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 PDF

Info

Publication number
CN105608744A
CN105608744A CN201510989164.6A CN201510989164A CN105608744A CN 105608744 A CN105608744 A CN 105608744A CN 201510989164 A CN201510989164 A CN 201510989164A CN 105608744 A CN105608744 A CN 105608744A
Authority
CN
China
Prior art keywords
cos
utilize
value
tetrahedral
scan line
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201510989164.6A
Other languages
Chinese (zh)
Other versions
CN105608744B (en
Inventor
余泽云
范树迁
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chongqing Institute of Green and Intelligent Technology of CAS
Original Assignee
Chongqing Sailing Science And Technology Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chongqing Sailing Science And Technology Co Ltd filed Critical Chongqing Sailing Science And Technology Co Ltd
Priority to CN201510989164.6A priority Critical patent/CN105608744B/en
Publication of CN105608744A publication Critical patent/CN105608744A/en
Application granted granted Critical
Publication of CN105608744B publication Critical patent/CN105608744B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/30Polynomial surface description

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

The internal void method for designing of the imitative cycle minimal surface based on tetrahedral grid
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.
CN201510989164.6A 2015-12-24 2015-12-24 The internal void design method of imitative period minimal surface based on tetrahedral grid Active CN105608744B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201510989164.6A CN105608744B (en) 2015-12-24 2015-12-24 The internal void design method of imitative period minimal surface based on tetrahedral grid

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201510989164.6A CN105608744B (en) 2015-12-24 2015-12-24 The internal void design method of imitative period minimal surface based on tetrahedral grid

Publications (2)

Publication Number Publication Date
CN105608744A true CN105608744A (en) 2016-05-25
CN105608744B CN105608744B (en) 2018-10-02

Family

ID=55988655

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201510989164.6A Active CN105608744B (en) 2015-12-24 2015-12-24 The internal void design method of imitative period minimal surface based on tetrahedral grid

Country Status (1)

Country Link
CN (1) CN105608744B (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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
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

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102087676B (en) * 2010-12-13 2012-07-04 上海大学 Pore network model (PNM)-based bionic bone scaffold designing method
CN102426711A (en) * 2011-09-08 2012-04-25 上海大学 Three-dimensional porous bone scaffold discrete model construction method capable of controlling discrete interval
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

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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
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

Also Published As

Publication number Publication date
CN105608744B (en) 2018-10-02

Similar Documents

Publication Publication Date Title
Zhou et al. Topology repair of solid models using skeletons
Pahr et al. From high-resolution CT data to finite element models: development of an integrated modular framework
CN102184567B (en) Method for constructing three-dimensional blood vessel model based on ball B-spline curve
CN106373168A (en) Medical image based segmentation and 3D reconstruction method and 3D printing system
Anastasiou et al. 3D printing: Basic concepts mathematics and technologies
Holdstein et al. Three-dimensional surface reconstruction using meshing growing neural gas (MGNG)
US8384716B2 (en) Image processing method
CN102087676A (en) Pore network model (PNM)-based bionic bone scaffold designing method
CN107615279B (en) Virtual three-dimensional model generation based on virtual hexahedron model
CN107391784A (en) A kind of cancellous bone loose structure modeling method based on topological optimization technology
CN105608744A (en) Internal pore design method of simulation periodic minimum surface based on tetrahedral mesh
CN104657519B (en) The method for establishing the statistical average model of dento enamel junction
CN105740533B (en) CT gray scale-material properties assignment the finite element modeling method orthopedic for osteotomy
Pasko et al. Procedural function-based spatial microstructures
JP2005293021A (en) Triangular mesh generation method using maximum opposite angulation, and program
Raut et al. An approach for patient-specific multi-domain vascular mesh generation featuring spatially varying wall thickness modeling
CN106863785B (en) The preparation method and device of bone model
CN105279794A (en) Reservoir stratum rock core multi-organizational model constructing method based on Micro-CT technology
KR101978316B1 (en) 3D volume mesh generation method for arterial blood flow dynamics simulation using the mesh morphing technique
Arefin et al. Computational design generation and evaluation of beam-based tetragonal bravais lattice structures for tissue engineering
EP2631877A2 (en) Mesh generating apparatus and method
CN108694282A (en) A kind of grid of ship surface partitioning method and device for Calculation of Hydrodynamic
Guo et al. Efficient collision detection with a deformable model of an abdominal aorta
Li et al. New modeling technique for bionic space grid structures
Rodrigues et al. A user-editable C1-continuous 2.5 D space deformation method for 3D models

Legal Events

Date Code Title Description
PB01 Publication
C06 Publication
SE01 Entry into force of request for substantive examination
C10 Entry into substantive examination
TA01 Transfer of patent application right

Effective date of registration: 20180115

Address after: No. 266, fangzheng Avenue, water and soil Town, Beibei District, Chongqing City, Chongqing

Applicant after: Chongqing Institute of Green and Intelligent Technology of the Chinese Academy of Sciences

Address before: 400714 Beibei City, soil and water district, the town of Fangzheng Avenue, No. 256

Applicant before: CHONGQING SAILING SCIENCE AND TECHNOLOGY CO., LTD.

TA01 Transfer of patent application right
GR01 Patent grant
GR01 Patent grant