Computational design of tissue engineering scaffolds. (English) Zbl 1125.74031

Summary: Tissue engineering utilizes porous biomaterial scaffolds to deliver biological factors that accelerate tissue healing. These two functions require scaffolds be designed for mechanical loading and mass transport. The purpose of this paper was to apply both ad hoc and topology optimization homogenization based design approaches to create scaffold architectures, and to determine how these architectures compare to theoretical bounds on effective stiffness. Open cell scaffold architectures demonstrated a wide range of permeability, but were all below isotropic effective stiffness bounds. Wavy fiber architectures provide a means to approach the lower bounds. Using image-based techniques, designed architectures may be incorporated in anatomic shapes.


74L15 Biomechanical solid mechanics
74Q20 Bounds on effective properties in solid mechanics
74P15 Topological methods for optimization problems in solid mechanics
92C10 Biomechanics
Full Text: DOI


[1] Langer, R.; Vacanti, J., Tissue engineering, Science, 260, 920-926, (1993)
[2] Hollister, S.J., Porous scaffold design for tissue engineering, Nat. mater., 4, 518-524, (2005)
[3] Hutmacher, D.W., Scaffold design and fabrication technologies for engineering tissues – start of the art and future perspectives, J. biomater. sci., polym. ed., 12, 107-124, (2001)
[4] Torquato, S., Random heterogenous materials: architecture and material properties, (2002), Springer-Verlag New York
[5] Milton, G.W., The theory of composites, (2001), Cambridge University Press Cambridge · Zbl 0631.73011
[6] Avellaneda, M., Optimal bounds and microgeometries for elastic two-phase composites, SIAM J. appl. math., 47, 1216-1228, (1987) · Zbl 0632.73079
[7] O. Sigmund, On the optimality of bone architecture, in: P. Pedersen, M.P. Bendsoe (Eds.), Synthesis in Biosolid Mechanics, 1999, pp. 221-234.
[8] Hashin, Z.; Shritkman, S., A variational approach to the theory of the elastic behaviour of multiphase materials, J. mech. phys. solids, 11, 127-140, (1963) · Zbl 0108.36902
[9] Sigmund, O., Materials with prescribed constitutive parameters – an inverse homogenization problem, Int. J. solids struct., 31, 2329-2513, (1994) · Zbl 0946.74557
[10] Hollister, S.J.; Maddox, R.D.; Taboas, J.M., Optimal design and fabrication of scaffolds to mimic tissue properties and satisfy biological constraints, Biomaterials, 23, 4095-4103, (2002)
[11] Wettergreen, M.A.; Bucklen, B.S.; Sun, W.; Liebschner, M.A., Computer-aided tissue engineering of a human vertebral body, Ann. biomed. engrg., 10, 1333-1343, (2005)
[12] Sanchez-Palencia, E., Non-homogeneous media and vibration theory, (1980), Springer-Verlag Berlin · Zbl 0432.70002
[13] Hollister, S.J.; Kikuchi, N., Homogenization theory and digital imaging: a basis for studying the mechanics and design principles of bone tissue, Biotechnol. bioengrg., 43, 586-596, (1994)
[14] Terada, K.; Kikuchi, N., Characterization of the mechanical behaviors of solid – fluid mixture by the homogenization method, Comput. method appl. mech. engrg., 153, 223-257, (1998) · Zbl 0926.74097
[15] Terada, K.; Miura, T.; Kikuchi, N., Digital image-based modeling applied to the homogenization analysis of composite materials, Comput. mech., 20, 331-346, (1997) · Zbl 0898.73045
[16] Lin, C.Y.; Kikuchi, N.; Hollister, S.J., A novel method for biomaterial scaffold internal architecture design to match bone elastic properties with desired porosity, J. biomech., 37, 623-636, (2004)
[17] Svanberg, K., The method of moving asymptotes – a new method for structural optimization, Int. J. numer. methods engrg., 24, 359-373, (1987) · Zbl 0602.73091
[18] C.Y. Lin, PhD Dissertation, The University of Michigan, 2005.
[19] Steven, G.P.; Li, Q.; Xie, Y.M., Evolutionary topology and shape design for general physical field problems, Comput. mech., 26, 129-139, (2000) · Zbl 0961.74050
[20] Bendsoe, M.P.; Sigmund, O., Topology optimization: theory, methods and applications, (2003), Springer-Verlag · Zbl 0957.74037
[21] Guedes, J.M.; Rodrigues, H.C.; Bendsoe, M.P., A material optimization model to approximate energy bounds for cellular materials under multiload conditions, Struct. multidisc. optim., 25, 446-452, (2003) · Zbl 1243.74139
[22] Diaz, A.R.; Benard, A., Designing materials with prescribed elastic properties using polygonal cells, Int. J. numer. meth. engrg., 57, 301-314, (2003) · Zbl 1062.74521
[23] Karande, T.S.; Ong, J.L.; Agrawal, C.M., Diffusion in musculoskeletal tissue engineering scaffolds: design issues related to porosity, permeability, architecture and nutrient mixing, Ann. biomed. engrg., 32, 1728-1743, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.