CN105608744A - Internal pore design method of simulation periodic minimum surface based on tetrahedral mesh - Google Patents
Internal pore design method of simulation periodic minimum surface based on tetrahedral mesh Download PDFInfo
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Abstract
The invention provides an internal pore design method of a simulation periodic minimum surface based on a tetrahedral mesh. The method comprises the steps of (1) extracting an image, (2) generating a tetrahedral mesh, (3) carrying slicing processing, (4) selecting a layer of slicing plane, (5) obtaining scanning lines in particular directions, (6) finding the tetrahedrons T from all scanning line starting points to end points, (7) calculating the intersection starting points A and the intersection end points B of the tetrahedrons T which intersect with each scanning line, (8) establishing a four-variable implicit function by using the four vertices of the tetrahedrons T, (9) comparing a sampling point function value and a set value C, and skipping if the sampling point function value is larger then the set value C, otherwise going to a step (10), (10) carrying a sampling point function value into a 3D printing path, (11) judging whether the processing of the slicing plane is completed or not, outputting the 3D printing path if so, otherwise selecting another slicing plane, and going to the step (5). According to the method, the deficiency of the existing triply periodic minimum surface technology is made up.
Description
Technical field
The present invention relates to technical field of biological materials, be specifically related to a kind of internal void method for designing of the imitative cycle minimal surface based on tetrahedral grid.
Background technology
Biomedical tissue engineering, as an emerging medical technology, is progressively moved towards in actual medical application from laboratory. Its general principle is to utilize a kind of good biocompatibility, 3D support (scaffolds) rational in infrastructure to cultivate normal human tissue cell outward at human body, then the disease damage position of cultured cell and support complex implant into body tissue or organ, with the histocyte natural fusion in vivo of human body self, to reach the object of repairing wound.
An important step in biomedical tissue engineering is to design and manufacture 3D support. This class support need to have the internal void structure of complexity and fully connection grow therein and form functional organization for cell conventionally. It is traditional that to subtract material manufacture method difficult in the time that processing has the geometrical body of complex internal structure. The 3D coming into vogue gradually recent years prints (or increasing material manufacturing technology) provides the method for a feasible manufacture complex internal structure stand, but corresponding support Design method concentrates on three cycle minimal surfaces (TriplyPeriodicMinimalSurfaces or TPMS) technology mostly. This internal void generation technique is based on the single cuboid domain of definition, simplicity of design flexibly but exist several obvious deficiencies: 1,, in the time processing the parts of complex surface shape, we will carry out 3D solid subdivision to parts conventionally. Compared to tetrahedral grid division and optimized algorithm and the software of current maturation, hexahedral mesh subdivision method has reduced flexibility and more difficult standardization. 2, TPMS is defined in the single cuboid domain of definition, and hexahedron in hexahedral mesh may be arbitrarily. May there is very large shape distortion from cuboid to any hexahedral TPMS Function Mapping. 3, in 3D prints, a crucial step is Slicing Algorithm (slicing), calculates a plane and the intersecting area that is printed body surface grid. TPMS is as a kind of implicit expression function representation method, and we do not need clearly to define a huge body surface grid, thereby and only needs each hexahedral crossing corresponding with TPMS of Calculation Plane to determine the region that will print. But plane is with general hexahedral crossing complicated more than plane and tetrahedral crossing situation. This complexity has not only reduced the reliability of algorithm, and has greatly increased calculation cost.
