CN112037334A - Fracture healing simulation method based on ultrasonic effect and mechanical environment - Google Patents
Fracture healing simulation method based on ultrasonic effect and mechanical environment Download PDFInfo
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Abstract
The invention discloses a fracture healing simulation method based on ultrasonic action and force environment, which specifically comprises the following steps: establishing a three-dimensional model of a fracture part; carrying out grid division on the obtained geometric model, and establishing a finite element model of bones and callus; analyzing and resolving the finite element model to solve expansion strain and distortion strain of the fracture area; establishing an ultrasonic three-dimensional diffusion model of a fracture area; finite element calculation is carried out on the ultrasonic three-dimensional diffusion model, and the sound field distribution of the fracture area is solved: establishing a fuzzy mathematical model for force and ultrasonic sound field distribution combined control; calculating new material properties within the tissue; and (4) establishing a fracture healing simulation process based on the ultrasonic action and the mechanical environment according to the steps, judging whether the material property in the tissue reaches the material property value of the bone according to the tissue material property value obtained by calculation in the step eight, finishing the simulation if the material property value of the bone is reached, and updating the tissue material property value and entering the next iteration simulation if the material property value of the tissue is not reached.
Description
Technical Field
The invention relates to a fracture healing simulation method based on an ultrasonic effect and a mechanical environment.
Background
In recent years, with the rapid development of industries such as buildings and traffic and the current aging of the population in China, the number of patients suffering from construction injuries, traffic injuries and senile osteoporosis fracture is rapidly increased every year. As shown by traffic accident statistics in 2015, a car accident 10597358 occurred in 2015, with 98.5% of people being injured; according to the big health data of the aged in China in 2015, osteoporosis jumps to the seventh place of common diseases and frequently encountered diseases. Wherein the prevalence rate of people over 60 years old is 56%, and the prevalence rate of women is 60% -70%. The incidence of bone fracture in these diseases is nearly one third of the total data, and the annual medical cost is high and generally requires 150 billion RMB, which brings heavy economic burden to the society and families. However, not all fractures can be repaired, some people of old age or some people suffer from diseases which can cause negative influence on fracture repair, the fracture of the part of people can not be repaired or delayed to be repaired, the fracture is delayed to be healed or not healed, pain and dysfunction of affected limbs are caused, and great pain can be brought to patients. On the other hand, researchers find that ultrasound has a positive effect on promoting fracture healing, and when the ultrasound acts on a fracture part, the ultrasound can cause the function or the structure of a biological system to be changed, so that healing of fresh fracture can be accelerated, and healing and nonunion of fracture can be delayed and treated. 385 cases of patients with delayed union and nonunion of fracture are treated by pulse ultrasound, the result healing rate is 85%, and 951 cases of patients with delayed union of fracture are treated, and 91% of the patients are successfully treated; 366 patients with nonunion fractures were treated with 86% success. The effect of ultrasonic waves on fracture healing is gradually paid attention and paid attention to by people due to low cost, no infection, no wound, simple treatment, no adverse reaction and ideal effect.
At present, a computer simulation model which can express that the ultrasound plays such an important role in the fracture healing process is lacked, and firstly, the influence of the ultrasound effect on the proliferation and differentiation of cells in tissues in the fracture healing process is not considered; secondly, the mode of energy used for the ultrasonic wave to reach the bottom is not considered to be transmitted to the fracture part; there is also no suitable mathematical model to express the positive role of ultrasound in the fracture healing process.
Disclosure of Invention
The invention aims to provide a dynamic simulation method for a fracture healing process with an ultrasonic effect so as to solve the problems.
A fracture healing simulation method based on ultrasonic action and mechanical environment comprises the following steps:
the method comprises the following steps: establishing a three-dimensional geometric model of a fracture part;
step two: carrying out grid division on the obtained geometric model, and establishing a finite element model of bones and callus;
step three: assigning a value to a material property at an initial moment in the callus and applying a force stimulus;
step four: analyzing and resolving the finite element model to solve expansion strain and distortion strain of the fracture area;
step five: establishing an ultrasonic three-dimensional diffusion model of a fracture area;
step six: finite element calculation is carried out on the ultrasonic three-dimensional diffusion model, and the sound field distribution of the fracture area is solved;
step seven: establishing a fuzzy mathematical model for force and ultrasonic sound field distribution combined control, wherein the fuzzy mathematical model for force and ultrasonic sound field distribution combined control comprises membership and a fuzzy control rule;
step eight: calculating new material properties within the tissue;
step nine: and (4) establishing a fracture healing simulation process based on the ultrasonic action and the mechanical environment according to the steps, judging whether the material property in the tissue reaches the material property value of the bone according to the tissue material property value obtained by calculation in the step eight, finishing the simulation if the material property value of the bone is reached, and updating the tissue material property value and entering the next iteration simulation if the material property value of the tissue is not reached.
