CN109033641A - A kind of Virtual cropping algorithm based on silica gel healed model - Google Patents
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- 239000000741 silica gel Substances 0.000 title claims abstract description 53
- 229910002027 silica gel Inorganic materials 0.000 title claims abstract description 53
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 title claims abstract description 52
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 25
- 230000035876 healing Effects 0.000 claims abstract description 54
- 238000005520 cutting process Methods 0.000 claims abstract description 38
- 210000004872 soft tissue Anatomy 0.000 claims abstract description 23
- 238000009877 rendering Methods 0.000 claims abstract description 10
- 239000011159 matrix material Substances 0.000 claims description 31
- 238000000034 method Methods 0.000 claims description 16
- 238000006073 displacement reaction Methods 0.000 claims description 13
- 210000001519 tissue Anatomy 0.000 claims description 9
- 238000013016 damping Methods 0.000 claims description 7
- 238000002474 experimental method Methods 0.000 claims description 4
- 239000000463 material Substances 0.000 claims description 4
- 238000004826 seaming Methods 0.000 claims description 4
- 230000002269 spontaneous effect Effects 0.000 claims description 3
- 210000004204 blood vessel Anatomy 0.000 claims description 2
- 238000006243 chemical reaction Methods 0.000 claims description 2
- 238000001514 detection method Methods 0.000 abstract description 2
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- 238000010586 diagram Methods 0.000 description 3
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- 230000009286 beneficial effect Effects 0.000 description 2
- 238000004364 calculation method Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000003993 interaction Effects 0.000 description 1
- 230000002452 interceptive effect Effects 0.000 description 1
- 230000035515 penetration Effects 0.000 description 1
- 229920001296 polysiloxane Polymers 0.000 description 1
- 238000000926 separation method Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000001356 surgical procedure Methods 0.000 description 1
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Abstract
The invention proposes a kind of Virtual cropping algorithms based on silica gel healed model, specifically comprise the following steps: that step 1) establishes finite element governing equation；Step 2 detects cutting condition and generates notch, and generates the grid model for being included in silica gel healed model in real time；The detection of step 3) real-time status；Step 4) real-time rendering: real-time rendering is carried out to notch, shows healing effect.The utility model has the advantages that incorporating silica gel healed model, wherein biologic soft tissue is the fundamental characteristics of biologic soft tissue to the frictional force of analog scalpel, carries out simulating cut there are frictional force and is more in line with reality, is more advantageous to surgical doctor and holds force degree.
Description
Technical Field
The invention belongs to the technical field of medical simulation, and particularly relates to a virtual cutting algorithm based on a silica gel healing model.
Background
In recent years, with the continuous development of virtual reality technology, the simulation of surgical training through a virtual reality platform is possible. Virtual surgery gives medical personnel very big facility, and they can use this technique to carry out repeated simulation exercise, promote own technique. The current virtual surgery presents the process of the simulated surgery on a platform through modeling, rendering and calculation, and uses a finite element model, a non-grid model and the like. However, currently, the aspects of virtual surgery technology are still not comprehensive, and reality is still insufficient. In the process of virtual cutting, the friction force of the biological soft tissue on the scalpel influences the grasping force application degree of the operating doctor, and the difficulty degree of cutting is different at different parts of the body, so that the operating doctor needs to grasp the force to grasp the cutting depth; the self-healing ability of biological soft tissue is also very important, and the incision types are roughly divided into two types according to the difference of incision size, shape and depth: the former needs to sew up the incision to heal it and the latter can heal it naturally.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a virtual cutting algorithm based on a silica gel healing model, which can better realize force feedback and enable an operator to control the operation force through an improved grid model under the condition of not reducing the deformation precision, wherein the obtained model has more authenticity and is specifically realized by the following technical scheme:
the virtual cutting algorithm based on the silica gel healing model specifically comprises the following steps:
step 1) establishing a finite element control equation;
step 2) detecting cutting conditions to generate cuts, and generating a grid model incorporated into the silica gel healing model in real time;
step 3), detecting the real-time state;
step 4), real-time rendering: and rendering the incision in real time and showing the healing effect.
