Page 52 - IJB-9-6

International Journal of Bioprinting Sub-regional design of the bionic bone scaffolds

Figure 4. The as-designed models where a = 4000 μm and a = 2000 μm are held constant and the set of values of C , C , and ε are respectively (a) 50%,
2
1
1
2
90%, and 0.47 and (b) 20%, 80%, and 0.06.
the scaling of Voronoi face (Figure 3a) and of Voronoi solve the problem, this study proposed a solution through
cell (Figure 3b) with respect to their corresponding the following relational formula:
centers. d
C face = C + C − C cell = C − i ( C − C ) (IV)
In addition, the bionic bone scaffolds should have i 1 2 i 2 d max 2 1
specific regional functionality; this will require that the Then, the final 3D porous interconnection structure
graded distribution of pore locations should be considered, was obtained by the Boolean operation between the initial
and more importantly, the graded porosity should also be 3D Voronoi cell structure and the scaling results. Finally,
taken into account. A distance-to-scale coefficient mapping Weaverbird v.0.9.0.1 was used to soften the trabecular-like
} to sub-
model, based on the shortest distance from {P 1 S N mesh model. Figure 4 shows the as-designed models with
i i 1=
region A, was computed, where its core is calculating different design variables. It is clear that each characteristic
the shortest distance d (i = 1, 2, …, N) from each point
i parameter has achieved the predetermined design goal.
} to the topological model that is
in the point set {P 1 S N It is important to mention that the porosity of the
i i 1=
determined. The values were ordered from smallest to bionic bone scaffolds can be parametrically modified by
largest and the maximum value d max in d was determined. changing C and C . Similarly, the specific surface area
i
Thus, C , corresponding to the i-th nucleating point, can can be adjusted, when needed, at constant porosity by
1
cell
2
be described as follows: controlling the dot pitch and the scale coefficient. Equation
d IV brings an extremely great improvement to the specific
C cell = C + i ( C − C ) (III)
1
i
d 2 1 surface area in sub-region B, which positively induces the
max
where C represents the lower limit of the predefined adhesion and proliferation of osteoblasts. The effect of
1
value of the scale coefficient while C corresponds to its specific surface area on permeability will be investigated
in a future work. The aperture D (defined by the equivalent
2
upper limit. The value C = C was set for the Voronoi diameter method) of the bionic bone scaffolds is affected by
cell
1
cells in sub-region A while in sub-region B, the value of the synergy of C and the design variables of the combined
face
C was set to a graded value ranging between C and C , probability sphere model. The target aperture range can be
cell
2
1
depending on the mapping model. The gradient setting of obtained by adjusting C when the probability sphere
face
C in sub-region B was aimed to maximize the mechanical model is determined. Furthermore, it is worth pointing out
cell
continuity and enhance the regional functionality of cell that our approach is applicable to any type of 3D printers.
adhesion, especially alleviating the mutation phenomenon
at the junction of the two sub-regions.
2.2 Finite element analysis of the bionic bone
Almost all studies did not distinguish between C and scaffolds
cell
C , which exhibited a lack of adaptability to this bionic As mentioned in section 2.1, the graded Voronoi
face
bone scaffold. Previous work has shown that the dot pitch nucleating points have a random distribution, and the
is the most important factor influencing the aperture at randomness arises from the combined probability sphere
a certain scale coefficient [12,13] . Due to the introduction of model. In order to evaluate the effect of randomness on the
the combined probability sphere model, the nucleating mechanical properties and the porosity, four as-designed
points were mainly concentrated in sub-region A, which models, denoted as randomness series, were generated
already resulted in a graded distribution of aperture. using four different random seeds. Other design parameters
When the same scale coefficient used for C is applied to were kept the same where a = 4000 μm, a = 2000 μm, C
cell
1
2
1
C , it will lead to a large increase in aperture less than = 50%, C = 90%, and ε = 0.47. Moreover, the dot pitch
face
2
60 μm and greater than 1200 μm, significantly reducing a was supposed to be another possible factor that affect
t
the functionality of the scaffolds to induce osteoblasts in the mechanical properties of the bionic bone scaffolds.
order to proliferate and differentiate in sub-region B. To Two series of the as-designed models with different a
1
Volume 9 Issue 6 (2023) 44 https://doi.org/10.36922/ijb.0222