Summary of the invention
The present invention is the deficiency that makes up existing TPMS technology, a kind of implicit expression function representation method of utilizing tetrahedron element has been proposed, greatly improve the applicability that generates the internal void structure of arbitrary surface shape, arrive any hexahedral Function Mapping with respect to cuboid, rule tetrahedron is comparatively succinct to any tetrahedral Function Mapping, and the shape distortion bringing is thus less. The internal void method for designing of the surrounding phase minimal surface (QuadruplyPeriodicMinimalSurfaces or QPMS) based on tetrahedral grid, the concrete steps of employing are as follows:
Step 1: utilize medical imaging and image processing techniques to extract the three-dimensional exterior contour image of patient's diseased region;
Step 2: the inside tetrahedral grid that utilizes tetrahedral grid generation technique generating three-dimensional contour images profile;
Step 3: set 3D Print direction, and three-D profile image is carried out to slicing treatment;
Step 4: one deck slice plane of selected three-D profile image;
Step 5: utilize scanning line method to obtain the scan line of specific direction in selected slice plane;
Step 6: find out all tetrahedron T between scan line origin-to-destination;
Step 7: the crossing starting point A and the crossing terminal B that calculate the each tetrahedron T crossing with scan line;
Step 8: utilize four summits of tetrahedron T, set up quaternary implicit expression function, and utilize this quaternary implicit expression function to calculate the functional value of starting point A to all sampled points of terminal B;
Step 9: sampled point functional value is compared with setting value C, be greater than setting value C and skip, be less than and enter step 10;
Step 10: functional value is less than to that section of scan line that sets value C and counts 3D printing path;
Step 11: judging whether slice plane is disposed, is to export 3D printing path, otherwise, select the next slice plane of three-D profile image, enter step 5.
Wherein said step 8 is specially, by tetrahedral four summits for being made as V1,V2,V3,V4, summit V1To opposite, leg-of-mutton vertical range is d1, the like, we can obtain four vertical range d1,d2,d3,d4, utilizing this four distance values, we can define a quaternary implicit expression function: cos (D1)+cos(D2)+cos(D3)+cos(D4)+cos(D1)cos(D2)cos(D3)cos(D4)=C has defined implicit surface, wherein a D1＝2πk1d1,D2＝2πk2d2,D3＝2πk3d3,D4＝2πk4d4。k1,k2,k3,k4Be four positive integers, determining the periodic function change frequency along four axis directions, when changing k1,k2,k3,k4Or when constant C in step 9, also there is variation in corresponding pore radius and complexity.
Beneficial effect of the present invention is: have at present a lot of effectively algorithms and software to carry out tetrahedral grid subdivision and optimization to the object of arbitrary surfaces shape almost, but three traditional cycle minimal surfaces (TPMS) can not directly be processed the tetrahedron domain of definition. Surrounding phase minimal surface (QPMS) method that the present invention proposes is based upon on tetrahedral grid basis, so can generate easily and effectively the solid geometric pattern with complex internal pore structure. In conjunction with at present popular 3D printing technique and the development of material science gradually, some tissue or objects with natural hole that the method for complex internal pore structure that the present invention proposes can be used for design and copy occurring in nature, and this geometry designs is controlled. The design that a most important application is at present the artificial bone tissue of high emulation and 3D print. Method of the present invention can be used for design and have highly personalized bone profile and the bone tissue of complex internal pore structure, then utilizes the titanium alloy material of current comparative maturity and 3D printing technique to produce the bone object tool that makes children next life. Near normal bone cell adhering to, growing and merging in the artifical bone's support this bone tissue (support) with complex internal pore structure can guide well.
Brief description of the drawings
Fig. 1 is flow chart of the present invention;
Fig. 2 is tetrahedral structural representation in quaternary implicit expression function of the present invention;
Fig. 3 is the space radius structure schematic diagram that in quaternary implicit expression function of the present invention, C equals 0;
Fig. 4 is k in quaternary implicit expression function of the present invention1＝k2＝k3＝k4=3 space radius structure schematic diagram;
Fig. 5 is the space radius structure schematic diagram that in quaternary implicit expression function of the present invention, C equals 0.5.
Detailed description of the invention
Below in conjunction with accompanying drawing, preferred embodiment of the present invention is described in detail, thereby so that advantages and features of the invention can be easier to be it will be appreciated by those skilled in the art that, protection scope of the present invention is made to more explicit defining.
