Soft tissue pressing and clamping simulation method for real-time virtual surgery

Abstract

The present invention relates to real-time surgical simulation in the field of virtual reality. Disclosed is a soft tissue pressing and clamping simulation method for real-time virtual surgery. Pressing and clamping are two common operations during surgery, and for the operation simulation requirements, a multi-scale model is adopted in the present invention for deformation interaction simulation of the soft organ: a coarse-scale mesh is a tetrahedral mesh and is used for simulating the overall deformation of the organ; a fine-scale mesh is a surface triangular mesh and is used for simulating fine deformation during the interaction of the organ and a surgical instrument; a ball tree model is used for calculating directions in which vertexes are discharged after contact. For pressing operation simulation, collision positions of a surgical tool and the soft tissue are obtained by means of continuous collision detection, and after a collision occurs, a guide vector is used to calculate the discharge directions of vertex positions, ensuring that there is no penetration between the surgical tool and the soft tissue surface. For clamping operation simulation, dynamic attachment constraint is used to realize fine interaction between jaws and the soft tissue.

Description

A simulation method for soft tissue compression and clamping in real-time virtual surgery Technical Field

[0001] The present invention relates to the technical field of multi-scale model joint deformation methods, and in particular to a soft tissue pressing and clamping simulation method for real-time virtual surgery. Background Art

[0002] Humans require a higher frequency for force perception to feel smooth than for visual perception. For example, 60Hz image output is sufficient for a smooth experience, while force perception requires at least 500Hz to avoid noticeable jitter. Because soft body deformation typically requires more computation and a lower output frequency, while feedback force output typically requires less computation but has a higher output frequency requirement, to enable force feedback interaction between humans and objects in a virtual environment, current mainstream implementations divide the interaction process into two parts: soft body deformation simulation and feedback force calculation.

[0003] Projective Dynamics is a commonly used framework for soft body deformation simulation. Soft body deformation can be understood as the process of gradually updating a model's vertices. Projective Dynamics creates constraints between model vertices and updates vertex positions by minimizing the energy defined by these constraints, thus achieving the effect of soft body deformation.

[0004] Constraint solving can be divided into two steps: local constraint solving and global constraint solving. Local constraint solving calculates the energy gradient at the associated vertex for a single constraint (used to update the vertex position). Global solving combines the results of multiple local constraint solving operations to obtain the updated vertex position.

[0005] Projective Dynamics uses a Jacobi iterative solver to find an intermediate solution among multiple constraints that satisfies all constraints as much as possible, thus avoiding the problem of the final result jumping between multiple constraints. The Projective Dynamics method uses projection to project the vertex position onto the zero potential energy hyperplane of the constraint. The distance between the vertex and the projection point of the zero potential energy surface is used as the constraint measurement method. The definition of constraint energy has the following form:

[0006] ;

[0007] in, is the stiffness coefficient of the constraint, 、 is the system parameter matrix corresponding to constraint i, The selection matrix for selecting vertices related to the current constraint. Constraint energy is the shortest Euclidean distance metric for projecting the vertex onto the zero potential energy surface of the constraint energy. Minimizing the constraint energy is the optimization goal for solving the constraint. By projecting the vertex to be optimized onto the zero potential energy manifold of the constraint, most of the nonlinear part of the constraint is left on the zero potential energy manifold of the constraint, so that the method can express the energy of the constraint in a very simple square distance manner. Multiple constraint energies can exist simultaneously on a soft tissue vertex. , the total energy of multiple constraints and the zero potential energy surface projection point corresponding to each constraint can be obtained by accumulating .

[0008] This method accumulates the energy of multiple local solutions and then obtains the final vertex position through global solution. The global solution can be expressed as follows:

[0009] ;

[0010] in, is the system mass matrix, The unknown quantity is . Solving the above linear equations yields the updated soft tissue vertex positions, and vertex displacements can achieve soft tissue deformation. This local-global solution method efficiently solves vertex constraints. Furthermore, due to the use of Jacobi iteration, this constraint solving algorithm can find a compromise solution among multiple constraints, preventing the local solution from oscillating back and forth between multiple constraints.

[0011] Existing feedback force calculation methods can be divided into two categories: direct feedback force calculation methods and virtual matching methods.

[0012] The direct feedback force calculation method calculates the force generated by each point that collides with the tool, and finally outputs the resultant force on the virtual tool to the force feedback device.

[0013] The virtual matching method maintains a virtual tool pose that does not collide with the object, and calculates the feedback force by the difference between the pose of the virtual tool and the pose of the physical tool.

[0014] The key to this feedback force calculation method is to determine the virtual tool pose that avoids collision with the object. Mainstream methods include: solving a quadratic programming problem to obtain a virtual tool pose that is completely free of object insertion; and gradually updating the virtual tool pose by solving force balance equations.

