CN107610781A - A kind of union emulation mode based on tissue oxygen atmosphere and mechanical environment - Google Patents
A kind of union emulation mode based on tissue oxygen atmosphere and mechanical environment Download PDFInfo
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Abstract
The invention discloses a kind of union emulation mode based on tissue oxygen atmosphere and mechanical environment, following steps are specifically included：Establish the 3-D geometric model of fracture site；Obtained geometrical model is subjected to mesh generation, establishes bone and the FEM model of poroma；Analysis resolving is carried out to FEM model, solves the inclined strain of fracture area；Stimulated according to power, establish the angiogenic growth model of fracture area；Establish each cell proliferation and differentiation model of fracture area；Establish the oxygen transportation model of fracture area；New material properties in computation organization；Establish the union iteration simulation process of power biological regulation algorithm；Organization material property value according to being calculated judges whether the material properties in tissue reach the material properties value of bone, and completion is emulated if the material properties value of bone is reached, and otherwise updates organization material property value and enters following iteration emulation.
Description
Technical field
It is more particularly to a kind of based on tissue oxygen atmosphere and mechanical environment the present invention relates to biomedical engineering field
Union emulation mode.
Background technology
With the aggravation of development and the aging population of the industries such as traffic, building, cause traffic accident injury, building wound and old age
Patients with osteoporotic bone fracture quickly increases.It has been shown that, get into an accident altogether according to the statistics of traffic accidents of 2015 within 2015
10597358, wherein 98.5% people is by wound；Shown according to Chinese Aged health big data in 2015, osteoporosis
Leapt to common disease, the 7th of frequently-occurring disease.The prevalence of more than 60 years old be 56%, the women incidence of disease be 60%-
70%.Wherein for incidence of fracture close to 1/3rd, annual medical expense needs RMB 15,000,000,000 by most conservative estimation.One
Denier fracture occurs, and heavy financial burden is all brought to society and family.
Fracture is a kind of frequently-occurring wound, and this make it that the research to union mechanism is particularly urgent.Union
Journey is long-term and complex biology repair process, and wherein mechanics factor and biological factor is particularly important.When fracture occurs, bone
Folding part position makes vascular injury cause to fail timely and sufficient offer enough oxygen and nutriment, damage location due to wound
Gradually become anoxic, surrounding tissue starts to degrade.This triggering inflammatory cell, the invasion and attack of macrophage and leucocyte, indicates inflammation
The beginning of disease phase.Meanwhile the Porcine HGF in perihematoma and surrounding tissue and cell factor attraction fibroblast,
Mesenchymal stem cells (mesenchymal stem cells MSCs) and endothelial cell are to wound site.Mesenchymal stem cells MSCs starts to break up, bone
Poroma filling granulation tissue is rolled over, forms cartilage scab.It is aerobic at cortex bone, medulla mesenchyma is dry thin in periosteal region
Born of the same parents directly break up to Gegenbaur's cell.The Gegenbaur's cell of these new formation produces braiding bone matrix (i.e. intermembranous ossification).In anoxic
Fracture region is entreated, mesenchymal stem cells MSCs is divided into cartilage cell and produces cartilage, fracture region mechanically stable first.Blood vessel invades this
Individual cartilaginous areas indicates the beginning of os osseum scab formation stages, and emerging zona vascuiosa carrys out mineralising woven bone caused by Gegenbaur's cell
Matrix sclerous tissues poroma (i.e. endochondral ossification), when poroma bridge fracture gap, reach clinical healing.In last remodelling phase,
Hard scab is by osteoclast and Gegenbaur's cell transformation, progressively substitutes jejune lamellar bone, woven bone and bone and returns to original
Shape, size and intensity.Cause severe depletion of oxygen if fracture site severe ischemic, cell death can be caused, postpone cartilage
The differentiation of cell and Gegenbaur's cell, and union are damaged.Because oxygen participates in multiple basic cell processes, for normal
Union is critically important.The simulation model of current union has the following disadvantages：
(1) material impact of the fracture healing process oxygen atmosphere to tissue inner cell Proliferation, Differentiation is not accounted for.