The virtual cutting algorithm based on the silica gel healing model is further designed in that the step 1) comprises the following steps:
step 1-1) obtaining a vectorized form of a finite element control equation according to formula (1):
where M is the quality matrix of the element, U is the displacement vector of the node, Fext，Fint，FdampRespectively representing external force, internal force and damping force on a single node;
step 1-2) adopting a triangular mesh as a finite element of the virtual blood vessel model, and introducing a local rigidity matrix of a single triangular unit as shown in formula (2):
[ke]＝∫[B]T[E][B]dS (2)
wherein ,keIs a global stiffness matrix of a single unit, B is the strain of the displacement matrix, E is the elastic modulus matrix of the tissue properties;
step 1-3) setting each node in the triangular unit to have three degrees of freedom, and setting the position of each node as xi(i ═ 1,2,3,4), the position matrix of the finite elements is as in (3):
step 1-4) the quality of the triangle is distributed to each node according to a quality concentration mechanism, and the quality of one triangle is obtained from an equation according to the formula (4):
wherein ,mIRepresenting the mass of the ith triangle, e is composed of all triangle finite elements adjacent to the ith node, ρ is the density of the tissue material, SeA region represented by a triangular finite element e;
steps 1-5) give System t0Known position x (t)0) And speedCalculating to obtain a system t according to a dynamic equation of the system0Position x (t) of + h0+ h) and speed
The virtual cutting algorithm based on the silica gel healing model is further designed in that the blood vessel surfaces are set to be equidistant in the step 1-2), and then the elastic modulus matrix of the tissue characteristics is expressed as:
where λ and μ are the lam é constants.
The virtual cutting algorithm based on the silica gel healing model is further designed in that the steps 1-4) zhong1 discretizes the dynamic equation (1) on each node according to equation (6):
wherein ,μI(t)＝[μI(t),υI(t),ωI(t)]TIs the displacement vector of the I-th node;
the internal force of the I-th node is obtained according to equation (7):
the damping force at the I-th node is obtained according to equation (8):
wherein ,representing the velocity of the ith node;
the virtual cutting algorithm based on the silica gel healing model is further designed in the following steps 1-5), firstly, the model is expressed by a time-varying partial differential equation, and then the dispersed partial differential equation is used as an ordinary differential equation, as shown in formula (9):
wherein, the vector X represents the position of the soft model, the diagonal matrix M X represents the mass distribution of the soft model, e represents the internal energy of the model, and F represents other forces acting on the model;
then according to Newton's law, the kinetic equation of the system is obtained as follows:
by subsequently defining the velocity v of the system asConversion to a first order differential equation:
the implicit forward euler method defines the discrete dynamic equation as:
in the formula, Δ ν represents a velocity difference between adjacent positions, and Δ x represents a distance between adjacent positions;
a taylor series expansion is applied to f and a first order approximation is made according to equation (13):
remolding formula (13) according to formula (14);
finally, Δ x — h (ν) is calculated0+ Δ ν) to calculate the next position x (t)0+h)＝x0+ Δ x and velocity v (t)0+h)＝υ0+Δυ。
The virtual cutting algorithm based on the silica gel healing model is further designed in that in the step 2), the cutting process is divided into three stages, a deformation model containing nonlinear viscoelasticity is adopted,
a plane equation is constructed according to equation (15):
Ax+By+Cz+D＝0 (15)
when C ≠ 0, there is:
definition ofComprises the following steps:
z＝a0x+a1y+a2 (17)
setting n collision points Pi(xi,yi,zi) And the formed cutting surface:
when in useWhen the formula (18) reaches the minimum value, the formulae (19) and (20) are obtained
Solving the equations (19) and (20) to obtain the coefficient a0,a1,a2And then a cut surface is obtained.
The virtual cutting algorithm based on the silica gel healing model is further designed in that a grid model added into the silica gel healing model is generated in time along with the cutting of the virtual scalpel in the step 2): and generating a grid model on the contact surface of the grid and the scalpel in real time, and adding a layer of silica gel on the surface of the grid model.
The virtual cutting algorithm based on the silica gel healing model is further designed in that the friction force of the biological soft tissue to the scalpel is simulated through the friction force between the silica gel and the scalpel in the step 3), and the spontaneous healing phenomenon of the biological soft tissue is simulated through the viscosity of the silica gel, and the method specifically comprises the following steps of:
defining the friction force generated in the cutting process as sliding friction force, and defining:
Ff＝μFN1(21)
wherein ,FfMu is a friction factor which is the friction force of the current silica gel to the scalpel, and is obtained by experiments and represents the linear relation between the positive pressure and the generated friction force, FN1Representing the positive pressure of the current cutting force against the mesh face. Constructing a force model according to the formula (22) and the formula (23):
wherein ,F1In order to provide the cutting force,half of the apex angle of the incision, f2Is the component of the cutting force parallel to the cutting plane. And setting the overlapped part of the top end of the incision and the overlapped part of the seaming point and the top end of the incision in the seaming graph to represent the contact of the silica gel, wherein the formula (24):
α＝f(t) (24)
where α represents the degree of healing (in percent), t represents time, and f represents a piecewise function that can be expressed as:
wherein ,k1,k2Is two constants, t1And obtaining corresponding displacement and speed according to the control equation as a constant so as to obtain a model at the next moment.
