CN104462723A - Personalized interbody fusion cage design method based on topological optimization and bony reconstitution simulation - Google Patents
Personalized interbody fusion cage design method based on topological optimization and bony reconstitution simulation Download PDFInfo
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Abstract
The invention relates to a personalized interbody fusion cage design method based on topological optimization and bony reconstitution simulation. The method includes the steps of conducting CT/MRI scanning on a vertebral body, segmenting a CT/MRI continuous cross-sectional image of the vertebral body, establishing a three-dimensional model, establishing a finite element model through the substeps of grid dividing and smoothing, material assignment, boundary condition setting, mechanical loading and the like, conducting the topological optimization design on an interbody fusion cage through a density-variable method, and evaluating whether the design is reasonable or not by conducting bony reconstitution numerical analogue simulation on the vertebral body and the cage bone filling area according to the adaptation bony reconstitution theory on the basis of the strain energy density.
Description
Technical field
The present invention relates to a kind of personalized Invasive lumbar fusion device method for designing, more particularly relate to a kind ofly carry out the method for personalized design based on topological optimization and bone remoulding simulation evaluation to Invasive lumbar fusion device.
Background technology
In clinical interbody fusion, implantation, size, spatial form and the neurotrosis of Invasive lumbar fusion device, implant stability, intervertebral bone graft amount is closely related.But, because differing greatly of physiological parameter and internal milieu individualized feature, standardization, mass, the Invasive lumbar fusion device of serializing production and the interaction of human body are difficult to optimization, cause some Invasive lumbar fusion devices to enter after in body, excessive wear, fatigue failure etc. occur.Therefore, the design of Invasive lumbar fusion device must be personalized.
At present, Invasive lumbar fusion device is on the market mostly shape of threads fusion device and box-shaped fusion device, and its outside is entity, and centre is the hole of up/down perforation, in order to fill bone graft.In interbody fusion, BAK on the one hand requirement will have enough mechanical strengths to maintain disc height, and namely entity part volume is large as far as possible, to provide enough mechanical support; Requirement can be convenient to merge by implantable bone as much as possible on the other hand, and namely entity part volume is little as far as possible, and the hole for implantable bone is enough large.In order to solve above-mentioned contradiction, be necessary that introducing Topology Optimization Method is optimized design to fusion device.
Finite element simulation evaluation study for Invasive lumbar fusion device is existing a lot, and the instant stress after fusion device implantation is substantially all paid close attention in existing research.But the effect at once produced in the fusion device of mechanics better performances or the long-term after surgery rejuvenation of modes of emplacement under state is not necessarily better.In fact fusion device can change original biomechanical environment after implanting, thus brings out bone remoulding process, causes the change of sclerotin around implant.In a lot of situation, mechanical signal can stimulate the formation of bone in suitable situation, and bone tissue can show healing ability and carry out restore funcitons.Therefore, in order to better evaluate the long-term effect of fusion device, it is necessary for adding in the evaluation of Invasive lumbar fusion device finite element simulation by bone remoulding theory.
Summary of the invention
In order to meet the personalized design demand of current most Invasive lumbar fusion device, the invention discloses a kind of Invasive lumbar fusion device method for designing, described method is by utilizing CT/MRI 3-dimensional reconstruction technology, under digital virtual environment, go back the anatomical structure feature of prevertebrate, use Topology Optimization Method and bone remoulding emulation to carry out personalized design and the evaluation of Invasive lumbar fusion device on this basis.
The present invention according to actual needs, the view data such as CT/MRI are imported in developed software AdvancedCageDesigner, automatically carry out the segmentation of spinal vertebral, set up the geometric model of backbone, automatically carry out the FEM meshing of model, then adopt Topology Optimization Method to carry out the personalized design of Invasive lumbar fusion device, finally adopt bone remoulding emulation mode to carry out assay and improvement to designed fusion device.
The invention discloses a kind of personalized Invasive lumbar fusion device method for designing, specifically comprise the following steps:
1) image acquisition and pre-service
Vertebra is carried out CT/MRI scanning, and the raw data of the vertebra then CT/MRI scanning obtained to import in software and carries out auto-sequencing and judgement according to the numbering of image to image.Then medium filtering, gaussian filtering and binary conversion treatment are carried out to the CT image imported.