[0015] The first type of method is prone to the situation where there is no reasonable virtual tool posture in a narrow space, resulting in errors in the calculation of feedback force.

[0016] The second method gradually updates the virtual tool's position by solving the force balance equation. According to Newton's third law, the force exerted by the physical body on the virtual tool and the force exerted by the virtual tool on the physical body are equal and opposite in magnitude. This means that the resultant force of the collision force and the virtual matching force on the virtual tool is zero. As the physical tool moves, this resultant force no longer equals zero. Therefore, the virtual tool's position is updated to return the resultant force of the collision and virtual matching forces to zero.

[0017] Collision detection can be categorized as discrete collision detection and continuous collision detection. Discrete collision detection examines whether objects overlap in space at a given moment. Continuous collision detection determines whether two objects collide based on their motion trajectories. If the sampling frequency is low, the objects are thin, or the objects are moving quickly, a collision occurs between two adjacent frames, but no collision occurs in two consecutive time frames. Discrete collision detection will miss any collision results. Continuous collision detection takes into account the objects' motion trajectories and can detect collisions that might be missed in discrete collision detection.

[0018] Collision response refers to the change in the state of the colliding objects according to the collision. The changed object posture should avoid overlapping in space.

[0019] During the collision detection process, the incorrect direction of the soft body vertex discharge will cause penetration and adhesion problems; when the rigid body tool clamps the soft body, the soft body will deform, but the deformation effect at the clamped position and its surroundings is unnatural and discontinuous. Summary of the Invention

[0020] The purpose of this invention is to provide a soft tissue compression and gripping simulation method for real-time virtual surgery. This method can handle collision detection and collision response in complex environments such as inserting soft objects, avoiding penetration and adhesion issues caused by incorrect vertex ejection directions during collision detection. During the gripping process, discrete collision detection projects the colliding vertices onto the collision surface of the clamp. The interaction between the surface mesh and the tetrahedral mesh creates a more natural surface shape around the gripping location.

[0021] To achieve the above objectives, the present invention provides a soft tissue compression and clamping simulation method for real-time virtual surgery, comprising the following steps:

[0022] S1. The soft tissue simulation model consists of three parts: a surface triangular mesh, a tetrahedral mesh, and a ball tree. The interaction between the surface triangular mesh, the tetrahedral mesh, and the ball tree is as follows:

[0023] S11, synchronization between ball tree and tetrahedral mesh;

[0024] S12, the tetrahedron vertices are constrained by the positions of the vertices from the surface triangle mesh;

[0025] S13, the surface triangle mesh vertices are constrained by the positions of the tetrahedron vertices;

[0026] S2. During the compression simulation, the collision space of the surgical tools is constructed in two adjacent frames, the expulsion direction is optimized by the guidance vector, and the position constraint coefficient is dynamically adjusted;

[0027] S3. Clamping simulation operation based on dynamic attachment constraints, specifically including:

[0028] S31, calculating the position of the soft tissue vertex that collided using the bounding box of the surgical tool, and calculating the relative position and local coordinates of the soft tissue vertex that collided on the surgical tool; selectively performing step S32 or step S33 according to the closed state of the surgical tool;

[0029] S32, if the surgical tool is still not closed, discrete collision detection is performed using the soft tissue vertices and the bounding box of the surgical tool, and attachment constraints are applied to the soft tissue vertices that collide;

[0030] S33: If the surgical tool is already closed, then an attachment constraint is applied to the soft tissue vertices that can be captured when the surgical tool is pre-calculated to be closed.

[0031] Preferably, in step S11, the synchronization between the ball tree and the tetrahedral grid is as follows:

[0032] S111. The ball tree organizes the spheres in a tree structure and calculates the center coordinates of the sphere center in the tetrahedral grid. The position of the sphere center can be expressed as follows:

[0033] (1)

[0034] in, is the center position of the sphere bound to the tetrahedron mesh, The positions of the four vertices bound to the ball, is the weight of the four vertex positions of the tetrahedral mesh to the center position of the sphere;

[0035] S112, the tetrahedron mesh vertices and the surface triangle mesh vertices are bound to the ball in the ball tree, and the guidance vector is calculated based on the position of the ball center to which the soft tissue vertex is bound. The guidance vector of the soft tissue vertex To point from the soft tissue vertex to the center of the sphere to which the soft tissue vertex is bound, the guidance vector is defined as follows:

[0036] (2)

[0037] Indicates the location of the soft tissue apex;

[0038] S113. After each soft tissue deformation calculation is completed, the guidance vectors of the ball center position and the soft tissue vertex in the ball tree are updated.

