A method for motion interaction between liver parenchyma and intrahepatic blood vessels and blood in a virtual surgery scene

Abstract

The application discloses a method for motion interaction of liver parenchyma and intrahepatic blood vessels and blood in a virtual surgery scene, mainly comprising: generation of a visual liver body model and an intrahepatic blood vessel body model; generation of a liver parenchyma body model; generation of a dense mesh of the intrahepatic blood vessel body model by means of a gmsh software, and generation of an intra-blood vessel blood model composed of a blood flow particle set; establishment of a liver parenchyma motion model based on PBD, and motion trends of the liver parenchyma and the intrahepatic blood vessels under the action of an external force, which are used to represent the motion of the liver parenchyma under the action of the external force, and the motion of the blood vessels and the blood particles caused by the deformation of the liver parenchyma, and simultaneously contain the flow of the blood particles under the condition of cutting; and realization of the motion constraints between the intrahepatic blood vessels and the liver parenchyma, and the motion constraint conditions of the blood flow in the blood vessels under the action of the external force in the virtual surgery scene. The method fully considers the motion characteristics of the liver and the blood vessels under the action of the force.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of virtual reality technology and medical technology, and particularly relates to a control system of a surgical simulator. BACKGROUND

[0002] The surgical simulator is used for helping doctors to train before surgery and improve surgical skills. Meanwhile, the motion displacement of internal blood vessels of tissues is also a part that doctors focus on during surgery. Therefore, how to correctly reflect the motion of internal blood vessels of tissues under the action of force in a virtual surgery simulation environment is also very important.

[0003] The existing method considering the interaction between intrahepatic blood vessels and liver motion often considers the blood vessels and liver as the same object, and does not fully consider the material properties of the blood vessels and the motion characteristics of the blood flow in the blood vessels. SUMMARY

[0004] In view of the above prior art, the present application provides a method for motion interaction between liver parenchyma and intrahepatic blood vessels and blood in a virtual surgery scene, so as to realize the motion constraint between intrahepatic blood vessels and liver parenchyma and the motion constraint of blood flow in the blood vessels when the liver is subjected to external force in the virtual surgery scene.

[0005] In order to solve the above technical problems, the present application provides a method for motion interaction between liver parenchyma and intrahepatic blood vessels and blood in a virtual surgery scene, which comprises the following steps:

[0006] Step 1, generation of a liver body model and an intrahepatic blood vessel body model: obtaining a liver outer surface model and an intrahepatic blood vessel outer surface model from preoperative CT, converting the liver outer surface model and the blood vessel outer surface model into stp format respectively by using solidworks, and generating a liver body model and an intrahepatic blood vessel body model each composed of a plurality of tetrahedrons, converting the stp format file into a body model data in gmsh software, and generating the body model data containing node spatial position information, two connected node information, and node belonging to tetrahedron information; transmitting all the information to Unity software to realize visualization of the model;

[0007] Step 2, generation of a liver parenchyma body model: detecting the nodes of the liver body model located inside the intrahepatic blood vessel body model by using the barycentric method, deleting the tetrahedrons containing the nodes from the liver body model according to the node information, and forming a liver parenchyma body model;

[0008] Step 3, generation of intravascular blood model: the intravascular model of liver obtained in step 1 is generated into a dense mesh by means of the gmsh software, all node spatial position information in the mesh is obtained, for each node, the Euclidean distance d from the nearest node is calculated respectively, and a small ball with a diameter of d is generated respectively, the small ball represents the blood flow particle in the blood vessel for describing the blood flow in the blood vessel, and the blood flow particle constitutes the intravascular blood model;

[0009] Step 4, movement trend of liver parenchyma and intravascular under the action of external force, which is used to represent the movement of liver parenchyma under the action of external force, and the movement of blood vessels and blood particles caused by the deformation of liver parenchyma, and also includes the flow of blood particles under the condition of cutting, and the liver model is generated by combining the liver parenchyma model, the intravascular model and the intravascular blood model;

[0010] Step 5, movement of blood in blood vessel: the tetrahedron information in the liver parenchyma model is obtained, and the circumscribed sphere is generated based on the liver parenchyma tetrahedron information, the circumscribed sphere is used to constrain the movement of blood particles in the intravascular blood model, and the blood particles will be driven to move in the correct direction when the blood particles move normally,

[0011] When the blood particles collide, the speed of the blood particles does not change, and a force F is applied to the two blood particles colliding, the direction of the force F is from the center of the circumscribed sphere to the center of the blood particle, and the blood particle is driven to move;

[0012] When the blood particles collide with the circumscribed sphere in the liver parenchyma model, the liver parenchyma does not change, the intravascular does not drive the movement of the blood particles, and a collision force is applied to the blood particles colliding to drive the blood particles to move;

[0013] When facing tissue resection, the tetrahedron in the liver parenchyma model is separated or deleted, the movement barrier composed of the circumscribed sphere of the tetrahedron is cut, so that the blood particles have no movement constraint at this position, and the blood particles flow to the outside, forming the visual effect of blood outflow.