2) foundation of centrum Iamge Segmentation and three-dimensional model
First manually select an initial lamella to start cutting procedure at software level face view area, the centrum general profile of the initial lamella of manual drawing, then adopt Level Set Method to obtain the centrum precise boundary of initial lamella through iteration.After this cutting procedure will be that starting point carries out cutting operation from upper and lower both direction to all lamellas with reference layer.Because the amplitude of variation of centrum CT image adjacent sheets target is less, thus can the segmentation result gained profile of handy processed lamella as the initial profile of adjacent sheets, then use Level Set Method to obtain the precise boundary of all centrums.Finally, manual method can be adopted to revise obtained profile.For the result of segmentation, adopt object plotting method to draw, and show in the window.
3) foundation of finite element model
The Meshing Method based on voxel is adopted to carry out stress and strain model to centrum.The fusion device model of design to be optimized can be existing fusion device model on the market, also can be the original fusion device model that system generates automatically.The region that the original fusion device model that system generates automatically surrounds according to fibrous ring in intervertenral space is formed.For the stress and strain model of fusion device, the original fusion device model that system generates automatically adopts the Meshing Method based on voxel to carry out stress and strain model, and existing fusion device model directly imports the fusion device grid model of inp form on the market.
After completing FEM meshing, corresponding material properties and boundary condition are set, apply corresponding Mechanical loading, complete the foundation of finite element model.
4) topology optimization design
The target of Invasive lumbar fusion device topology optimization design is under given design volume mark constraint, makes strain energy minimum (namely rigidity is maximum).Density variable method is adopted to carry out topology optimization design.The basic thought of density variable method is the material artificially having introduced a kind of imaginary variable density, relation between its relative density and elastic modulus is also supposition, the relative density of each unit is design variable, structural Topology Optimization problem is converted into material Optimal Distribution design problem.Therefore, be m at design volume mark
fconstraint condition under, the topology optimization design of Invasive lumbar fusion device can represent as follows:
Objective function:
Constraint condition:
Wherein x
ifor unit relative density, be independent variable, C (x) is strain energy, d
ifor element displacement, k
0for initial cell stiffness matrix, v
ifor unit volume, V
0for initial volume, V (x) is volume after design, and N is unit number, m
ffor volume fraction.X
ivalue between (0,1), x
irepresent this unit close to 0 need remove, x
ineed to retain close to 1 representative.
After setting up above-mentioned Optimized model, adopt Method of Optimality Criteria solving-optimizing model.Method of Optimality Criteria is one indirectly optimization method, its not direct optimization object function, but based on Kuhn-Tucker condition, is formed the update scheme of design variable, complete solving of Optimized model by iteration by structure Lagrange function.After having solved of Optimized model, by x
iremove close to the unit of 0, realize the optimal design of fusion device.
5) bone remoulding simulation evaluation
When mechanical environment residing for bone changes, bone tissue can produce adaptive change, adopts the adaptability bone remoulding theory based on strain energy density to fill bone region to centrum and fusion device and carries out bone remoulding Numerical Simulation.
In modeling effort, adopt the bone remoulding governing equation of piecewise function form to carry out analyses and prediction bone remoulding result, the change of bone density is defined as the function that bone remoulding stimulates, formula is:
Wherein Δ ρ is bone density increment; B is bone remoulding rate constant, gets empirical value 1 (g/cm3)/MPa; U is bone remoulding values, and the strain energy density namely in unit mass, is expressed as:
Wherein ε is von Mises strain tensor, and σ is von Mises stress tensor, and ρ is bone density, and s is the reference width (in inertia area, ostosis and bone information are mobile equilibrium, and bone density does not change) of inertia area, gets empirical value 0.1; K is bone remoulding parametric excitation, gets empirical value 0.004; Δ t is time increment.
