Soft tissue deformation simulation method based on finite element spring

Abstract

The invention relates to a soft tissue deformation simulation method based on a finite element spring, and the method comprises the steps: constructing a soft tissue spring model based on the structure parameters of a to-be-simulated soft tissue, the soft tissue spring model comprises a structure spring used for maintaining the structure, a bending spring used for preventing the soft tissue from being excessively bent, and a shearing spring used for simulating the shearing characteristic. Dampers are added between the two ends of the structural springs, and each damper is connected with the corresponding structural spring in parallel; based on the constructed soft tissue spring model, calculating an elastic coefficient of a spring and a damping coefficient of a damper by utilizing soft tissue finite element parameters, and describing a stress-strain relationship of the soft tissue by adopting a piecewise function; and based on the constructed soft tissue spring model, simulating the deformation process of the soft tissue, determining the position coordinates of the mass points of the soft tissue spring model in the deformation process, and realizing soft tissue deformation simulation. Compared with the prior art, the method has the advantages that the authenticity of a finite element method and the real-time performance of spring simulation are combined, and the like.

Description

Technical Field

[0001] The invention relates to the technical field of soft tissue simulation, and in particular to a soft tissue deformation simulation method based on a finite element spring. Background Art

[0002] Due to advances in medical technology and increased complexity of surgeries, hospitals have continuously increased their requirements for doctors' surgical skills in recent years. However, the traditional surgical training model is costly and inefficient. The fundamental reason is that the training materials cannot be reused and there are differences between the materials and the human body.

[0003] In recent years, based on the development of computer graphics and computer hardware conditions, virtual surgery systems use computer technology to build a three-dimensional virtual environment and use medical images to establish human organ models. Through tactile and visual devices, they simulate the surgical process, allowing doctors to obtain a realistic training experience, greatly improving efficiency and reducing costs.

[0004] The ultimate effect of the surgical simulation system requires a trade-off between authenticity and real-time performance. In order to achieve the realism of real-time interaction and enhance the practical value of virtual surgical training, soft tissue simulation is its core. The key to soft tissue modeling is whether it can simulate the deformation of soft tissue in real time and realistically.

[0005] In the construction of the mechanical model of the virtual surgery system, the most commonly used are the mass spring model (MSM) and the finite element model. The mass spring model has a simple structure, fast calculation speed, and good real-time performance, but it has poor stability and is prone to model collapse and slow deformation recovery when the deformation range is large. The finite element model (FEM) discretizes the model into units, analyzes each unit and then synthesizes them. It has high simulation accuracy and strong realism, but it is complex in calculation, poor in real-time performance, and has high hardware requirements. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a soft tissue deformation simulation method based on finite element spring with high real-time performance, strain relaxation and more realistic model.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A soft tissue deformation simulation method based on finite element spring comprises the following steps:

[0009] Based on the structural parameters of the soft tissue to be simulated, a soft tissue spring model is constructed, wherein the soft tissue spring model includes a structural spring for maintaining the structure, a bending spring for preventing excessive bending of the soft tissue, and a shear spring for simulating shear characteristics;

[0010] Add dampers between the two ends of the structural spring, and each damper is connected in parallel with the corresponding structural spring;

[0011] Based on the constructed soft tissue spring model, the elastic coefficient of the spring and the damping coefficient of the damper are calculated using the soft tissue finite element parameters, and a piecewise function is used to describe the stress-strain relationship of the soft tissue.

[0012] Based on the constructed soft tissue spring model, the deformation process of the soft tissue is simulated, the position coordinates of the mass points of the soft tissue spring model during the deformation process are determined, and the soft tissue deformation simulation is realized.

[0013] Furthermore, the structural springs are distributed in the horizontal direction and the vertical direction, and masses are provided at both ends of each structural spring. The bending spring is located between two masses with a mass in the middle, and the shear spring connects the two mass points in the diagonal direction.

[0014] Furthermore, the piecewise function expression of the elastic coefficient of the spring is:

[0015]

[0016] In the formula, k s is the elastic coefficient of the spring, v is the Poisson's ratio of the soft tissue material, A is the cross-sectional area of ​​the soft tissue, E0 is the initial Young's modulus of the soft tissue material, is the initial length of the spring, ε0 is the strain threshold, ε is the strain magnitude, and is determined by the length of the spring x ij Determine, a is the coefficient, which is determined by Poisson's ratio v, Young's modulus E and strain size ε.

[0017] Furthermore, the calculation expression of the damping coefficient of the damper is:

[0018] k d =ηk s

[0019] In the formula, k d is the damping coefficient of the damper, η is the linear coefficient of the damping coefficient and the spring coefficient, k s is the elastic constant of the spring.

[0020] Furthermore, the calculation expression of the elastic force exerted by the spring in the soft tissue spring model is:

[0021]

[0022] In the formula, f si is the elastic force applied by the spring corresponding to mass point i, k s is the elastic constant of the spring, x ij is the length of the spring between mass point i and mass point j, is the initial length of the spring.

