Skip to main content
Log in

Advanced porous scaffold design using multi-void triply periodic minimal surface models with high surface area to volume ratios

  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

Creating biophysically and biologically desirable porous scaffolds has always been one of the greatest challenges in tissue engineering (TE). Advanced additive manufacture (AM) methods such as three-dimensional (3D) printing techniques have established remarkable improvements in the fabrication of porous scaffolds and structures close in architecture to biological tissue. Such fabrication techniques have opened new areas of research in TE. Recently, it was shown that porous scaffolds which are mathematically designed by using triply periodic minimal surface (TPMS) pore geometry and fabricated through 3D printing techniques have remarkably high cell viability and mechanical strength when compared with conventional scaffolds. The enhanced cell adhesion, migration, and proliferation of TPMS-based scaffolds arise from the high surface area to volume ratio (SA/V ratio) that is a basic and fundamental concept of biology. Here, we report the design of multi-void TPMS-based scaffolds that dramatically increase the SA/V ratio of conventional TPMS scaffolds. Our findings suggest that the proposed novel design methodology can be applied to create a variety of computational models for prototyping and printing of biomimetic scaffolds and bioartificial tissues.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Starly, B., Lau, W., Bradbury, T., and Sun, W., “Internal Architecture Design and Freeform Fabrication of Tissue Replacement Structures,” Computer-Aided Design, Vol. 38, No. 2, pp. 115–124, 2006.

    Article  Google Scholar 

  2. Sun, W., Starly, B., Nam, J., and Darling, A., “Bio-CAD Modeling and Its Applications in Computer-Aided Tissue Engineering,” Computer-Aided Design, Vol. 37, No. 11, pp. 1097–1114, 2005.

    Article  Google Scholar 

  3. Wettergreen, M. A., Bucklen, B. S., Starly, B., Yuksel, E., Sun, W., and Liebschner, M. A. K., “Creation of a Unit Block Library of Architectures for Use in Assembled Scaffold Engineering,” Computer-Aided Design, Vol. 37, No. 11, pp. 1141–1149, 2005.

    Article  Google Scholar 

  4. Tuan, H. S. and Hutmacher, D. W., “Application of Micro CT and Computation Modeling in Bone Tissue Engineering,” Computer-Aided Design, Vol. 37, No. 11, pp. 1151–1161, 2005.

    Article  Google Scholar 

  5. Naing, M. W., Chua, C. K., Leong, K. F., and Wang, Y., “Fabrication of Customised Scaffolds using Computer-Aided Design and Rapid Prototyping Techniques,” Rapid Prototyping Journal, Vol. 11, No. 4, pp. 249–259, 2005.

    Article  Google Scholar 

  6. Wang, C. S., Wang, W. H. A., and Lin, M. C., “STL Rapid Prototyping Bio-CAD Model for CT Medical Image Segmentation,” Computers in Industry, Vol. 61, No. 3, pp. 187–197, 2010.

    Article  Google Scholar 

  7. Cheah, C. M., Chua, C. K., Leong, K. F., and Chua, S. W., “Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 1: Investigation and Classification,” The International Journal of Advanced Manufacturing Technology, Vol. 21, No. 4, pp. 291–301, 2003.

    Article  Google Scholar 

  8. Cheah, C. M., Chua, C. K., Leong, K. F., and Chua, S. W., “Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 2: Parametric Library and Assembly Program,” The International Journal of Advanced Manufacturing Technology, Vol. 21, No. 4, pp. 302–312, 2003.

    Article  Google Scholar 

  9. Cheah, C. M., Chua, C. K., Leong, K. F., Cheong, C. H., and Naing, M. W., “Automatic Algorithm for Generating Complex Polyhedral Scaffold Structures for Tissue Engineering,” Tissue Engineering, Vol. 10, No. 3–4, pp. 595–610, 2004.

    Article  Google Scholar 

  10. Sudarmadji, N., Tan, J. Y., Leong, K. F., Chua, C. K., and Loh, Y. T., “Investigation of The Mechanical Properties and Porosity Relationships in Selective Laser-Sintered Polyhedral for Functionally Graded Scaffolds,” Acta Biomaterialia, Vol. 7, No. 2, pp. 530–537, 2011.

