Porous Structure Design Using Parameterized Hexahedral Meshes and Triply Periodic Minimal Surfaces

Chen, Huawei; Guo, Ye; Rostami, Reihaneh; Fan, Shuqian; Tang, Kanglai; Yu, Zeyun

doi:10.1145/3208159.3208174

Cited by 5 publications

(4 citation statements)

References 30 publications

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“…presented a different approach to generating TPMS porous scaffolds based on T-spline [29]. More recently, Chen et al attempted to map regular TPMS into parameterized hexahedral mesh using the Laplace's equation [30]. Even though the benefits of TPMS and its applications have been widely discussed in the literature, it might not always be the best tool when manufacturing porous structures.…”

Section: Tpms Surface Typementioning

confidence: 99%

“…As mentioned in Section 2, TPMS couldn't produce a porous structure fitting any irregular complex shape unless some mapping techniques, such as the distance field [31], T-spline [29], or hexahedral parameterization [30], is integrated. Unlike TPMS, a significant advantage of the proposed tetrahedral implicit surface method is that it can generate surfaces with same morphological features inside the tetrahedron of any shape.…”

Section: Continuity Analysis Of Tetrahedral Implicit Surfacementioning

confidence: 99%

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Tetrahedron-Based Porous Scaffold Design for 3D Printing

Guo

Liu

2019

Designs

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Tissue repairing has been the ultimate goal of surgery, especially with the emergence of reconstructive medicine. A large amount of research devoted to exploring innovative porous scaffold designs, including homogeneous and inhomogeneous ones, have been presented in the literature. The triply periodic minimal surface has been a versatile source of biomorphic structure design due to its smooth surface and high interconnectivity. Nonetheless, many 3D models are often rendered in the form of triangular meshes for its efficiency and convenience. The requirement of regular hexahedral meshes then becomes one of limitations of the triply periodic minimal surface method. In this paper, we make a successful attempt to generate microscopic pore structures using tetrahedral implicit surfaces. To replace the conventional Cartesian coordinates, a new coordinates system is built based on the perpendicular distances between a point and the tetrahedral faces to capture the periodicity of a tetrahedral implicit surface. Similarly to the triply periodic minimal surface, a variety of tetrahedral implicit surfaces, including P-, D-, and G-surfaces are defined by combinations of trigonometric functions. We further compare triply periodic minimal surfaces with tetrahedral implicit surfaces in terms of shape, porosity, and mean curvature to discuss the similarities and differences of the two surfaces. An example of femur scaffold construction is provided to demonstrate the detailed process of modeling porous architectures using the tetrahedral implicit surface.

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Section: Tpms Surface Typementioning

confidence: 99%

Section: Continuity Analysis Of Tetrahedral Implicit Surfacementioning

confidence: 99%

Tetrahedron-Based Porous Scaffold Design for 3D Printing

Guo

Liu

2019

Designs

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“…Feng et al [8] proposed a method to design porous scaffold based on solid Tsplines and TPMS, and analyzed the parameter influences on the volume specific surface area and porosity. In addition, a heterogenous methodology for modeling porous scaffolds using a parameterized hexahedral mesh and TPMS was developed by Chen et al [10].…”

Section: Related Workmentioning

confidence: 99%

“…In the first class of methods, a volume mesh model is embedded in an ambient TPMS, and the intersection of them is taken as the porous scaffold [5][6][7][8]. In the second class of methods, a regular TPMS unit is transformed into each hexahedron of a hexahedron mesh model, thus generating a porous scaffold [9][10][11]. However, the first class of methods can generate incomplete TPMS units near the boundary of a volume mesh model, and the second class of methods may cause discontinuities between two adjacent TPMS units.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous porous scaffold generation in trivariate B-spline solid with triply periodic minimal surface in the parametric domain

Hu,

Lin

2019

Preprint

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A porous scaffold is a three-dimensional network structure composed of a large number of pores, and triply periodic minimal surfaces (TPMSs) are one of conventional tools for designing porous scaffolds. However, discontinuity, incompleteness, and high storage space requirements are the three main shortcomings of TPMSs for porous scaffold design. In this study, we developed an effective method for heterogeneous porous scaffold generation to overcome the abovementioned shortcomings of TPMSs. The input of the proposed method is a trivariate B-spline solid (TBSS) with a cubic parameter domain. The proposed method first constructs a threshold distribution field (TDF) in the cubic parameter domain, and then produces a continuous and complete TPMS within it. Moreover, by mapping the TPMS in the parametric domain to the TBSS, a continuous and complete porous scaffold is generated in the TBSS. In addition, if the TBSS does not satisfy engineering requirements, the TDF can be locally modified in the parameter domain, and the porous scaffold in the TBSS can be rebuilt. We also defined a new storage space-saving file format based on the TDF to store porous scaffolds. The experimental results presented in this paper demonstrate the effectiveness and efficiency of the method using a TBSS as well as the superior space-saving of the proposed storage format.

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Porous Structure Design in Tissue Engineering Using Anisotropic Radial Basis Functions

Guo

Liu²,

2018

Advances in Visual Computing

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Porous Structure Design Using Parameterized Hexahedral Meshes and Triply Periodic Minimal Surfaces

Cited by 5 publications

References 30 publications

Tetrahedron-Based Porous Scaffold Design for 3D Printing

Tetrahedron-Based Porous Scaffold Design for 3D Printing

Heterogeneous porous scaffold generation in trivariate B-spline solid with triply periodic minimal surface in the parametric domain

Porous Structure Design in Tissue Engineering Using Anisotropic Radial Basis Functions

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