[0023] Furthermore, the deformation process of the simulated soft tissue is specifically as follows: in a virtual environment, when the soft tissue spring model interacts with the outside world, the interaction point is used as the force point, and then the deformation of all springs is detected and calculated within the force area formed by the force point, and the spring force is calculated based on a piecewise function of the elastic coefficient of the spring; according to the synthesis of all spring forces, the displacement of each particle at the next moment is derived based on the numerical integration method, and the particle position is updated to realize the deformation simulation of the soft tissue.

[0024] Furthermore, the interaction point is determined using a nearest neighbor method of collision detection.

[0025] Furthermore, the soft tissue spring model is constructed based on surface node information of the soft tissue to be simulated.

[0026] Furthermore, when the external force acting on the soft tissue spring model disappears, each particle gradually returns to an undeformed state.

[0027] Furthermore, the method displays the deformation simulation process of the soft tissue by means of real-time image drawing.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] (1) The present invention integrates the soft tissue modeling methods of the finite element method and the mass spring method. By setting a structural spring for maintaining the structure, a bending spring for preventing excessive bending of the soft tissue, and a shear spring for simulating shear characteristics, the surface node information of the soft tissue can be simulated. The damper is connected in parallel with the structural spring to simulate the strain relaxation and hysteresis in the viscoelasticity of the soft tissue, which well simulates the nonlinearity and viscoelasticity of the soft tissue. The spring elastic parameters and the damper damping parameters are selected through the finite element constitutive equation, and the piecewise function is used to simulate the nonlinearity of the soft tissue deformation. The model is more realistic, which effectively solves the problem of low authenticity and real-time performance of the virtual simulation model.

[0030] (2) The present invention combines the authenticity of the finite element method and the real-time nature of the spring simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A schematic flow chart of a soft tissue deformation simulation method based on a finite element spring provided in an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of a topological structure of a spring model provided in an embodiment of the present invention;

[0033] Figure 3 A schematic diagram of a spring damping model provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0035] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0036] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0037] Example 1

[0038] like Figure 1 As shown, this embodiment provides a soft tissue deformation simulation method based on a finite element spring, comprising the following steps:

[0039] S1: Based on the structural parameters of the soft tissue to be simulated, a soft tissue spring model is constructed. The soft tissue spring model includes a structural spring for maintaining the structure, a bending spring for preventing the soft tissue from excessive bending, and a shear spring for simulating shear characteristics. These mass spring models are used to simulate the surface node information of the soft tissue;

[0040] Optionally, the structural springs are distributed in the horizontal direction and the vertical direction, each structural spring has a mass point at both ends, the bending spring is located between two mass points with a mass point in the middle, and the shear spring connects the two mass points in the diagonal direction;

[0041] S2: Add dampers between the two ends of the structural spring. Each damper is connected in parallel with the corresponding structural spring. These dampers are used to simulate the strain relaxation and hysteresis in the viscoelasticity of soft tissue.

[0042] S3: Based on the constructed soft tissue spring model, the elastic coefficient of the spring and the damping coefficient of the damper are calculated using the soft tissue finite element parameters, and a piecewise function is used to describe the stress-strain relationship of the soft tissue;

[0043] S4: Based on the constructed soft tissue spring model, the deformation process of the soft tissue is simulated, the position coordinates of the mass points of the soft tissue spring model during the deformation process are determined, and the soft tissue deformation simulation is realized.

[0044] In step S1 of this embodiment, the following is established: Figure 2 The topological structure shown constructs a soft tissue model. The horizontal and vertical directions are structural springs that maintain the structure of the soft tissue model. The spring between two particles separated by one particle is a bending spring that prevents excessive bending of the soft tissue. The spring connected in the diagonal direction is a shear spring that imitates the shear properties of the soft tissue.

[0045] In step S2, a damper is connected in parallel to each spring of the horizontal and vertical structures, such as Figure 3 shown.

[0046] In step S3, the specific calculation process is as follows:

[0047] According to Newton's second law, the forces acting on the model are divided into external forces and internal forces. The internal forces can be divided into the elastic force f exerted by the spring si and the damping force f applied by the damper di According to Hooke's theorem of the spring and the finite element constitutive equation, the relationship between the elastic force can be obtained:

[0048]

[0049] where k s is the elastic constant of the spring, x ij is the length of the spring between mass point i and mass point j, is the initial length of the spring, v is the Poisson's ratio of the soft tissue material, E is the Young's modulus of the soft tissue material, and A is the cross-sectional area of ​​the soft tissue. Considering the nonlinearity of the soft tissue, a piecewise function is used to describe the stress-strain relationship of the soft tissue. The Young's modulus of the linear part is constant, and the stress-strain relationship is linear. The stress-strain relationship of the nonlinear part is an exponential relationship:

[0050]

