CN113297688A - Bone-like support structure based on Voronoi diagram and design and preparation method thereof - Google Patents
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Abstract
The invention provides a bone-like support structure based on a Voronoi diagram and a design and preparation method thereof, wherein the bone-like support structure comprises the following steps: creating a three-dimensional space, placing N random discrete points, and extracting coordinate values of all the random points; converting the coordinate value into a unique corresponding characteristic value within 0-1, controlling the gradient distribution of the characteristic value within 0-1 by using a Bezier curve, and restraining the discrete points to present the gradient distribution; converting the characteristic value into an actual coordinate value, reconstructing a space coordinate of the discrete point, and generating a Voronoi subspace; exploding the subspace, setting a scaling factor and specifically selecting mark points, wherein the mark points form a mark surface; associating the selected mark surfaces, reconstructing a new boundary of a subspace, and generating an initial polyhedral scaffold by inclusion; subdividing the lattice epidermis of the stent, softening the surface and the nodules of the stent; the invention designs the bone-like scaffold by using the Voronoi diagram, realizes the gradient distribution of the scaffold by adding distribution constraint to discrete points, controls the volume fraction of the scaffold by using a scaling factor, softens the surface and the nodes and practically simulates the natural structure of the trabecula.
Description
Technical Field
The invention belongs to the field of computer aided design, 3D printing and biological scaffolds, and particularly relates to a bone-like scaffold structure based on a Venuo diagram and a design and preparation method thereof.
Background
Voronoi diagrams (Voronoi diagrams) are based on the expansion of polygons or polyhedrons at a constant rate to fill a space, using discrete points randomly distributed in a finite space, with the growth of the polygons or polyhedrons outwards, ending when adjacent polygons or polyhedrons collide with each other, generating boundaries consisting of straight lines in a two-dimensional space, and planes in a three-dimensional space. Thus, the whole body is divided into a plurality of sub areas or subspaces with different shapes. The voronoi diagram is applied to environmental maps, electronic networks and other angles.
The lightweight support is an application hotspot in a plurality of fields such as aerospace, building, medical treatment and the like. The design goal of lightweight stents is to attempt to improve mechanical properties while reducing material usage and weight through design and optimization of structural distribution. For the biological scaffold, the distribution of the scaffold in the scaffold needs to be considered, and the distribution is related to the attachment and the growth of osteoblasts. Because the boundary interweaving and nodule condition in the Voronoi diagram has high similarity with the trabecula in the skeleton, the three-dimensional Voronoi diagram has better applicability in the design and manufacture of the bone-like scaffold. The density distribution of the trabeculae has the characteristic of gradient distribution, when the unordered irregularly-segmented Voronoi diagram is applied to the design and manufacture of the bone-like support, further optimization and adjustment are needed, and a method for designing and manufacturing the gradient bone-like support structure by restricting the scattered point distribution in the Voronoi diagram is not found in the prior art.
Disclosure of Invention
Aiming at the technical problems, the invention provides a bone-like support structure based on a Voronoi diagram and a design and preparation method thereof, the Voronoi diagram is utilized to design the bone-like support, the idea of restricting the distribution of discrete points is utilized to control the gradient distribution, the distribution restriction is added to the discrete points to realize the adjustable gradient distribution of the support from a core to a shell, the idea of scaling factors is utilized to control the volume fraction of the support, the idea of subdivision surfaces is utilized to soften the surface and the nodes, the natural structure of a trabecula ossis practically simulated, and the advantages of the Voronoi diagram on the design of the bionic support are fully embodied.