The flow process of bone remoulding emulation is: first from finite element model, calculate quantity of stimulus U and strain energy density, and then judge the relation of U and bone uptake and bone information threshold value.Judge rear numerical evaluation of carrying out bone density according to corresponding reconstructed formula.If reach convergence state, termination of iterations through the final bone density value of successive ignition, do not restrain, the material properties upgrading bone continues to calculate until bone density reaches convergence.In the renewal of bone tissue material properties, the formula between bone density and elastic modulus is:
E＝3790·ρ
3
Wherein E unit is MPa, and the unit of corresponding ρ is g/cm3.
Determine that whether design is reasonable according to the result of bone remoulding emulation, for irrational design, turn back to step 4 and design is modified.The personalized Invasive lumbar fusion device of final design is with STL formatted output.
The present invention's personalized Invasive lumbar fusion device method for designing advantage comprises:
1, consider the fusion device designing requirement that rigidity is maximum when volume is little as far as possible in the design comprehensively, topological optimization technology is incorporated in the personalized design of Invasive lumbar fusion device.
2, bone remoulding theory is added in the evaluation of Invasive lumbar fusion device finite element simulation, the long-term effect of fusion device in interbody fusion can better be evaluated;
3, method for designing is simple and practical, and the running time is short, is easy to clinical expansion.
Accompanying drawing explanation
Fig. 1 is that personalized Invasive lumbar fusion device according to an embodiment of the invention designs concrete implementing procedure figure;
Fig. 2 is the concrete implementing procedure figure of topological optimization according to an embodiment of the invention;
Fig. 3 is that bone remoulding according to an embodiment of the invention emulates concrete implementing procedure figure;
Fig. 4 is the initial Invasive lumbar fusion device model of one embodiment of the present of invention;
Fig. 5 is the centrum finite element model being implanted with Invasive lumbar fusion device of one embodiment of the present of invention;
Fig. 6 is the Invasive lumbar fusion device model relative density distribution plan after the topological optimization of one embodiment of the present of invention;
Fig. 7 is the Invasive lumbar fusion device model after the optimization of one embodiment of the present of invention.
Embodiment
As shown in Figure 1, be that personalized Invasive lumbar fusion device according to an embodiment of the invention designs concrete implementing procedure figure, comprise the following steps:
Step 101: image acquisition and pre-service.
Spiral CT scan is carried out to vertebra, obtains vertebra CT image.The raw image data of the vertebra of acquisition to be imported in software and according to the numbering of image, auto-sequencing and judgement to be carried out to image.Then medium filtering, gaussian filtering and binary conversion treatment are carried out to the CT image imported.
Step 102: the foundation of centrum Iamge Segmentation and three-dimensional model.
First manually select an initial lamella to start cutting procedure at software level face view area, the centrum general profile of the initial lamella of manual drawing, then adopt Level Set Method to obtain the centrum precise boundary of initial lamella through iteration.After this cutting procedure will be that starting point carries out cutting operation from upper and lower both direction to all lamellas with reference layer.Because the amplitude of variation of centrum CT image adjacent sheets target is less, thus can the segmentation result gained profile of handy processed lamella as the initial profile of adjacent sheets, then use Level Set Method to obtain the precise boundary of all centrums.Finally, manual method can be adopted to revise obtained profile.For the result of segmentation, adopt object plotting method to draw, and show in the window.
Step 103: the foundation of finite element model.
The Meshing Method based on voxel is adopted to carry out stress and strain model to centrum.First by the different coded representation of the pixel of each several part; Then adjacent for levels 8 pixels are connected into 1 voxel as node, remove the voxel of redundancy, using the hexahedral element of remaining voxel as eight nodes.The pixel coder of eight nodes of the unit in model surface and different materials interface is different, now adopt the method for mirror image subdivision that each border hexahedral element is decomposed into 5 tetrahedron elements, then carry out the level and smooth of interface by the node of these tetrahedron elements mobile; In order to reduce calculated amount, some unit consistent for material will merge as required.
The fusion device model of design to be optimized can be existing fusion device model on the market, also can be the original fusion device model that system generates automatically.The region that the original fusion device model that system generates automatically surrounds according to fibrous ring in intervertenral space is formed.The initial Invasive lumbar fusion device model that the system being illustrated in figure 4 one embodiment of the present of invention generates automatically.For the stress and strain model of fusion device, the original fusion device model that system generates automatically adopts the Meshing Method based on voxel to carry out stress and strain model, and existing fusion device model directly imports the fusion device grid model of inp form on the market.