[0039] Preferably, in step S12, the positions of the tetrahedron vertices are constrained by the positions of the vertices from the surface triangle mesh as follows:

[0040] Use the surface triangle model vertices to constrain the tetrahedron model vertices, and impose position constraints on some of the tetrahedron model vertices:

[0041] (3)

[0042] (4)

[0043] Among them, W Tri The energy function representing the position constraints imposed on the vertices of the tetrahedron model. represents the vertex position of the tetrahedral mesh, is the vertex position of the surface triangle model, is the distance from the tetrahedron vertex to the surgical tool, is the stiffness coefficient of the surface triangular mesh position constraint, which is related to the distance from the tetrahedral mesh vertex to the surgical tool. If the surgical tool does not collide with the soft tissue, the stiffness coefficient is 0. The surface triangular mesh does not impose position constraints on the tetrahedral mesh. If the surgical tool collides with the soft tissue, the stiffness coefficient of the constraint is calculated according to formula (4), and the surface triangular mesh position constraint is imposed on the vertex of the tetrahedral mesh. The maximum value of the stiffness coefficient set by the user.

[0044] Preferably, in step S13, the surface triangle mesh vertices are constrained by the positions of the tetrahedron mesh vertices as follows:

[0045] The energy function of the tetrahedral mesh position constraint is shown in (5):

[0046] (5)

[0047] (6)

[0048] Among them, W Tet Energy function representing the position constraint of the tetrahedral mesh, Indicates the position of the current surface triangle mesh vertex, Represents the skin position of the surface triangle mesh vertex calculated based on the vertex position after the tetrahedron mesh is deformed. is the distance from the vertex of the surface triangle mesh to the surgical tool, is the stiffness coefficient of the tetrahedral mesh position constraint, is the basic weight value of the stiffness coefficient, The user-set stiffness coefficient for the surface triangle mesh vertices to be constrained from the tetrahedron mesh vertex positions when no collision occurs.

[0049] Preferably, in step S2, the collision space of the surgical tool is constructed between two adjacent frames, the ejection direction is optimized by the guidance vector, and the position constraint coefficient is dynamically adjusted:

[0050] Set ε as the threshold set by the user to determine whether to construct the spatial signed distance field between the front and back frame poses of the surgical tool, d q Represents the distance between the front and back frame poses of the surgical tool. The space between the front and back frame poses of the surgical tool is called the swept volume:

[0051] When , a signed distance field is constructed on the front frame and back frame pose scan volume of the surgical tool, including:

[0052] Construct a non-orthogonal coordinate system M (X, Y, Z) on the scanned volume through which the surgical tool passes in the previous and next frames, where X is the central axis vector of the surgical tool, Y is the direction from the current frame pose of the surgical tool to the previous frame pose of the surgical tool, and Z is the normal vector of the central axis of the surgical tool across the plane A.

[0053] For soft tissue model vertices ( ), first calculate the coordinate values ​​of the soft tissue vertices in the local coordinate system of the scanned volume ( ), the length of the surgical tool is L and the radius is R, and it is divided into four cases according to the position of the soft tissue vertex in the scan volume;

[0054] When constructing the non-embedding constraint on the soft tissue vertices, different repulsion directions are applied to the vertices at different positions of the scanned body, which are respectively pointing to the direction of the surgical tool pose in the current frame and the direction of the surgical tool pose in the previous frame. The repulsion direction is , the repulsive ray equation is expressed as ,in is the distance to the starting point of the ray, and the center position of the bottom surface of the surgical tool cylinder is , the cylinder axis vector is , the new ray equation in the local coordinate system of the cylinder is expressed as:

[0055] (7)

[0056] Solve the following equation :

[0057] (8)

[0058] After solving the equation, we get the position where the soft tissue vertex is expelled to the surface , the normal vector at the location ;

[0059] Where R is the radius of the surgical tool cylinder, The ray equation representing the expulsion of soft tissue vertices, represents the vertex coordinates in the local coordinate system of the surgical tool, represents the direction of the ray in the local coordinate system of the surgical tool, Represents the position of the vertex in the global coordinate system.

[0060] Preferably, in step S2, the distance between the front frame and the back frame of the surgical tool is , the front and back frame poses of the surgical tool are considered to overlap, and the signed distance field of the front frame pose of the surgical tool is constructed, and discrete collision detection is performed between the model vertices and the cylinder signed distance field:

[0061] First, calculate the projection of the soft tissue vertex on the central axis of the surgical tool , , the soft tissue vertex collides with the surgical tool, otherwise no collision occurs; for the soft tissue vertex that collides, the repulsion direction of the soft tissue is set to , the soft tissue apex is to be discharged to the discharge position on the surface of the cylinder , the surface normal vector at the discharge location ;

[0062] in, is the current collision vertex position, d t is the center axis direction vector of the surgical tool cylinder.