The technical scheme of the invention is as follows: a bone-like support structure design method based on a Voronoi diagram comprises the following steps:
s1: creating a three-dimensional space, placing N random discrete points, and extracting coordinate values (X) of each random pointn,Yn,Zn)，n＝1,2…,N-1,N；
S2: converting the coordinate value into a unique corresponding characteristic value within 0-1, controlling the gradient distribution of the characteristic value within 0-1 by using a Bezier curve, and restraining the discrete points to present the gradient distribution;
s3: converting the characteristic value into an actual coordinate value, reconstructing a space coordinate of the discrete point, accessing a Voronoi3D calculator, and dividing the original space to generate a Veno subspace;
s4: exploding subspaces, extracting boundary lines of the subspaces, automatically capturing multiple mark points with equal distances on the boundary lines, setting a scaling factor to specifically select the mark points, and forming a mark surface by the mark points;
s5: associating the selected mark surfaces, reconstructing a new boundary of a subspace, generating an initial polyhedral scaffold by inclusion, and adjusting a scaling factor to control the volume fraction of the whole scaffold;
s6: subdividing the lattice epidermis of the stent, softening the surface and the nodules of the stent.
In the foregoing scheme, the S1 specifically is: creating a three-dimensional space, randomly placing discrete points in the space, setting the number N of the discrete points and the seed number S, and extracting the coordinate values (X) of all the discrete pointsn,Yn,Zn)，n＝1,2…,N-1,N。
In the foregoing scheme, the S2 specifically is: and converting X, Y, Z coordinate values of all discrete points into uniquely corresponding values in 0-1, respectively establishing a characteristic value set of an X coordinate, a Y coordinate and a Z coordinate of the discrete points, inputting the characteristic value set into a Bezier curve, respectively adjusting the distribution density of the characteristic value set of the X coordinate, the Y coordinate and the Z coordinate in the 0-1 value, enabling the distribution situation of the characteristic values in the 0-1 interval to present a gradient trend, and controlling the gradient distribution of the discrete points.
In the above-described embodiment, the bezier curve b (t) ═ P in step S2o(1-t)3+3P1t(1-t)2+3P2t2(1-t)+P3t3,t∈[0,1]From four control points Po、P1、P2、P3And controlling, wherein the Bezier curve can be changed by adjusting the position of the control point, so that the distribution density of the characteristic value of the coordinates of the discrete point X, Y, Z in a value of 0-1 is adjusted.
In the foregoing scheme, the S3 specifically is: and reconstructing a space coordinate of the discrete point according to the adjusted X, Y, Z characteristic value set, and generating a regulated and distributed Veno subspace in the original three-dimensional space according to the reconstructed discrete point.
A preparation method of a bone-like support structure based on a Voronoi diagram is provided, and the bone-like support structure based on the Voronoi diagram is designed according to a design method of the bone-like support structure based on the Voronoi diagram.
In the scheme, the bone-like support structure based on the Veno diagram is prepared by adopting 3D printing.
The bone-like scaffold structure based on the Voronoi diagram is prepared by a preparation method of the bone-like scaffold structure based on the Voronoi diagram.
Compared with the prior art, the invention has the beneficial effects that: the invention realizes the gradient distribution of the stent by using the idea of restricting the discrete point distribution, adjusts the branch diameter and the volume fraction of the stent by using the idea of scaling factors, softens the surface and the nodes of the stent by using the idea of subdividing a curved surface, and further optimizes the application of the Voronoi diagram in the design and manufacture of the bionic stent. The method has the advantages of high speed and high efficiency for preparing the bracket, can quickly adjust the volume fraction of the bracket by using the scaling factor, quickly adjust the gradient distribution mode of the bracket by using the Bezier curve, and has important significance for industrial application.
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FIG. 1 is a flow chart of a bone-like scaffold structure design based on a Voronoi diagram and a preparation method thereof.
Fig. 2 is an implementation process according to embodiment 1 of the present invention. Where Perspective refers to a three-dimensional schematic, Front refers to a Front view, and Top refers to a Top view. Wherein FIGS. 2(a) to (f) correspond to the operation results of steps S1 to S6, respectively.
Fig. 3 is an implementation process according to embodiment 2 of the present invention. Where Perspective refers to a three-dimensional schematic, Front refers to a Front view, and Top refers to a Top view. Wherein (a) to (f) of FIG. 3 correspond to the operation results of steps S1 to S6, respectively.