The method comprises the following steps of:
1) obtaining a plurality of images with a DICOM format by medical image CT scanning;
2) then, importing the three-dimensional reconstruction into the Minics software to carry out three-dimensional reconstruction;
3) and introducing the three-dimensional reconstructed model into Geomagic software for smoothing and materializing to obtain a three-dimensional geometric model of the fracture part.
And step two, importing the obtained geometric model into Hypermesh for grid division, and establishing a finite element model of the linear elastic bone and callus.
In the third step, the material attribute value of the callus at the initial moment is assigned as the material attribute value of the granulation tissue, and the applied force is the maximum value of the force which can be borne by the fracture part during normal action.
Wherein, the four finite element calculation processes are as follows:
the stress-strain relationship of the callus unit is established based on the basic equation of elasticity mechanics, and is shown in formula (1):
σ＝D (1)
in the formula, σ is a stress matrix, D is an elastic matrix, and D is a strain matrix, and the formula (1) is developed into a formula (2):
according to the generalized hooke's law and related experiments, the elastic matrix D is determined by the mechanical parameters elastic modulus E and poisson ratio v, and then the elastic matrix D can be expressed as:
wherein E is the elastic modulus, and ν is the Poisson's ratio;
in the process of fracture healing, the fibrous tissue concentration, the cartilage tissue concentration and the bone tissue concentration are constantly changed, the tissue concentration and the elastic modulus of each tissue determine the elastic modulus of the callus unit, and the tissue concentration and the Poisson ratio of each tissue determine the Poisson ratio of the callus unit. The elastic modulus and Poisson's ratio of the unit are calculated as shown in formulas (4) and (5):
v＝vboneCbone+vcartCcart+vcontCcont (5)
wherein E is the modulus of elasticity of the callus unit, EboneIs the modulus of elasticity of bone, EcartIs the elastic modulus of cartilage, EcontElastic mould for fibrous tissueAmount, CboneIs the bone tissue concentration, CcartIs cartilage tissue concentration, CcontIs fibrous tissue concentration, v is Poisson's ratio of callus units, vboneIs the poisson's ratio of bone, vcartPoisson's ratio, v, of cartilagecontIs the poisson's ratio of the fibrous tissue;
after finite element calculation, the expansion strain and the distortion strain are solved as shown in formula (6) and formula (7):
in the formula, strain is a first variable0The change in volume is expressed as expansion strain. A second strain variable gamma0To distort strain, a change in shape is indicated,1is the first principal strain, and is,2is the second principal strain, and is,3is the third principal strain.
The five-step ultrasonic three-dimensional diffusion model establishment process comprises the following steps:
the fracture part tissue can generate sound flow under the action of the ultrasound, namely, the tissue flows slightly, so the fracture part is regarded as micro-fluid, and the absorption degree of the ultrasound by different tissues of the fracture part is different, so the distribution of the ultrasound sound pressure at the fracture part is very uneven, and the establishment of the ultrasound three-dimensional diffusion needs to make the following assumptions:
1) acoustic waves, as a substance, do not exist off time, and therefore, ultrasound propagation is assumed to be continuous;
2) although the fracture site is considered as microfluidic, the flow rate is not too fast, is not an order of magnitude at all with the propagation rate of ultrasound, and the microfluidic flow rate is approximately negligible, thus, assuming the background fluid is stationary;
3) there is heat in any form of energy, and ultrasound propagation is no exception, but for model simplification and to highlight the role of ultrasound pressure in fracture healing, heat exchange is temporarily not taken into account;
the propagation process of the ultrasonic wave is a macroscopic physical phenomenon, and a Newton motion equation, a mass conservation equation and a physical state equation are necessarily applicable in the process of ultrasonic propagation;
the motion equation of ultrasonic wave propagation in an ideal medium is as shown in formula (8):
in the formula, ρ0Is the density of the fluid medium, v0The flow velocity of the fluid medium is shown, and P is the sound pressure of ultrasound;
the simplified equation of motion is as in equation (9):
the simplified physical state equation of ultrasonic wave propagation in an ideal medium is shown as the formula (10):
dP＝c2dρ0 (10)
wherein P is the sound pressure of ultrasound, c2For the propagation velocity of the ultrasonic waves in an ideal medium,
k0is the bulk modulus, ρ, of the fluid medium0Is the fluid medium density;
the continuity equation of ultrasonic propagation in an ideal medium is as in equation (11):
wherein P is the sound pressure of ultrasound, ρ0Is the density of the fluid medium, v0Is the flow rate of the fluid medium;
based on three basic equations of a formula (9), a formula (10) and a formula (11), a three-dimensional wave equation of the small-amplitude sound wave in the ideal medium is obtained as a formula (12):
wherein P is the sound pressure of ultrasound, c2For the propagation velocity of the ultrasonic waves in an ideal medium,
k0is the bulk modulus, ρ, of the fluid medium0In order to be the density of the fluid medium,
in order to be the laplacian operator,
the finite element calculation process of the ultrasonic three-dimensional diffusion model in the sixth step is as follows: setting an initial value of ultrasonic sound pressure, setting boundary conditions of the three-dimensional model, solving by using a finite volume difference method due to different absorption degrees of ultrasonic waves by tissues, obtaining sound field distribution in the three-dimensional model, obtaining sound pressure of all grid nodes, and solving an average value of sound pressure at periosteal callus, an average value of sound pressure at cortical bony callus and an average value of sound pressure at intraosseous callus.
