A biological soft tissue virtual simulation method, system and medium

Abstract

The present invention relates to a method, system, and medium for virtual simulation of biological soft tissue, wherein the method comprises the following steps: constructing a three-dimensional soft tissue model based on medical imaging data, discretizing it into a particle system and binding initial constraint parameters; detecting collisions between particles and surgical instruments using signed distance field technology; if no collision is detected, outputting the particle position and generating simulation results; if a collision is detected, applying a repulsive force to the particle to correct the deformation path; determining whether the forces are balanced or the maximum number of iterations has been reached; if so, returning to collision detection; otherwise, updating the particle velocity in real time, predicting the particle motion trend using an implicit time integration algorithm, employing a Gauss-Seidel iteration method to couple and solve position constraints, volume constraints, shape constraints, and physical constraints, dynamically adjusting the constraint stiffness to match real tissue characteristics, and updating the particle position. Compared with the existing technology, the present invention has the advantages of ensuring that deformation conforms to the laws of real physical changes.

Description

Technical Field

[0001] The present invention relates to the technical field of soft tissue simulation modeling, and in particular to a biological soft tissue virtual simulation method, system and medium. Background Art

[0002] Biological soft tissue modeling and simulation technology is a core technology in fields such as medical training and virtual surgery. Existing techniques primarily use medical imaging data to construct soft tissue models and simulate their deformation behavior. Traditional methods rely primarily on geometric modeling, simulating deformation by extracting soft tissue surface contour features. While simple to implement, these methods focus solely on morphological changes and fail to reflect the true biomechanical properties of soft tissue, such as viscoelasticity and nonlinear deformation, resulting in insufficient simulation accuracy. Especially when dealing with dynamic interactions, the models are prone to distortion or logical errors, making them difficult to meet the requirements of high-precision surgical simulation.

[0003] To enhance realism, existing technologies have introduced physical modeling methods, which simulate the stress distribution and energy conduction of soft tissues through mechanical equations. However, such methods are extremely demanding on computing resources and typically rely on high-performance hardware for real-time solutions, significantly increasing system costs. Furthermore, physical modeling requires complex parameter settings and relies on extensive experimental data for calibration. In practical applications, this leads to long debugging cycles, poor versatility, and lengthy computational times, making it difficult to meet the demands of real-time interaction.

[0004] Position dynamics-based simulation methods optimize the deformation process through geometric constraints. Although this method improves computational efficiency, its core flaw lies in its lack of physical accuracy. For example, CN107330972A discloses a real-time soft tissue deformation method that simulates biomechanical properties, which includes the following steps: generating soft tissue physical model data based on three-dimensional visualization data of soft tissue organs; generating collision detection model data based on the soft tissue physical model data; loading the physical model data and collision detection model data through a game engine to perform collision detection; and calculating the deformed state of the soft tissue using a constrained optimization solution method. However, this method cannot accurately describe the true biomechanical properties of soft tissue, resulting in significant deviations between the deformation simulation results and the actual biological tissue response. In particular, when dealing with complex deformations or dynamic interactions, the model is prone to non-physical mutations or energy non-conservation phenomena, making it difficult to meet the requirements for rigorous simulation results in medical scenarios. Summary of the Invention

[0005] The purpose of the present invention is to provide a method, system and medium for virtual simulation of biological soft tissue, which introduces biomechanical parameters and physical properties into the traditional simulation framework based on position dynamics, and solves the problems of simulation distortion, insufficient accuracy and dynamic response mismatch caused by the lack of material property mapping mechanism in traditional methods.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A biological soft tissue virtual simulation method comprises the following steps:

[0008] Constructing 3D soft tissue models based on medical imaging data;

[0009] Discretize the three-dimensional soft tissue model into a particle system and bind the initial constraint parameters;

[0010] The collision between particles and surgical instruments is detected based on the signed distance field technology. If no collision is detected, the particle position is output and the simulation results are generated. If a collision is detected,

[0011] A repulsive force is applied to the particles to correct the deformation path, and it is determined whether the force is balanced or the maximum number of iterations has been reached. If so, collision detection is returned. Otherwise, the particle velocity is updated in real time, and the particle motion trend is predicted through an implicit time integration algorithm. The Gauss-Seidel iteration method is used to couple the position constraints, volume constraints, shape constraints, and physical constraints, and the constraint stiffness is dynamically adjusted to match the actual tissue characteristics, and the particle position is updated. Among them, in the physical constraints, the biomechanical parameters are converted into constraint weight coefficients through a parameterized mapping mechanism to support rapid switching and high-precision simulation of different tissue types.