    Article  Google Scholar 

  11. Sun, W. and Lal, P., “Recent Development on Computer Aided Tissue Engineering-A Review,” Computer Methods and Programs in Biomedicine, Vol. 67, No. 2, pp. 85–103, 2002.

    Article  Google Scholar 

  12. Sun, W., Starly, B., Darling, A., and Gomez, C., “ComputerAided Tissue Engineering: Application to Biomimetic Modelling and Design of Tissue Scaffolds,” Biotechnology and Applied Biochemistry, Vol. 39, No. 1, pp. 49–58, 2004.

    Article  Google Scholar 

  13. Chu, W. S., Kim, C. S., Lee, H. T., Choi, J. O., Park, J. I., et al., “Hybrid Manufacturing in Micro/Nano Scale: A Review,” Int. J. Precis. Eng. Manuf.-Green Tech., Vol. 1, No. 1, pp. 75–92, 2014.

    Article  Google Scholar 

  14. Rajagopalan, S. and Robb, R. A., “Schwarz Meets Schwann: Design and Fabrication of Biomorphic and Durataxic Tissue Engineering Scaffolds,” Medical Image Analysis, Vol. 10, No. 5, pp. 693–712, 2006.

    Article  Google Scholar 

  15. Melchels, F. P. W., Bertoldi, K., Gabbrielli, R., Velders, A. H., Feijen, J., and Grijpma, D. W., “Mathematically Defined Tissue Engineering Scaffold Architectures Prepared by Stereolithography,” Biomaterials, Vol. 31, No. 27, pp. 6909–6916, 2010.

    Article  Google Scholar 

  16. Melchels, F. P. W., Barradas, A. M. C., Van Blitterswijk, C. A., De Boer, J., Feijen, J., and Grijpma, D. W., “Effects of the Architecture of Tissue Engineering Scaffolds on Cell Seeding and Culturing,” Acta Biomaterialia, Vol. 6, No. 11, pp. 4208–4217, 2010.

    Article  Google Scholar 

  17. Yoo, D. J., “Computer-Aided Porous Scaffold Design for Tissue Engineering Using Triply Periodic Minimal Surfaces,” Int. J. Precis. Eng. Manuf., Vol. 12, No. 1, pp. 61–71, 2011.

    Article  MathSciNet  Google Scholar 

  18. Yoo, D. J., “Porous Scaffold Design using the Distance Field and Triply Periodic Minimal Surface Models,” Biomaterials, Vol. 32, No. 31, pp. 7741–7754, 2011.

    Article  Google Scholar 

  19. Kapfer, S. C., Hyde, S. T., Mecke, K., Arns, C. H., and Schröder-Turk, G. E., “Minimal Surface Scaffold Designs for Tissue Engineering,” Biomaterials, Vol. 32, No. 29, pp. 6875–6882, 2011.

    Article  Google Scholar 

  20. Yoo, D. J., “Heterogeneous Minimal Surface Porous Scaffold Design using the Distance Field and Radial Basis Functions,” Medical Engineering & Physics, Vol. 34, No. 5, pp. 625–639, 2012.

    Article  Google Scholar 

  21. Yoo, D. J., “Heterogeneous Porous Scaffold Design for Tissue Engineering using Triply Periodic Minimal Surfaces,” Int. J. Precis. Eng. Manuf., Vol. 13, No. 4, pp. 527–537, 2012.

    Article  Google Scholar 

  22. Yoo, D. J., “New Paradigms in Internal Architecture Design and Freeform Fabrication of Tissue Engineering Porous Scaffolds,” Medical Engineering & Physics, Vol. 34, No. 6, pp. 762–776, 2012.

    Article  Google Scholar 

  23. Yoo, D. J., “New Paradigms in Hierarchical Porous Scaffold Design for Tissue Engineering,” Materials Science and Engineering: C, Vol. 33, No. 3, pp. 1759–1772, 2013.