(2) current model can not be emulated for the specific different types of union of patient's different parts.
(3) selection to fixator is greatly limited, and existing model is emulated just for a kind of fixed form, no
The preferred of fixator can be realized, and then hinders doctor and provides more preferable therapeutic scheme for patient.
The content of the invention
It is an object of the invention to provide it is a kind of based on tissue oxygen atmosphere and mechanical environment union emulation mode,
It is dry thin invention emulates the angiogenic growth situation of fracture area under oxygen atmosphere in tissue and mechanical environment and mesenchyma
Born of the same parents, cartilage cell, Gegenbaur's cell and fibroblastic Proliferation, Differentiation process, simulate the complicated dynamic mistake of union
Journey.
A kind of union emulation mode based on tissue oxygen atmosphere and mechanical environment, comprises the following steps：
Step 1：Establish the 3-D geometric model of fracture site；
Step 2：Obtained geometrical model is subjected to mesh generation, establishes bone and the FEM model of poroma；
Step 3：Assignment is carried out to the material properties of initial time in poroma；
Step 4：Analysis resolving is carried out to FEM model, solves the inclined strain of fracture area；
Step 5：Stimulated according to the power being calculated, establish the angiogenic growth model of fracture area；
Step 6：Establish fracture area cell proliferation and differentiation model, including mescenchymal stem cell Proliferation, Differentiation model, cartilage
Cell proliferation and differentiation model, fibroblast proliferation differentiation model and bone cell proliferation differentiation model；
Step 7：Establish the oxygen transportation model of fracture area；
Step 8：New material properties in computation organization；
Step 9：The union iteration simulation process of power biological regulation algorithm is established according to above step, according to step
The eight organization material property values being calculated judge whether the material properties in tissue reach the material properties value of bone, if reaching bone
Material properties value then emulate completion, otherwise update organization material property value and enter following iteration emulate.
Wherein, in step 1 fracture site 3-D geometric model to establish process as follows：
1) image that multiple forms are DICOM is obtained by medical imaging CT scan,
2) it is then introduced into Mimics softwares and carries out three-dimensional reconstruction,
3) it will be smoothed in the model importing Geomagic softwares after three-dimensional reconstruction and hypostazation operate, obtained
The 3-D geometric model of fracture site.
Wherein, obtained geometrical model is imported into Hypermesh in step 2 and carries out mesh generation, establish the bone of linear elasticity
And the FEM model of poroma.
Wherein, the material properties of initial time are entered as the material properties value of granulation tissue in poroma in step 3.
Wherein, the solution formula that fracture area strains partially in step 4 is as follows：
In formula, εdStrained partially for poroma unit, ε1For the first principal strain in unit, ε2For the second principal strain in unit,
ε3For the 3rd principal strain in unit.
Wherein, step 5 medium vessels growth model is as follows：
In formula, CvesselFor vascular concentration, DvesselFor blood vessel diffusion coefficient in poroma, represent new blood vessel and grown in poroma
Speed, t is the time, and x, y, z is respectively the x-axis of three Cartesian coordinates, and y-axis, z-axis, the diffusion source of angiogenic growth is marrow
At chamber and cortex periosteum.
Wherein, mesenchymal stem cell proliferation differentiation model, chondrocyte proliferation differentiation model, fibroblast among step 6
Proliferation, Differentiation model and bone cell proliferation differentiation model are as follows：
(1) mescenchymal stem cell Proliferation, Differentiation model is：
In formula, CmFor mescenchymal stem cell concentration in poroma unit, DmFor the diffusion coefficient of mescenchymal stem cell in poroma,
FmFor the death rate of mescenchymal stem cell in poroma unit；
(2) chondrocyte proliferation differentiation model is：
In formula, CcFor cartilage cell's concentration in poroma unit, DcFor the diffusion coefficient of cartilage cell in poroma, FcFor poroma
Cartilage cell's death rate in unit；
(3) fibroblast proliferation differentiation model is：
In formula, CfFor fibroblast concentration in poroma unit, DfFor fibroblastic diffusion coefficient, F in poromafFor
Fibroblastic death rate in poroma unit；
(4) bone cell proliferation differentiation model is：
In formula, CbFor poroma unit in-seam cell concentration, DbFor poroma in-seam cellular invasion coefficient, FbFor in poroma unit
Bone cell death rate.
