CN109033641B - Virtual cutting algorithm based on silica gel healing model - Google Patents
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- 230000035876 healing Effects 0.000 title claims abstract description 57
- 239000000741 silica gel Substances 0.000 title claims abstract description 45
- 229910002027 silica gel Inorganic materials 0.000 title claims abstract description 45
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 title claims abstract description 44
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 24
- 238000005520 cutting process Methods 0.000 claims abstract description 38
- 210000004872 soft tissue Anatomy 0.000 claims abstract description 24
- 238000009877 rendering Methods 0.000 claims abstract description 10
- 238000001514 detection method Methods 0.000 claims abstract description 4
- 239000011159 matrix material Substances 0.000 claims description 30
- 238000000034 method Methods 0.000 claims description 19
- 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
- 229920001296 polysiloxane Polymers 0.000 claims description 7
- 238000002474 experimental method Methods 0.000 claims description 4
- 239000000463 material Substances 0.000 claims description 4
- 230000002269 spontaneous effect Effects 0.000 claims description 3
- 238000006243 chemical reaction Methods 0.000 claims description 2
- 230000002792 vascular Effects 0.000 claims 1
- 230000009286 beneficial effect Effects 0.000 abstract description 3
- 238000004088 simulation Methods 0.000 description 6
- 238000010586 diagram Methods 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- 210000004204 blood vessel Anatomy 0.000 description 1
- 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
- 238000013152 interventional procedure Methods 0.000 description 1
- 230000035515 penetration Effects 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 provides a virtual cutting algorithm based on a silica gel healing model, which specifically comprises the following steps: step 1), establishing a finite element control equation; step 2) detecting a cutting condition to generate a notch, and generating a grid model which is incorporated into a silica gel healing model in real time; step 3) real-time state detection; step 4) real-time rendering: and rendering the incision in real time, and displaying the healing effect. The beneficial effects are that: the silica gel healing model is incorporated, wherein the friction force of the biological soft tissue to the virtual scalpel is a basic characteristic of the biological soft tissue, and the simulated cutting by the friction force is more practical and is more beneficial to the operator to grasp the force application 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, simulation of surgical training by a virtual reality platform is possible. Virtual surgery gives great convenience to medical staff, and they can use the technique to carry out repeated simulation exercises, thereby improving their own technique. The current virtual surgery presents the process of simulating the surgery on a platform through modeling, rendering and calculation, and a finite element model, a mesh-free model and the like are used. However, the aspects considered by the current virtual surgery techniques are still not comprehensive and the reality is still insufficient. In the process of virtual cutting, the friction force of biological soft tissues on a scalpel influences the force application degree of a surgeon, and the difficulty degree of cutting is often different at different parts of the body, so that the surgeon is required to grasp the force so as to grasp the cutting depth; the self-healing ability of biological soft tissues is also a very important ring, and the incision types are roughly divided into two types according to the size, shape and depth of the incision: the incision needs to be sutured, the former needs to be sutured and repaired, and the latter can be self-healed.
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 through an improved grid model and enable an operator to control operation force under the condition of not reducing deformation precision, and 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 a cutting condition to generate a notch, and generating a grid model which is incorporated into a silica gel healing model in real time;
step 3) real-time state detection;
step 4) real-time rendering: and rendering the incision in real time, and displaying 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 version of the finite element control equation according to equation (1):
wherein M is a mass matrix of elements, U is a displacement vector of the node, F ext ，F int ，F damp Respectively representing external force, internal force and damping force on a single node;
step 1-2) adopting a triangular mesh as a finite element of a virtual blood vessel model, and introducing a local stiffness matrix of a single triangular unit as shown in formula (2):
[k e ]＝∫[B] T [E][B]dS (2)
wherein ,ke Is the global stiffness matrix of the single unit, B is the strain of the displacement matrix, E is the elastic modulus matrix of the tissue characteristics;
step 1-3) setting three degrees of freedom for each node in the triangle unit, and setting the position of each node as x i (i=1, 2,3, 4), a finite element positional matrix such as (3):
step 1-4) assigning the mass of the triangle to each node according to a mass concentration mechanism, deriving the mass of a triangle from the equation according to equation (4):
wherein ,mI Representing 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, S e A region represented by a triangle finite element e;
step 1-5) System t is given 0 Is (t) 0 ) And speed of
Calculating according to a dynamic equation of the system to obtain a system t 0 Position x (t) of +h 0 +h) and velocity->
The virtual cutting algorithm based on the silica gel healing model is further designed in that the blood vessel surface is set to be equidistant in the step 1-2), and then the elastic modulus matrix of the tissue characteristics is expressed as follows:
where λ and μ are lame constants.