[0014] Further, the virtual surgery scene of the liver parenchyma and the intravascular and blood movement interaction method of the application, wherein,

[0015] In step 2, the method for detecting the nodes of the liver body model inside the intrahepatic blood vessel body model by using the gravity center method is as follows: a node O in the liver body model is connected with the four nodes of a tetrahedron ABCD in the intrahepatic blood vessel body model respectively, four tetrahedrons containing node P are formed respectively, if the volume of the four tetrahedrons is the same as the volume of the tetrahedron ABCD, it is considered that the node O is inside the intrahepatic blood vessel body model, and the node is recorded; the above process is repeated, and finally the node information of all nodes inside the intrahepatic blood vessel body model is obtained.

[0016] In step 3, the intrahepatic blood vessel body model obtained in step 1 is generated into a dense mesh by means of the gmsh software, and the number of tetrahedrons in the intrahepatic blood vessel body model after the dense mesh is 5-10 times that of the original.

[0017] The step 4 mainly includes: establishing a liver parenchyma motion model based on PBD; generating an inscribed sphere of a tetrahedron based on the spatial coordinates of the nodes of the liver parenchyma model and the intrahepatic blood vessel body model, and respectively calculating the inscribed sphere center and diameter of the liver parenchyma model and the intrahepatic blood vessel body model; generating a collision sphere according to the spatial coordinates of the nodes of the liver parenchyma motion model, and calculating the motion condition of the intrahepatic blood vessel.

[0018] Compared with the prior art, the method has the following beneficial effects:

[0019] (1) The method can correctly reflect the correct interactive motion condition of the liver parenchyma, the intrahepatic blood vessel and the blood flow in the virtual scene.

[0020] (2) When the cutting experiment is carried out in the virtual scene, when the blood vessel is cut, the method can correctly show the flow effect of the blood flow in the blood vessel. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a flow chart of the method of the application;

[0022] Figure 2 is a schematic view of deleting the nodes of the liver model in the blood vessel in the embodiment;

[0023] Figure 3 is a tetrahedron calculation example in the embodiment. DETAILED DESCRIPTION

[0024] The method for the motion interaction of the liver parenchyma, the intrahepatic blood vessel and the blood in the virtual surgery scene provided by the application comprises the following steps as shown in the figure: Figure 1 The method comprises the following steps:

[0025] Step 1, generation of a liver body model and an intrahepatic blood vessel body model.

[0026] The liver outer surface model and the intrahepatic blood vessel outer surface model are obtained from preoperative CT, the two models are respectively converted into stp format by using solidworks to form the liver body model and the intrahepatic blood vessel body model which are both composed of several tetrahedrons, the stp format files are transferred into the gmsh software to generate the body model data, the body model data contains node space position information, two connected node information and node belonging tetrahedron information; all the information is transmitted to the Unity software to realize the visualization of the model.

[0027] Step 2, generation of the liver parenchyma body model.

[0028] The nodes of the liver body model located in the intrahepatic blood vessel body model are detected by using the barycenter method, and the tetrahedrons containing the nodes are deleted from the liver body model according to the node information to form the liver parenchyma body model.

[0029] Since the liver generates the body model, a large number of space nodes are in the interior of the liver, and the nodes are also in the interior of the blood vessel model, because the liver and its blood vessel soft tissue characteristics are to be given according to the node information, so it is necessary to delete the liver body model nodes in the blood vessel, as shown in Figure 2 The body model data of the blood vessel is obtained, mainly the tetrahedron data in the body model data,

[0030] In the application, the method for detecting the nodes of the liver body model located in the intrahepatic blood vessel body model by using the barycenter method is that a node O in the liver body model is connected with four nodes of a tetrahedron ABCD in the intrahepatic blood vessel body model to form four tetrahedrons containing node P respectively, if the volume of the four tetrahedrons is the same as the volume of the tetrahedron ABCD, it is considered that the node O is located in the intrahepatic blood vessel body model, and the node is recorded; the above process is repeated to finally obtain all the node information located in the intrahepatic blood vessel body model. According to the recorded node information, all the tetrahedron models containing the nodes in the liver model are deleted. Thus, the liver parenchyma body model is formed. The volume calculation formula of the tetrahedron is: As shown in Figure 3 .