[0063] Preferably, in step S2, the time step of the soft tissue vertex movement is adjusted according to the movement speed of the surgical tool for the soft tissue vertex that collides, and the weight of the time step expansion is It is expressed as follows:

[0064] (9)

[0065] in, is the current surgical tool movement rate, The motion rate threshold set by the user.

[0066] Preferably, in step S32, if the surgical tool is still not closed, discrete collision detection is performed using the soft tissue vertices and the bounding box of the surgical tool, and attachment constraints are applied to the colliding soft tissue vertices, including:

[0067] For soft tissue vertices that collide, use the soft tissue vertex guidance vector Project the location of the soft tissue vertices that collided onto the closing surface of the surgical tool , then build an attachment constraint between the colliding soft tissue vertex and the projection position, and the energy function formula on the collision vertex is:

[0068] (10)

[0069] in, represents the stiffness coefficient of the constraint, Indicates the distance from the collided soft tissue vertex to the axis of the surgical tool, The maximum value of the constraint stiffness coefficient set by the user, Indicates the current position of the vertex on the soft tissue surface that is collided, u g Indicates the position of the currently colliding soft tissue vertex projected onto the closing surface of the surgical tool.

[0070] Preferably, in step S33, the surgical tool is completely closed, the user controls the grasping forceps to drag the soft tissue, and pre-calculates the local coordinates of the projection position in the grasping forceps local coordinate system. After the surgical tool moves, the current position of the surgical tool is obtained first, and the three axis vectors X, Y, and Z of the local coordinate system of the current surgical tool are calculated. According to the pre-calculated local coordinates, the position where the soft tissue vertex to be grasped at the current moment is projected is calculated. , and then build attachment constraints between the clamped soft tissue vertices and the projected positions.

[0071] Therefore, the present invention adopts the above-mentioned soft tissue compression and clamping simulation method for real-time virtual surgery, and its technical effects are as follows:

[0072] (1) When pressing soft tissue, reduce the penetration and adhesion between the tool and the soft tissue, and improve the realism of the simulation results;

[0073] (2) The surface shape of the clamping area is made to fit the actual surface position of the surgical tool, making the clamping simulation effect more natural;

[0074] (3) The use of a multi-scale joint deformation strategy can make the surface deformation more natural while avoiding surface adhesion and penetration.

[0075] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] FIG1 is a schematic diagram of a continuous collision detection collision body constructed;

[0077] Figure 2 is a schematic diagram of vertex repulsion direction;

[0078] Figure 3 is a schematic diagram of the collision and discharge with a cylinder;

[0079] FIG4 is a schematic diagram of tetrahedron position constraints;

[0080] Figure 5 is a flow chart of the step-by-step crawling scheme;

[0081] FIG6 is a schematic diagram of clamping constraints. DETAILED DESCRIPTION

[0082] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0083] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0084] Example 1

[0085] As shown in the figure, the present invention provides a soft tissue compression and clamping simulation method for real-time virtual surgery, comprising the following steps:

[0086] S1. The soft tissue simulation model consists of three parts: a surface triangular mesh, a tetrahedral mesh, and a ball tree. The interaction between the surface triangular mesh, the tetrahedral mesh, and the ball tree is as follows:

[0087] S11, synchronization between ball tree and tetrahedral mesh;

[0088] The synchronization between the ball tree and the tetrahedral mesh is as follows:

[0089] S111. The ball tree organizes the spheres in a tree structure and calculates the center coordinates of the sphere center in the tetrahedral mesh to represent the contribution value of the tetrahedral mesh vertex position to the center of gravity position. The sphere center position can be expressed as follows:

[0090] (1)

[0091] in, is the center position of the sphere bound to the tetrahedron mesh, The positions of the four vertices bound to the ball, is the weight of the four vertex positions of the tetrahedral mesh to the center position of the sphere;

[0092] S112, the tetrahedron mesh vertices and the surface triangle mesh vertices are bound to the ball in the ball tree, and the guidance vector is calculated based on the position of the ball center to which the soft tissue vertex is bound. The guidance vector of the soft tissue vertex To point from the soft tissue vertex to the center of the sphere to which the soft tissue vertex is bound, the guidance vector is defined as follows:

[0093] (2)

[0094] Indicates the location of the soft tissue apex;

[0095] S113. After each soft tissue deformation calculation is completed, the guidance vectors of the ball center position and the soft tissue vertex in the ball tree are updated.