The virtual cutting algorithm based on the silica gel healing model is further designed in that step 1-4) zhong1 discretizes the dynamic equation (1) on each node according to equation (6):
wherein ,μI (t)＝[μ I (t),υ I (t),ω I (t)] T Is the displacement vector of the I node;
the internal force to obtain node I according to equation (7) is:
the damping force at node I is obtained according to equation (8):
wherein ,
representing the speed of the I-th node;
the virtual cutting algorithm based on the silica gel healing model is further designed in the steps 1-5), wherein in the step, the advancing of the model is firstly represented by a time-varying partial differential equation, and then the discretized partial differential equation is used as a normal differential equation, as shown in the formula (9):
where vector X represents the position of the soft model, diagonal matrix M X represents the mass distribution of the soft model, e represents the internal energy of the model, and F represents the other forces acting on the model;
and then according to Newton's law, the dynamics equation of the obtained system is as follows:
then by defining the velocity v of the system as
Conversion to a first order differential equation:
implicit forward euler method defines discrete dynamic equations as:
wherein Deltav represents the speed difference between adjacent positions, and Deltax represents the interval distance between adjacent positions respectively;
applying a taylor series expansion to f and making a first order approximation according to equation (13):
remolding the form (13) according to formula (14);
finally, Δx=h (v) 0 +Δν) to calculate the next position x (t 0 +h)＝x 0 +Δx and velocity v (t) 0 +h)＝υ 0 +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,
constructing a plane equation according to equation (15):
Ax+By+Cz+D＝0 (15)
when C.noteq.0, there are:
definition of the definition
The method comprises the following steps:
z＝a 0 x+a 1 y+a2 (17)
setting n collision points P i (x i ,y i ,z i ) The cutting surface is formed by:
when (when)
When formula (18) reaches a minimum value, formulas (19) and (20) are obtained
Solving the equation (19) and the equation (20) to obtain the coefficient a 0 ,a 1 ,a 2 Further, a cut surface was obtained.
The virtual cutting algorithm based on the silica gel healing model is further designed in that in the step 2), along with the cutting of the virtual scalpel, a grid model added into the silica gel healing model is generated in time: generating a grid model in real time on the contact surface of the grid and the scalpel, 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 in the step 3), the friction force of the biological soft tissue to the scalpel is simulated through the friction force between the silica gel and the scalpel, and the spontaneous healing phenomenon of the biological soft tissue is simulated through the viscosity of the silica gel, specifically:
defining that friction force generated in the cutting process is sliding friction force, and defining that:
F f ＝μF N1 (21)
wherein ,Ff For the friction force of the current silica gel to the scalpel, mu is a friction factor, and the linear relation between positive pressure and generated friction force is shown by experiments, F N1 Indicating 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 ,F1 In order for the cutting force to be sufficient,
is half of the vertex angle of the notch, f 2 Is the component of the cutting force parallel to the cutting plane. The overlapping portion of the incision tip and the overlapping portion of the suture point and the incision tip in the suture map are set to represent the contact of the silicone, as in formula (24):
α＝f(t) (24)
where α represents the degree of healing (expressed in percent), t represents time, and f represents a piecewise function, which can be expressed as:
wherein ,k1 ,k 2 Is two constants, t 1 And obtaining corresponding displacement and speed according to the control equation as constants, and further obtaining a model at the next moment.