Fig. 4 is a stent model generated according to example 1 and example 2 of the present invention. Fig. 4(a) is a stent model generated in example 1, and fig. 4(b) is a stent model generated in example 2.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
As shown in fig. 1, the implementation flowchart of the bone-like scaffold structure design based on voronoi diagram and the preparation method thereof includes the following steps:
s1, creating a three-dimensional space, placing N random discrete points, and extracting coordinate values (X) of each random pointn,Yn,Zn)，n＝1,2…,N-1,N；
S2, converting the coordinate value into a unique corresponding characteristic value within 0-1, controlling the gradient distribution of the characteristic value within 0-1 by using a Bezier curve, and restraining discrete points to present gradient distribution;
s3, converting the characteristic value into an actual coordinate value, reconstructing a space coordinate of the discrete point, accessing a Voronoi3D calculator, and dividing the original space to generate a Voronoi subspace;
s4, exploding the subspaces, extracting boundary lines of the subspaces, automatically capturing multiple mark points with equal distances on the boundary lines, setting a scaling factor to specifically select the mark points, and forming mark surfaces by the mark points;
s5, correlating the selected mark face, reconstructing a new boundary of the subspace, generating an initial polyhedral stent by inclusion, and adjusting a scaling factor to control the volume fraction of the whole stent;
s6, subdividing the lattice epidermis of the stent, and softening the surface and the nodules of the stent.
Preferably, the bone-like scaffold structure designed by the bone-like scaffold structure design method based on the Veno diagram is prepared by 3D printing.
Preferably, the bone-like scaffold structure design method based on the voronoi diagram mainly comprises the following steps:
s1, creating a three-dimensional space, placing N random discrete points, and extracting the coordinates (X) of each random pointn,Yn,Zn)(n＝1,2…,N-1,N)。
The S1 specifically includes: creating a solid model in the Rhino, randomly placing discrete points in space by using a Populate 3D command in Grasshopper, setting the number N and the seed number S of the discrete points, and extracting coordinate values (X) of all the discrete points by using a Deconstruct commandn,Yn,Zn)，n＝1,2…,N-1,N。
And S2, converting the coordinate values into unique corresponding characteristic values within 0-1, controlling the gradient distribution of the characteristic values within 0-1 by using a Bezier curve, and restraining discrete points to present the gradient distribution.
The S2 specifically includes: for X, Y, Z coordinate values of all discrete points, converting a Construct Domain command and a Bounds command into uniquely corresponding values in 0-1, and respectively establishing a characteristic value set of X coordinates, Y coordinates and Z coordinates of the discrete points. And drawing a Bezier curve path by using a Mapper instruction, and respectively adjusting the distribution density degree of the characteristic value sets of the X coordinate, the Y coordinate and the Z coordinate within a value range of 0-1, so that the distribution condition of the characteristic values within a range of 0-1 presents a gradient trend, namely the gradient distribution of discrete points is controlled to realize the gradient distribution of the support.
The Bessel curve B (t) ═ Po(1-t)3+3P1t(1-t)2+3P2t2(1-t)+P3t3,t∈[0,1]From four control points Po、P1、P2、P3And controlling, wherein the Bezier curve can be changed by adjusting the position of the control point, so that the distribution density of the characteristic value of the coordinates of the discrete point X, Y, Z in a value of 0-1 is adjusted.
And S3, converting the characteristic value into an actual coordinate value, reconstructing a space coordinate of the discrete point, accessing the discrete point into a Voronoi3D calculator, and dividing the original space to generate the Voronoi subspace.
The S3 specifically includes: mapping the adjusted X, Y, Z characteristic value set by using a RemapNumbers instruction, then reconstructing a discrete Point coordinate by using a Construct Point command according to the X, Y, Z characteristic value set, simultaneously accessing the original limited space and the reconstructed discrete Point to a Voronoi3D instruction, and generating a regulated and distributed Veno subspace.
S4, exploding the subspaces, extracting boundary lines of the subspaces, automatically capturing multiple mark points with equal distances on the boundary lines, setting a scaling factor to specifically select the mark points, and forming mark surfaces by the mark points.
The S4 specifically includes: and (3) exploding each subspace by using Deconstruct Brep, extracting faces and angular points, equally dividing a plurality of equal parts of mark points by using an Average command, setting a scaling factor by using a Scale command, and selecting the mark points and mark faces.