The virtual cutting algorithm based on the silica gel healing model is further designed in that the healing degree is increased along with the increase of time in the step 3), the fixed vertex angle is unchanged in the incision image, the vertex moves upwards along with the healing degree, and the model is updated; in the suture map, the fixed suture point is fixed, the vertex angle at the suture point and the vertex angle of the incision are kept unchanged, the vertex angle at the incision moves upwards along with the healing degree, and the model is updated.
The invention has the following advantages:
(1) the method incorporates a silica gel healing model into the existing grid, wherein the friction force of the biological soft tissue to the virtual scalpel is the basic characteristic of the biological soft tissue, and the simulation cutting of the friction force is more practical, so that the method is more beneficial for operating doctors to grasp the force application degree.
(2) The method simulates the automatic healing condition of the incision along with time by using the viscosity of the silica gel, is more practical and is suitable for operations such as suturing and the like.
(3) The silica gel healing model provided by the method has stronger robustness, is suitable for most virtual operations, and is beneficial for operating doctors to rub the operation skills in a virtual reality system.
Drawings
Fig. 1 is a schematic diagram of cutting.
Fig. 2 is a diagram of a silica gel healing mesh model.
Fig. 3 is a side view of a model of the silica gel healing grid shown in fig. 2.
FIG. 4 is a force model schematic.
Fig. 5 is a schematic view of a cut.
FIG. 6 is a schematic view of a suture.
In the figure, 1-grid, 2-silica gel, 3-suture point, 4-incision to be healed, 5-contact surface and 6-virtual scalpel.
Detailed Description
The technical solution of the present invention is further explained with reference to the specific embodiments and the accompanying drawings.
As shown in fig. 1, the virtual cutting algorithm based on the silica gel healing model according to the embodiment of the present invention mainly includes the steps of establishing a finite element control equation, detecting a cutting condition to generate a cut, detecting a real-time state, and rendering in real time, which are specifically as follows:
step 1: and establishing a finite element control equation.
Physical simulation is a key part of the virtual world of a surgical simulator, and a physical-based volumetric model provides users with more realistic and interactive performance. However, organizing the large amount of data of the model leads to relatively complex computational problems, since computing the stiffness matrix of the finite elements or the entire model reduces the fluency and efficiency of the simulation system. MSM can easily overcome this problem and model volumetric virtual models in a more efficient way, but the modeling parameters of MSM are not real tissue properties. The tensor-mass model is as efficient as the MSM model in computational complexity, but its parameters are physically based and applied to our vessel model in the interventional surgical simulator. A virtual cutting algorithm is provided based on a triangle tensor-mass model and combined with a silica gel healing model.
The vectorized form of the finite element control equation can be expressed as:
where M is the quality matrix of the element, U is the displacement vector of the node, Fext，Fint，FdampRespectively representing the external force, internal force and damping force at a single node. Fext and FdampDerived in the following form:
where K is the global stiffness matrix and C is the damping force matrix, the relationship between them is expressed as:
{C}＝α[M]+β[K](3)
where α, β are Rayleigh coefficients.
The key idea of TMM is to simply combine local element stiffness matrices to form a global stiffness matrix, breaking the traditional constraints. The TMM method decomposes the stiffness matrix into a node component and an edge component, and accumulates the two components onto the node and edge, respectively. The triangular mesh is used as a finite element of a virtual blood vessel model, and referring to fig. 2 and 3, a local stiffness matrix of a single unit is introduced:
[ke]＝∫[B]T[E][B]dS (4)
wherein ,keIs the global stiffness matrix of the individual elements, B is the strain of the displacement matrix, and E is the elastic modulus matrix (young's modulus) of the tissue properties. Assuming that the vessel surfaces are equidistant, the properties of the soft tissue have the same performance in any direction. The young's modulus matrix of the finite elements is expressed as:
where λ and μ are the lammei constants (lame constants), two material-related quantities in the stress-strain relationship.