[0031] Step 3, generation of the blood vessel blood model.

[0032] Firstly, the dense mesh of the intrahepatic blood vessel model is generated by means of the gmsh software, all node space position information in the dense mesh is acquired, for each node, the Euclidean distance d from the nearest node is calculated respectively, and a small ball with a diameter of d is generated respectively, for each node, the distance of the nearest node is calculated according to the above method, and the small ball is generated, the small ball represents the blood flow particle in the blood vessel and is used for describing the blood flow in the blood vessel, and the blood flow particle constitutes the blood model in the blood vessel; in the application, the number of tetrahedrons in the intrahepatic blood vessel model after the dense mesh is 5-10 times of the original number.

[0033] Step 4, under the action of external force, the movement trend of liver parenchyma and intrahepatic blood vessels.

[0034] The movement of the liver under the action of external force, the movement of the liver parenchyma, and the movement of the blood vessels and blood particles caused by the deformation of the liver parenchyma are mainly described, and the flow of the blood particles in the cutting condition is also included, the PBD (Position-based Dynamics) is used for modeling the liver parenchyma, when the liver parenchyma is subjected to external force, the nodes in contact with the liver parenchyma change, the distance constraint and the volume constraint are used to drive the movement of the remaining nodes in the model, and the liver model is generated by combining the liver parenchyma model, the intrahepatic blood vessel model and the blood model in the blood vessel.

[0035] 4-1) Establishing a liver parenchyma movement model based on PBD:

[0036] When the liver parenchyma is subjected to external force, the positions of the nodes in contact with each other in the liver parenchyma change, and the distance constraint and the volume constraint are used to drive the movement of the remaining nodes in the liver parenchyma model;

[0037] According to the node information of the distance constraint condition: Figure 2

[0038]

[0039] A' = A + ΔA

[0040] Wherein, A represents the space coordinates of node A, B represents the space coordinates of node B; represents the gradient of the direction vector from node A to node B, represents the gradient of the direction vector from node B to node A; λ represents the Lagrange multiplier, C represents the distance change between node A and node B, l0 represents the original length from node A to node B, l represents the length from node A to node B after being subjected to force, w a represents the weight parameter of the position of node A, w b represents the weight parameter of the position of node B, and the w a and w b ​A' represents the spatial coordinates of node A after distance constraint;

[0041] Similarly, the spatial coordinates of node B after distance constraint B' are obtained;

[0042] Volume constraint condition (to Figure 2 Position information calculation of the above four nodes:

[0043] C v = 6 (V-V o ) = [(B'-A') x (C'-A')] · (D'-A') - 6V

[0044]

[0045] Wherein, V represents the volume of the tetrahedron after deformation, V o represents the volume of the tetrahedron before deformation, C v represents the change of the volume of the tetrahedron before and after deformation, represents the volume constraint on D point;

[0046] Similarly, the spatial coordinates of node B after volume constraint B" are obtained.

[0047]

[0048] A" = A + ΔA' i

[0049] Wherein, λ is the Lagrange multiplier, w i represents the weight parameter of each node in the tetrahedron, represents the volume constraint on node i, i represents the node position, and A" represents the spatial coordinates of node A after volume constraint;

[0050] Similarly, the spatial coordinates of node B after volume constraint B" are obtained.

[0051] The displacement of the four nodes under the volume constraint condition can be obtained. The displacement of the nodes inside the liver parenchyma under the action of external force is realized.