[0012] The three-dimensional soft tissue model constructed based on medical imaging data is specifically as follows: based on the medical imaging data, the target soft tissue area is segmented and three-dimensionally reconstructed to generate a three-dimensional tetrahedral mesh model, and the mesh vertex coordinates, normal vectors, topological connection relationships and tetrahedral unit information are defined so that the geometric structure of the model is consistent with the real anatomical features, thereby obtaining a three-dimensional soft tissue model.

[0013] The discretization of the three-dimensional soft tissue model into a particle system is specifically as follows:

[0014] Each vertex of the mesh is mapped to a dynamic particle. The particle number corresponds to the vertex number one by one. The initial position of the particle directly inherits the vertex coordinates. The initial velocity is set to zero. The mass of each particle is calculated by evenly dividing the adjacent tetrahedral units.

[0015] The position constraint is expressed as:

[0016] ,

[0017] in, Represent the two vertex positions in any tetrahedral unit, a , b =1,2,3,4, d is the initial distance calibrated by the rest spring length.

[0018] The volume constraint is to maintain the volume conservation of the tetrahedron unit, which is expressed as:

[0019] ,

[0020] in, , , are the four vertex positions of any tetrahedron unit, is the initial volume of the tetrahedron, , , .

[0021] The shape constraint is expressed as:

[0022] ,

[0023] in, n Represents the total number of particles in the cluster, without considering the edge connectivity of the tetrahedron. A cluster is a set of particles in a 3D grid. and Represents the first i The particle positions before and after deformation, R represents the rotation matrix, and Represents the translation vector before and after deformation, and are the predicted rotation matrix and translation vector.

[0024] The physical constraints are expressed as:

[0025] ,

[0026] in, is the deformation gradient, and are the first and second parameters of the Lamé constant, respectively. The elastic energy density of the Neo-Hookean material is expressed as , is the energy that resists compression and expansion, It is the energy that resists deformation.

[0027] The biomechanical parameters include Young's modulus and Poisson's ratio.

[0028] A biological soft tissue virtual simulation system, used to implement the above method, the system comprises:

[0029] 3D soft tissue model construction module: constructs 3D soft tissue models based on medical imaging data;

[0030] Particle system construction and initialization module: discretizes the 3D soft tissue model into a particle system and binds initial constraint parameters;

[0031] Collision detection module: Detects collisions between particles and surgical instruments based on signed distance field technology. If no collision is detected, the particle position is output and simulation results are generated. If a collision is detected, the particle update module is called.

[0032] Particle update module: applies repulsive force to particles to correct the deformation path, determines whether the force is balanced or the maximum number of iterations is reached, and if so, calls the collision detection module for collision detection; otherwise, updates the particle velocity in real time, and predicts the particle motion trend through the implicit time integration algorithm. The Gauss-Seidel iteration method is used to couple the position constraints, volume constraints, shape constraints and physical constraints, dynamically adjusts the constraint stiffness to match the actual tissue characteristics, and updates the particle position; among the physical constraints, the biomechanical parameters are converted into constraint weight coefficients through a parameterized mapping mechanism to support rapid switching and high-precision simulation of different tissue types.

[0033] A storage medium stores a program, which implements the above method when executed.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] (1) Real-time: This paper adopts a deep fusion of the position dynamics framework and the implicit integration algorithm, and realizes fast constraint convergence through Gauss-Seidel iteration. Compared with the traditional physical simulation model, it significantly improves the computational efficiency and achieves real-time performance.

