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Additive manufacturing of bone scaffolds
minimal surfaces were more easily wetted with higher lower than 74%. Beyond this critical point, the solid
permeability, leading to deeper cells into growth as well phase turned disconnected.
as more uniform cell distribution, as compared with a Another typical mathematical modeling is Voronoi-
salt-leached scaffold with a random-pore architecture . Tessellation method, which constructs porous models
[69]
Kapfer et al. investigated two kinds of TPMS-based using a Voronoi diagram. A typical scaffold design
[68]
structure, including network solids and sheet solids. In the principle based on Voronoi-Tessellation method is
network solids, the minimal surface constructs the solid/ depicted in Figure 5. In particular, a set of points (or seeds)
void interface, whereas in sheet solids, porous solids are are positioned randomly inside the design volume to fulfill
constructed by inflating the minimal surfaces to sheets a partition of the space in regions. Then, a thickness is
with a predefined thickness. Finite element analysis assigned to the edges of the partitioned regions to obtain a
confirmed that the sheet solids possessed considerably porous scaffold [79,80] . The design of porous structure based
higher mechanical stiffness than that of network solids on Voronoi diagram could be traced back to Kou and
for identical volume fractions (Figure 4B and C) and Tan [81,82] , where they first proposed to use Voronoi vertices
Poisson’s ratio (Figure 4D). Moreover, the sheet solids as the control points of a closed B-spline curve to create
also exhibited higher material utilization and provided a convex-shaped cell. Besides, a porous structure was
relatively more surface area and pore space for cell obtained by merging the adjacent cells. However, they
migration and activity. only studied the 2D pore structure. While Chow et al.
[83]
TPMS has been explored for its possibility to construct organized Voronoi seeds in concentric circles and formed
gradient, heterogeneous, hybrid, and irregular porous a 2D shape region. Subsequently, a 3D porous structure
[38]
structures. Melchels et al. reported that the design was constructed by expanding the time dimension of the
of a gradient porous structure can be constructed based dynamic pattern in the third dimension of the 2D shape
on TPMS by adding a linear function. Feng et al. region.
[31]
designed heterogeneous porous scaffolds with non- In recent years, researchers have conducted a more in-
uniform threshold, period, and unit by combining TPMS depth study on Voronoi-Tessellation-based scaffold
and solid T-splines. In addition, Yang et al. proposed design and have achieved great progress. For example,
[70]
two CAD methods to prepare hybrid porous structures for Fantini et al. combined CAD 3D software Rhinoceros
[84]
biomimetic design purposes that combine different TPMS- with its Plug-in Grasshopper to design bone scaffolds
based structures with given transition boundaries. Using based on Voronoi-Tessellation method. This work
his approach, it is able to place TPMS-based substructures successfully correlated to the input parameters, including
on given 3D subspaces with perfect transitions to their the number of seeds, porosity, and the pore size of
adjacent substructures within a scaffold domain. A series the structure . Gómez et al. proposed a bone-like
[85]
[86]
of multiscale and multimorphology porous scaffolds trabecular structure design based on Voronoi-Tessellation
were presented in their further studies [71-74] . For similar principle. The seeds of Voronoi diagram were extracted
goals, Yoo et al. [75-77] combined a kind of distance field from the micro-CT images of the trabecular bone. The
with TPMS-based functions to effectively construct obtained isotropic porous scaffolds were then perfectly
pseudorandom porous scaffolds. Yang et al. utilized matched the main histomorphometric indices of nature
[78]
coordinate transformation based on TPMS to construct bone. More importantly, the final properties could
an gradient and full irregular porous structure, extending be tailored during the design stage by changing the
TPMS to irregular design areas. However, the stochastic trabecular separation and thickness. Wang et al. put
[87]
porous structure constructed by this method had porosities forward a probability sphere method to generate random
seeds based on the Voronoi-Tessellation. In this study,
a scale coefficient K was introduced to control the pore
size and strut thickness, which successfully achieved the
balance between “irregularity” and “controllability.” As
a result, highly mimic scaffolds with porosities ranging
from 60% to 95% and pore size ranging from 200 to
1200 μm were designed precisely. In addition, a porosity
gradient ranging from 0.03 to 0.54 was also obtained. In
this regard, it is clear that Voronoi-Tessellation method
combines the advantages of reverse modeling method
and topology optimization method. It cannot only realize
Figure 5. A schematic diagram showing the scaffold design the bionic structure design of bone scaffold but also
principle based on Voronoi-Tessellation method and as-built optimize the structure to achieve desirable properties,
scaffolds . such as porosity, permeability, and mechanical strength.
[87]
6 International Journal of Bioprinting (2019)–Volume 5, Issue 1