Skip to main content
SpringerLink
Log in

Heterogeneous porous scaffold design for tissue engineering using triply periodic minimal surfaces

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

Abstract

Recently, a paradigm shift is taking place in tissue engineering scaffold design from homogeneous porous scaffolds to functionally graded scaffolds that have heterogeneous internal structures with controlled porosity levels and architectures. This paper presents a new heterogeneous modeling methodology for designing tissue engineering scaffolds with precisely controlled porosity and internal architectures using triply periodic minimal surfaces. The internal architectures and porosity at the spatial locations of the scaffolds are determined based on a given distribution of architectures and porosity levels specified at a few selected points on the model. After generating the hexahedral elements for a 3D anatomical shape using the distance field algorithm, the unit cell libraries composed of triply periodic minimal surfaces are mapped into the subdivided hexahedral elements using the shape function widely used in the finite element method. By simply allocating parameter values related to the porosity and architecture type to the corner nodes in each hexahedral element, we can easily and precisely control the pore size, porosity, and architecture type at each region of the scaffold while preserving perfectly interconnected pore networks across the entire scaffold.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Das, S., Beama, J. J., Wohlert, M. and Bourell, D. L., “Direct laser freeform fabrication of high performance metal components,” Rapid Prototyping Journal, Vol. 4, No. 3, pp. 112–117, 1998.

    Article  Google Scholar 

  2. Simchi, A., Petzoldt, F. and Pohl, H., “On the development of direct metal laser sintering for rapid tooling,” Journal of Materials Processing Technology, Vol. 141, No. 3, pp. 319–328, 2003.

    Article  Google Scholar 

  3. Hutmacher, D. W., Sittinger, M. and Risbud, M. V., “Scaffoldbased tissue engineering: rationale for computer-aided design and solid free-form fabrication systems,” TRENDS in Biotechnology, Vol. 22, No. 7, pp. 354–362, 2004.

    Article  Google Scholar 

  4. Ma, P. X., “Scaffolds for tissue fabrication,” Materials Today, Vol. 7, No. 5, pp. 30–40, 2004.

    Article  Google Scholar 

  5. Hollister, S. J., “Porous scaffold design for tissue engineering,” Nature Materials, Vol. 4, No. 7, pp. 518–524, 2005.

    Article  Google Scholar 

  6. Gomez, C., Shokoufandeh, A. and Sun, W., “Unit-Cell Based Design and Modeling in Tissue Engineering Applications,” Computer-Aided Design & Applications, Vol. 4, No. 5, pp. 649–659, 2007.

    Google Scholar 

  7. Fang, Z., Starly, B. and Sun, W., “Computer-aided characterization for effective mechanical properties of porous tissue scaffolds,” Computer-Aided Design, Vol. 37, No. 1, pp. 65–72, 2005.

    Article  Google Scholar 

  8. 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 

  9. Adachi, T., Osako, Y., Tanaka, M., Hojo, M. and Hollister, S. J., “Framework for optimal design of porous scaffold microstructure by computational simulation of bone generation,” Biomaterials, Vol. 27, No. 21, pp. 3964–3972, 2006.

    Article  Google Scholar 

  10. 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 

  11. 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 

  12. 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 

  13. Naing, M. W., Chua, C. K., Leong, K. F. and Wang, Y., “Fabrication of customized scaffolds using computer-aided design and rapid prototyping techniques,” Rapid Prototyping Journal, Vol. 11, No. 4, pp. 249–259, 2005.

    Article  Google Scholar 

  14. Wang, C. S., Wang, W. H. 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 

  15. Leong, K. F., Chua, C. K., Sudarmadji, N. and Yeong, W. Y., “Engineering functionally graded tissue engineering scaffolds,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 1, No. 2, pp. 140–152, 2008.

    Article  Google Scholar 

  16. Sogutlu, S. and Koc, B., “Stochastic Modeling of Tissue Engineering Scaffolds with Varying Porosity Levels,” Computer-Aided Design & Applications, Vol. 4, No. 5, pp. 661–670, 2007.