As shown in Figure 1: a kind of internal void method for designing of the imitative cycle minimal surface based on tetrahedral grid, the concrete steps of employing are as follows;
Step 1: input image data (CT, MRI etc.), utilize medical imaging and image processing techniques to extract the three-dimensional exterior contour image of patient's diseased region or wound site, this three-dimensional exterior contour represents with the form of triangular mesh;
Step 2: the inside tetrahedral grid that utilizes tetrahedral grid generation technique generating three-dimensional contour images profile;
Step 3: set 3D Print direction, and three-D profile image is carried out to slicing treatment;
Step 4: the bottom slice plane of selected three-D profile image;
Step 5: utilize scanning line method (scanninglines) to obtain the scan line of a series of specific directions in selected slice plane;
Step 6: find out all tetrahedron T between scan line origin-to-destination;
Step 7: the crossing starting point A and the crossing terminal B that calculate the tetrahedron T crossing with every scan line;
Step 8: utilize four summits of tetrahedron T, set up quaternary implicit expression function, and utilize this quaternary implicit expression function to calculate the functional value of each starting point A to terminal B sampled point; As shown in Figure 2: be specially, by tetrahedral four summits for not being made as V1,V2,V3,V4, summit V1To opposite, leg-of-mutton vertical range is d1, the like, we can obtain four vertical range d1,d2,d3,d4, utilizing this four distance values, we can define a quaternary implicit expression function. Such as:
cos(D1)+cos(D2)+cos(D3)+cos(D4)+cos(D1)cos(D2)cos(D3)cos(D4)=C has defined implicit surface, wherein a D1＝2πk1d1,D2＝2πk2d2,D3＝2πk3d3,D4＝2πk4d4。k1,k2,k3,k4Be four positive integers, determining the periodic function change frequency along four axis directions. As shown in Figures 3 to 5: when changing constant C or k1,k2,k3,k4Time, also there is variation in corresponding pore radius and complexity.
Traditional TPMS technology is to utilize the coordinate figure of three major axes orientations to build a three dimensional implicit function, and different implicit expression functions obtain different pore structures. The implicit expression function definition corresponding such as P-curved surface is:
cos(2πk1x)+cos(2πk2y)+cos(2πk3Z)=C, C is a constant (being related to pore diameter size and porosity) here.
X above, y, z is [0,1]3Arbitrfary point in the domain of definition (square). k1,k2,k3Be three positive integers, determining the periodic function change frequency along three axis directions.
The grid that traditional TPMS and the QPMS of above-mentioned proposition generate is all suitable huge, especially in the time processing real medical data. Such as the skeletal sites of a pathology can extract three-D profile by CT image data conventionally, this three-D profile may include tens thousand of even hundreds thousand of hexahedrons (TPMS) or tetrahedron (QPMS). And each TPMS or QPMS comprise thousands of triangles. So want 3D to print a real tissue of patient or organ, the number of triangles of required processing will be extremely huge, the calculating to computer and storage capacity are formed very big challenge by this. Given this, pith of the present invention is to utilize implicit expression function mode represent three-dimension curved surface and do not need directly it to be described out with triangular mesh, and the 3D that can very effectively process thus the large-scale medical implant with complex internal pore structure prints.
Step 9: sampled point functional value is compared with setting value C, be greater than setting value C and skip, be less than and enter step 10;
Step 10: functional value is less than to that section of scan line that sets value C and counts 3D printing path;
Step 11: judging whether slice plane is disposed, is to export 3D printing path, otherwise, select a slice plane on three-D profile image, enter step 5.
