid physical properties on ink-jet printability. Langmuir 25, 2629–2635 (2009).

    Article 

    Google Scholar
     

  • Chávez-Madero, C. et al. Using chaotic advection for facile high-throughput fabrication of ordered multilayer micro- and nanostructures: continuous chaotic printing. Biofabrication 12, 035023 (2020).

    Article 

    Google Scholar
     

  • Liu, W. et al. Rapid continuous multimaterial extrusion bioprinting. Adv. Mater. https://doi.org/10.1002/adma.201604630 (2017).

  • Zhao, L. et al. Developing the optimized control scheme for continuous and layer-wise DLP 3D printing by CFD simulation. Int. J. Adv. Manuf. Technol. 125, 1511–1529 (2023). A foundational study combining computational simulations and experimental validations to analyse key parameters in DLP printing.

    Article 

    Google Scholar
     

  • Whyte, D. J., Doeven, E. H., Sutti, A., Kouzani, A. Z. & Adams, S. D. Volumetric additive manufacturing: a new frontier in layer-less 3D printing. Addit. Manuf. https://doi.org/10.1016/j.addma.2024.104094 (2024).

  • Vakilha, M. & Safdari Shadloo, M. A smoothed particle hydrodynamics method for two-phase electrohydrodynamics modeling with Nernst–Planck equations. Phys. Fluids https://doi.org/10.1063/5.0235072 (2024).

  • Sexton, Z. A. et al. Rapid model-guided design of organ-scale synthetic vasculature for biomanufacturing. Science 388, 1198–1204 (2025).

    Article 

    Google Scholar
     

  • Shi, J. et al. Study on performance simulation of vascular-like flow channel model based on TPMS structure. Biomimetics 8, 69 (2023).

    Article 

    Google Scholar
     

  • Florczak, S. et al. Adaptive and context-aware volumetric printing. Nature 645, 108–114 (2025).

    Article 

    Google Scholar
     

  • Sego, T. J. et al. Computational fluid dynamic analysis of bioprinted self-supporting perfused tissue models. Biotechnol. Bioeng. 117, 798–815 (2019).

    Article 

    Google Scholar
     

  • Bhattacharyya, A., Janarthanan, G. & Noh, I. Nano-biomaterials for designing functional bioinks towards complex tissue and organ regeneration in 3D bioprinting. Addit. Manuf. 37, 101639 (2021).


    Google Scholar
     

  • Kim, Y., Yuk, H., Zhao, R., Chester, S. A. & Zhao, X. Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558, 274–279 (2018).

    Article 

    Google Scholar
     

  • Arif, Z. U., Khalid, M. Y., Ahmed, W. & Arshad, H. A review on four-dimensional (4D) bioprinting in pursuit of advanced tissue engineering applications. Bioprinting 27, e00203 (2022).

    Article 

    Google Scholar
     

  • De Giorgi, A. et al. Diffusion of curcumin in PLGA-based carriers for drug delivery: a molecular dynamics study. J. Mol. Model. 30, 219 (2024).

    Article 

    Google Scholar
     

  • dos Santos, B. C., Noritomi, P. Y., da Silva, J. V. L., Maia, I. A. & Manzini, B. M. Biological multiscale computational modeling: a promising tool for 3D bioprinting and tissue engineering. Bioprinting 28, e00234 (2022).

    Article 

    Google Scholar
     

  • Pearce, D., Fischer, S., Huda, F. & Vahdati, A. Applications of computer modeling and simulation in cartilage tissue engineering. Tissue Eng. Regen. Med. 17, 1–13 (2020).

    Article 

    Google Scholar
     

  • Starruß, J., De Back, W., Brusch, L. & Deutsch, A. Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology. Bioinformatics 30, 1331–1332 (2014).

    Article 

    Google Scholar
     

  • Ruberu, K. et al. Coupling machine learning with 3D bioprinting to fast track optimisation of extrusion printing. Appl. Mater. Today https://doi.org/10.1016/j.apmt.2020.100914 (2021).

  • Fu, Z., Angeline, V. & Sun, W. Evaluation of printing parameters on 3D extrusion printing of pluronic hydrogels and machine learning guided parameter recommendation. Int. J. Bioprinting https://doi.org/10.18063/ijb.v7i4.434 (2024).

  • An, J., Chua, C. K. & Mironov, V. Application of machine learning in 3D bioprinting: focus on development of big data and digital twin. Int. J. Bioprinting 7, 342 (2021).

    Article 

    Google Scholar
     

  • Wang, D. et al. Microfluidic bioprinting of tough hydrogel-based vascular conduits for functional blood vessels. Sci. Adv. 8, eabq6900 (2022).