    Google Scholar 

  17. Takano, N., Zako, M., Kubo, F. and Kimura, K., “Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling,” International Journal of Solids and Structures, Vol. 40, No. 5, pp. 1225–1242, 2003.

    Article  MATH  Google Scholar 

  18. Schroeder, C., Regli, W. C., Shokoufandeh, A. and Sun, W., “Computer-aided design of porous artifacts,” Computer-Aided Design, Vol. 37, No. 3, pp. 339–353, 2005.

    Article  Google Scholar 

  19. Zang, J., Wu, L., Jing, D. and Ding, J., “A comparative study of porous scaffolds with cubic and spherical macropores,” Polymer, Vol. 46, No. 13, pp. 4979–4985, 2005.

    Article  Google Scholar 

  20. Sung, H. J., Meredith, C., Johnson, C. and Galis, Z. S., “The effect of scaffold degradation rate on three dimensional cell growth and angiogenesis,” Biomaterials, Vol. 25, No. 26, pp. 5735–5742, 2004.

    Article  Google Scholar 

  21. Cai, S. and Xi, J., “A control approach for pore size distribution in the bone scaffold based on the hexahedral mesh refinement,” Computer-Aided Design, Vol. 40, No. 10–11, pp. 1040–1050, 2008.

    Article  Google Scholar 

  22. Lord, E. A., “Periodic minimal surfaces of cubic symmetry,” Curr. Sci., Vol. 85, No. 3, pp. 346–362, 2003.

    MathSciNet  Google Scholar 

  23. 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 

  24. 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 

  25. Wang, Y., “Periodic surface modeling for computer aided nano design,” Computer-Aided Design, Vol. 39, No. 3, pp. 179–189, 2007.

    Article  Google Scholar 

  26. 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  MathSciNet  MATH  Google Scholar 

  27. 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 

  28. Melchels, F. P. W., Bertoldi, K., Gabbielli, R., Velders, A. H. and Feijen, J., “Mathematically defined tissue engineering scaffold architectures prepared by stereolithography,” Biomaterials, Vol. 31, No. 27, pp. 6909–6916, 2010.

    Article  Google Scholar 

  29. 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 

  30. 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 

  31. 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 

  32. 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 

  33. 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 

  34. Barentzen, J. A. and Aanas, H., “Signed distance computation using the angle weighted pseudo-normal,” IEEE Transactions on Visualization and Computer Graphics, Vol. 11, No. 3, pp. 243–253, 2005.

    Article  Google Scholar 

  35. Gueziec, A., “Meshsweeper: Dynamic point-to-polygonal mesh distance and applications,” IEEE Transactions on Visualization and Computer Graphics, Vol. 7, No. 1, pp. 47–60, 2001.

    Article  Google Scholar 

  36. Sud, A., Otaduy, M. A. and Manocha, D., “DiFi: Fast 3D distance field computation using graphics hardware,” Proc. of Euro-graphics, Vol. 23, No. 3, pp. 557–566, 2004.

    Article  Google Scholar 

  37. Yoo, D. J., “Offsetting of triangular net using distance fields,” J. of the KSPE, Vol. 24, No. 9, pp. 148–157, 2007.

    Google Scholar 

  38. 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 

  39. 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 

  40. 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 

  41. 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 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Aided Mechanical Design Engineering, Daejin University, Seondan-dong, Pocheon-si, Gyeonggi-do, South Korea, 487-711

    Dong-Jin Yoo

Authors
  1. Dong-Jin Yoo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong-Jin Yoo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yoo, DJ. Heterogeneous porous scaffold design for tissue engineering using triply periodic minimal surfaces. Int. J. Precis. Eng. Manuf. 13, 527–537 (2012). https://doi.org/10.1007/s12541-012-0068-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-012-0068-5

Keywords

Search

Navigation