[0096] S12, the tetrahedron vertices are constrained by the positions of the vertices from the surface triangle mesh;

[0097] The positions of the tetrahedron vertices are constrained by the positions of the vertices from the surface triangle mesh as follows:

[0098] Use the surface triangle model vertices to constrain the tetrahedron model vertices, and impose position constraints on some of the tetrahedron model vertices:

[0099] (3)

[0100] (4)

[0101] Among them, W Tri Position constraints are imposed on the vertices of the tetrahedral model representing the part, represents the vertex position of the tetrahedral mesh, is the vertex position of the surface triangle model, is the distance from the tetrahedron vertex to the surgical tool, is the stiffness coefficient of the surface triangular mesh position constraint, which is related to the distance from the tetrahedral mesh vertex to the surgical tool. If the surgical tool does not collide with the soft tissue, the stiffness coefficient is 0. The surface triangular mesh does not impose position constraints on the tetrahedral mesh. If the surgical tool collides with the soft tissue, the stiffness coefficient of the constraint is calculated according to formula (4), and the surface triangular mesh position constraint is imposed on the vertex of the tetrahedral mesh. The maximum value of the stiffness coefficient set by the user.

[0102] S13, the surface triangle mesh vertices are constrained by the positions of the tetrahedron vertices;

[0103] The surface triangle mesh vertices are constrained to their positions from the tetrahedral mesh vertices as follows:

[0104] The energy function of the tetrahedral mesh position constraint is shown in (5):

[0105] (5)

[0106] (6)

[0107] Among them, W TetEnergy function representing the position constraint of the tetrahedral mesh, Indicates the position of the current surface triangle mesh vertex, Represents the skin position of the surface triangle mesh vertex calculated based on the vertex position after the tetrahedron mesh is deformed. is the distance from the vertex of the surface triangle mesh to the surgical tool, is the stiffness coefficient of the tetrahedral mesh position constraint, is the basic weight value of the stiffness coefficient, The user-set stiffness coefficient for the surface triangle mesh vertices to be constrained from the tetrahedron mesh vertex positions when no collision occurs.

[0108] Three models, surface triangulated mesh, tetrahedral mesh, and ball tree, are used to represent soft bodies in the simulation process. Surface triangulated mesh uses triangles to approximate the surface of the soft body model and is used for local fine deformation and rendering. Tetrahedral mesh uses tetrahedrons to fill the internal space of the soft body. By constructing tetrahedral volume constraints on the tetrahedrons, the soft body model can be deformed and return to its original shape. Ball tree represents the volume inside the soft tissue. Using spheres to fill the internal space of the soft tissue can be used for collision detection and anti-penetration processing during the interaction between surgical tools and soft tissue. Using three models to represent soft tissue at the same time, taking advantage of the advantages of different model representations, and designing the interaction method between models, a real-time soft body deformation effect for virtual surgery is achieved.

[0109] S2. During the pressing simulation, the collision space is constructed between two adjacent frames, the discharge direction is optimized through the guidance vector, and the position constraint coefficient is dynamically adjusted;

[0110] The concept of soft tissue vertex guidance vectors is introduced to standardize the direction of repulsion of soft tissue vertices after a collision with a surgical tool. During collision detection, when a soft tissue vertex passes through the center axis of the surgical tool, the direction in which the surgical tool expel the soft tissue vertex will change, making it more likely to penetrate. The guidance vector can provide a reference for the direction of expulsion when the soft tissue vertex is expelled by the surgical tool. The role of the guidance vector in the vertex expulsion direction is as follows:

[0111] When the angle between the soft tissue vertex discharge direction calculated by collision detection and the guidance vector of the soft tissue vertex is greater than 90°, the soft tissue vertex discharge direction obtained by collision detection is inconsistent with the distribution of soft tissue vertices around the collision area. At this time, using the vertex guidance vector as the discharge direction of the soft tissue vertex can reduce the abnormality of the soft tissue discharge direction caused by the excessive depth of vertex embedding, and avoid the penetration phenomenon during the interaction between surgical tools and soft tissue.

[0112] Set ε as the threshold set by the user to determine whether to construct the spatial signed distance field between the front and back frame poses of the surgical tool, dq Represents the distance between the front and back frame poses of the surgical tool. The space between the front and back frame poses of the surgical tool is called the swept volume:

[0113] When , a signed distance field is constructed on the front frame and back frame pose scan volume of the surgical tool, including:

[0114] A non-orthogonal coordinate system M(X, Y, Z) is constructed on the scanned volume through which the surgical tool passes in the previous and next frames, where X is the central axis vector of the surgical tool, Y is the direction from the current frame pose of the surgical tool to the previous frame pose of the surgical tool, and Z is the normal vector of the central axis of the surgical tool sweeping across the plane A. For the vertex of the soft tissue model ( ), first calculate the coordinate values ​​of the soft body vertex in the local coordinate system of the scanned body ( ), the length of the surgical tool is L and the radius is R. According to the position of the soft tissue vertex in the scan volume, it is divided into four cases, as shown in Table 1.