Establishing a fuzzy mathematical model for force and ultrasonic sound field distribution combined control, wherein the fuzzy mathematical model for force and ultrasonic sound field distribution combined control comprises membership and a fuzzy control rule; the specific process is as follows:
step seven, establishing a membership function;
setting 7 linguistic values of input 2 output linguistic variables, and establishing a membership function;
the 7 inputs are expansion strain, distortion strain, tissue sound pressure value, fibrous tissue concentration, cartilage concentration, bone concentration and adjacent unit bone concentration;
2 outputs are cartilage tissue concentration change quantity and bone tissue concentration change quantity;
seventhly, establishing a fuzzy control rule;
rules 1-3 describe that in the early stage of fracture, after the bone is wounded, the nutritive artery and its branches at the fracture part are torn, resulting in bleeding of different degrees, bleeding extravasates to the surrounding to form hematoma, osteoclasts invade and begin to clear dead bone, new blood vessels invade in fibrin network in hematoma and are accompanied with a great amount of mesenchymal stem cell proliferation, ultrasonic sound pressure just diffuses to the fracture part, and the energy is not yet released through tissue flow, so the sound pressure value is high, ultrasonic energy can play a role in enhancing the recruitment of osteoprogenitor mesenchymal stem cells to the fracture part and promoting the proliferation of fibrocyte, phagocytes gradually clear the hematoma, and the callus region quickly organizes to granulation tissue to form fibrous callus, so the concentration of cartilage and bone in callus is reduced;
rules 6-8 describe the process of cartilage generation, during the process of fracture healing, the generation of cartilage is promoted due to insufficient oxygen and nutrients, the large fracture end is micro-moved due to unstable mechanical environment, mesenchymal stem cells in tissues can be differentiated into chondrocytes to form cartilage, and ultrasonic energy can activate the activity of some active enzymes, so that the differentiation of mesenchymal stem cells into osteogenesis and chondrocytes is accelerated, and the acoustic streaming effect caused by ultrasonic sound pressure can also deliver oxygen and nutrients to osteoblasts and discharge cell secretions in time;
rules 9-14 describe the process of cartilage calcification and ossification, with the promotion of fracture healing by ultrasound and the accumulation of healing time, blood vessels have been approximately formed, sufficient oxygen is brought to bone tissues, cartilage is calcified, meanwhile, under stress stimulation, osteoblasts synthesize collagen and glycoprotein to form an organic matrix of bone, osteoblasts are embedded by the organic matrix and then converted into osteocytes, calcification gradually occurs, the bone matrix becomes harder bony callus, the cartilage cells are promoted by ultrasound during the process to secrete collagen, collagen fibers are deposited by calcium salt, the chondroblasts can denature and die, cartilage calcification occurs under intermittent high stress stimulation, during the process of cartilage calcification, the concentration of cartilage is reduced and the concentration of bone is increased, during ossification, vascular growth factors are released, the amount of angiogenesis is greatly increased, oxygen is sufficient, osteoblasts can release alkaline phosphatase and the activity of the alkaline phosphatase is increased rapidly, the alkaline phosphatase hydrolyzes organically combined phosphoric acid in plasma and releases phosphate to combine with calcium salt to form calcium carbonate, finally, bone is converted into bone tissue, the bone concentration is increased and the cartilage concentration is reduced in the process;
and step eight, calculating new material properties in the tissue:
v＝vboneCbone+vcartCcart+vcontCcont (5)
wherein E is the modulus of elasticity of the callus unit, EboneIs the modulus of elasticity of bone, EcartIs the elastic modulus of cartilage, EcontIs the modulus of elasticity, C, of the fibrous tissueboneIs the bone tissue concentration, CcartIs cartilage tissue concentration, CcontIs fibrous tissue concentration, v is Poisson's ratio of callus units, vboneIs the poisson's ratio of bone, vcartPoisson's ratio, v, of cartilagecontIs the poisson's ratio of the fibrous tissue;
judging whether the Young modulus E of the obtained unit is equal to that of the bone or not in the ninth stepboneIf the material attribute value in the tissue reaches the material attribute of the bone, the fracture healing is finished, and the simulation is finished, otherwise, the material attribute value of the tissue is updated and the next iterative simulation is carried out.