The virtual cutting algorithm based on the silica gel healing model is further designed in that in the step 3), the healing degree is increased along with the time increase, in the incision figure, the fixed vertex angle is unchanged, the vertex moves upwards along with the healing degree, and the model is updated; in the suture graph, 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 at the incision moves upwards along with the healing degree, and the model is updated.
The invention has the following advantages:
(1) The method comprises the step of incorporating a silica gel healing model into the existing grid, wherein the friction force of the biological soft tissue to the virtual scalpel is a basic characteristic of the biological soft tissue, and the simulation cutting by the friction force is more practical, so that the operator can grasp the force application degree more easily.
(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 the operation 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 to the operators to grind the operation skills in a virtual reality system.
Drawings
Fig. 1 is a schematic cutting view.
Fig. 2 is a graph of a silica gel healing mesh model.
Fig. 3 is a side view of the silica gel healing mesh model diagram shown in fig. 2.
Fig. 4 is a force model schematic.
Fig. 5 is a schematic illustration of a cut.
Fig. 6 is a schematic view of stitching.
In the figure, 1-mesh, 2-silica gel, 3-suture points, 4-incision to be healed, 5-contact surface, 6-virtual scalpel.
Detailed Description
The technical scheme of the invention is further described with reference to the specific embodiments and the attached drawings.
Referring to fig. 1, the main steps of the virtual cutting algorithm based on the silica gel healing model according to the method of the present embodiment include building a finite element control equation, detecting cutting conditions to generate cuts, detecting real-time states, and rendering in real time, which is specifically as follows:
step 1: and establishing a finite element control equation.
Physical simulation is a critical part of the virtual world of the surgical simulator, providing users with more realistic and interactive performance based on a physical volumetric model. However, the large amount of data that organizes the model results in relatively complex computational problems, as computing the stiffness matrix of the finite element or the entire model reduces the fluency and efficiency of the simulation system. MSM can easily overcome this problem and model the volumetric virtual model in a more efficient way, but the modeling parameters of MSM are not real tissue properties. Tensor-mass models are as efficient in computational complexity as MSM models, but their parameters are physically based and applied to our vessel model in interventional procedure simulators. Based on a triangle tensor-quality model and combined with a silica gel healing model, a virtual cutting algorithm is provided.
The vectorized version of the finite element control equation can be expressed as:
wherein M is a mass matrix of elements, U is a displacement vector of the node, F ext ，F int ，F damp Respectively, an external force, an internal force and a damping force at a single node. F (F) ext and Fdamp Derived in the following form:
where K is the global stiffness matrix and C is the damping force matrix, the relationship between the two is expressed as:
{C}＝α[M]+β[K] (3)
where α, β are Rayleigh coefficients.
The key idea of TMM is to simply combine the local cell stiffness matrices to form a global stiffness matrix to break the traditional constraints. The TMM method decomposes the stiffness matrix into node and edge components and adds the two components to the nodes and edges, respectively. Triangular meshes are adopted as finite elements of the virtual vessel model, see fig. 2 and 3, and a local stiffness matrix of a single unit is introduced:
[k e ]＝∫[B] T [E][B]dS (4)
wherein ,ke Is the global stiffness matrix of the individual cells, B is the strain of the displacement matrix, and E is the elastic modulus matrix (young's modulus) of the tissue properties. The properties of soft tissue have the same properties in any direction, provided that the vessel surfaces are equidistant. The young's modulus matrix of the finite element is expressed as:
where λ and μ are lamee constants (lamee constants) and are two material related quantities in the stress-strain relationship.