    Google Scholar 

  24. Yoo, D. J., “Heterogeneous Porous Scaffold Design using the Continuous Transformations of Triply Periodic Minimal Surface Models,” Int. J. Precis. Eng. Manuf., Vol. 14, No. 10, pp. 1743–1753, 2013.

    Article  Google Scholar 

  25. Schwarz, H., Uber Minimalflachen, Monatsber. Berlin Akad., Apr 1865; Gesammelte Mathematische Abhandlungen, Vol. 1, Springer, Berlin, 1890.

    Google Scholar 

  26. Schoen, A. H., “Infinite Periodic Minimal Surfaces without Self-Intersections,” NASA Technical Report TN D-5541, 1970.

    MATH  Google Scholar 

  27. Lord, E. A. and Mackay, A. L., “Periodic Minimal Surfaces of Cubic Symmetry,” Current Science, Vol. 85, No. 3, pp. 346–362, 2003.

    MathSciNet  Google Scholar 

  28. Wohlgemuth, M., Yufa, N., Hoffman, J., and Thomas, E. L., “Triply Periodic Bicontinuous Cubic Microdomain Morphologies by Symmetries,” Macromolecules, Vol. 34, No. 17, pp. 6083–6089, 2001.

    Article  Google Scholar 

  29. Gandy, P. J. F., Bardhan, S., Mackay, A. L., and Klinowski, J., “Nodal Surface Approximations to the P, G, D and I-WP Triply Periodic Minimal Surfaces,” Chemical Physics Letters, Vol. 336, No. 3, pp. 187–195, 2001.

    Article  Google Scholar 

  30. Wang, Y., “Periodic Surface Modeling for Computer Aided Nano Design,” Computer-Aided Design, Vol. 39, No. 3, pp. 179–189, 2007.

    Article  Google Scholar 

  31. Jung, Y., Chu, K. T., and Torquato, S., “A Variational Level Set Approach for Surface Area Minimization of Triply-Periodic Surfaces,” Journal of Computational Physics, Vol. 223, No. 2, pp. 711–730, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  32. Yoo, D. J., “Filling Holes in Large Polygon Models using an Implicit Surface Scheme and the Domain Decomposition Method,” Int. J. Precis. Eng. Manuf., Vol. 8, No. 1, pp. 3–10, 2007.

    Google Scholar 

  33. Yoo, D. J., “Three-Dimensional Morphing of Similar Shapes using a Template Mesh,” Int. J. Precis. Eng. Manuf., Vol. 10, No. 1, pp. 55–66, 2009.

    Article  Google Scholar 

  34. Yoo, D. J., “Rapid Surface Reconstruction from a Point Cloud using the Least-Squares Projection,” Int. J. Precis. Eng. Manuf., Vol. 11, No. 2, pp. 273–283, 2010.

    Article  Google Scholar 

  35. Yoo, D. J. and Kwon, H. H., “Shape Reconstruction, Shape Manipulation, and Direct Generation of Input Data from Point Clouds for Rapid Prototyping,” Int. J. Precis. Eng. Manuf., Vol. 10, No. 1, pp. 103–113, 2009.

    Article  Google Scholar 

  36. Yoo, D. J., “Three-Dimensional Human Body Model Reconstruction and Manufacturing from CT Medical Image Data using a Heterogeneous Implicit Solid Based Approach,” Int. J. Precis. Eng. Manuf., Vol. 12, No. 2, pp. 293–301, 2011.

    Article  Google Scholar 

  37. Yoo, D. J., “Three-Dimensional Surface Reconstruction of Human Bone using a B-Spline based Interpolation Approach,” Computer-Aided Design, Vol. 43, No. 8, pp. 934–947, 2011.

    Article  MathSciNet  Google Scholar 

  38. Baerentzen, J. A. and Aanaes, H., “Signed Distance Computation using the Angle Weighted Pseudonormal,” IEEE Transactions on Visualization and Computer Graphics, Vol. 11, No. 3, pp. 243–253, 2005.

    Article  Google Scholar 

  39. Guezlec, A., ““Meshsweeper”: Dynamic Point-to-Polygonal Mesh Distance and Applications,” IEEE Transactions on Visualization and Computer Graphics, Vol. 7, No. 1, pp. 47–61, 2001.