[0036] (2) Accuracy: The present invention is based on a multi-constraint coupled iterative optimization mechanism. Through the coordinated correction of volume conservation, shape matching, particle spacing stability and hyperelastic response, it ensures that the simulated deformation trajectory is strictly consistent with the nonlinear mechanical response of real biological tissues, reduces the theoretical and experimental deviations caused by modeling, and improves the accuracy of simulation modeling.

[0037] (3) Physical reality: The present invention inputs hyperelastic material constraint functions and biomechanical parameters with physical properties, so that the dynamic simulation has the physical material properties of the tissue, which is consistent with the physical real world.

[0038] (4) Diversity: This invention adjusts the initial value of the constraint by adjusting the Young's modulus, viscoelastic coefficient, etc., and accurately matches the stress relaxation and creep effects of different tissues such as tumors and muscles. It breaks through the limitation of the single mechanical properties of traditional methods and supports rapid switching and high-precision simulation of different tissue types. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the method of the present invention;

[0040] Figure 2 This is a schematic diagram of the iterative process when a collision is detected in the present invention. DETAILED DESCRIPTION

[0041] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0042] This embodiment provides a method for virtual simulation of biological soft tissue, which combines a position dynamics framework with physical constraint functions and a biomechanical parameter mapping mechanism to provide a high-precision physical model, thereby solving the problems of insufficient accuracy, low efficiency and dynamic response distortion in soft tissue deformation simulation using traditional methods.

[0043] Specifically, such as Figure 1 As shown, the method includes the following steps:

[0044] Step 1) Construct a 3D soft tissue model based on medical imaging data.

[0045] Specifically, based on medical imaging data, the target soft tissue area is segmented and three-dimensionally reconstructed to generate a three-dimensional tetrahedral mesh model. The model must fully represent the geometric morphology of the target soft tissue (such as liver, muscle, etc.), define the mesh vertex coordinates, normal vectors, topological connection relationships and tetrahedral unit information, so that the geometric structure of the model is consistent with the actual anatomical features, and obtain a three-dimensional soft tissue model.

[0046] Step 2) Discretize the 3D soft tissue model into a particle system and bind the initial constraint parameters.

[0047] Specifically, each vertex of the mesh is mapped to a dynamic particle, with particle numbers corresponding to vertex numbers. The initial positions of the particles are directly inherited from the vertex coordinates. The initial velocities of all particles are set to zero, and the mass of each particle is calculated by dividing the mass equally among the adjacent tetrahedral elements. Next, the initial positions of the particles are directly assigned to the mesh vertex coordinates, ensuring full consistency with the input 3D soft tissue model geometry.

[0048] Step 3) During surgical procedures such as cutting and suturing, collisions may occur in biological soft tissues, and external forces may be applied to the particles. Therefore, this step uses signed distance field technology to detect collisions between particles and surgical instruments. If no collision is detected, the particle position is output and the simulation results are generated. If a collision is detected, the process jumps to step 4).

[0049] In this embodiment, signed distance field technology is used to monitor the spatial interaction between particles and surgical instruments in real time, detect penetration areas, and calculate penetration depth, ensuring submillimeter detection accuracy. The core function of this module is to use a signed distance function to calculate the minimum distance between objects to determine whether a collision has occurred. Once a collision is detected, the module uses a collision detection algorithm to handle interactions between fast-moving objects and avoid penetration errors. The management of the collision response is based on the distance and normal information provided by the signed distance field, including the calculation of the rebound direction, the adjustment of the penetration depth, and the appropriate modification of the dynamic response, such as the adjustment of velocity and angular momentum.

[0050] In a preferred embodiment, generating simulation results specifically includes the following steps:

[0051] It uses physically based real-time rendering technology to accurately simulate soft tissue surfaces (such as wrinkles and subcutaneous scattering), dynamically calculate light source reflection and soft shadows, and intuitively present stress distribution through color gradients (red high-stress areas, blue low-stress areas). It supports high-resolution multi-view dynamic observation.