[0052] Because the liver blood vessels and the liver parenchyma are two models, the nodes of the two are not connected with each other, so the motion of the liver blood vessels is calculated according to the liver parenchyma,

[0053] 4-2) Based on the spatial coordinates of the nodes of the liver parenchyma model and the liver blood vessel model, the inscribed sphere of the tetrahedron is generated;

[0054] Because the liver blood vessel and the liver parenchyma are two models, the nodes of the two models are not connected with each other, so the movement of the liver blood vessel is calculated according to the liver parenchyma. First, according to the information of all tetrahedrons in the liver parenchyma model obtained in step 1, the inscribed sphere of each tetrahedron is made; according to the inscribed sphere of each tetrahedron, the coordinates of four nodes of a tetrahedron are set as:

[0055] A(Ax, Ay, Az), B(Bx, By, Bz), C(Cx, Cy, Cz), D(Dx, Dy, Dz);

[0056] The center of the inscribed sphere of the tetrahedron is O(x, y, z), and the radius of the inscribed sphere is R;

[0057]

[0058] Wherein, V is the volume of the tetrahedron, and S is the surface area of the tetrahedron;

[0059]

[0060] S = S ABC + S BCD + S ACD + S ABD

[0061]

[0062] The coordinates of the center of the inscribed sphere O are:

[0063]

[0064] That is, the center coordinates and the radius of the inscribed sphere are obtained.

[0065] Similarly, according to the information of all tetrahedrons in the liver blood vessel model obtained in step 1, the inscribed sphere of each tetrahedron is made, and the center and the diameter of the inscribed sphere of the liver blood vessel model are obtained by using the calculation method of the center and the diameter of the inscribed sphere of the liver parenchyma model.

[0066] 4-3) According to the space coordinates of the nodes of the liver parenchyma movement model, the collision sphere is generated, and the movement of the liver blood vessel is calculated;

[0067] When the liver parenchyma has motion interaction, the nodes in the liver have motion, and the position and size of the inscribed sphere also have motion. When the inscribed sphere of the liver parenchyma contacts the inscribed sphere of the intrahepatic blood vessel, the relative position of the two is adjusted, the position of the inscribed spheres in contact is adjusted using distance constraints, the distance to be moved by the sphere center is calculated, which is a vector, and the four nodes constituting the two inscribed spheres are added with the vector respectively to realize the motion of the nodes. The intrahepatic blood vessel is also modeled using the PBD method, and distance constraints and volume constraints are used to ensure the motion of the model. The specific process is as follows:

[0068] An inscribed sphere O1 in the liver parenchyma model obtained from step 4-2) and an inscribed sphere O2 in the intrahepatic blood vessel model are used to calculate the Euclidean distance between the sphere centers of the two inscribed spheres. If the distance is less than the radius of the two inscribed spheres, it is considered that the two inscribed spheres are in contact. Let the coordinates of the sphere centers of the inscribed spheres O1 and O2 be P1 and P2 respectively. The spatial coordinates P1' and P2' of P1 and P2 after motion are calculated using the distance constraint condition in step 4-1). The spatial coordinate change of the four nodes of the tetrahedron where the inscribed sphere O1 is located is equal to the spatial coordinate change of the sphere center of the inscribed sphere O1, and the spatial coordinate change of the four nodes of the tetrahedron where the inscribed sphere O2 is located is equal to the spatial coordinate change of the sphere center of the inscribed sphere O2. The position criteria of the remaining nodes of the liver parenchyma model and the intrahepatic blood vessel model are calculated according to the distance constraint and the volume constraint of the PBD method

[0069] Step 5, the motion of the blood in the blood vessel:

[0070] Obtain the tetrahedron information in the liver parenchyma model, generate an inscribed sphere based on the liver parenchyma tetrahedron information, the sphere center coordinates of the inscribed sphere are (x0, y0, z0), and the radius of the inscribed sphere is R o ;

[0071] The expression of the inscribed sphere is: (x-x0) 2 +(y-y0) 2 +(z-z0) 2 =R o 2 .

[0072] Expand as:

[0073] Convert to: x 2 +y 2 +z 2 +ax+by+cz+d=0

[0074] Finally, the coordinates of the four nodes of the tetrahedron inside the inscribed sphere are brought into the conversion formula to solve the values of a, b, c, and d, and thus the coordinates of the center of the inscribed sphere are obtained:

[0075]

[0076] The radius of the circumscribed sphere is:

[0077]

[0078] The circumscribed sphere is used to constrain the movement of blood particles in the blood model in the blood vessel, and the blood particles in the blood vessel are given a certain force according to their normal movement to make them move in the correct direction, and when the blood particles collide, the speed of the blood particles does not change, and a certain force F is given to the blood particles according to the direction of the centers of the two colliding particles, to drive the blood particles to move, and the direction of the force F is from the center of the circumscribed sphere to the center of the blood particle. When the blood particles collide with the circumscribed sphere in the liver parenchyma model, the liver parenchyma does not change, and the blood particles are given a certain collision force according to the contact condition to drive the blood particles to move. The blood vessels in the liver do not drive the movement of the blood particles. When facing tissue resection, the tetrahedron in the liver parenchyma model is separated or deleted, and when the liver parenchyma near the blood vessel is separated, the movement barrier composed of the circumscribed sphere of the tetrahedron is cut, resulting in that the blood particles have no movement constraint at this place, and flow out of the blood vessel to the outside, forming a visual effect of blood outflow.

