Page 266 - IJB-10-5

International Journal of Bioprinting A TPMS framework for complete dentures

2. Methods level-set approximation equations, a hyperboloid can be
formed by solving -c ≤ φ(x,y,z) ≤ c. The space surrounded
2.1. Functionally graded TPMS framework design for by two surfaces is the solid part of the TPMS porous
implant-supported fixed complete dentures
structure as depicted in Figure 1C.
2.1.1. Sheet-network gyroid structure designs
The four most common TPMS structures are illustrated
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in Figure 1A. According to the study by Castro et al., 2.1.2. Gradient porous gyroid structure designs
sheet-network gyroid structures, compared to other TPMS The internal structure of a tooth exhibits a hierarchical
porous structures, exhibit higher surface area, better organization, comprising three primary components:
manufacturability, superior energy absorption, and load- enamel, dentin, and pulp. This hierarchical organization
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bearing capabilities. These structures have smooth surfaces results in a gradient variation in the mechanical
with an average curvature of 0 to effectively reduce local properties of teeth, from the interior to the exterior
stress concentration. Consequently, we employed the sheet- regions. Additionally, density and unit cell size are crucial
network gyroid lattice as the research object (Figure 1B). parameters affecting the mechanical properties of TPMS
The level-set approximation equation is the most porous structures. They jointly control the wall thickness,
commonly used method to describe TPMS. The equation thereby influencing the structures’ elastic modulus and
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for gyroid is compressive performance. Therefore, this study adopted
a radial gradient variation method based on the gyroid
φ = cos(X) sin(Y) + cos (Y) (I) structure (including variations in porosity and cell size
G
gradients) to design a biomimetic framework for IFCDs.
sin(Z) + cos(Z) sin(X) = c
This study combines two design types: (i) relative density
gradient variation and (ii) cell size gradient variation.
where X = 2πx/t, Y = 2πy/t, and Z = 2πz/t refer to the The former is controlled by parameter c, and the latter is
periodic changes in the x, y, and z directions, respectively, t influenced by parameter t.
is a parameter that determines the size of the unit cell, and
c indicates the value of the surface offset that governs the The relative density is a crucial parameter in TPMS-
internal void morphology of the lattice structures. In the based porous structures, as it not only determines pore

Figure 1. Four kinds of three-periodic minimal surface (TPMS) and the formation principle of the sheet-networks gyroid structures. (A) Four types
of three-periodic minimal surface (TPMS) structures. (B) The sheet-network gyroid structure. (C) Construction of sheet-network gyroid structures.
Abbreviation: I-WP, Schoen’s I-graph-wrapped package.

Volume 10 Issue 5 (2024) 258 doi: 10.36922/ijb.3453