The elastic modulus of range site node densitometer calculated unit, arranges model thickness of cortex of bone and Minor articulus friction factor, supposes that cancellous bony material is isotropy, adopts face-face to contact between Invasive lumbar fusion device with centrum.The all degree of freedom of lower soleplate of hypocentrum are all fixed, and choose the upper soleplate central point R of centrum, by applying downward pressure simulation centrum load-bearing on R, apply torque simulation anteflexion, after stretch, lateral bending, torsion.By above-mentioned steps, complete the foundation (Fig. 5) of the centrum finite element model being implanted with Invasive lumbar fusion device.
Step 104: topology optimization design.
The target of Invasive lumbar fusion device topology optimization design is under given design volume mark constraint, makes strain energy minimum (namely rigidity is maximum).Adopt density variable method to carry out building topology Optimized model, adopt Method of Optimality Criteria solving-optimizing model.
As shown in Figure 2, be the concrete implementing procedure figure of topological optimization according to an embodiment of the invention, step is as follows:
A), be first call in the finite element model that step 103 sets up, and the volume fraction of In-put design;
B), adopt voxel finite element model to solve conventional algorithm EBE-PCG (element by element precon-ditioned conjugate gradient) algorithm to solve, obtain transposed matrix d;
C), transposed matrix d as input, obtain strain energy change rate dc;
D), dc as input parameter, the unit relative density x after utilizing Method of Optimality Criteria to obtain renewal;
E), after x meets the requirements of precision, stop circulation, finishing iteration, otherwise forward step b to) continue circulation;
F) the rear unit relative density x of optimization and distribution plan thereof, is exported.A fructufy of the Invasive lumbar fusion device model relative density distribution plan after topological optimization is such as shown in Fig. 6.
To the element deletion of rear unit relative density close to 0 be optimized, the Invasive lumbar fusion device model (Fig. 7) after being optimized.
Step 105: bone remoulding simulation evaluation.
Adopt the adaptability bone remoulding theory based on strain energy density to fill bone region to centrum and fusion device and carry out bone remoulding Numerical Simulation.In modeling effort, the bone remoulding governing equation of piecewise function form is adopted to carry out analyses and prediction bone remoulding result.
As shown in Figure 3, that bone remoulding according to an embodiment of the invention emulates concrete implementing procedure figure, step is as follows: first from finite element model, calculate quantity of stimulus U and strain energy density, and then judge the relation of U and bone uptake and bone information threshold value, judge rear numerical evaluation of carrying out bone density according to corresponding reconstructed formula, if reach convergence state, termination of iterations through the final bone density value of successive ignition, do not restrain, the material properties upgrading bone continues to calculate until bone density reaches convergence.
Determine that whether design is reasonable according to the result of bone remoulding emulation, for irrational design, turn back to step 104 and design is modified.The personalized Invasive lumbar fusion device of final design is with STL formatted output.
The design of the personalized lumbar intervertebral fusion device of embodiment
L3-L4 lumbar vertebrae is carried out Spiral CT scan, sweep parameter: thickness 0.63mm, layer is apart from 0.63mm, bulb voltage 120kV, and electric current 225mAs, resolution 512*512pxl, obtain 150 lumbar vertebrae CT images.Medium filtering, gaussian filtering and binary conversion treatment is carried out by these 150 CT data importing softwares.
First a picture with centrum and vertebral arch is manually selected as initial lamella to start cutting procedure at software level face view area, the centrum general profile of the initial lamella of manual drawing, then adopts Level Set Method to obtain the centrum precise boundary of initial lamella through iteration.After this cutting procedure will be that starting point carries out cutting operation from upper and lower both direction to all lamellas with reference layer.For the result of segmentation, adopt object plotting method to draw, and show in the window.