Wherein, the oxygen transportation model of step 7 is as follows：
Qm=qmCmO/KmO (8)
Qc=qcCcO/KcO (9)
Qf=qfCfO/KfO (10)
Qb=qbCbO/KbO (11)
In formula, O be poroma in oxygen concentration, DoxygenFor the diffusion coefficient of oxygen in poroma, QmFor mescenchymal stem cell
Oxygen consumption, QcFor cartilage cell's oxygen consumption, Q in poromafFor fibroblast oxygen consumption, Q in poromabFor osteocyte oxygen consumption, q in poromamFor
The consumption rate of mescenchymal stem cell, KmFor when mescenchymal stem cell consumption rate reaches mescenchymal stem cell maximum consumption rate half
The concentration of oxygen, qcFor the consumption rate of cartilage cell, KcTo reach cartilage cell's maximum consumption rate half when cartilage cell's consumption rate
When oxygen concentration, qfFor fibroblastic consumption rate, KfTo reach the maximum consumption of fibroblast when fibroblast consumption rate
The concentration of oxygen, q during oxygen rate halfbFor the consumption rate of osteocyte, KbTo reach osteocyte maximum consumption rate when osteocyte consumption rate
The concentration of oxygen during half.
Wherein, material properties value is calculated as follows in being organized in step 9：
E=Cmax-Cp/CmaxEg+Cp/CmaxEt (12)
ν=Cmax-Cp/Cmaxνg+Cg/Cmaxνt (13)
In formula, E be unit Young's modulus, CmaxFor cell concentration maximum in unit, CpIt is dense for average cell in unit
Degree, EgFor the modulus of elasticity of granulation tissue, EtFor the Young's modulus value organized in last iterate to calculate, ν is the Poisson of unit
Than νgFor the Poisson's ratio of granulation tissue, νtFor the Poisson's ratio organized in last iterate to calculate.
Wherein, judgment step eight calculates the Young's modulus E whether gained unit Young's modulus E is equal to bone in step 10bone,
If the material properties value in tissue reaches the material properties value of bone, union is completed, and emulation terminates, and otherwise, updates tissue
Material properties value and carry out next iteration emulation.
The beneficial effects of the invention are as follows：The influence of mechanical environment and oxygen atmosphere to union, mould are taken into full account
The growing state of fracture healing process medium vessels is intended, mescenchymal stem cell, cartilage are thin in the supply of oxygen and tissue in tissue
Mescenchymal stem cell in born of the same parents, Gegenbaur's cell, fibroblast metabolism oxygen consumption and tissue, cartilage cell, Gegenbaur's cell, into fiber
The Proliferation, Differentiation process of cell, union this dynamic process is more accurately simulated, take injection stem cell to control for doctor
Treatment mode and the appropriate oxygen environment therapeutic modality of offer provide reference frame.
Brief description of the drawings
Fig. 1 is the flow chart of the union emulation mode based on tissue oxygen atmosphere and mechanical environment.
Embodiment
In order to more specifically describe the present invention, below in conjunction with the accompanying drawings and embodiment to the present invention based on tissue
The union emulation mode of oxygen atmosphere and mechanical environment is described in detail.