[0052] Three-dimensional images are presented through display devices such as virtual reality or augmented reality, supporting gesture interaction to adjust the viewing angle, and synchronizing deformation state and stress distribution in real time to achieve fully immersive visualization.

[0053] Step 4) Apply repulsive force to the particles to correct the deformation path and determine whether the forces are balanced or the maximum number of iterations has been reached. If so, return to collision detection. Otherwise, perform constrained iterative optimization. Through four powerful constraints, the object's motion is made consistent with the real physical world and the particle position is updated.

[0054] In this embodiment, the process of constrained iterative optimization is as follows: Figure 2 As shown, the following steps are included:

[0055] Particle velocities are updated in real time, and particle motion trends are predicted using an implicit time integration algorithm. The Gauss-Seidel iteration method is used to couple position, volume, shape, and physical constraints. The constraint stiffness is dynamically adjusted to match the actual tissue properties, and the particle position is updated. The system then re-evaluates whether force equilibrium has occurred or the maximum number of iterations has been reached. Prior to this step, experimentally calibrated biomechanical parameters such as Young's modulus and Poisson's ratio are loaded. These biomechanical parameters are then converted into physical constraint weight coefficients through a parameterized mapping mechanism to support rapid switching between different tissue types and high-precision simulation.

[0056] The position constraint is expressed as:

[0057] ,

[0058] in, Represent the two vertex positions in any tetrahedral unit, a , b =1,2,3,4, d is the initial distance calibrated by the rest spring length.

[0059] The volume constraint is to maintain the volume conservation of the tetrahedron unit, which is expressed as:

[0060] ,

[0061] Among them, because the 3D grid used in this embodiment is composed of tetrahedrons, , , are the four vertex positions of a tetrahedron unit, is the initial volume of the tetrahedron, 、 、 .

[0062] The shape constraint is expressed as:

[0063] ,

[0064] in, n Represents the total number of particles in the cluster, without considering the edge connectivity of the tetrahedron. A cluster is a set of particles in a 3D grid. and Represents the first i The particle positions before and after deformation, R represents the rotation matrix, and Represents the translation vector before and after deformation, and is the final minimized objective function Get the predicted rotation matrix and translation vector.

[0065] The physical constraints are expressed as:

[0066] ,

[0067] in, is the deformation gradient, and are the first and second parameters of the Lamé constant, respectively. The elastic energy density of the Neo-Hookean material is expressed as , is the energy that resists compression and expansion, It is the energy that resists deformation.

[0068] The dynamics solution process begins with the application of external forces. When the surgical instrument interacts with soft tissue (e.g., cutting or puncturing), the force feedback from the haptic device updates the particle velocity in real time. An implicit integration algorithm is then used to predict the particle's displacement trend. During this process, four types of physical constraints are applied sequentially to iteratively correct the predicted position. First, volume constraints maintain the volume conservation of the tetrahedral elements to prevent tissue collapse or expansion. Shape constraints align the local geometry before and after deformation to ensure structural stability. Position constraints adjust the spacing between adjacent particles to their initial length to eliminate excessive deformation. Finally, the nonlinear stress-strain response of the soft tissue is simulated based on physical constraints (hyperelastic material constraints) to ensure that the mechanical properties conform to real-world biological tissue behavior. After each iteration, the particle system is checked for equilibrium or the maximum number of iterations has been reached. If these conditions are not met, corrections are continued until dynamic equilibrium is reached or the process is forced to terminate. During this process, biomechanical parameters such as Young's modulus and Poisson's ratio are dynamically mapped to constraint stiffness coefficients, enabling real-time adaptation from experimental data to simulation parameters. This ensures that the mechanical differences between different tissue types (e.g., normal liver tissue and tumors) are accurately represented in the simulation.