And S5, correlating the selected mark surface, reconstructing a new boundary of the subspace, generating an initial polyhedral stent by inclusion, and adjusting the scaling factor to control the volume fraction of the whole stent.
The S5 specifically includes: and associating all the marked point surfaces by using the Merge command, reconstructing each surface of the subspace by using the Construct Mesh, and generating the bracket of the bracket by using the space sandwiched between the reduced subspace and the subspace interface.
S6, subdividing the lattice epidermis of the stent, and softening the surface and the nodules of the stent.
The S6 specifically includes: combining a plurality of grid vertexes which are combined together into a single node by using a Join messages and Weld command, unifying the normal direction of a grid surface by using a MeshUnifyNormals command, subdividing the surface of the grid of the support by using a Catmull-ClarkSubdivision command, and softening the surface and the nodes of the support.
Example 1
A bone-like support structure design method based on a Voronoi diagram comprises the following steps:
in step S1, a three-dimensional space of 20mm × 20mm × 40mm is created, and discrete points are randomly placed in the space using a Populate 3D command, the number of discrete points beingN is 100, the seed S is 1, and coordinate values (X) of the discrete point are extracted by a Deconstruct command1,Y1,Z1)～(X100,Y100,Z100). As shown in fig. 2(a), fig. 2(a) represents randomly discrete points distributed in a finite space.
In step S2, two Construct Domain commands are used to extract the X coordinates and the Y coordinates of 100 discrete points, the Bounds commands are used to convert the coordinate values into uniquely corresponding values in 0-1, a characteristic value set of the X coordinates and a characteristic value set of the Y coordinates are established, two Mapper commands are used to pull a bezier curve path, and the distribution density of the discrete points X coordinates and Y coordinates characteristic values between 0-1 values is adjusted, so that the discrete points exhibit spatial distribution with sparse core and dense shell. The coordinates of the control points of the Bezier curve are respectively Po(0，0)、P1(0.2，0.8)、P2(0.8，0.2)、P3(1, 1), as shown in FIG. 2(b), FIG. 2(b) shows the discrete points after constraint distribution.
In step S3, the adjusted X, Y feature value set is mapped by using the Remap Numbers instruction, and discrete Point coordinates are reconstructed by using the Construct Point command according to the X, Y feature value set and the original Z value set. The original space and the reconstruction point are accessed into a Voronoi3D instruction to generate a Voronoi subspace after the regulation distribution, as shown in FIG. 2(c), and the generated Voronoi subspace is shown in FIG. 2 (c).
In step S4, 100 subspaces are exploded by Deconstruct Brep, faces and corners are extracted, Average commands are used to divide the mark points and mark faces equally, Scale commands are used to set the scaling factor F to 0.25, and corresponding mark points and mark faces are selected, as shown in fig. 2(d), fig. 2(d) shows the mark points selected by the scaling factor.
In step S5, the Merge command is used to associate all the mark point faces, the Construct Mesh is used to reconstruct each face of the subspace, and the space sandwiched between the reduced subspace and the subspace interface generates an initial polyhedral scaffold of the scaffold, as shown in fig. 2(e), fig. 2(e) represents the initial polyhedral scaffold of the scaffold.
In step S6, Mesh documents and Weld commands are used to merge the combined Mesh vertices into a single node, Mesh UnifyNormals commands are used to unify the normal directions of the Mesh surfaces, and Catmull-Clark Subdivision commands are used to subdivide the stent Mesh surface, thereby softening the stent surface and the nodes, as shown in fig. 2(f), fig. 2(f) shows the softened stent.
A preparation method of a bone-like support structure based on a Voronoi diagram is characterized in that a designed bone-like support structure is output to STL file format and input to three-dimensional model printing software for processing, and the support structure is printed in 3D.
The scaffold volume fraction obtained by the above procedure was 17.27%.
The scaling factors F-0.40 and F-0.55 were adjusted to control the volume fraction of the scaffold as a whole, and the resulting scaffold volume fractions were 24.46% and 31.36% respectively, with the other parameters and settings being the same.