As shown in figure 1, a kind of union emulation mode based on tissue oxygen atmosphere and mechanical environment, including it is as follows
Embodiment：
Embodiment one：Establish the 3-D geometric model of fracture site；
Fracture site 3-D geometric model to establish process as follows：
(1) image that multiple forms are DICOM is obtained by medical imaging CT scan,
(2) it is then introduced into Mimics softwares and carries out three-dimensional reconstruction,
(3) it will be smoothed in the model importing Geomagic softwares after three-dimensional reconstruction and hypostazation operate, obtained
To the 3-D geometric model of fracture site；
Embodiment two：It will obtain obtained geometrical model importing Hypermesh progress mesh generations, establish line
The bone of elasticity and the FEM model of poroma；
Embodiment three：Assignment is carried out to the material properties of initial time in poroma, the material of initial time in poroma
Expect the material properties value that attribute assignment is granulation tissue；
Embodiment four：Analysis resolving is carried out to FEM model, solves the inclined strain of fracture area；
The solution formula that fracture area strains partially is as follows：
In formula, εdStrained partially for poroma unit, ε1For the first principal strain in unit, ε2For the second principal strain in unit,
ε3For the 3rd principal strain in unit.
Embodiment five：Stimulated according to the power being calculated, establish the angiogenic growth model of fracture area；
Angiogenic growth model is as follows：
In formula, CvesselFor vascular concentration, DvesselFor blood vessel diffusion coefficient in poroma, represent new blood vessel and grown in poroma
Speed, t is the time, and x, y, z is respectively the x-axis of three Cartesian coordinates, and y-axis, z-axis, the diffusion source of angiogenic growth is marrow
At chamber and cortex periosteum.
Embodiment six：Establish fracture area cell proliferation and differentiation model, including mescenchymal stem cell Proliferation, Differentiation
Model, chondrocyte proliferation differentiation model, fibroblast proliferation differentiation model and bone cell proliferation differentiation model；
Mescenchymal stem cell Proliferation, Differentiation model, chondrocyte proliferation differentiation model, fibroblast proliferation differentiation model
And bone cell proliferation differentiation model is as follows：
(1) mescenchymal stem cell Proliferation, Differentiation model is：
In formula, CmFor mescenchymal stem cell concentration in poroma unit, DmFor the diffusion coefficient of mescenchymal stem cell in poroma,
FmFor the death rate of mescenchymal stem cell in poroma unit；
(2) chondrocyte proliferation differentiation model is：
In formula, CcFor cartilage cell's concentration in poroma unit, DcFor the diffusion coefficient of cartilage cell in poroma, FcFor poroma
Cartilage cell's death rate in unit；
(3) fibroblast proliferation differentiation model is：
In formula, CfFor fibroblast concentration in poroma unit, DfFor fibroblastic diffusion coefficient, F in poromafFor
Fibroblastic death rate in poroma unit；
(4) bone cell proliferation differentiation model is：
In formula, CbFor poroma unit in-seam cell concentration, DbFor poroma in-seam cellular invasion coefficient, FbFor in poroma unit
Bone cell death rate.
Embodiment seven：Establish the oxygen transportation model of fracture area；
Oxygen transportation model is as follows：
Qm=qmCmO/KmO (8)
Qc=qcCcO/KcO (9)
Qf=qfCfO/KfO (10)
Qb=qbCbO/KbO (11)
In formula, O be poroma in oxygen concentration, DoxygenFor the diffusion coefficient of oxygen in poroma, QmFor mescenchymal stem cell
Oxygen consumption, QcFor cartilage cell's oxygen consumption, Q in poromafFor fibroblast oxygen consumption, Q in poromabFor osteocyte oxygen consumption, q in poromamFor
The consumption rate of mescenchymal stem cell, KmFor when mescenchymal stem cell consumption rate reaches mescenchymal stem cell maximum consumption rate half
The concentration of oxygen, qcFor the consumption rate of cartilage cell, KcTo reach cartilage cell's maximum consumption rate half when cartilage cell's consumption rate
When oxygen concentration, qfFor fibroblastic consumption rate, KfTo reach the maximum consumption of fibroblast when fibroblast consumption rate
The concentration of oxygen, q during oxygen rate halfbFor the consumption rate of osteocyte, KbTo reach osteocyte maximum consumption rate when osteocyte consumption rate
The concentration of oxygen during half.