There are three nodes in a triangle unit, each node having three degrees of freedom (DOF). Setting the position of each node as x i (i=1, 2,3, 4), the location matrix of the finite element can be expressed as:
the strain and displacement matrix B is represented as the following array:
[B]＝[B 1 B 2 B 3 ] (7)
bringing (7) into (4) yields an array of 3 x 3 local cell stiffness matrices, expressed as:
wherein ,
is the tensor in TMM model, +.>
Represents the ith node, +.>
Representing edges ij, i and j as local indices of nodes in a triangle finite element, tensors of the local triangle finite element are combined into a global tensor, denoted K, in TMM mechanical model IJ I, J are globally defined.
Another mechanism is quality concentration, which assigns the quality of triangles to each node. The mass of a triangle is obtained from the equation:
wherein ,mI Representing 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, S e The area represented by the triangle finite element e. The mass matrix M obtained by the mass concentration method is symmetrical about a diagonal line. Discretizing the dynamic equation (1) at each node:
wherein ,μI (t)＝[μ I (t),υ I (t),ω I (t)] T Is the displacement vector of the I-th node. The internal forces of the I-th node are:
the damping force at node I is:
wherein ,
indicating the speed of the I-th node.
Most of the methods of advancing simulators have in common that they can be expressed as a time-varying partial differential equation which is solved as a normal differential equation after discretization:
where vector X and diagonal matrix M represent the position and mass distribution of the soft model, E represents the internal energy of the model, and F represents the other forces acting on the model.
Giving a system t 0 Is (t) 0 ) And speed of
The purpose is to obtain a system t 0 Position x (t) of +h 0 +h) and velocity->
To calculate a new state using implicit techniques, the dynamic equations of the system need to be solved. The kinetic equation of the system can be expressed as:
by defining the velocity v of the system as
It can be converted into a first order differential equation:
implicit forward euler method defines discrete dynamic equations as:
apply a taylor series expansion to f and make a first order approximation:
remolding (18) with (19) to obtain:
calculate Δx=h (v) 0 +Δν) to calculate the next position x (t 0 +h)＝x 0 +Δx and velocity v (t) 0 +h)＝υ 0 +Δυ。
Step 2) detecting the cutting condition to generate an incision (fig. 1), and generating a grid model (fig. 2 and 3) incorporating the silica gel healing model in real time.
In true cutting, the following two important interactions occur during the penetration of the soft tissue by the scalpel. 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 applied to the soft tissue reaches the breaking stress, the soft tissue will be incised and begin to expand rapidly with a sharp decrease in cutting force. Once the soft tissue is incised, the soft tissue will deform in a direction opposite to the center of the cutting plane. Thus, the cutting process can be divided into three stages. Deformation is more realistically represented using a deformation model that includes nonlinear viscoelasticity.
The knife typically cuts only soft tissue in the direction of the blade, so the cut surface must be determined before the soft tissue deformation is calculated. Since the cut surface is imaginary, the point obtained by collision detection is 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.noteq.0, there are:
definition of the definition
The method comprises the following steps:
z＝a 0 x+a 1 y+a2 (22)
assume that there are n collision points P i (x i ,y i ,z i ) The cut surface formed by these points meets the requirements:
when (when)
When the above equation reaches a minimum. Thus:
solving the above to obtain the coefficient a 0 ,a 1 ,a 2 Further, a cut surface was obtained.
Along with the cutting of the virtual scalpel, a grid model added into a silica gel healing model is timely generated: 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.
Step 3: and detecting the real-time state.
When the biological soft tissue is cut by the scalpel, a small friction force is generated on the scalpel; the opening created by the incision will spontaneously heal locally due to the viscoelastic properties of biological soft tissue, etc. These two points are added in the virtual operation system, so that the reality can be better simulated, and an operator can better grind the technology.
The friction force of the biological soft tissue to the surgical knife and the spontaneous healing phenomenon of the biological soft tissue are respectively simulated by the viscosity of the silica gel and the knife.