As shown in fig. 4(a), the solid graph of the stent is represented by F ═ 0.25, F ═ 0.40, and F ═ 0.55 from left to right.
Example 2
A bone-like support structure design method based on a Voronoi diagram comprises the following steps:
in step S1, a space of 20mm × 20mm × 40mm is created, discrete points are randomly placed in the space using a popup 3D command, the number N of discrete points is 500, the seed S is 5, and coordinates of the discrete points are extracted using a Deconstruct command (X is X)1,Y1,Z1)～(X500,Y500,Z500) Fig. 3(a) shows randomly discrete points distributed in a finite space, as shown in fig. 3 (a).
In step S2, the X coordinates and the Y coordinates of 500 discrete points are extracted by using two Construct Domain commands, the coordinate values are converted into uniquely corresponding values in 0 to 1 by using Bounds commands, a characteristic value set of the X coordinates and a characteristic value set of the Y coordinates are established, a bezier curve path is drawn by using two Mapper instructions, and the distribution density of the characteristic values of the X coordinates and the Y coordinates of the discrete points between 0 to 1 values is adjusted, so that the discrete points exhibit spatial distribution with sparse cores and dense shells. The coordinates of the control points of the Bezier curve are respectively Po(0，0)、P1(0.8，0.2)、P2(0.2，0.8)、P3(1，1) As shown in fig. 3(b), fig. 3(b) shows the discrete points after the distribution is constrained.
In step S3, the adjusted X, Y feature value set is mapped by using the Remap Numbers instruction, and discrete Point coordinates are reconstructed by using the Construct Point command according to the X, Y feature value set and the original Z value set. The original space and the reconstruction point are accessed into a Voronoi3D instruction to generate a Weinuo subspace after the regulation distribution, as shown in FIG. 3(c), and the generated Weinuo subspace is shown in FIG. 3 (c).
In step S4, 500 subspaces are exploded by Deconstruct Brep, faces and corners are extracted, Average commands are used to divide the mark points and mark faces equally, Scale commands are used to set the scaling factor F to 0.25, and corresponding mark points and mark faces are selected, as shown in fig. 3(d), fig. 3(d) shows the mark points selected by the scaling factor.
In step S5, the Merge command is used to associate all the mark point faces, the Construct Mesh is used to reconstruct each face of the subspace, and the space sandwiched between the reduced subspace and the subspace interface generates an initial polyhedral scaffold of the scaffold, as shown in fig. 3(e), fig. 3(e) represents the initial polyhedral scaffold of the scaffold.
In step S6, Mesh documents and Weld commands are used to merge the combined Mesh vertices into a single node, Mesh UnifyNormals commands are used to unify the normal directions of the Mesh surfaces, and Catmull-Clark Subdivision commands are used to subdivide the stent Mesh surface, thereby softening the stent surface and the nodes, as shown in fig. 3(f), fig. 3(f) shows the softened stent.
A preparation method of a bone-like support structure based on a Voronoi diagram is characterized in that a designed bone-like support structure is output to STL file format and input to three-dimensional model printing software for processing, and the support structure is printed in 3D.
The volume fraction of the scaffold obtained by the steps is 18.07%, and the gradient distribution is g1。
Adjusting the control point of the Bezier curve to be Po(0，0)、P1(0.7，0.3)、P2(0.3，0.7)、P3(1, 1) and Po(0，0)、P1(0.6，0.4)、P2(0.4，0.6)、P3(1, 1) obtaining a gradient size distribution g2、g3The support structure of (1).
As shown in fig. 4(b), the gradient g is 0.25F from left to right1、g2、g3The scaffold entity map of (1).
The above example 1 shows that the scaffold with gradient direction from inside to outside is prepared by the present invention, and the example 2 shows that the scaffold with gradient direction from outside to inside is prepared by the present invention, so that the adjustable gradient distribution of the scaffold from the core to the shell is realized, and the natural structure of trabecula ossis is simulated practically. The two examples aim to illustrate that the invention can rapidly adjust the distribution morphology of the stent by adjusting the Bezier curve, realize gradient distribution in various different modes and fully embody the advantages of the Voronoi diagram in the design of the bionic stent.