The invention has the beneficial effects that: the method has the advantages that the influence of the ultrasonic effect on fracture healing is considered, the differentiation effect of the mechanical environment on bone tissues is also considered, the fracture healing process controlled by the ultrasonic effect and the mechanical environment in a combined mode is simulated, the proliferation and differentiation processes of fibroblasts, chondrocytes and osteoblasts in the fracture healing process are shown, the optimal treatment parameters can be determined through different combinations of the treatment parameters of the fracture healing affected by the ultrasonic effect, the prediction of the complex fracture healing process can be realized, guidance is provided for a doctor to make an operation scheme, and then the operation success rate is improved, and the fracture healing quality is improved.
Drawings
FIG. 1 is a flow chart of a fracture healing simulation method based on ultrasound and mechanical environment;
FIG. 2 is a schematic diagram of membership functions for 7 input 2 output linguistic variables: wherein, 2(a) is a schematic diagram of expansion strain membership function, 2(b) is a schematic diagram of distortion strain membership function, 2(c) is a schematic diagram of tissue sound pressure value membership function, 2(d) is a schematic diagram of fiber tissue, cartilage and bone membership function, 2(e) is a schematic diagram of adjacent unit membership function, 2(f) is a schematic diagram of cartilage concentration change membership function, and 2(g) is a schematic diagram of bone concentration change membership function;
FIG. 3 is a schematic diagram of a fuzzy mathematical model for the combined control of force and ultrasonic sound field distribution;
Detailed Description
For more specific description of the present invention, the fracture healing simulation method based on ultrasound and mechanical environment according to the present invention will be described in detail with reference to the accompanying drawings and the detailed description.
A fracture healing simulation method based on ultrasonic action and mechanical environment comprises the following specific implementation modes:
the first embodiment is as follows: establishing a three-dimensional geometric model of a fracture part; the process of establishing the three-dimensional geometric model of the fracture part is as follows:
1) obtaining a plurality of images with a DICOM format by medical image CT scanning;
2) then, importing the three-dimensional reconstruction into the Minics software to carry out three-dimensional reconstruction;
3) and introducing the three-dimensional reconstructed model into Geomagic software for smoothing and materializing to obtain a three-dimensional geometric model of the fracture part.
The second embodiment is as follows: and introducing the obtained geometric model into Hypermesh for grid division, and establishing a finite element model of the linear elastic bone and callus.
The third concrete implementation mode: the material property value of the granulation tissue is assigned to the material property value of the initial moment in the callus, and the applied force is the maximum value of the force which can be borne by the fracture part during normal action.
The fourth concrete implementation mode: the finite element solution process is as follows:
the stress-strain relationship of the callus unit is established based on the basic equation of elasticity mechanics, and is shown in formula (1):
σ＝D (1)
in the formula, σ is a stress matrix, D is an elastic matrix, and D is a strain matrix, and the formula (1) is developed into a formula (2):
according to the generalized hooke's law and related experiments, the elastic matrix D is determined by the mechanical parameters elastic modulus E and poisson ratio v, and then the elastic matrix D can be expressed as:
wherein E is the elastic modulus and v is the Poisson's ratio;
in the process of fracture healing, the fibrous tissue concentration, the cartilage tissue concentration and the bone tissue concentration are constantly changed, the tissue concentration and the elastic modulus of each tissue determine the elastic modulus of the callus unit, and the tissue concentration and the Poisson ratio of each tissue determine the Poisson ratio of the callus unit. The elastic modulus and Poisson's ratio of the unit are calculated as shown in formulas (4) and (5):
v＝vboneCbone+vcartCcart+vcontCcont (5)
wherein E is the modulus of elasticity of the callus unit, EboneIs the modulus of elasticity of bone, EcartIs the elastic modulus of cartilage, EcontIs the modulus of elasticity, C, of the fibrous tissueboneIs the bone tissue concentration, CcartIs cartilage tissue concentration, CcontIs fibrous tissue concentration, v is Poisson's ratio of callus units, vboneIs the poisson's ratio of bone, vcartPoisson's ratio, v, of cartilagecontIs the poisson's ratio of the fibrous tissue;
after finite element calculation, the expansion strain and the distortion strain are solved as shown in formula (6) and formula (7):
in the formula, strain is a first variable0The change in volume is expressed as expansion strain. A second strain variable gamma0To distort strain, a change in shape is indicated,1is the first principal strain, and is,2is the second principal strain, and is,3is the third principal strain.