[0079] In summary, the method fully considers the movement characteristics of the liver and the blood vessels under the action of force, and realizes the movement constraint between the blood vessels in the liver and the liver parenchyma, and the movement constraint of the blood flow in the blood vessels under the action of external force in the virtual surgery scene through the above process.

[0080] Although the present application has been described in conjunction with the accompanying drawings, the present application is not limited to the specific embodiments described above, and the specific embodiments described above are only illustrative but not limiting, and those skilled in the art can make many improvements and changes under the inspiration of the present application without departing from the purpose of the present application, and these all belong to the protection of the present application.

Claims

1. A method for motion interaction of liver parenchyma and intrahepatic blood vessels and blood in a virtual surgery scene, characterized in that, The method comprises the following steps: Step 1, generation of a liver body model and an intrahepatic blood vessel body model: Obtain a liver outer surface model and an intrahepatic blood vessel outer surface model from preoperative CT, convert the liver outer surface model and the blood vessel outer surface model into stp format respectively by using solidworks to form a liver body model and an intrahepatic blood vessel body model each composed of a plurality of tetrahedrons, convert the stp format file into gmsh software to generate body model data, wherein the body model data comprises node spatial position information, two connected node information, and node tetrahedron information; transmit all information to Unity software to realize visualization of the model; Step 2, generation of a liver parenchyma body model: Detect the nodes of the liver body model inside the intrahepatic blood vessel body model by using the barycentric method, delete the tetrahedrons containing the nodes from the liver body model according to the node information to form a liver parenchyma body model; Step 3, generation of a blood vessel blood model: The hepatic intravascular body model obtained in step 1 is generated into a dense mesh by means of the gmsh software, all node space position information in the mesh is obtained, for each node, the Euclidean distance from the nearest node is calculated respectively , and small balls with a diameter of are generated respectively, the small balls represent blood flow particles in the blood vessels for describing blood flow in the blood vessels, and the blood flow in the blood vessels is constituted by a collection of the blood flow particles; Step 4, movement trend of liver parenchyma and intrahepatic blood vessels under external force, used to represent the movement of liver parenchyma under external force and the movement of blood vessels and blood particles caused by deformation of liver parenchyma, and also include the flow of blood particles under cutting condition, generate a liver model in combination with the liver parenchyma body model, the intrahepatic blood vessel body model and the blood vessel blood model; specifically comprising: Step 4-1) establish a liver parenchyma movement model based on PBD, When the liver parenchyma is subjected to external force, the positions of the nodes in contact with each other in the liver parenchyma change, and distance constraint and volume constraint are used to drive the movement of the remaining nodes in the liver parenchyma model; Distance constraint condition: ； ； ； ； ； wherein A represents the spatial coordinates of node A, B represents the spatial coordinates of node B; represents the gradient of the direction vector from node A to node B, represents the gradient of the direction vector from node B to node A; represents the Lagrange multiplier, C represents the distance variation between node A and node B, represents the original length from node A to node B, represents the length from node A to node B after being stressed, represents the weight parameter of the position of node A, represents the weight parameter of the position of node B, and the and are used to represent the motion characteristics of the nodes under the action of stress; represents the spatial coordinates of node A after the distance constraint. Similarly, the spatial coordinates of the Node B after the distance constraint are obtained ; Volume constraint condition: ； ； wherein, represents the volume of the tetrahedron after deformation, represents the volume of the tetrahedron before deformation, represents the volume change of the tetrahedron before and after deformation, represents the volume constraint on the D point; By analogy, we obtain ; ； ； ； wherein, Lagrange multipliers, denotes a weight parameter for each node in the tetrahedron, denotes a volume constraint for node i, i denotes a node position, denotes the spatial coordinates of node A after the volume constraint; Similarly, the spatial coordinates of the node B after the volume constraint are obtained ; Step 4-2) generate an inscribed sphere of a tetrahedron based on the spatial coordinates of each node of the liver parenchyma model and the intrahepatic blood vessel body model; According to the information of all tetrahedrons in the liver parenchyma model obtained in step 1, make an inscribed sphere of each tetrahedron; Let the coordinates of the four nodes of a tetrahedron be: ； The center of the inscribed sphere of the tetrahedron is O , the radius of the inscribed sphere R; ； wherein is the volume of the tetrahedron, is the surface area of the tetrahedron; ； ； ； ； ； ； The coordinates of the center O of the inscribed sphere are: ； ； ； According to the information of all tetrahedrons in the intrahepatic blood vessel body model obtained in step 1, make an inscribed sphere of each tetrahedron, and obtain the center and diameter of the inscribed sphere of the intrahepatic blood vessel body model by using the calculation method of the center and diameter of the inscribed sphere of the liver parenchyma model; Step 4-3) generate a collision sphere according to the spatial coordinates of each node of the liver parenchyma movement model to calculate the movement of the intrahepatic blood vessels; The Euclidean distance between the centers of the two inscribed spheres O1 and O2 in the liver parenchyma model obtained from step 4-2) and the liver blood vessel model is calculated. If the distance is less than the sum of the radii of the two inscribed spheres, it is considered that the two inscribed spheres are in contact. Let the coordinates of the centers of the inscribed spheres O1 and O2 be P1 and P2, respectively. The spatial coordinates P1' and P2' of P1 and P2 after movement are calculated using the distance constraint in step 4-1). The spatial coordinate changes of the four nodes of the tetrahedron where the inscribed sphere O1 is located are equal to the spatial coordinate changes of the center of the inscribed sphere O1. The spatial coordinate changes of the four nodes of the tetrahedron where the inscribed sphere O2 is located are equal to the spatial coordinate changes of the center of the inscribed sphere O2. The position criteria of the remaining nodes of the liver parenchyma model and the liver blood vessel model are calculated according to the distance constraint and the volume constraint of the PBD method. Step 5, the movement of blood in the blood vessels: Obtain the tetrahedron information in the liver parenchyma model, and generate an inscribed sphere based on the liver parenchyma tetrahedron information. The inscribed sphere is used to constrain the movement of blood particles in the blood vessel blood model. When the blood particles move normally, they will be subject to a force that drives them to move in the correct direction, When the blood particles collide, the speed of the blood particles remains unchanged. A force F is applied to the two blood particles that collide, and the direction of the force F is from the center of the inscribed sphere to the center of the blood particle, driving the blood particle to move. When the blood particles collide with the inscribed sphere in the liver parenchyma model, the liver parenchyma does not change, and the liver blood vessels do not drive the movement of the blood particles. A collision force is applied to the colliding blood particles to drive the blood particles to move. When facing tissue resection, the tetrahedron in the liver parenchyma model is separated or deleted, and the movement barrier composed of the inscribed sphere of the tetrahedron is cut, resulting in no movement constraint for the blood particles at this point, and the blood particles flow out of the blood vessels to the outside, forming a visual effect of blood outflow.