There are three nodes in a triangle cell, each node having three degrees of freedom (DOF). Setting the position of each node to xi(i ═ 1,2,3,4), the position matrix of the finite element can be represented as:
the strain and displacement matrix B is represented as the following array:
[B]＝[B1B2B3](7)
substituting (7) into (4) results in a 3 × 3 array of local cell stiffness matrices, expressed as:
wherein ,is the tensor in the TMM model,it is shown that the node of the i-th node,representing edges ij, i and j as local indices of nodes in a triangular finite element, the tensors of the local triangular finite element are combined into a global tensor, denoted as K, in the TMM mechanical modelIJI, J are globally defined.
Another mechanism is quality concentration, which assigns the quality of a triangle to each node. The mass of a triangle is derived from the equation:
wherein ,mIRepresenting the mass of the ith triangle, e is composed of all triangle finite elements adjacent to the ith node, ρ is the density of the tissue material, SeThe triangular finite element e. The mass matrix M obtained by the mass concentration method is symmetric about a diagonal. Discretizing the equation of dynamics (1) on each node:
wherein ,μI(t)＝[μI(t),υI(t),ωI(t)]TIs the displacement vector of the I-th node. The internal force of the ith node is:
the damping force at the I-th node is:
wherein ,representing the velocity of the ith node.
Most methods of advancing the simulator have in common that they can be expressed as a time-varying partial differential equation which is solved after discretization as an ordinary differential equation:
wherein, the vector X and the diagonal matrix M represent the position and mass distribution of the soft model, E represents the internal energy of the model, and F represents other forces acting on the model.
Give the system t0Known position x (t)0) And speedThe purpose is to obtain a system t0Position x (t) of + h0+ h) and speedTo compute a new state using implicit techniques, the dynamic equations of the system need to be solved. According to newton's law, the kinetic equation of the system can be expressed as:
by defining the velocity v of the system asIt can be converted into a first order differential equation:
the implicit forward euler method defines the discrete dynamic equation as:
apply a Taylor series expansion to f and make a first order approximation:
reshaping (18) with (19) yields:
Δ x-h (ν) was calculated0+ Δ ν) to calculate the next position x (t)0+h)＝x0+ Δ x and velocity v (t)0+h)＝υ0+Δυ。
Step 2) detecting the cutting conditions to generate an incision (as shown in figure 1), and generating a grid model (as shown in figures 2 and 3) including the silica gel healing model in real time.
In a true cut, the following two important interactions occur during penetration of the scalpel through soft tissue. First, as the cutting force increases, deformation of the soft tissue continues to occur. Separation does not occur until the cutting force applied to the soft tissue exceeds a threshold level. Second, when the stress exerted on the soft tissue reaches the fracture stress, the soft tissue will be incised and begin to expand rapidly as the cutting force drops sharply. Once the soft tissue is incised, it will deform in the opposite direction to the center of the cutting plane. Thus, the cutting process can be divided into three stages. The deformation is more closely represented using a deformation model that includes nonlinear viscoelasticity.
The scalpel typically cuts the soft tissue only in the direction of the blade, so the cut plane must be determined before calculating the soft tissue deformation. Since the cut surface is imaginary, the points obtained by the collision detection are used to adapt the cut surface. In geometry, the equation for a plane can be expressed as:
Ax+By+Cz+D＝0 (20)
when C ≠ 0, there is:
definition ofComprises the following steps:
z＝a0x+a1y+a2 (22)
suppose there are n collision points Pi(xi,yi,zi) The cutting surface formed by the points meets the requirement:
when in useThen the above equation reaches a minimum. Thus:
solving the above equation, the coefficient a can be obtained0,a1,a2And then a cut surface is obtained.
Along with the cutting of virtual scalpel, in time produce the mesh model that adds the silica gel healing model: and generating a grid model on the contact surface of the grid scalpel in real time, and adding a layer of silica gel on the surface of the grid model.
And step 3: and detecting the state in real time.
When the biological soft tissue is cut by the scalpel, a small friction force is generated on the scalpel; and the opening generated by cutting is spontaneously and locally healed due to the viscoelasticity and the like of the biological soft tissue. The two points are added into the virtual operation system, so that the reality can be better simulated, and the operating doctor can better mill the technology.
The friction force of the biological soft tissue to the scalpel and the spontaneous healing phenomenon of the biological soft tissue are simulated respectively by the friction force between the silica gel and the scalpel and the viscosity of the silica gel.