[0051] This function is used to simulate the elasticity of soft tissue materials. It simulates the nonlinear characteristics of materials through function segmentation, where ε is the strain size, which can be obtained through the length x of the spring. ij a can be determined by Poisson's ratio v, elastic modulus E and strain size ε. ε0 is the threshold value, which can be determined by the soft tissue material properties. The hysteresis and stress relaxation of the soft tissue material are simulated by the damper. The damping coefficient is linearly related to the spring coefficient, and the linear coefficient is η:

[0052] k d =ηk s

[0053] The η value can be selected according to the soft tissue material, generally 0.1 to 0.3, and finally the key parameters can be established according to the finite element parameters of different soft tissues, such as Poisson's ratio v, elastic modulus E, cross-sectional area A, and strain threshold;

[0054] The deformation simulation process in step S4 includes: in the virtual environment, when the model interacts with the outside world, the interaction point is used as the force point. The interaction point is determined by the nearest neighbor method of collision detection. After the force point is determined, all springs in the force area are detected to calculate the deformation. If the deformation is within the set threshold, the linear model is used to calculate the spring force; if it exceeds the threshold, the nonlinear model is used. According to the synthesis of all spring forces, the displacement of each particle at the next moment is derived based on the numerical integration method. The particle position is updated to achieve the deformation of the soft tissue.

[0055] When the external force is removed, the tissue will gradually return to its undeformed state. The entire simulation process is intuitively presented by redrawing the image in real time.

[0056] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A soft tissue deformation simulation method based on finite element spring, characterized in that: The following steps are involved: Based on the structural parameters of the soft tissue to be simulated, a soft tissue spring model is constructed, wherein the soft tissue spring model includes a structural spring for maintaining the structure, a bending spring for preventing excessive bending of the soft tissue, and a shear spring for simulating shear characteristics; Add dampers between the two ends of the structural spring, and each damper is connected in parallel with the corresponding structural spring; Based on the constructed soft tissue spring model, the elastic coefficient of the spring and the damping coefficient of the damper are calculated using the soft tissue finite element parameters, and a piecewise function is used to describe the stress-strain relationship of the soft tissue. Based on the constructed soft tissue spring model, the deformation process of the soft tissue is simulated, the position coordinates of the mass points of the soft tissue spring model during the deformation process are determined, and the soft tissue deformation simulation is realized.

2. The soft tissue deformation simulation method based on finite element spring according to claim 1, characterized in that: The structural springs are distributed in the horizontal direction and the vertical direction. Both ends of each structural spring are provided with mass points. The bending spring is located between two mass points with a mass point in the middle. The shear spring connects the two mass points in the diagonal direction.

3. The soft tissue deformation simulation method based on finite element spring according to claim 1, characterized in that: The piecewise function expression of the elastic coefficient of the spring is: In the formula, k s is the elastic coefficient of the spring, v is the Poisson's ratio of the soft tissue material, A is the cross-sectional area of ​​the soft tissue, E0 is the initial Young's modulus of the soft tissue material, is the initial length of the spring, ε0 is the strain threshold, ε is the strain magnitude, and is determined by the length of the spring x ij Determine, a is the coefficient, which is determined by Poisson's ratio v, Young's modulus E and strain size ε.

4. The soft tissue deformation simulation method based on finite element spring according to claim 3, characterized in that: The calculation expression of the damping coefficient of the damper is: k d =ηk s In the formula, k d is the damping coefficient of the damper, η is the linear coefficient of the damping coefficient and the spring coefficient, k s is the elastic constant of the spring.

5. The soft tissue deformation simulation method based on finite element spring according to claim 3, characterized in that: The calculation expression of the elastic force exerted by the spring in the soft tissue spring model is: In the formula, f si is the elastic force applied by the spring corresponding to mass point i, k s is the elastic constant of the spring, x ij is the length of the spring between mass point i and mass point j, is the initial length of the spring.

6. The soft tissue deformation simulation method based on finite element spring according to claim 3, characterized in that: The soft tissue deformation simulation process is specifically as follows: in a virtual environment, when the soft tissue spring model interacts with the outside world, the interaction point is used as a force point, and then the deformation of all springs is detected and calculated within the force area formed by the force point, and the spring force is calculated based on a piecewise function of the elastic coefficient of the spring; according to the synthesis of all spring forces, the displacement of each particle at the next moment is derived based on the numerical integration method, and the particle position is updated to realize the deformation simulation of the soft tissue.

7. The soft tissue deformation simulation method based on finite element spring according to claim 6, characterized in that: The interaction points are determined using the nearest neighbor method of collision detection.

8. The soft tissue deformation simulation method based on finite element spring according to claim 6, characterized in that: The soft tissue spring model is constructed based on the surface node information of the soft tissue to be simulated.

9. The soft tissue deformation simulation method based on finite element spring according to claim 6, characterized in that: When the external force on the soft tissue spring model disappears, each mass point gradually returns to an undeformed state.

10. The soft tissue deformation simulation method based on finite element spring according to claim 6, characterized in that: The method displays the deformation simulation process of the soft tissue by means of real-time image drawing.

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