2. The method of claim 1, wherein the liver parenchyma and the intrahepatic blood vessels and blood are interacted with each other in motion in the virtual surgical scene. In step 2, the method for detecting the nodes of the liver model inside the liver blood vessel model using the barycentric method is as follows: connect a node O in the liver model with the four nodes of a tetrahedron ABCD in the liver blood vessel model to form four tetrahedrons containing node P, respectively. If the volume of the four tetrahedrons is the same as the volume of tetrahedron ABCD, it is considered that the node O is located inside the liver blood vessel model, and the node is recorded. Repeat the above process to finally obtain all the node information inside the liver blood vessel model. 3.The method of claim 1, wherein, In step 3, the liver blood vessel model obtained in step 1 is generated into a dense mesh using the gmsh software. The number of tetrahedrons in the liver blood vessel model after dense meshing is 5-10 times that of the original.

4. The method of claim 1, wherein the liver parenchyma and the intrahepatic blood vessels and blood are interacted with each other in motion in the virtual surgical scene. The center coordinates of the circumscribed sphere in step 5 are (x0, y0, z0), and the radius of the circumscribed sphere is ; The expression of the circumscribed enclosing sphere is: . Unfolded is: ; Transforms to: ; Finally, the coordinates of the four nodes of the tetrahedron inscribed in the circumscribed sphere are brought into the conversion formula, and the value of is solved, thus obtaining the coordinates of the center of the circumscribed sphere: ； The radius of the inscribed sphere is: 。

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