Claims (2)
1. an internal void method for designing for the imitative cycle minimal surface based on tetrahedral grid, is characterized in that, the concrete steps of employing are as follows:
Step 1: utilize medical imaging and image processing techniques to extract the three-dimensional exterior contour image of patient's diseased region;
Step 2: the inside tetrahedral grid that utilizes tetrahedral grid generation technique generating three-dimensional contour images profile;
Step 3: set 3D Print direction, and three-D profile image is carried out to slicing treatment;
Step 4: one deck slice plane of selected three-D profile image;
Step 5: utilize scanning line method to obtain the scan line of specific direction in selected slice plane;
Step 6: find out all tetrahedron T between scan line origin-to-destination;
Step 7: the crossing starting point A and the crossing terminal B that calculate the each tetrahedron T crossing with scan line;
Step 8: utilize four summits of tetrahedron T, set up quaternary implicit expression function, and utilize this quaternary implicit expression function to calculate and open the functional value of an A to terminal B sampled point;
Step 9: sampled point functional value is compared with setting value C, be greater than setting value C and skip, be less than and enter step 10;
Step 10: functional value is less than to that section of scan line that sets value C and counts 3D printing path;
Step 11: judging whether slice plane is disposed, is to export 3D printing path, otherwise, select the next slice plane of three-D profile image, enter step 5.
2. the internal void method for designing of the surrounding phase minimal surface based on tetrahedral grid according to claim 1, is characterized in that: described step 8 is specially, and tetrahedral four summits are made as to V1,V2,V3,V4, summit V1To opposite, leg-of-mutton vertical range is d1, the like, we can obtain four vertical range d1,d2,d3,d4, utilize this four distance values, determine quaternary implicit expression function:
cos(D1)+cos(D2)+cos(D3)+cos(D4)+cos(D1)cos(D2)cos(D3)cos(D4)=C has defined implicit surface, wherein a D1＝2πk1d1,D2＝2πk2d2,D3＝2πk3d3,D4＝2πk4d4，k1,k2,k3,k4Be four positive integers, determining the periodic function change frequency along four axis directions, when changing k1,k2,k3,k4Or when constant C in step 9, also there is variation in corresponding pore radius and complexity.
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| CN108327287A (en) * | 2018-01-16 | 2018-07-27 | 浙江大学 | A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile |
| CN109446549A (en) * | 2018-09-13 | 2019-03-08 | 大连理工大学 | A kind of labyrinth color cap design and implementation methods suitable for 3D printing |
| CN109622958A (en) * | 2018-12-20 | 2019-04-16 | 华中科技大学 | A method of titanium alloy implant is prepared using minimal surface porous structure |
| CN111899346A (en) * | 2020-07-16 | 2020-11-06 | 天津理工大学 | Mathematical modeling method of controllable porous bone tissue engineering scaffold |
| CN115194931A (en) * | 2022-09-14 | 2022-10-18 | 中电建冀交高速公路投资发展有限公司 | Planning method, device and equipment for concrete 3D printing path and storage medium |
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| CN104537164A (en) * | 2014-12-19 | 2015-04-22 | 上海大学 | Integrated system and method for bone defect repair |
| CN105014971B (en) * | 2015-07-31 | 2017-02-01 | 创生医疗器械（中国）有限公司 | 3D printing method |
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| CN108327287A (en) * | 2018-01-16 | 2018-07-27 | 浙江大学 | A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile |
| CN108327287B (en) * | 2018-01-16 | 2019-06-25 | 浙江大学 | A kind of rapid generation of three periods minimal surface 3 D-printing slicing profile |
| CN109446549A (en) * | 2018-09-13 | 2019-03-08 | 大连理工大学 | A kind of labyrinth color cap design and implementation methods suitable for 3D printing |
| CN109446549B (en) * | 2018-09-13 | 2022-09-20 | 大连理工大学 | Design and implementation method of complex-structure colored lampshade suitable for 3D printing |
| CN109622958A (en) * | 2018-12-20 | 2019-04-16 | 华中科技大学 | A method of titanium alloy implant is prepared using minimal surface porous structure |
| CN109622958B (en) * | 2018-12-20 | 2020-06-02 | 华中科技大学 | Method for preparing titanium alloy implant by adopting minimum curved surface porous structure |
| CN111899346A (en) * | 2020-07-16 | 2020-11-06 | 天津理工大学 | Mathematical modeling method of controllable porous bone tissue engineering scaffold |
| CN115194931A (en) * | 2022-09-14 | 2022-10-18 | 中电建冀交高速公路投资发展有限公司 | Planning method, device and equipment for concrete 3D printing path and storage medium |
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