Considering that the friction force generated in the cutting process is sliding friction force, and not considering the situation that static friction force is generated due to incapability of cutting, defining:
F f ＝μF N1 (26)
wherein ,Ff For the friction force of the current silica gel to the scalpel, mu is a friction factor, and the linear relation between positive pressure and generated friction force is shown by experiments, F N1 Indicating the positive pressure of the current cutting force against the mesh face.
The force model diagram of fig. 4, wherein:
wherein ,F1 In order for the cutting force to be sufficient,
is half of the vertex angle of the notch, f 2 Is the component of the cutting force parallel to the cutting plane.
The overlapping portion of the incision tip in the incision figure (see fig. 5) and the overlapping portion of the suture point and the incision tip in the suture figure (see fig. 6) represent the contact of the silicone, defining:
α＝f(t) (29)
where α represents the degree of healing (expressed in percent), t represents time, and f represents a piecewise function, which can be expressed as:
wherein ,k1 ,k 2 Is two constants, and t is obtained by experiment 1 Is constant, and the degree of healing is 100% at this time. And (3) combining the control equation established in the step one 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, the fixed vertex angle is unchanged in the incision diagram, the vertex moves upwards along with the healing degree, and the model is updated; in the suture graph, 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 at the incision moves upwards along with the healing degree, and the model is updated.
Step 4: and rendering in real time, namely rendering the incision in real time and displaying the healing effect.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (8)
1. The virtual cutting algorithm based on the silica gel healing model is characterized by comprising the following steps of:
step 1), establishing a finite element control equation;
step 2) detecting a cutting condition to generate a notch, and generating a grid model which is incorporated into a silica gel healing model in real time;
step 3) real-time state detection;
step 4) real-time rendering: rendering the incision in real time, and displaying healing effect; the step 1) comprises the following steps:
step 1-1) obtaining a vectorized version of the finite element control equation according to equation (1):
wherein M is a mass matrix of elements, U is a displacement vector of the node, F ext ，F int ，F damp Respectively representing external force, internal force and damping force on a single node;
step 1-2) adopting a triangular mesh as a finite element of a virtual blood vessel model, and introducing a local stiffness matrix of a single triangular unit as shown in formula (2):
wherein B is the strain of the displacement matrix, E is the elastic modulus matrix of the tissue characteristic;
is the tensor in TMM model, +.>
Representing edges ij, i and j as local indices of nodes in a triangle finite element, tensors of the local triangle finite element are combined into a global tensor, denoted k, in TMM mechanical model ij I, j are globally defined;
step 1-3) setting three degrees of freedom for each node in the triangle unit, and setting the position of each node as x i (i=1, 2,3, 4), a finite element positional matrix such as (3):
step 1-4) assigning the mass of the triangle to each node according to a mass concentration mechanism, deriving the mass of a triangle from the equation according to equation (4):
wherein ,mI Representing 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, S e A region represented by a triangle finite element e;
step 1-5) System t is given 0 Is (t) 0 ) And speed of
Calculating according to a dynamic equation of the system to obtain a system t 0 Position x (t) of +h 0 +h) and velocity->
2. The virtual cutting algorithm based on a silicone healing model according to claim 1, wherein the setting of the vascular surface in step 1-2) is equidistant, and the elastic modulus matrix of the tissue characteristics is expressed as:
where λ and μ are lame constants.
3. The virtual cutting algorithm based on the silica gel healing model according to claim 1, wherein the dynamic equation (1) at each node is discretized according to equation (6) in steps 1-4):
wherein ,μI (t)＝[μ I (t),υ I (t),ω I (t)] T Is the displacement vector of the I node;
the internal force to obtain node I according to equation (7) is:
the damping force at node I is obtained according to equation (8):
wherein ,
indicating the speed of the I-th node.