    Article 

    Google Scholar
     

  • Acosta-Vélez, G. F., Linsley, C. S., Craig, M. C. & Wu, B. M. Photocurable bioink for the inkjet 3D pharming of hydrophilic drugs. Bioengineering 4, 11 (2017).

    Article 

    Google Scholar
     

  • Gudapati, H., Parisi, D., Colby, R. H. & Ozbolat, I. T. Rheological investigation of collagen, fibrinogen, and thrombin solutions for drop-on-demand 3D bioprinting. Soft Matter 16, 10506–10517 (2020).

    Article 

    Google Scholar
     

  • You, S., Wang, P., Schimelman, J., Hwang, H. H. & Chen, S. High-fidelity 3D printing using flashing photopolymerization. Addit. Manuf. 30, 100834 (2019).


    Google Scholar
     

  • Hakim Khalili, M. et al. Additive manufacturing and physicomechanical characteristics of PEGDA hydrogels: recent advances and perspective for tissue engineering. Polymers 15, 2341 (2023).

    Article 

    Google Scholar
     

  • Gregory, T. et al. Rheological characterization of cell-laden alginate-gelatin hydrogels for 3D biofabrication. J. Mech. Behav. Biomed. Mater. 136, 105474 (2022).

    Article 

    Google Scholar
     

  • Ng, W. L. et al. Controlling droplet impact velocity and droplet volume: key factors to achieving high cell viability in sub-nanoliter droplet-based bioprinting. Int. J. Bioprinting 8, 424 (2021).

    Article 

    Google Scholar
     

  • You, S. et al. High cell density and high-resolution 3D bioprinting for fabricating vascularized tissues. Sci. Adv. 9, eade7923 (2023).

    Article 

    Google Scholar
     

  • 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. 419, 116685 (2024).

    Article 
    MathSciNet 

    Google Scholar
     

  • Shaukat, U., Rossegger, E. & Schlögl, S. A review of multi-material 3D printing of functional materials via vat photopolymerization. Polymers https://doi.org/10.3390/polym14122449 (2022).

  • Miri, A. K. et al. Microfluidics-enabled multimaterial maskless stereolithographic bioprinting. Adv. Mater. https://doi.org/10.1002/adma.201800242 (2018).

  • Wu, C., Zhang, R., Zhao, P., Li, L. & Zhang, D. Curing simulation and data-driven curing curve prediction of thermoset composites. Sci. Rep. 14, 31860 (2024).

    Article 

    Google Scholar
     

  • Hölzl, K. et al. Bioink properties before, during and after 3D bioprinting. Biofabrication https://doi.org/10.1088/1758-5090/8/3/032002 (2016).

  • Mardles, E. W. J. Viscosity of suspensions and the einstein equation. Nature 145, 970–970 (1940).

    Article 

    Google Scholar
     

  • Diamantides, N., Dugopolski, C., Blahut, E., Kennedy, S. & Bonassar, L. J. High density cell seeding affects the rheology and printability of collagen bioinks. Biofabrication 11, 045016 (2019).

    Article 

    Google Scholar
     

  • Majumder, N., Mishra, A. & Ghosh, S. Effect of varying cell densities on the rheological properties of the bioink. Bioprinting https://doi.org/10.1016/j.bprint.2022.e00241 (2022).

  • Boothe, T. et al. A tunable refractive index matching medium for live imaging cells, tissues and model organisms. eLife 6, e27240 (2017).

    Article 

    Google Scholar
     

  • Matsson, J. E. An Introduction to Ansys Fluent 2023 (SDC Publications, 2023).

  • Tezduyar, T. E. Finite element methods for flow problems with moving boundaries and interfaces. Arch. Comput. Methods Eng. 8, 83–130 (2001).

    Article 

    Google Scholar
     

  • Chen, G. et al. OpenFOAM for computational fluid dynamics. Not. Am. Math. Soc. 61, 354–363 (2014).

    Article 
    MathSciNet 

    Google Scholar
     

  • Brindha, J., Edwina, R. G. P., Rajesh, P. & Rani, P. Influence of rheological properties of protein bio-inks on printability: a simulation and validation study. Mater. Today: Proc. 3, 3285–3295 (2016).


    Google Scholar
     

  • Mark, A., Rundqvist, R. & Edelvik, F. Comparison between different immersed boundary conditions for simulation of complex fluid flows. Fluid Dyn. Mater. Process. 7, 241–258 (2011).


    Google Scholar
     

  • Comments

    No comments yet. Why don’t you start the discussion?

    Leave a Reply

    Your email address will not be published. Required fields are marked *