Embodiment eight：New material properties in computation organization；
Material properties value is calculated as follows in tissue：
E=Cmax-Cp/CmaxEg+Cp/CmaxEt (12)
ν=Cmax-Cp/Cmaxνg+Cg/Cmaxνt (13)
In formula, E be unit Young's modulus, CmaxFor cell concentration maximum in unit, CpIt is dense for average cell in unit
Degree, EgFor the modulus of elasticity of granulation tissue, EtFor the Young's modulus value organized in last iterate to calculate, ν is the Poisson of unit
Than νgFor the Poisson's ratio of granulation tissue, νtFor the Poisson's ratio organized in last iterate to calculate.
Embodiment nine：The union iteration simulation process of power biological regulation algorithm is established according to above step,
Whether unit Young's modulus E is equal to the Young's modulus E of bone according to obtained by calculating judgment step eightboneIf the material category in tissue
Property value reach the material properties value of bone, then union is completed, and emulation terminates, and otherwise, more neoblastic material properties value is gone forward side by side
Row next iteration emulates.
Claims (10)
1. a kind of union emulation mode based on tissue oxygen atmosphere and mechanical environment, comprises the following steps：
Step 1：Establish the 3-D geometric model of fracture site；
Step 2：Obtained geometrical model is subjected to mesh generation, establishes bone and the FEM model of poroma；
Step 3：Assignment is carried out to the material properties of initial time in poroma；
Step 4：Analysis resolving is carried out to FEM model, solves the inclined strain of fracture area；
Step 5：Stimulated according to the power being calculated, establish the angiogenic growth model of fracture area；
Step 6：Establish fracture area cell proliferation and differentiation model, including mescenchymal stem cell Proliferation, Differentiation model, cartilage cell
Proliferation, Differentiation model, fibroblast proliferation differentiation model and bone cell proliferation differentiation model；
Step 7：Establish the oxygen transportation model of fracture area；
Step 8：New material properties in computation organization；
Step 9：The union iteration simulation process of power biological regulation algorithm is established according to above step, according to step 8 meter
Obtained organization material property value judges whether the material properties in tissue reach the material properties value of bone, if reaching the material of bone
Material property value then emulates completion, otherwise updates organization material property value and enters following iteration emulation.
2. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
In step 1 fracture site 3-D geometric model to establish process as follows：
1) image that multiple forms are DICOM is obtained by medical imaging CT scan,
2) it is then introduced into Mimics softwares and carries out three-dimensional reconstruction,
3) it will be smoothed in the model importing Geomagic softwares after three-dimensional reconstruction and hypostazation operate, fractured
The 3-D geometric model at position.
3. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
In step 2 by obtained geometrical model import Hypermesh carry out mesh generation, establish linear elasticity bone and poroma it is limited
Meta-model.
4. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
The material properties of initial time are entered as the material properties value of granulation tissue in poroma in step 3.
5. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
The solution formula that fracture area strains partially in step 4 is as follows：
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In formula, εdStrained partially for poroma unit, ε1For the first principal strain in unit, ε2For the second principal strain in unit, ε3For
The 3rd principal strain in unit.
6. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
Step 5 medium vessels growth model is as follows：
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In formula, CvesselFor vascular concentration, DvesselFor blood vessel diffusion coefficient in poroma, the speed that new blood vessel grows in poroma is represented
Degree, t are the time, x, y, and z is respectively the x-axis of three Cartesian coordinates, y-axis, z-axis, the diffusion source of angiogenic growth for pulp cavity and
At cortex periosteum.
7. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
Mesenchymal stem cell proliferation differentiation model, chondrocyte proliferation differentiation model, fibroblast proliferation differentiation model among step 6
And bone cell proliferation differentiation model is as follows：
(1) mescenchymal stem cell Proliferation, Differentiation model is：
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In formula, CmFor mescenchymal stem cell concentration in poroma unit, DmFor the diffusion coefficient of mescenchymal stem cell in poroma, FmFor
The death rate of mescenchymal stem cell in poroma unit；
(2) chondrocyte proliferation differentiation model is：
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<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>C</mi>
<mi>c</mi>
</msub>
<mo>-</mo>
<msub>
<mi>F</mi>
<mi>c</mi>
</msub>
<msub>
<mi>C</mi>
<mi>c</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, CcFor cartilage cell's concentration in poroma unit, DcFor the diffusion coefficient of cartilage cell in poroma, FcFor poroma unit
Interior cartilage cell's death rate；
(3) fibroblast proliferation differentiation model is：
<mrow>
<msub>
<mi>dC</mi>
<mi>f</mi>
</msub>
<mo>/</mo>
<mi>d</mi>
<mi>t</mi>
<mo>=</mo>
<msub>
<mi>D</mi>
<mi>f</mi>
</msub>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>c</mi>
<mi>f</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>c</mi>
<mi>f</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>c</mi>
<mi>f</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>C</mi>
<mi>f</mi>
</msub>
<mo>-</mo>
<msub>
<mi>F</mi>
<mi>f</mi>
</msub>
<msub>
<mi>C</mi>
<mi>f</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, CfFor fibroblast concentration in poroma unit, DfFor fibroblastic diffusion coefficient, F in poromafFor poroma
Fibroblastic death rate in unit；
(4) bone cell proliferation differentiation model is：
<mrow>
<msub>
<mi>dC</mi>
<mi>b</mi>
</msub>
<mo>/</mo>
<mi>d</mi>
<mi>t</mi>
<mo>=</mo>
<msub>
<mi>D</mi>
<mi>b</mi>
</msub>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>c</mi>
<mi>b</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>c</mi>
<mi>b</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>c</mi>
<mi>b</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<msub>
<mi>C</mi>
<mi>b</mi>
</msub>
<mo>-</mo>
<msub>
<mi>F</mi>
<mi>b</mi>
</msub>
<msub>
<mi>C</mi>
<mi>b</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, CbFor poroma unit in-seam cell concentration, DbFor poroma in-seam cellular invasion coefficient, FbIt is thin for poroma unit in-seam
Born of the same parents' death rate.
8. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
The oxygen transportation model of step 7 is as follows：
<mrow>
<mi>d</mi>
<mi>O</mi>
<mo>/</mo>
<mi>d</mi>
<mi>t</mi>
<mo>=</mo>
<msub>
<mi>D</mi>
<mrow>
<mi>o</mi>
<mi>x</mi>
<mi>y</mi>
<mi>g</mi>
<mi>e</mi>
<mi>n</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<mi>o</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<mi>o</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>y</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<msup>
<mo>&part;</mo>
<mn>2</mn>
</msup>
<mi>o</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<msup>
<mi>z</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mi>O</mi>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mi>m</mi>
</msub>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mi>c</mi>
</msub>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mi>f</mi>
</msub>
<mo>-</mo>
<msub>
<mi>Q</mi>
<mi>b</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
Qm=qmCmO/KmO (8)
Qc=qcCcO/KcO (9)
Qf=qfCfO/KfO (10)
Qb=qbCbO/KbO (11)
In formula, O be poroma in oxygen concentration, DoxygenFor the diffusion coefficient of oxygen in poroma, QmFor mescenchymal stem cell oxygen consumption,
QcFor cartilage cell's oxygen consumption, Q in poromafFor fibroblast oxygen consumption, Q in poromabFor osteocyte oxygen consumption, q in poromamFilled for
The consumption rate of matter stem cell, KmFor the oxygen when mescenchymal stem cell consumption rate reaches mescenchymal stem cell maximum consumption rate half
Concentration, qcFor the consumption rate of cartilage cell, KcFor the oxygen when cartilage cell's consumption rate reaches cartilage cell's maximum consumption rate half
The concentration of gas, qfFor fibroblastic consumption rate, KfTo reach fibroblast maximum consumption rate when fibroblast consumption rate
The concentration of oxygen, q during halfbFor the consumption rate of osteocyte, KbTo reach osteocyte maximum consumption rate half when osteocyte consumption rate
When oxygen concentration.
9. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：It is described
Material properties value is calculated as follows in being organized in step 9：
E=Cmax-Cp/CmaxEg+Cp/CmaxEt (12)
ν=Cmax-Cp/Cmaxνg+Cg/Cmaxνt (13)
In formula, E be unit Young's modulus, CmaxFor cell concentration maximum in unit, CpFor average cell concentration, E in unitg
For the modulus of elasticity of granulation tissue, EtFor the Young's modulus value organized in last iterate to calculate, ν is the Poisson's ratio of unit, νgFor
The Poisson's ratio of granulation tissue, νtFor the Poisson's ratio organized in last iterate to calculate.
10. the union emulation mode according to claim 1 based on oxygen and mechanical environment, it is characterised in that：Institute
State judgment step eight in step 10 and calculate the Young's modulus E whether gained unit Young's modulus E is equal to boneboneIf in tissue
Material properties value reaches the material properties value of bone, then union is completed, and emulation terminates, otherwise, more neoblastic material properties
It is worth and carries out next iteration emulation.
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| CN108565027A (en) * | 2018-04-09 | 2018-09-21 | 哈尔滨理工大学 | A kind of analogue system of simulation fracture healing process |
| CN109033742A (en) * | 2018-06-21 | 2018-12-18 | 哈尔滨理工大学 | It is a kind of for simulating the shear-deformable hyperelastic model of soft tissue |
| CN110379518A (en) * | 2019-06-05 | 2019-10-25 | 东南大学 | A kind of emulation mode that the bone based on immunoregulation is grown in porous support |
| CN112037334A (en) * | 2019-12-12 | 2020-12-04 | 哈尔滨理工大学 | Fracture healing simulation method based on ultrasonic effect and mechanical environment |
| CN113361181A (en) * | 2021-07-02 | 2021-09-07 | 哈尔滨理工大学 | Fracture healing simulation method based on nutrition diffusion and mechanical environment |
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| CN106777582A (en) * | 2016-12-01 | 2017-05-31 | 哈尔滨理工大学 | A kind of long bone fracture healing analogue system based on tissue differentiation |
| CN106777583A (en) * | 2016-12-01 | 2017-05-31 | 哈尔滨理工大学 | A kind of union emulation mode based on cellular activity |
| CN106777584A (en) * | 2016-12-01 | 2017-05-31 | 哈尔滨理工大学 | A kind of analogue system for simulating fracture healing process |
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| CN106777582A (en) * | 2016-12-01 | 2017-05-31 | 哈尔滨理工大学 | A kind of long bone fracture healing analogue system based on tissue differentiation |
| CN106777583A (en) * | 2016-12-01 | 2017-05-31 | 哈尔滨理工大学 | A kind of union emulation mode based on cellular activity |
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| CN108565027A (en) * | 2018-04-09 | 2018-09-21 | 哈尔滨理工大学 | A kind of analogue system of simulation fracture healing process |
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| CN110379518A (en) * | 2019-06-05 | 2019-10-25 | 东南大学 | A kind of emulation mode that the bone based on immunoregulation is grown in porous support |
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| CN112037334A (en) * | 2019-12-12 | 2020-12-04 | 哈尔滨理工大学 | Fracture healing simulation method based on ultrasonic effect and mechanical environment |
| CN113361181A (en) * | 2021-07-02 | 2021-09-07 | 哈尔滨理工大学 | Fracture healing simulation method based on nutrition diffusion and mechanical environment |
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