[0115] Table 1 Intersection calculation table of soft tissue vertices and surgical tool scan volume

[0116] ;

[0117] When constructing the non-embedding constraint on the soft body vertices, different repulsion directions are applied to the vertices at different positions of the scanned body, which are respectively pointing to the direction of the surgical tool pose in the current frame and the direction of the surgical tool pose in the previous frame. The repulsion direction is , the repulsive ray equation is expressed as ,in is the distance to the starting point of the ray, and the center position of the bottom surface of the surgical tool cylinder is , the cylinder axis vector is , the new ray equation in the local coordinate system of the cylinder is expressed as

[0118] (7)

[0119] Solve the following equation :

[0120] (8)

[0121] After solving the equation, we get the position where the soft tissue vertex is expelled to the surface , the normal vector at the location ;

[0122] Where, The ray equation representing the expulsion of soft tissue vertices, represents the vertex coordinates in the local coordinate system of the surgical tool, represents the direction of the ray in the local coordinate system of the surgical tool, Represents the position of the soft tissue vertex in the global coordinate system. The ray equation refers to the ray equation starting from the current soft body vertex and the direction of the ray.

[0123] The distance between the front and back frame poses of the surgical tool , the front frame and the back frame poses of the surgical tool are overlapped, the signed distance field of the front frame pose of the surgical tool is constructed, and discrete collision detection is performed between the model vertex and the cylinder signed distance field:

[0124] First, calculate the projection of the soft tissue vertex on the central axis of the surgical tool , , the soft tissue vertex collides with the surgical tool, otherwise no collision occurs; for the soft tissue vertex that collides, the repulsion direction of the soft tissue is set to , the soft tissue apex is to be discharged to the discharge position on the surface of the cylinder , the surface normal vector at the discharge location ;

[0125] in, is the current collision vertex position, R is the radius of the surgical tool cylinder; d t is the center axis direction vector of the surgical tool cylinder.

[0126] According to the movement speed of the surgical tool, the time step of the soft tissue vertex movement is adjusted for the soft tissue vertex that collides, so that the soft body vertex that collides responds faster to the pressure from the surgical tool and produces corresponding deformation. It is expressed as follows:

[0127] (9)

[0128] in, is the current surgical tool movement rate, A user-defined motion rate threshold. This method allows the soft body to deform faster when the surgical tool is pressed down quickly, while maintaining stability when the surgical tool is pressed down continuously and remains stationary.

[0129] S3. Clamping simulation operation based on dynamic attachment constraints, specifically including:

[0130] S31, precalculating vertices that can be captured when the surgical tool is closed, and then determining whether the surgical tool is closed;

[0131] The positions of the soft tissue vertices that collided are calculated using the bounding box of the surgical tool. The relative positions and local coordinates of the vertices on the surgical tool are then calculated. Depending on the closed state of the surgical tool, either step S32 or step S33 is selectively performed. This allows the coordinates of the vertices in the local coordinate system of the surgical tool's gripper to be determined, thereby determining the binding positions of the attachment constraints.

[0132] S32, if the surgical tool is still not closed, discrete collision detection is performed using the soft tissue vertices and the bounding box of the surgical tool, and attachment constraints are applied to the soft tissue vertices that collide;

[0133] In step S32, if the surgical tool is still not closed, discrete collision detection is performed using the soft tissue vertices and the bounding box of the surgical tool, and attachment constraints are applied to the colliding soft tissue vertices, including:

[0134] For soft tissue vertices that collide, use the soft tissue vertex guidance vector Project the location of the soft tissue vertices that collided onto the closing surface of the surgical tool , then build an attachment constraint between the colliding soft tissue vertex and the projection position, and the energy function formula on the collision vertex is:

[0135] (10)

[0136] in, represents the stiffness coefficient of the constraint, Indicates the distance from the collided soft tissue vertex to the axis of the surgical tool, The maximum value of the constraint stiffness coefficient set by the user, Indicates the current position of the vertex on the soft tissue surface that is collided, u g Indicates the position of the currently colliding soft tissue vertex projected onto the closing surface of the surgical tool;

[0137] S33: If the surgical tool is already closed, then an attachment constraint is applied to the soft tissue vertices that can be captured when the surgical tool is pre-calculated to be closed.

[0138] The surgical tool is completely closed, and the user controls the grasping forceps to drag the soft tissue. Because the surgical tool will move away from the soft tissue during the dragging operation, the projection position calculated according to the method in the previous stage will not move with the grasping forceps. Therefore, at this stage, the present invention will pre-calculate the local coordinates of the projection position in the local coordinate system of the grasping forceps. , so that when the surgical tool moves, first obtain the current position of the surgical tool, and calculate the three axis vectors X, Y, Z of the local coordinate system of the current operation. In this way, the position where the soft tissue vertex to be captured at the current moment is projected can be calculated based on the pre-calculated local coordinates , then build attachment constraints between the soft tissue vertices and the projected position. Because the projected position moves with the movement of the gripper, the gripping points subject to the attachment constraints will also move with the gripper, and the soft tissue will also deform accordingly.