It should be understood that although the present description has been described in terms of various embodiments, not every embodiment includes only a single embodiment, and such description is for clarity purposes only, and those skilled in the art will recognize that the embodiments described herein may be combined as suitable to form other embodiments, as will be appreciated by those skilled in the art.
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.
Claims (8)
1. A bone-like support structure design method based on a Voronoi diagram is characterized by comprising the following steps:
s1: creating a three-dimensional space, placing N random discrete points, and extracting coordinate values (X) of each random pointn,Yn,Zn)，n＝1,2…,N-1,N；
S2: converting the coordinate value into a unique corresponding characteristic value within 0-1, controlling the gradient distribution of the characteristic value within 0-1 by using a Bezier curve, and restraining the discrete points to present the gradient distribution;
s3: converting the characteristic value into an actual coordinate value, reconstructing a space coordinate of the discrete point, accessing a Voronoi3D calculator, and dividing the original space to generate a Veno subspace;
s4: exploding subspaces, extracting boundary lines of the subspaces, automatically capturing multiple mark points with equal distances on the boundary lines, setting a scaling factor to specifically select the mark points, and forming a mark surface by the mark points;
s5: associating the selected mark surfaces, reconstructing a new boundary of a subspace, generating an initial polyhedral scaffold by inclusion, and adjusting a scaling factor to control the volume fraction of the whole scaffold;
s6: subdividing the lattice epidermis of the stent, softening the surface and the nodules of the stent.
2. The method for designing a bone-like scaffold structure based on a voronoi diagram according to claim 1, wherein the S1 is specifically: creating a three-dimensional space, randomly placing discrete points in the space, setting the number N of the discrete points and the seed number S, and extracting the coordinate values (X) of all the discrete pointsn,Yn,Zn)，n＝1,2…,N-1,N。
3. The method for designing a bone-like scaffold structure based on a voronoi diagram according to claim 1, wherein the S2 is specifically: and converting X, Y, Z coordinate values of all discrete points into uniquely corresponding values in 0-1, respectively establishing a characteristic value set of an X coordinate, a Y coordinate and a Z coordinate of the discrete points, inputting the characteristic value set into a Bezier curve, respectively adjusting the distribution density of the characteristic value set of the X coordinate, the Y coordinate and the Z coordinate in the 0-1 value, enabling the distribution situation of the characteristic values in the 0-1 interval to present a gradient trend, and controlling the gradient distribution of the discrete points.
4. The method for designing a voronoi diagram-based bone-like scaffold structure according to claim 1, wherein the bezier curve b (t) P in step S2o(1-t)3+3P1t(1-t)2+3P2t2(1-t)+P3t3,t∈[0,1]From four control points Po、P1、P2、P3And controlling, wherein the Bezier curve can be changed by adjusting the position of the control point, so that the distribution density of the characteristic value of the coordinates of the discrete point X, Y, Z in a value of 0-1 is adjusted.
5. The method for designing a bone-like scaffold structure based on a voronoi diagram according to claim 1, wherein the S3 is specifically: and reconstructing a space coordinate of the discrete point according to the adjusted X, Y, Z characteristic value set, and generating a regulated and distributed Veno subspace in the original three-dimensional space according to the reconstructed discrete point.
6. A preparation method of a voronoi diagram-based bone-like scaffold structure, characterized in that the voronoi diagram-based bone-like scaffold structure is designed according to the voronoi diagram-based bone-like scaffold structure design method of any one of claims 1-5.
7. The method of claim 6, wherein the Voronoi diagram-based bone-like scaffold is prepared by 3D printing.
8. A voronoi diagram-based osteoid scaffold, characterized in that the voronoi diagram-based osteoid scaffold is prepared by the voronoi diagram-based osteoid scaffold preparation method of claim 6.
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| CN110974488A (en) * | 2019-12-31 | 2020-04-10 | 吉林大学 | Preparation method of Thiessen polygonal bionic artificial bone structure based on fractured bone surface |
| CN112220588A (en) * | 2020-10-15 | 2021-01-15 | 北京理工大学 | Method and system for generating controllable gradient bone tissue engineering scaffold |
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