    Article  Google Scholar 

  40. Sud, A., Otaduy, M. A., and Manocha, D., “DiFi: Fast 3D Distance Field Computation using Graphics Hardware,” Proc. of Computer Graphics Forum, Vol. 23, No. 3, pp. 557–566, 2004.

    Article  Google Scholar 

  41. Yoo, D. J., “General 3D Offsetting of a Triangular Net using an Implicit Function and the Distance Fields,” Int. J. Precis. Eng. Manuf., Vol. 10, No. 4, pp. 131–142, 2009.

    Article  Google Scholar 

  42. Min, B. M., Lee, G., Kim, S. H., Nam, Y. S., Lee, T. S., and Park, W. H., “Electrospinning of Silk Fibroin Nanofibers and Its Effect on the Adhesion and Spreading of Normal Human Keratinocytes and Fibroblasts in Vitro,” Biomaterials, Vol. 25, No. 7, pp. 1289–1297, 2004.

    Article  Google Scholar 

  43. Chen, C. S., Mrksich, M., Huang, S., Whitesides, G. M., and Ingber, D. E., “Geometric Control of Cell Life and Death,” Science, Vol. 276, No. 5317, pp. 1425–1428, 1997.

    Article  Google Scholar 

  44. Sun, C., Fang, N., Wu, D., and Zhang, X., “Projection Micro-Stereolithography Using Digital Micro-Mirror Dynamic Mask,” Sensors and Actuators A: Physical, Vol. 121, No. 1, pp. 113–120, 2005.

    Article  Google Scholar 

  45. Lu, Y., Mapili, G., Suhali, G., Chen, S., and Roy, K., “A Digital MicroMirror Devicebased System for the Microfabrication of Complex, Spatially Patterned Tissue Engineering Scaffolds,” Journal of Biomedical Materials Research Part A, Vol. 77, No. 2, pp. 396–405, 2006.

    Article  Google Scholar 

  46. Park, I. B., Ha, Y. M., Kim, M. S., and Lee, S. H., “Fabrication of a Micro-Lens Array with a Nonlayered Method in Projection Microstereolithography,” Int. J. Precis. Eng. Manuf., Vol. 11, No. 3, pp. 483–490, 2010.

    Article  Google Scholar 

  47. Jung, J. W., Kang, H.-W., Kang, T.-Y., Park, J. H., Park, J., and Cho, D.-W., “Projection Image-Generation Algorithm for Fabrication of a Complex Structure using Projection-based Microstereolithography,” Int. J. Precis. Eng. Manuf., Vol. 13, No. 3, pp. 445–449, 2012.

    Article  Google Scholar 

  48. Gauvin, R., Chen, Y. C., Lee, J. W., Soman, P., Zorlutuna, P., et al., “Microfabrication of Complex Porous Tissue Engineering Scaffolds using 3D Projection Stereolithography,” Biomaterials, Vol. 33, No. 15, pp. 3824–3834, 2012.

    Article  Google Scholar 

  49. Dean, D., Wallace, J., Siblani, A., Wang, M. O., Kim, K., et al., “Continuous Digital Light Processing (cDLP): Highly Accurate Additive Manufacturing of Tissue Engineered Bone Scaffolds: This Paper Highlights the Main Issues Regarding the Application of Continuous Digital Light Processing (cDLP) for the Production of Highly Accurate PPF Scaffolds with Layers as thin as 60 m for Bone Tissue Engineering,” Virtual and Physical Prototyping, Vol. 7, No. 1, pp. 13–24, 2012.

    Article  Google Scholar 

  50. Jang, D., Meza, L. R., Greer, F., and Greer, J. R., “Fabrication and Deformation of Three-Dimensional Hollow Ceramic Nanostructures,” Nature Materials, Vol. 12, No. 10, pp. 893–898, 2013.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dong-Jin Yoo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yoo, DJ. 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, 1657–1666 (2014). https://doi.org/10.1007/s12541-014-0516-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-014-0516-5

Keywords

Navigation