[0069] In this embodiment, the Gauss-Seidel method is used to constrain iterative optimization, calling volume, shape, distance and hyperelastic constraints in sequence, correcting the particle position step by step, eliminating non-physical deformation, and ensuring that the mechanical response conforms to the real tissue characteristics. The Gauss-Seidel method is a method for solving a system of linear equations. First, there is a system of n linear equations. The square system of and is known, If the value is unknown, this method can be used to iteratively approximate vector, the initial guess is usually ,in .use The kth iteration of The approximate value of The next (i.e. k+1) iteration of The specific element-level formula iteration is as follows:

[0070]

[0071] While applying a normal repulsive force to the penetrating particles to correct their motion trajectory, a friction suppression mechanism is introduced to eliminate non-physical slippage, ensuring a stable and non-penetrating deformation process. The specific implementation of this module is based on measuring real-world parameters such as the friction coefficient and air resistance, and ultimately multiplying these damping factor coefficients when calculating the external force, thereby ensuring compliance with the real laws of motion in the physical world.

[0072] This invention, for the first time, integrates biomechanical parameters and physical properties into a traditional position-based dynamics simulation framework, addressing the simulation distortion, inaccuracy, and dynamic response mismatch inherent in traditional methods due to the lack of a material property mapping mechanism. By embedding biomechanical parameters such as Young's modulus, Poisson's ratio, and viscoelastic coefficient into the constraint function's iterative parameters, these parameters are directly mapped into the constraint function, ultimately satisfying stiffness, damping, and energy attenuation properties. This establishes a physically consistent link from microscopic particle interactions to macroscopic tissue deformation. When soft tissue is subjected to external forces (such as cutting or puncturing), volume constraints are prioritized to maintain tissue density stability and prevent non-physical collapse. Subsequently, local stiffness is dynamically adjusted based on a hyperelastic model to simulate the mechanical differences between tumors and normal tissue. A viscoelastic attenuation function is also introduced to modify constraint weights to replicate stress relaxation and creep effects in soft tissue. During the iterative solution process, biomechanical parameters drive constraint corrections in real time, ensuring that the deformation process strictly adheres to physical laws. Ultimately, this provides a highly reliable simulation tool for virtual surgical training.

[0073] In this embodiment, the implicit time integration algorithm is used to predict the particle motion trend. The implicit integration position prediction is based on Newton's second law. The implicit integration algorithm is used to predict the particle displacement trend and update the position and velocity for subsequent constraint iterations. This law is based on the energy potential. The force derived from the equation , and perform implicit position-level time discretization on the equation, expressed as a time step index t:

[0074]

[0075] Where M is the mass matrix, a is the acceleration, and x is the position of the particle. Note that the gradient operator ∇ is a row vector containing partial derivatives.

[0076] The above is an introduction to the method embodiment. The following further illustrates the solution of the present invention through a system embodiment.

[0077] A biological soft tissue virtual simulation system, used to implement the above method, the system comprising:

[0078] 3D soft tissue model construction module: constructs 3D soft tissue models based on medical imaging data;

[0079] Particle system construction and initialization module: discretizes the 3D soft tissue model into a particle system and binds initial constraint parameters;

[0080] Collision detection module: Detects collisions between particles and surgical instruments based on signed distance field technology. If no collision is detected, the particle position is output and simulation results are generated. If a collision is detected, the particle update module is called.

[0081] Particle update module: applies repulsive force to particles to correct the deformation path, determines whether the force is balanced or the maximum number of iterations is reached, and if so, calls the collision detection module for collision detection; otherwise, updates the particle velocity in real time, and predicts the particle motion trend through the implicit time integration algorithm. The Gauss-Seidel iteration method is used to couple the position constraints, volume constraints, shape constraints and physical constraints, dynamically adjusts the constraint stiffness to match the actual tissue characteristics, and updates the particle position; among the physical constraints, the biomechanical parameters are converted into constraint weight coefficients through a parameterized mapping mechanism to support rapid switching and high-precision simulation of different tissue types.