The fifth concrete implementation mode: the ultrasonic three-dimensional diffusion model establishment process is as follows:
the fracture part tissue can generate sound flow under the action of the ultrasound, namely, the tissue flows slightly, so the fracture part is regarded as micro-fluid, and the absorption degree of the ultrasound by different tissues of the fracture part is different, so the distribution of the ultrasound sound pressure at the fracture part is very uneven, and the establishment of the ultrasound three-dimensional diffusion needs to make the following assumptions:
1) acoustic waves, as a substance, do not exist off time, and therefore, ultrasound propagation is assumed to be continuous;
2) although the fracture site is considered as microfluidic, the flow rate is not too fast, is not an order of magnitude at all with the propagation rate of ultrasound, and the microfluidic flow rate is approximately negligible, thus, assuming the background fluid is stationary;
3) there is heat in any form of energy, and ultrasound propagation is no exception, but for model simplification and to highlight the role of ultrasound pressure in fracture healing, heat exchange is temporarily not taken into account;
the propagation process of the ultrasonic wave is a macroscopic physical phenomenon, and a Newton motion equation, a mass conservation equation and a physical state equation are necessarily applicable in the process of ultrasonic propagation;
the motion equation of ultrasonic wave propagation in an ideal medium is as shown in formula (8):
in the formula, ρ0Is the density of the fluid medium, v0The flow velocity of the fluid medium is shown, and P is the sound pressure of ultrasound;
the simplified equation of motion is as in equation (9):
the simplified physical state equation of ultrasonic wave propagation in an ideal medium is shown as the formula (10):
dP＝c2dρ0 (10)
wherein P is the sound pressure of ultrasound, c2For the propagation velocity of the ultrasonic waves in an ideal medium,
k0is the bulk modulus, ρ, of the fluid medium0Is the fluid medium density;
the continuity equation of ultrasonic propagation in an ideal medium is as in equation (11):
wherein P is the sound pressure of ultrasound, ρ0Is the density of the fluid medium, v0Is the flow rate of the fluid medium;
based on three basic equations of a formula (9), a formula (10) and a formula (11), a three-dimensional wave equation of the small-amplitude sound wave in the ideal medium is obtained as a formula (12):
wherein P is the sound pressure of ultrasound, c2For the propagation velocity of the ultrasonic waves in an ideal medium,
k0is the bulk modulus, ρ, of the fluid medium0In order to be the density of the fluid medium,
in order to be the laplacian operator,
the sixth specific implementation mode: the finite element calculation process of the ultrasonic three-dimensional diffusion model comprises the following steps: setting an initial value of ultrasonic sound pressure, setting boundary conditions of the three-dimensional model, solving by using a finite volume difference method due to different absorption degrees of ultrasonic waves by tissues, obtaining sound field distribution in the three-dimensional model, obtaining sound pressure of all grid nodes, and solving an average value of sound pressure at periosteal callus, an average value of sound pressure at cortical bony callus and an average value of sound pressure at intraosseous callus.
The seventh embodiment: establishing a fuzzy mathematical model for force and ultrasonic sound field distribution combined control, wherein the fuzzy mathematical model for force and ultrasonic sound field distribution combined control comprises membership and a fuzzy control rule; the specific process is as follows:
step seven, establishing a membership function;
setting 7 linguistic values of input 2 output linguistic variables, and establishing a membership function;
the 7 inputs are expansion strain, distortion strain, tissue sound pressure value, fibrous tissue concentration, cartilage concentration, bone concentration and adjacent unit bone concentration;
2 outputs are cartilage tissue concentration change quantity and bone tissue concentration change quantity;
seventhly, establishing a fuzzy control rule;
fuzzy control rules mainly describe the tissue transformation process in the healing process, the rules are the basis of a fuzzy model, and the research adopts the statement description of if A and B then C, and the main form of the statement is shown in Table 1.
