Page 373 - IJB-10-5

International Journal of Bioprinting Tunable anisotropic gyroid bioscaffolds

mechanical properties. The geometrical properties of the Graded gyroid scaffold that mimics the anisotropic
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structure can be manipulated by controlling the parameters structure of natural bone can be beneficial for mitigating
of the level-set equations of the structure, which are a stress shielding effect and promoting cell growth.
combination of trigonometric functions that satisfy the Graded porosity and structural anisotropy were achieved
equation φ (x, y, z) = c. The sheet gyroids can be described by adjusting the parameters of the level-set equation
by the following level-set equation: (Equation (I)), specifically by defining the parameters for
the unit cell dimension and a function for the iso-value
sin(2απx) cos(2βπy) + sin(2βπy) (I) c = C (x, y, z). Gyroid structures with varying aspect ratios of
cos(2γπz) + sin(2γπz) cos(2απx) = c the unit cell were constructed by controlling the parameter γ
(Figure 2a). It is noteworthy that the value of ϕ in the sheet
gyroid structure remained independent of the γ value but
where the geometric parameters α, β, and γ control showed a positive correlation with the c value (Figure 2b).
the unit cell dimensions in the x, y, and z directions, A radially graded porosity within the gyroid scaffold was
respectively; c is a function that defines the iso-surface of achieved by assigning a control function to C (x, y, z) as follows:
the sheet gyroid structure which controls the thickness of
the sheet and therefore affects the solid volume fraction (ϕ) 2 2 2
of the structure. To create a solid domain, a double iso- C (x, y, z) = a(x + y + z ) + b (II)
surface can be defined by solving –c ≤ φ ≥ c. Scaffold with
gy
interconnected pores is desirable to mimic the biological To mimic the pore distribution of natural bone, which
bone tissue, as it promotes nutrient diffusion, and facilitates has a denser outer part (cortical bone) and a more porous
cell attachment, differentiation, and colonization. Studies inner part (cancellous bone), the center porosity of the
3
have shown that TPMS scaffolds with 30–60% porosity gyroid structure is set to 60% ((C ϕ=60% = 0.91) and the outer
exhibit reduced stress shielding effect. Therefore, the porosity to 40% (C ϕ=40% = 0.62), the coefficients value can
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parameters α, β, and γ were fixed at 0.50, and the value of c be obtained as follows:
ranging from 0.62 to 0.91 was identified to achieve desired
ϕ (40–60%) of the gyroid structure. Figure 1 illustrates


the 8 × 8 × 8 mm sheet gyroid structures with different  C x== = 0 = C φ = 60% = 091. 
3
y z
value of ϕ, including 40% (40VF-gy), 50% (50VF-gy), 60%  C = C = 062.  (III)
(60VF-gy), and their corresponding c values.   x= y = zd= / 2 φ = 40%  

Figure 1. 3D models for the gyroid structure with different volume fractions ϕ: 40VF-gy (ϕ = 40%, c = 0.62), 50VF-gy (ϕ = 50%, c = 0.76), and 60VF-gy
(ϕ = 60%, c = 0.91).

Volume 10 Issue 5 (2024) 365 doi: 10.36922/ijb.3609