[0139] Therefore, the present invention utilizes the aforementioned soft tissue compression and gripping simulation method for real-time virtual surgery, capable of handling collision detection and response in complex environments such as inserting soft objects, avoiding penetration and adhesion issues caused by incorrect vertex ejection directions during collision detection. During the gripping process, discrete collision detection projects the collided vertices onto the collision surface of the clamp. The interaction between the surface mesh and the tetrahedral mesh creates a more natural surface shape around the gripping location.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A soft tissue compression and clamping simulation method for real-time virtual surgery, characterized in that: The following steps are involved: S1. The soft tissue simulation model consists of three parts: a surface triangular mesh, a tetrahedral mesh, and a ball tree. The interaction between the surface triangular mesh, the tetrahedral mesh, and the ball tree is as follows: S11, synchronization between ball tree and tetrahedral mesh; S12, the tetrahedron vertices are constrained by the positions of the vertices from the surface triangle mesh; S13, the surface triangle mesh vertices are constrained by the positions of the tetrahedron vertices; S2. During the compression simulation, the collision space of the surgical tools is constructed in two adjacent frames, the expulsion direction is optimized by the guidance vector, and the position constraint coefficient is dynamically adjusted; S3. Clamping simulation operation based on dynamic attachment constraints, specifically including: S31, calculating the position of the soft tissue vertex that collided using the bounding box of the surgical tool, and calculating the relative position and local coordinates of the soft tissue vertex that collided on the surgical tool; selectively performing step S32 or step S33 according to the closed state of the surgical tool; S32, if the surgical tool is still not closed, discrete collision detection is performed using the soft tissue vertices and the bounding box of the surgical tool, and attachment constraints are applied to the soft tissue vertices that collide; S33: If the surgical tool is already closed, then an attachment constraint is applied to the soft tissue vertices that can be captured when the surgical tool is pre-calculated to be closed.

2. A soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 1, characterized in that: In step S11, the synchronization between the ball tree and the tetrahedral mesh is as follows: S111. The ball tree organizes the spheres in a tree structure and calculates the center coordinates of the sphere center in the tetrahedral grid. The position of the sphere center can be expressed as follows: （1） in, is the center position of the sphere bound to the tetrahedron mesh, The positions of the four vertices bound to the ball, is the weight of the four vertex positions of the tetrahedral mesh to the center position of the sphere; S112, the tetrahedron mesh vertices and the surface triangle mesh vertices are bound to the ball in the ball tree, and the guidance vector is calculated based on the position of the ball center to which the soft tissue vertex is bound. The guidance vector of the soft tissue vertex To point from the soft tissue vertex to the center of the sphere to which the soft tissue vertex is bound, the guidance vector is defined as follows: （2） Indicates the location of the soft tissue apex; S113. After each soft tissue deformation calculation is completed, the guidance vectors of the ball center position and the soft tissue vertex in the ball tree are updated.

3. The soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 2, characterized in that: In step S12, the positions of the tetrahedron vertices are constrained by the positions of the vertices from the surface triangle mesh as follows: Use the surface triangle model vertices to constrain the tetrahedron model vertices, and impose position constraints on some of the tetrahedron model vertices: （3） （4） Among them, W Tri The energy function representing the position constraints imposed on the vertices of the tetrahedron model. represents the vertex position of the tetrahedral mesh, is the vertex position of the surface triangle model, is the distance from the tetrahedron vertex to the surgical tool, is the stiffness coefficient of the surface triangular mesh position constraint, which is related to the distance from the tetrahedral mesh vertex to the surgical tool. If the surgical tool does not collide with the soft tissue, the stiffness coefficient is 0. The surface triangular mesh does not impose position constraints on the tetrahedral mesh. If the surgical tool collides with the soft tissue, the stiffness coefficient of the constraint is calculated according to formula (4), and the surface triangular mesh position constraint is imposed on the vertex of the tetrahedral mesh. The maximum value of the stiffness coefficient set by the user.

4. The soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 3, characterized in that: In step S13, the surface triangle mesh vertices are constrained by the positions of the tetrahedral mesh vertices as follows: The energy function of the tetrahedral mesh position constraint is shown in (5): （5） （6） Among them, W Tet Energy function representing the position constraint of the tetrahedral mesh, Indicates the position of the current surface triangle mesh vertex, Represents the skin position of the surface triangle mesh vertex calculated based on the vertex position after the tetrahedron mesh is deformed. is the distance from the vertex of the surface triangle mesh to the surgical tool, is the stiffness coefficient of the tetrahedral mesh position constraint, is the basic weight value of the stiffness coefficient, The user-set stiffness coefficient for the surface triangle mesh vertices to be constrained from the tetrahedron mesh vertex positions when no collision occurs.