4. The virtual cutting algorithm based on a silicone healing model according to claim 1, wherein in step 1-5),
firstly, the advancing of a model is represented by a time-varying partial differential equation, and then the discretized partial differential equation is used as a normal differential equation, as shown in the formula (9):
where vector X represents the position of the soft model, diagonal matrix M X represents the mass distribution of the soft model, e represents the internal energy of the model, and F represents the other forces acting on the model;
and then according to Newton's law, the dynamics equation of the obtained system is as follows:
then by defining the velocity v of the system as
Conversion to a first order differential equation:
implicit forward euler method defines discrete dynamic equations as:
wherein Deltav represents the speed difference between adjacent positions, and Deltax represents the interval distance between adjacent positions respectively;
applying a taylor series expansion to f and making a first order approximation according to equation (13):
remolding the form (13) according to formula (14);
finally, Δx=h (v) 0 +Δν) to calculate the next position x (t 0 +h)＝x 0 +Δx and velocity v (t) 0 +h)＝υ 0 +Δυ。
5. The virtual cutting algorithm based on the silicone healing model according to claim 1, wherein in the step 2), the cutting process is divided into three stages, a deformation model including nonlinear viscoelasticity is used, and a plane equation is constructed according to the formula (15):
Ax+By+Cz+D＝0 (15)
when C.noteq.0, there are:
definition of the definition
The method comprises the following steps:
z＝a 0 x+a 1 y+a2 (17)
setting n collision points P i (x i ,y i ,z i ) The cutting surface is formed by:
when (when)
When formula (18) reaches a minimum value, formulas (19) and (20) are obtained
Solving the equation (19) and the equation (20) to obtain the coefficient a 0 ,a 1 ,a 2 Further, a cut surface was obtained.
6. The virtual cutting algorithm based on the silica gel healing model according to claim 1, wherein in the step 2), as the virtual scalpel cuts, a mesh model added to the silica gel healing model is generated in time: generating a grid model in real time on the contact surface of the grid and the scalpel, and adding a layer of silica gel on the surface of the grid model.
7. The virtual cutting algorithm based on a silicone healing model according to claim 1, wherein in the step 3)
The friction force of the biological soft tissue to the scalpel is simulated by the friction force between the silica gel and the scalpel, and the spontaneous healing phenomenon of the biological soft tissue is simulated by the viscosity of the silica gel, specifically:
defining that friction force generated in the cutting process is sliding friction force, and defining that:
F f ＝μF N1 (21)
wherein ,Ff Is at presentThe friction force of silica gel to the scalpel, mu is a friction factor, and is obtained by experiments and represents the linear relation between positive pressure and generated friction force, F N1 Positive pressure of current cutting force on grid surface; constructing a force model according to the formula (22) and the formula (23):
wherein ,F1 In order for the cutting force to be sufficient,
is half of the vertex angle of the notch, f 2 A component of the cutting force parallel to the cutting plane; the overlapping portion of the incision tip and the overlapping portion of the suture point and the incision tip in the suture map are set to represent the contact of the silicone, as in formula (24):
α＝f(t) (24)
where α represents the degree of healing (expressed in percent), t represents time, and f represents a piecewise function, which can be expressed as:
wherein ,k1 ,k 2 Is two constants, t 1 And obtaining corresponding displacement and speed according to the control equation as constants, and further obtaining a model at the next moment.
8. The virtual cutting algorithm based on the silica gel healing model according to claim 1, wherein the healing degree increases with time in the step 3), the vertex is fixed and moves upwards with the healing degree in the incision figure, and the model is updated; in the suture graph, 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 at the incision moves upwards along with the healing degree, and the model is updated.
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| CN104318056B (en) * | 2014-09-24 | 2017-05-03 | 北京航空航天大学 | Soft tissue deformation and cutting simulation method based on position dynamics |
| CN105302974B (en) * | 2015-11-06 | 2018-06-08 | 北京航空航天大学 | A kind of real-time cutting simulation method of flexible article analyzed based on finite element and time-varying modal |
| CN105559887B (en) * | 2015-12-11 | 2018-01-30 | 哈尔滨工业大学 | The surgical cut training system and method based on force feedback for operating robot |
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