Rules 1-3 describe that in the early stage of fracture, after the bone is wounded, the nutritive artery and its branches at the fracture part are torn, resulting in bleeding of different degrees, bleeding extravasates to the surrounding to form hematoma, osteoclasts invade and begin to clear dead bone, new blood vessels invade in fibrin network in hematoma and are accompanied with a great amount of mesenchymal stem cell proliferation, ultrasonic sound pressure just diffuses to the fracture part, and the energy is not yet released through tissue flow, so the sound pressure value is high, ultrasonic energy can play a role in enhancing the recruitment of osteoprogenitor mesenchymal stem cells to the fracture part and promoting the proliferation of fibrocyte, phagocytes gradually clear the hematoma, and the callus region quickly organizes to granulation tissue to form fibrous callus, so the concentration of cartilage and bone in callus is reduced;
rules 6-8 describe the process of cartilage generation, during the process of fracture healing, the generation of cartilage is promoted due to insufficient oxygen and nutrients, the large fracture end is micro-moved due to unstable mechanical environment, mesenchymal stem cells in tissues can be differentiated into chondrocytes to form cartilage, and ultrasonic energy can activate the activity of some active enzymes, so that the differentiation of mesenchymal stem cells into osteogenesis and chondrocytes is accelerated, and the acoustic streaming effect caused by ultrasonic sound pressure can also deliver oxygen and nutrients to osteoblasts and discharge cell secretions in time;
rules 9-14 describe the process of cartilage calcification and ossification, with the promotion of fracture healing by ultrasound and the accumulation of healing time, blood vessels have been approximately formed, sufficient oxygen is brought to bone tissues, cartilage is calcified, meanwhile, under stress stimulation, osteoblasts synthesize collagen and glycoprotein to form an organic matrix of bone, osteoblasts are embedded by the organic matrix and then converted into osteocytes, calcification gradually occurs, the bone matrix becomes harder bony callus, the cartilage cells are promoted by ultrasound during the process to secrete collagen, collagen fibers are deposited by calcium salt, the chondroblasts can denature and die, cartilage calcification occurs under intermittent high stress stimulation, during the process of cartilage calcification, the concentration of cartilage is reduced and the concentration of bone is increased, during ossification, vascular growth factors are released, the amount of angiogenesis is greatly increased, oxygen is sufficient, osteoblasts can release alkaline phosphatase and the activity of the alkaline phosphatase is increased rapidly, the alkaline phosphatase hydrolyzes organically combined phosphoric acid in plasma and releases phosphate to combine with calcium salt to form calcium carbonate, finally, bone is converted into bone tissue, the bone concentration is increased and the cartilage concentration is reduced in the process;
the specific implementation mode is eight: calculating new material properties within the tissue:
v＝vboneCbone+vcartCcart+vcontCcont (5)
wherein E is the modulus of elasticity of the callus unit, EboneIs the modulus of elasticity of bone, EcartIs the elastic modulus of cartilage, EcontIs the modulus of elasticity, C, of the fibrous tissueboneIs the bone tissue concentration, CcartIs cartilage tissue concentration, CcontIs fibrous tissue concentration, v is Poisson's ratio of callus units, vboneIs the poisson's ratio of bone, vcartPoisson's ratio, v, of cartilagecontIs the poisson's ratio of the fibrous tissue;
the specific implementation method nine: judging whether the Young's modulus E of the obtained unit is equal to that of the boneboneIf the material attribute value in the tissue reaches the material attribute of the bone, the fracture healing is finished, and the simulation is finished, otherwise, the material attribute value of the tissue is updated and the next iterative simulation is carried out.
This embodiment is only illustrative of the patent and does not limit the scope of protection thereof, and those skilled in the art can make modifications to its part without departing from the spirit of the patent.
Claims (10)
1. A fracture healing simulation method based on ultrasonic action and mechanical environment comprises the following steps:
the method comprises the following steps: establishing a three-dimensional geometric model of a fracture part;
step two: carrying out grid division on the obtained geometric model, and establishing a finite element model of bones and callus;
step three: assigning a value to a material property at an initial moment in the callus and applying a force stimulus;
step four: analyzing and resolving the finite element model to solve expansion strain and distortion strain of the fracture area;
step five: establishing an ultrasonic three-dimensional diffusion model of a fracture area;
step six: finite element calculation is carried out on the ultrasonic three-dimensional diffusion model, and the sound field distribution of the fracture area is solved;
step seven: establishing a fuzzy mathematical model for force and ultrasonic sound field distribution combined control, wherein the fuzzy mathematical model for force and ultrasonic sound field distribution combined control comprises membership and a fuzzy control rule;
step eight: calculating new material properties within the tissue;
step nine: and (4) establishing a fracture healing simulation process based on the ultrasonic action and the mechanical environment according to the steps, judging whether the material property in the tissue reaches the material property value of the bone according to the tissue material property value obtained by calculation in the step eight, finishing the simulation if the material property value of the bone is reached, and updating the tissue material property value and entering the next iteration simulation if the material property value of the tissue is not reached.
2. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: the process for establishing the three-dimensional geometric model of the fracture part comprises the following steps:
1) obtaining a plurality of images with a DICOM format by medical image CT scanning;
2) then, importing the three-dimensional reconstruction into the Minics software to carry out three-dimensional reconstruction;
3) and introducing the three-dimensional reconstructed model into Geomagic software for smoothing and materialization operation to obtain a three-dimensional geometric model of the fracture part.
3. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: and in the second step, the obtained geometric model is imported into Hypermesh for grid division, and a finite element model of the linear elastic bone and callus is established.
4. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: and in the third step, the material attribute at the initial moment in the callus is assigned as the material attribute value of granulation tissue, and the applied force is the maximum value of the force which can be borne by the fracture part during normal action.
5. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: the four finite element calculation process comprises the following steps:
the stress-strain relationship of the callus unit is established based on the basic equation of elasticity mechanics, and is shown in formula (1):
σ＝D (1)
in the formula, σ is a stress matrix, D is an elastic matrix, and D is a strain matrix, and the formula (1) is developed into a formula (2):
according to the generalized hooke's law and related experiments, the elastic matrix D is determined by the mechanical parameters elastic modulus E and poisson ratio v, and then the elastic matrix D can be expressed as:
wherein E is the elastic modulus and v is the Poisson's ratio;
in the process of fracture healing, the fibrous tissue concentration, the cartilage tissue concentration and the bone tissue concentration are constantly changed, the tissue concentration and the elastic modulus of each tissue determine the elastic modulus of the callus unit, and the tissue concentration and the Poisson ratio of each tissue determine the Poisson ratio of the callus unit. The elastic modulus and Poisson's ratio of the unit are calculated as shown in formulas (4) and (5):
v＝vboneCbone+vcartCcart+vcontCcont (5)
wherein E is the modulus of elasticity of the callus unit, EboneIs the modulus of elasticity of bone, EcartIs the elastic modulus of cartilage, EcontIs the modulus of elasticity, C, of the fibrous tissueboneIs the bone tissue concentration, CcartIs cartilage tissue concentration, CcontIs fibrous tissue concentration, v is Poisson's ratio of callus units, vboneIs the poisson's ratio of bone, vcartPoisson's ratio, v, of cartilagecontIs the poisson's ratio of the fibrous tissue;
after finite element calculation, the expansion strain and the distortion strain are solved as shown in formula (6) and formula (7):
in the formula, strain is a first variable0The change in volume is expressed as expansion strain. A second strain variable gamma0To distort strain, a change in shape is indicated,1is the first principal strain, and is,2is the second principal strain, and is,3is the third principal strain.
6. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: the five-step ultrasonic three-dimensional diffusion model establishment process is as follows:
the fracture part tissue can generate sound flow under the action of the ultrasound, namely, the tissue flows slightly, so the fracture part is regarded as the micro flow, and the different tissues of the fracture part have different absorption degrees of the ultrasound, so the distribution of the ultrasound sound pressure at the fracture part is very uneven, and the establishment of the ultrasound three-dimensional diffusion needs to make the following assumptions:
1) acoustic waves, as a substance, do not exist off time, and therefore, ultrasound propagation is assumed to be continuous;
2) although the fracture site is considered as microfluidic, the flow rate is not too fast, is not an order of magnitude at all with the propagation rate of ultrasound, and the microfluidic flow rate is approximately negligible, thus, assuming the background fluid is stationary;
3) heat exists in any form of energy, and ultrasonic transmission is no exception, but heat exchange is not considered for the simplification of a model and the role of ultrasonic sound pressure in fracture healing;
the propagation process of the ultrasonic wave is a macroscopic physical phenomenon, and a Newton motion equation, a mass conservation equation and a physical state equation are necessarily applicable in the process of ultrasonic propagation;
the motion equation of ultrasonic wave propagation in an ideal medium is as shown in formula (8):
in the formula, ρ0Is the density of the fluid medium, v0The flow velocity of the fluid medium is shown, and P is the sound pressure of ultrasound;
the simplified equation of motion is as in equation (9):
the simplified physical state equation of ultrasonic wave propagation in an ideal medium is shown as the formula (10):
dP＝c2dρ0 (10)
wherein P is the sound pressure of ultrasound, c2For the propagation velocity of the ultrasonic waves in an ideal medium,
k0is the bulk modulus of the fluid medium, p0Is the fluid medium density;
the continuity equation of ultrasonic propagation in an ideal medium is as in equation (11):
wherein P is the sound pressure of ultrasound, ρ0Is the density of the fluid medium, v0Is the flow rate of the fluid medium;
based on three basic equations of a formula (9), a formula (10) and a formula (11), a three-dimensional wave equation of the small-amplitude sound wave in the ideal medium is obtained as a formula (12):
wherein P is the sound pressure of ultrasound, c2For the propagation velocity of the ultrasonic waves in an ideal medium,
k0is the bulk modulus of the fluid medium, p0In order to be the density of the fluid medium,
in order to be the laplacian operator,
7. the method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: the sixth step of carrying out finite element calculation on the ultrasonic three-dimensional diffusion model comprises the following steps: setting an initial value of ultrasonic sound pressure, setting boundary conditions of the three-dimensional model, solving by using a finite volume difference method due to different absorption degrees of ultrasonic waves by tissues, obtaining sound field distribution in the three-dimensional model, obtaining sound pressure of all grid nodes, and solving an average value of sound pressure at periosteal callus, an average value of sound pressure at cortical bony callus and an average value of sound pressure at intraosseous callus.
8. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: establishing a fuzzy mathematical model for force and ultrasonic sound field distribution combined control, wherein the fuzzy mathematical model for force and ultrasonic sound field distribution combined control comprises membership and a fuzzy control rule; the specific process is as follows:
step seven, establishing a membership function;
setting 7 linguistic values of input 2 output linguistic variables, and establishing a membership function;
the 7 inputs are expansion strain, distortion strain, tissue sound pressure value, fibrous tissue concentration, cartilage concentration, bone concentration and adjacent unit bone concentration;
2 outputs are cartilage tissue concentration change quantity and bone tissue concentration change quantity;
seventhly, establishing a fuzzy control rule;
rules 1-3 describe that in the early stage of fracture, after the bone is wounded, the nutritive artery and branches of the fracture part are torn, bleeding is caused to different degrees, the bleeding extravasates to the periphery to form hematoma, osteoclast invades and begins to remove dead bone, new blood vessels invade in fibrin network in the hematoma and are accompanied by proliferation of a large amount of mesenchymal stem cells, ultrasonic sound pressure just diffuses to the fracture part, the energy is not yet released and is released through tissue flow, so the sound pressure value is high, ultrasonic energy can play a role in enhancing the recruitment of osteoprogenitor and mesenchymal stem cells to the fracture part and promoting the proliferation of the fibroblasts, hematoma is gradually removed by phagocytes, the callus region is organized to quickly form fibrous callus, and the concentration of cartilage and bone in the callus is reduced;
rules 4, 5 describe the process of intramembranous ossification, which is a direct osteogenesis procedure with no chondrogenesis; because the periosteum is aerobic, the connective tissue is directly converted into bone tissue, in the process, the mesenchymal stem cells are promoted to be differentiated into osteoblasts by ultrasound, and the osteoblasts are promoted to be continuously proliferated, so that the process of the stage is accelerated;
rules 6-8 describe the process of cartilage generation, during the process of fracture healing, the generation of cartilage is promoted due to insufficient oxygen and nutrients, the large fracture end is micro-moved due to unstable mechanical environment, mesenchymal stem cells in tissues can be differentiated into chondrocytes to form cartilage, and ultrasonic energy can activate the activity of some active enzymes, so that the differentiation of mesenchymal stem cells into osteogenesis and chondrocytes is accelerated, and the acoustic streaming effect caused by ultrasonic sound pressure can also deliver oxygen and nutrients to osteoblasts and discharge cell secretions in time;
rules 9-14 describe the process of cartilage calcification and ossification, with the promotion of fracture healing by ultrasound and the accumulation of healing time, blood vessels have been approximately formed, sufficient oxygen is brought to bone tissues, cartilage is calcified, meanwhile, under stress stimulation, osteoblasts synthesize collagen and glycoprotein to form an organic matrix of bone, osteoblasts are transformed into osteocytes after being embedded by the organic matrix, calcification gradually occurs, the bone matrix becomes harder bony callus, the cartilage cells are promoted by ultrasound during the process to secrete collagen, collagen fibers are deposited by calcium salt, the chondroblasts are degenerated and necrotized, cartilage calcification occurs under intermittent high stress stimulation, during the process of cartilage calcification, the concentration of cartilage is reduced, the concentration of bone is increased, during ossification, vascular growth factors are released, the angiogenesis amount is greatly increased, oxygen is sufficient, the osteoblasts release basic carbohydrase and the activity thereof is increased, the organic combined phosphoric acid in the plasma is hydrolyzed, and the phosphate is released to be combined with calcium salt to form calcium carbonate, so that the bone is converted into bone tissue, and in the process, the bone concentration is increased and the cartilage concentration is reduced;
rule 15 describes the process of tissue reconstruction, atrophy.
9. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: in said step eight new material properties within the tissue are calculated:
v＝vboneCbone+vcartCcart+vcontCcont (5)
wherein E is the modulus of elasticity of the callus unit, EboneIs the modulus of elasticity of bone, EcartIs the elastic modulus of cartilage, EcontIs the modulus of elasticity, C, of the fibrous tissueboneIs the bone tissue concentration, CcartIs cartilage tissue concentration, CcontIs fibrous tissue concentration, v is Poisson's ratio of callus units, vboneIs the poisson's ratio of bone, vcartPoisson's ratio, v, of cartilagecontIs the poisson's ratio of fibrous tissue.
10. The method for simulating fracture healing based on ultrasonic action and mechanical environment according to claim 1, wherein: judging whether the Young modulus E of the obtained unit is equal to that of the bone or notboneIf the material property value in the tissue reaches the material property of the bone, the fracture healing is finished, and the simulation is finished, otherwise, the material property value of the tissue is updated and the next iterative simulation is carried out.
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