5. The soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 4, characterized in that: In step S2, the collision space of the surgical tools is constructed between two adjacent frames, the ejection direction is optimized by the guidance vector, and the position constraint coefficient is dynamically adjusted: Set ε as the threshold set by the user to determine whether to construct the spatial signed distance field between the front and back frame poses of the surgical tool, d q Represents the distance between the front and back frame poses of the surgical tool. The space between the front and back frame poses of the surgical tool is called the swept volume: When , a signed distance field is constructed on the front frame and back frame pose scan volume of the surgical tool, including: Construct a non-orthogonal coordinate system M (X, Y, Z) on the scanned volume through which the surgical tool passes in the previous and next frames, where X is the central axis vector of the surgical tool, Y is the direction from the current frame pose of the surgical tool to the previous frame pose of the surgical tool, and Z is the normal vector of the central axis of the surgical tool across the plane A. For soft tissue model vertices ( ), first calculate the coordinate values ​​of the soft tissue vertices in the local coordinate system of the scanned volume ( ), the length of the surgical tool is L and the radius is R, and it is divided into four cases according to the position of the soft tissue vertex in the scan volume; When constructing the non-embedding constraint on the soft tissue vertices, different repulsion directions are applied to the vertices at different positions of the scanned body, which are respectively pointing to the direction of the surgical tool pose in the current frame and the direction of the surgical tool pose in the previous frame. The repulsion direction is , the repulsive ray equation is expressed as ,in is the distance to the starting point of the ray, and the center position of the bottom surface of the surgical tool cylinder is , the cylinder axis vector is , the new ray equation in the local coordinate system of the cylinder is expressed as: （7） Solve the following equation ： （8） After solving the equation, we get the position where the soft tissue vertex is expelled to the surface , the normal vector at the location ； Where R is the radius of the surgical tool cylinder, The ray equation representing the expulsion of soft tissue vertices, represents the vertex coordinates in the local coordinate system of the surgical tool, represents the direction of the ray in the local coordinate system of the surgical tool, Represents the position of the vertex in the global coordinate system.

6. The soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 5, characterized in that: In step S2, the distance between the front and back frame poses of the surgical tool , the front frame and the back frame pose of the surgical tool are considered to be overlapped. The signed distance field of the front frame pose of the surgical tool is constructed, and discrete collision detection is performed between the model vertices and the cylinder signed distance field: First, calculate the projection of the soft tissue vertex on the central axis of the surgical tool ， , the soft tissue vertex collides with the surgical tool, otherwise no collision occurs; for the soft tissue vertex that collides, the repulsion direction of the soft tissue is set to , the soft tissue apex is to be discharged to the discharge position on the surface of the cylinder , the surface normal vector at the discharge location ； in, is the current collision vertex position, d t is the center axis direction vector of the surgical tool cylinder.

7. The soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 6, characterized in that: In step S2, the time step of the soft tissue vertex movement is adjusted for the soft tissue vertex that collides with the surgical tool according to the movement speed of the surgical tool, and the weight of the time step expansion is It is expressed as follows: （9） in, is the current surgical tool movement rate, The motion rate threshold set by the user.

8. The soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 7, characterized in that: In step S32, if the surgical tool is still not closed, discrete collision detection is performed using the soft tissue vertices and the bounding box of the surgical tool, and attachment constraints are applied to the colliding soft tissue vertices, including: For soft tissue vertices that collide, use the soft tissue vertex guidance vector Project the location of the soft tissue vertices that collided onto the closing surface of the surgical tool , then build an attachment constraint between the colliding soft tissue vertex and the projection position, and the energy function formula on the collision vertex is: （10） in, represents the stiffness coefficient of the constraint, Indicates the distance from the collided soft tissue vertex to the axis of the surgical tool, The maximum value of the constraint stiffness coefficient set by the user, Indicates the current position of the vertex on the soft tissue surface that is collided, u g Indicates the position of the currently colliding soft tissue vertex projected onto the closing surface of the surgical tool.

9. The soft tissue compression and clamping simulation method for real-time virtual surgery according to claim 8, characterized in that: In step S33, the surgical tool is completely closed, and the user controls the forceps to drag the soft tissue, and pre-calculates the local coordinates of the projection position in the local coordinate system of the forceps. After the surgical tool moves, the current position of the surgical tool is obtained first, and the three axis vectors X, Y, and Z of the local coordinate system of the current surgical tool are calculated. According to the pre-calculated local coordinates, the position where the soft tissue vertex to be grasped at the current moment is projected is calculated. , and then build attachment constraints between the clamped soft tissue vertices and the projected positions.

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