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Application of Sierpinski and Pascal Fractals to Bone Scaffold Design

시어핀스키 및 파스칼 프랙탈의 뼈 스캐폴드 설계에의 응용

  • Received : 2017.01.16
  • Accepted : 2017.03.06
  • Published : 2017.06.01

Abstract

The fractal structures, which include Sierpinski and Pascal triangular fractals, have provided many mathematical interests. In this study, the hydrodynamic and mechanical properties of the triangular fractals were investigated, and their application to the design of various artificial bone scaffolds has been implemented via CAD modeling, computational analysis and mechanical testing. The study proved that the Sierpinski and Pascal triangular fractal structures could effectively be applied to bone scaffold design and manufacturing regarding permeability and mechanical stiffness.

Keywords

References

  1. Bamsley, M. F., 1993, Fractals Everywhere, 2nd ed., New York: Academic Press Professional.
  2. Peitgen, H. O., Jurgens, H. and Saupe, D., 2004, Chaos and Fractals: New Frontiers of Science, New York: Springer-Verlag.
  3. Carles Puente-Baliarda, Jordi Romeu, Rafael Pous, Angel Cardama, 1998, On the Behavior of the Sierpinski Multiband Fractal Antenna, IEEE Transactions of Antennas and Propagation, 46(4), pp.517-524. https://doi.org/10.1109/8.664115
  4. Jena, M.R., Mangaraj, B.B. and Pathak, R., 2014, Design of a Novel Sierpinski Fractal Antenna Arrays Based on Circular Shapes with Low Side Lobes for 3G Applications, American Journal of Electrical and Electronic Engineering, 2(4), pp.137-140. https://doi.org/10.12691/ajeee-2-4-3
  5. Sanchez-Molinaa, D., Velazquez-Ameijidea, J., Quintanaa, V., Arregui-Dalmasesa, C., Crandallb, J. R., Subitb, D. and Kerriganb, J.R., 2013, Fractal Dimension and Mechanical Properties of Human Cortical Bone, Medical Engineering & Physics, 35, pp.576-582. https://doi.org/10.1016/j.medengphy.2012.06.024
  6. Giannitelli, S.M., Accoto, D., Trombetta, M. and Rainer, A., 2014, Current Trends in the Design of Scaffolds for Computer-aided Tissue Engineering, Acta Biomaterialia, 10, pp.580-594. https://doi.org/10.1016/j.actbio.2013.10.024
  7. Langer, R. and Vacanti J.P., 1993, Tissue Engineering, Science, 260(5110), pp.920-926. https://doi.org/10.1126/science.8493529
  8. Park, J.W., Lee, J.H., Cho, H.U., Lee, S.H., Park, S.A. and Kim, W.D., 2012, Development of Scaffold Fabrication System using Multi-axis RP software Technique, Journal of the Korean Society for Precision Engineering, 29(1), pp.3340.
  9. Lipowiecki, M. et al., 2014, Permeability of Rapid Prototyped Artificial Bone Scaffold Structures, Journal of Biomedical Materials Research, 102A(11), pp.4127-4135.
  10. Asadi-Eydivand, M., Solati-Hashjin, M., Farzad, A. and Osman, N., 2016, Effect of Technical Parameters on Porous Structure and Strength of 3D Printed Calcium Sulfate Prototypes, Robotics and Computer-Integrated Manufacturing, 37, pp.57-67. https://doi.org/10.1016/j.rcim.2015.06.005
  11. Syahrom, A., Kadir, M., Abdullah, J. and Ochsner, A., 2013, Permeability Studies of Artificial and Natural Cancellous Bone Structures, Medical Engineering & Physics, 35, pp.792-799. https://doi.org/10.1016/j.medengphy.2012.08.011
  12. Gomez, S., Vlad, M.D., Lopez, J. and Fernandez, E., 2016, Design and Properties of 3D Scaffolds for Bone Tissue Engineering, Acta Biomaterialia, 42, pp.341-350. https://doi.org/10.1016/j.actbio.2016.06.032
  13. Li, X., 2010, Fabrication and Compressive Properties of Ti6Al4V Implant with Honeycomb-like Structure for Biomedical Applications, Rapid Prototyping Journal, 16(1), pp.44-49. https://doi.org/10.1108/13552541011011703
  14. Lee, S., Ahn, S.H. and Cho, Y., 2013, Assessment of Mechanical Characteristics of Scaffold via Computational Analysis and Compressive Test, Journal of Korean Society of Mechanical Technology, 15(6), pp.937-941. https://doi.org/10.17958/ksmt.15.6.201312.937
  15. Wieding, J., Souffrant, R., Mittelmeier, W. and Bader, R., 2013, Finite Element Analysis on the Biomechanical Stability of Open Porous Titanium Scaffolds for Large Segmental Bone Defects under Physiological Load Conditions, Medical Engineering & Physics, 35, pp.422-432. https://doi.org/10.1016/j.medengphy.2012.06.006
  16. Yang, S., Leong, K.F., Du, Z. and Chua, C.K., 2001, The Design of Scaffolds for use in Tissue Engineering. Part I. Traditional Factors, Tissue Eng., 7(6), pp.679-689. https://doi.org/10.1089/107632701753337645
  17. StudyBlue, https://www.studyblue.com/notes/note/n/list-7-1/deck/15834738, 2016.