Considering that the friction force generated in the cutting process is sliding friction force, and considering that the situation that static friction force is generated due to the fact that cutting cannot be performed is defined as follows:
Ff＝μFN1(26)
wherein ,FfMu is a friction factor which is the friction force of the current silica gel to the scalpel, and is obtained by experiments and represents the linear relation between the positive pressure and the generated friction force, FN1Representing the positive pressure of the current cutting force against the mesh face.
The force model diagram of fig. 4, wherein:
wherein ,F1In order to provide the cutting force,half of the apex angle of the incision, f2Is the component of the cutting force parallel to the cutting plane.
The overlapping portion of the incision top end in the incision figure (see fig. 5) and the overlapping portion of the suture point and the incision top end in the suture figure (see fig. 6) represent silicone contacts, defining:
α＝f(t) (29)
where α represents the degree of healing (in percent), t represents time, and f represents a piecewise function that can be expressed as:
wherein ,k1,k2Is two constants, derived from experiments, t1Constant, at which point the degree of healing is 100%. And (4) combining the control equation established in the first step to obtain corresponding displacement and speed so as to obtain a model at the next moment.
The healing degree is increased along with the increase of time, in the incision image, the fixed vertex angle is unchanged, the vertex moves upwards along with the healing degree, and the model is updated; in the suture map, the fixed suture point is fixed, the vertex angle at the suture point and the vertex angle of the incision are kept unchanged, the vertex angle at the incision moves upwards along with the healing degree, and the model is updated.
And 4, step 4: and (5) rendering in real time, namely rendering the incision in real time and showing a healing effect.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (9)
1. A virtual cutting algorithm based on a silica gel healing model is characterized by comprising the following steps:
step 1) establishing a finite element control equation;
step 2) detecting cutting conditions to generate cuts, and generating a grid model incorporated into the silica gel healing model in real time;
step 3), detecting the real-time state;
step 4), real-time rendering: and rendering the incision in real time and showing the healing effect.
2. The virtual cutting algorithm based on the silica gel healing model according to claim 1, wherein the step 1) comprises the steps of:
step 1-1) obtaining a vectorized form of a finite element control equation according to formula (1):
where M is the quality matrix of the element, U is the displacement vector of the node, Fext，Fint，FdampRespectively representing external force, internal force and damping force on a single node;
step 1-2) adopting a triangular mesh as a finite element of the virtual blood vessel model, and introducing a local rigidity matrix of a single triangular unit as shown in formula (2):
[ke]＝∫[B]T[E][B]dS (2)
wherein ,keIs a global stiffness matrix of a single unit, B is the strain of the displacement matrix, E is the elastic modulus matrix of the tissue properties;
step 1-3) setting each node in the triangular unit to have three degrees of freedom, and setting the position of each node as xi(i ═ 1,2,3,4), the position matrix of the finite elements is as in (3):
step 1-4) the quality of the triangle is distributed to each node according to a quality concentration mechanism, and the quality of one triangle is obtained from an equation according to the formula (4):
wherein ,mIRepresenting the mass of the ith triangle, e is composed of all triangle finite elements adjacent to the ith node, ρ is the density of the tissue material, SeA region represented by a triangular finite element e;
steps 1 to 5) Give the system t0Known position x (t)0) And speedCalculating to obtain a system t according to a dynamic equation of the system0Position x (t) of + h0+ h) and speed
3. The virtual cutting algorithm based on the silica gel healing model according to claim 2, wherein the blood vessel surfaces are set to be equidistant in the step 1-2), and then the elastic modulus matrix of the tissue characteristics is represented as:
where λ and μ are the lam é constants.
4. The virtual cutting algorithm based on the silica gel healing model according to claim 2, characterized in that the steps 1-4) zhong1 discretizes the dynamic equation (1) on each node according to equation (6):
wherein ,μI(t)＝[μI(t),υI(t),ωI(t)]TIs the displacement vector of the I-th node;
the internal force of the I-th node is obtained according to equation (7):
the damping force at the I-th node is obtained according to equation (8):
wherein ,representing the velocity of the ith node.