The region that the fusion device model of design to be optimized adopts system to surround according to fibrous ring in intervertenral space is formed (Fig. 4) automatically.The fusion device model of Meshing Method to centrum and design to be optimized based on voxel is adopted to carry out stress and strain model.Arranging Minor articulus friction factor is 0.1, supposes that cancellous bony material is isotropy, adopts face-face to contact between Invasive lumbar fusion device with centrum.The all degree of freedom of lower soleplate of L4 centrum are all fixed, and choose the upper soleplate central point R of L3 centrum, by applying 400N downward pressure simulation centrum load-bearing on R, apply 10N-m torque simulation anteflexion, after stretch, lateral bending, torsion.By above-mentioned steps, complete the foundation (Fig. 5) of the centrum finite element model being implanted with Invasive lumbar fusion device.
Setting volume fraction is 40%, and the volume of the Invasive lumbar fusion device after namely optimizing is 40% before optimizing.Adopt density variable method to carry out building topology Optimized model, adopt Method of Optimality Criteria solving-optimizing model, the unit relative density distribution plan (Fig. 6) after being optimized.To the element deletion of rear unit relative density close to 0 be optimized, the Invasive lumbar fusion device model (Fig. 7) after being optimized.Adopt the adaptability bone remoulding theory based on strain energy density to fill bone region to centrum and the fusion device after optimizing and carry out bone remoulding Numerical Simulation, determine that whether design is reasonable, for irrational design, turn back to step 104 and design is modified.The personalized Invasive lumbar fusion device of final design is with STL formatted output.
Should be understood that, just to illustrate but not determinate in the above description described and carry out the present invention in illustrating, and do not depart from as appended claims under the prerequisite of the present invention that limits, can various change, distortion be carried out to above-described embodiment and/or revise.
drawing reference numeral explanation
The foundation of 101, image acquisition and pre-service 102, centrum Iamge Segmentation and three-dimensional model
103, finite element model set up 104, topology optimization design
105, bone remoulding simulation evaluation.
Claims (5)
1., based on the personalized Invasive lumbar fusion device method for designing that topological optimization and bone remoulding emulate, it is characterized in that comprising the following steps:
1) image acquisition and pre-service: vertebra is carried out CT/MRI scanning, then carries out Image semantic classification by the vertebra raw data that CT/MRI scanning obtains, thus obtains centrum image;
2) foundation of centrum Iamge Segmentation and three-dimensional model: the segmentation being realized centrum image by automatic or manual segmentation, adopts object plotting method to complete reconstruction and the display of centrum three-dimensional model;
3) foundation of finite element model: respectively stress and strain model is carried out to centrum three-dimensional model and Invasive lumbar fusion device model, the material properties of centrum three-dimensional model each several part, boundary condition and Mechanical loading are set, complete the foundation of the centrum finite element model being implanted with Invasive lumbar fusion device model;
4) topology optimization design: under given design volume mark constraint, make model strain energy minimum, complete topology optimization design;
5) bone remoulding simulation evaluation: adopt the adaptability bone remoulding theory based on strain energy density to fill bone region to centrum and fusion device and carry out bone remoulding Numerical Simulation, and design is evaluated.
2. the personalized Invasive lumbar fusion device method for designing based on topological optimization and bone remoulding emulation according to claim 1, is characterized in that, the 1st) Image semantic classification described in step comprises medium filtering, gaussian filtering and binary conversion treatment.
3. the personalized Invasive lumbar fusion device method for designing emulated based on topological optimization and bone remoulding according to claim 1, it is characterized in that, 3rd) in the foundation of centrum finite element model described in step, the concrete steps of stress and strain model are: adopt the Meshing Method based on voxel to carry out stress and strain model to centrum, if the original fusion device model that selective system generates automatically, then the Meshing Method based on voxel is adopted to carry out stress and strain model; If select other existing fusion device model, then it is directly imported the grid model of inp form.
4. the personalized Invasive lumbar fusion device method for designing emulated based on topological optimization and bone remoulding according to claim 1, it is characterized in that, 4th) described in step, the concrete mode of topology optimization design is: adopt density variable method building topology Optimized model, adopts Method of Optimality Criteria solving-optimizing model.
5. the personalized Invasive lumbar fusion device method for designing emulated based on topological optimization and bone remoulding according to claim 1, it is characterized in that, the 5th) bone remoulding Numerical Simulation described in step adopts the bone remoulding governing equation of piecewise function form to carry out forecast analysis bone remoulding result.
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