Fig 1.
Spinal fusion system schematic.
A lattice with a solid shell acts as a tissue scaffold between adjacent vertebrae to facilitate bone fusion.
Fig 2.
Lattice design approach for tissue scaffolds.
(a) A defined topology is used to construct unit cells with (b) a specified porosity for (c) generating a lattice structure with desired pore sizes.
Fig 3.
Unit cells are grouped in (A) Cubic, (B) Octahedron, and (C) Truncated families based on their topology. Illustrated unit cells have porosity P = 0.8.
Fig 4.
Lattices with porosity P = 0.8 have overlaid squares indicating unit cell boundaries with beam diameters ø, unit cell length Lc, and circles indicating defined pores with diameter p.
Fig 5.
(a) Pore size p plotted for porosity P when beam diameter ø = 200μm and (b) surface-volume ratio S/V plotted as pore size increases from 250μm to 1500μm for lattices with P = 0.8 for all topologies.
Fig 6.
(a) Relative elastic modulus Er and (b) relative shear modulus Gr for porosity P for all topologies.
Fig 7.
(a) Permeability k for each topology when porosity P = 0.6 (open symbols; dotted lines) and P = 0.8 (closed symbols; solid lines) for surface-volume ratio S/V; lines reflect best fits for each unit cell family. (b) The Kozeny-Carmen relation k = K·P3 /(S/V)2 with lines of best fit for each unit cell family.
Fig 8.
Relative comparison of topologies with fixed porosity and pore size.
Properties of lattices with Porosity P = 0.8 and pore size p = 500μm are normalized to relative elastic modulus Er = 0.07, relative shear modulus Gr = 0.081, surface-volume ratio S/V = 7.0mm−1 and permeability k = 3.1 × 10−8m2.
Fig 9.
Relative comparison of topologies with fixed elastic modulus and pore size.
(a) Lattices were designed with relative elastic modulus Er = 0.03 and pore size p = 500μm and illustrated with a relative scaling. (b) Properties of lattices normalized to porosity P = 0.91, relative shear modulus Gr = 0.087, surface-volume ratio S/V = 6.9mm−1 and permeability k = 3.1 × 10−8m2.
Fig 10.
Trade-offs for printed BC-Cube topology for spinal cage applications.
(a) BC-Cube lattices were designed with a unit cell size Lc = 2mm, while increasing beam diameter for porosities between P = 0.45 to to P = 0.85; properties were normalized to relative elastic modulus Er = 0.11, relative shear modulus Gr = 0.24, surface-volume ratio S/V = 2.35mm−1, permeability k = 1.25 × 10−8m2, and porosity P = 0.85. (b) Designed structure generated by patterning unit cells with beam diameter ø = 500μm and (c) printed design with local reinforcement.