[0082] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the described module can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0083] If the above functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0084] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A biological soft tissue virtual simulation method, characterized in that: The following steps are involved: Constructing a 3D soft tissue model based on medical imaging data: Based on medical imaging data, the target soft tissue area is segmented and 3D reconstructed to generate a 3D tetrahedral mesh model. The mesh vertex coordinates, normal vectors, topological connection relationships, and tetrahedral unit information are defined to ensure that the model's geometric structure is consistent with the actual anatomical features, resulting in a 3D soft tissue model. Discretize the three-dimensional soft tissue model into a particle system and bind initial constraint parameters; wherein the discretization of the three-dimensional soft tissue model into a particle system specifically includes: mapping each vertex of the mesh into a dynamic particle, with the particle number corresponding to the vertex number one by one, the initial position of the particle directly inherits the vertex coordinates, the initial velocity is set to zero, and the mass of each particle is calculated by evenly dividing the adjacent tetrahedral units; The collision between particles and surgical instruments is detected based on the signed distance field technology. If no collision is detected, the particle position is output and the simulation results are generated. If a collision is detected, A repulsive force is applied to the particles to correct the deformation path, and it is determined whether the force is balanced or the maximum number of iterations has been reached. If so, collision detection is returned. Otherwise, the particle velocity is updated in real time, and the particle motion trend is predicted through an implicit time integration algorithm. The Gauss-Seidel iteration method is used to couple the position constraints, volume constraints, shape constraints, and physical constraints, and the constraint stiffness is dynamically adjusted to match the actual tissue characteristics, and the particle position is updated. Among them, in the physical constraints, the biomechanical parameters are converted into constraint weight coefficients through a parameterized mapping mechanism to support rapid switching and high-precision simulation of different tissue types.

2. A biological soft tissue virtual simulation method according to claim 1, characterized in that: The position constraint is expressed as: ， in, Represent the two vertex positions in any tetrahedral unit, a , b =1,2,3,4, d is the initial distance calibrated by the rest spring length.

3. A biological soft tissue virtual simulation method according to claim 1, characterized in that: The volume constraint is to maintain the volume conservation of the tetrahedron unit, which is expressed as: ， in, , , are the four vertex positions of any tetrahedron unit, is the initial volume of the tetrahedron, , , .

4. A biological soft tissue virtual simulation method according to claim 1, characterized in that: The shape constraint is expressed as: ， in, n Represents the total number of particles in the cluster, without considering the edge connectivity of the tetrahedron. A cluster is a set of particles in a 3D grid. and Represents the first i The particle positions before and after deformation, R represents the rotation matrix, and Represents the translation vector before and after deformation, and are the predicted rotation matrix and translation vector.

5. The biological soft tissue virtual simulation method according to claim 1, characterized in that: The physical constraints are expressed as: ， in, is the deformation gradient, and are the first and second parameters of the Lamé constant, respectively. The elastic energy density of the Neo-Hookean material is expressed as , is the energy that resists compression and expansion, It is the energy that resists deformation.

6. A biological soft tissue virtual simulation method according to claim 1, characterized in that: The biomechanical parameters include Young's modulus and Poisson's ratio.

7. A biological soft tissue virtual simulation system, characterized in that: For implementing the method according to any one of claims 1 to 6, the system comprises: 3D soft tissue model construction module: constructs 3D soft tissue models based on medical imaging data; Particle system construction and initialization module: discretizes the 3D soft tissue model into a particle system and binds initial constraint parameters; Collision detection module: Detects collisions between particles and surgical instruments based on signed distance field technology. If no collision is detected, the particle position is output and simulation results are generated. If a collision is detected, the particle update module is called. Particle update module: applies repulsive force to particles to correct the deformation path, determines whether the force is balanced or the maximum number of iterations is reached, and if so, calls the collision detection module for collision detection; otherwise, updates the particle velocity in real time, and predicts the particle motion trend through the implicit time integration algorithm. The Gauss-Seidel iteration method is used to couple the position constraints, volume constraints, shape constraints and physical constraints, dynamically adjusts the constraint stiffness to match the actual tissue characteristics, and updates the particle position; among the physical constraints, the biomechanical parameters are converted into constraint weight coefficients through a parameterized mapping mechanism to support rapid switching and high-precision simulation of different tissue types.

8. A storage medium having a program stored thereon, characterized in that: When the program is executed, the method according to any one of claims 1 to 6 is implemented.

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