5. The virtual cutting algorithm based on the silica gel healing model according to claim 2, wherein in the step 1-5),
firstly, representing the advancement of a model through a time-varying partial differential equation, and then taking the dispersed partial differential equation as an ordinary differential equation, as shown in formula (9):
wherein, the vector X represents the position of the soft model, the diagonal matrix M X represents the mass distribution of the soft model, e represents the internal energy of the model, and F represents other forces acting on the model;
then according to Newton's law, the kinetic equation of the system is obtained as follows:
by subsequently defining the velocity v of the system asConversion to a first order differential equation:
the implicit forward euler method defines the discrete dynamic equation as:
in the formula, Δ ν represents a velocity difference between adjacent positions, and Δ x represents a distance between adjacent positions;
a taylor series expansion is applied to f and a first order approximation is made according to equation (13):
remolding formula (13) according to formula (14);
finally, Δ x — h (ν) is calculated0+ Δ ν) to calculate the next position x (t)0+h)＝x0+ Δ x and velocity v (t)0+h)＝υ0+Δυ。
6. The virtual cutting algorithm based on the silica gel healing model according to claim 1, wherein in the step 2), the cutting process is divided into three stages, a deformation model containing nonlinear viscoelasticity is adopted,
a plane equation is constructed according to equation (15):
Ax+By+Cz+D＝0 (15)
when C ≠ 0, there is:
definition ofComprises the following steps:
z＝a0x+a1y+a2 (17)
setting n collision points Pi(xi,yi,zi) And the formed cutting surface:
when in useWhen k is 0,1,2, formula (18) reaches the minimum value, and thus formula (19) and formula (20) are obtained
Solving the equations (19) and (20) to obtain the coefficient a0,a1,a2And then a cut surface is obtained.
7. The virtual cutting algorithm based on the silica gel healing model according to claim 1, characterized in that the mesh model added to the silica gel healing model is generated in time as the virtual scalpel cuts in step 2): and generating a grid model on the contact surface of the grid and the scalpel in real time, and adding a layer of silica gel on the surface of the grid model.
8. The virtual cutting algorithm based on the silica gel healing model as claimed in claim 1, wherein the step 3) is performed in
The frictional force of biological soft tissue to the scalpel is simulated through the frictional force between silica gel and the sword, and the spontaneous healing phenomenon of biological soft tissue is simulated through the viscidity of silica gel, specifically is:
defining the friction force generated in the cutting process as sliding friction force, and defining:
Ff＝μFN1(21)
wherein ,FfMu is a friction factor which is the friction force of the current silica gel to the scalpel, and is obtained by experiments and represents the linear relation between the positive pressure and the generated friction force, FN1Representing the positive pressure of the current cutting force against the mesh face. Constructing a force model according to the formula (22) and the formula (23):
wherein ,F1In order to provide the cutting force,half of the apex angle of the incision, f2Is the component of the cutting force parallel to the cutting plane. And setting the overlapped part of the top end of the incision and the overlapped part of the seaming point and the top end of the incision in the seaming graph to represent the contact of the silica gel, wherein the formula (24):
α＝f(t) (24)
where α represents the degree of healing (in percent), t represents time, and f represents a piecewise function that can be expressed as:
wherein ,k1,k2Is two constants, t1And obtaining corresponding displacement and speed according to the control equation as a constant so as to obtain a model at the next moment.
9. The virtual cutting algorithm based on the silica gel healing model according to claim 1, wherein the healing degree increases with the increase of time in the step 3), the fixed vertex angle is unchanged in the incision map, and the vertex moves upwards with the healing degree to update the model; in the suture map, the fixed suture point is fixed, the vertex angle at the suture point and the vertex angle of the incision are kept unchanged, the vertex angle at the incision moves upwards along with the healing degree, and the model is updated.
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| CN104318056A (en) * | 2014-09-24 | 2015-01-28 | 北京航空航天大学 | Soft tissue deformation and cutting simulation method based on position dynamics |
| CN105302974A (en) * | 2015-11-06 | 2016-02-03 | 北京航空航天大学 | Real-time cutting simulation method of flexible object on the basis of finite element and time-variant modal analysis |
| CN105559887A (en) * | 2015-12-11 | 2016-05-11 | 哈尔滨工业大学 | Operation cutting training system and method based on force feedback and used for surgical robot |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN104318056A (en) * | 2014-09-24 | 2015-01-28 | 北京航空航天大学 | Soft tissue deformation and cutting simulation method based on position dynamics |
| CN105302974A (en) * | 2015-11-06 | 2016-02-03 | 北京航空航天大学 | Real-time cutting simulation method of flexible object on the basis of finite element and time-variant modal analysis |
| CN105559887A (en) * | 2015-12-11 | 2016-05-11 | 哈尔滨工业大学 | Operation cutting training system and method based on force feedback and used for surgical robot |
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