CN114693892A - Modeling method for cutting bleeding model in virtual surgery - Google Patents

Abstract

The invention discloses a modeling method of a cutting bleeding model in a virtual operation, which realizes the reality of cutting bleeding simulation in the virtual operation. The method comprises the following steps: firstly, before the soft tissue is cut open, according to the extrusion direction, angle and position of a scalpel, simulating to generate local small deformation and calculating feedback force; secondly, calculating sliding friction force and generating an incision after the soft tissue is incised; then, introducing a mathematical function to calculate real-time blood flow generated by the cutting part and generating corresponding amount of bleeding particles; finally, an improved hybrid depth visual rendering (IMDR) method is employed to render the blood surface. According to the modeling method of the cutting bleeding model in the virtual operation, provided by the invention, the local small deformation of the soft tissue before cutting, the cut formed after cutting, the real-time feedback force of the cutting process and the bleeding are fused, so that a vivid cutting bleeding simulation effect is realized.

Description

Modeling method for cutting bleeding model in virtual surgery

Technical Field

The invention belongs to the technical field of virtual operations in virtual reality, and particularly relates to a modeling method of a cutting bleeding model in a virtual operation.

Background

Virtual Reality (VR) is a interdisciplinary subject that integrates multiple technologies such as simulation, multimedia, and sensing technologies. Virtual surgery is used as VR, and a convenient and efficient method is provided for training surgeons. The surgeon can perform repeated operation training under the virtual operation scene provided by the virtual operation system so as to improve the success rate of the operation.

In a real surgical procedure, cutting is one of the most common surgical procedures. A good cutting model is crucial to reproduce a realistic cutting surgery simulation.

Early, most surgical simulators used Finite Element Methods (FEM) to implement cutting simulation. Node capture methods, vertex replication segmentation algorithms, tetrahedral removal methods, tetrahedral subdivision methods, and the like are early common finite element methods applied to cutting simulation. These methods are easy to implement, but it is very grid dependent, and a distorted or low quality grid can cause instability of the system. The advent of the Meshless Method (MM) just addressed the shortcomings of the finite element method. The method adopts a point cloud structure model, does not need complex topological structures of points and points, and has no direct association between elements of each point. Also, all point elements are not constrained by the grid, making them suitable for discontinuous scenes. Compared with the finite element method, the meshless method has the characteristic of strong self-adaption and is suitable for large deformation and cutting simulation.

Bleeding inevitably accompanies cutting during surgery. It not only interferes with the surgical operation of the surgeon, but may even risk excessive blood loss to the patient. Therefore, bleeding simulation is also an important part of a virtual surgical system, which is extremely important for training surgeons in their ability to deal with unexpected bleeding.

The marching cubes algorithm (MC) is the most common geometric method used to render bleeding. The method is a classic iso-surface rendering method. Because of its simple implementation, it is commonly used to simulate bleeding, particularly gushing-like bleeding. However, if a typical cutting operation does not cut large blood vessels such as arteries, then the bleeding created by the soft tissue damage is generally slow flowing on the soft tissue surface. In this case, the MC method hardly exhibits a sense of depth. The hybrid depth visual rendering Method (MDR) just makes up the defects of the MC algorithm, and the method can well show the depth visual effect of blood flowing on the surface of soft tissue. Moreover, the real-time performance of the MDR far exceeds that of the MC algorithm.

Although the prior art methods have achieved considerable research results for the simulation of cutting and bleeding, cutting and bleeding often occur independently of each other. In fact, cutting and bleeding are two interrelated modules whose fidelity interact. Also, the location of bleeding production and blood flow volume are key factors in simulating realistic bleeding.

Disclosure of Invention

Aiming at the defects and problems in the prior art, the invention aims to provide a modeling method for a cutting bleeding model in a virtual operation. The invention aims to improve the authenticity of the cutting bleeding simulation effect.

The invention is realized by the following technical scheme:

a modeling method for a cutting bleeding model in virtual surgery comprises the following steps:

step one, setting a maximum bearing force threshold maxforce for soft tissues.

And step two, generating local small deformation according to the position, the angle and the direction of the soft tissue extruded by the virtual scalpel, and calculating the feedback force.

And step three, when the acting force applied to the soft tissue by the scalpel exceeds maxforce, calculating the sliding friction force in the cutting process, and rendering the cut.

And step four, reasonably setting the maximum bleeding amount (namely the maximum particle generation amount) according to the cutting condition, and introducing a mathematical function to calculate the real-time blood flow (the particle amount generated in unit time).

And step five, adopting an improved mixed depth visual rendering (IMDR) method to render the blood surface.

Preferably, the method for generating the local small deformation in the second step comprises the following two processes:

(1) traversing all the point elements, judging whether the point elements are positioned in the deformation range, wherein the judgment conditions are as follows:

in the formula, l is the extrusion direction vector of the virtual scalpel, P is the coordinate position of the scalpel tip, T is the coordinate position of the point element, and R is the radius of the deformation range.

(2) And calculating the displacement of the point element in the deformation range according to the following calculation formula:

where dep is the depth of extrusion along the vector l, l_x、l_y、l_zFor the components of the vector l, n is a constant parameter that determines the degree of deformation.

Preferably, the formula for calculating the deformation feedback force in the second step is:

wherein k is the Hooke's law elastic coefficient.

Preferably, the formula for calculating the sliding friction force of the cutting process in the third step is as follows:

where eta is the coefficient of sliding friction, v_x、v_y、v_zThe component of the cutting movement speed, δ is a non-negative number less than 1.

Preferably, the function of calculating the real-time blood flow in step four is:

in the formula of lambda₁、λ₂、λ₃Constant for controlling blood flow, t₀To create a bleeding time.

Preferably, the IMDR method in step five specifically includes the following steps:

(1) establishing a smooth height field; the establishment process is as follows:

firstly, establishing a uniform two-dimensional height field grid for a blood flow area, and setting an initial height threshold value for all grids;

secondly, carrying out stress analysis on the particles, including pressure, viscous force and surface tension, and calculating position coordinates of the particles;

determining the grid position of the particle according to the coordinate of the particle;

if the height value of the particle exceeds the threshold value of the grid where the particle is located, updating the threshold value of the grid by using the height value of the particle; otherwise, updating is not carried out;

smoothing the threshold values of all the grids;

sixthly, connecting the central points of each grid, wherein the height of the central point is the height of the grid;

(2) repairing the boundary grid;

(3) calculating RGB values of blood colors; the calculation formula is as follows:

wherein (C)_R,C_G,C_B) RGB value corresponding to blood color at time t, (C)_R0,C_G0,C_B0) At an initial time t ═ t₀The RGB values corresponding to the color of the blood,

are respectively control C_R,C_G,C_BConstants of rates of change of three component values, T₀The temperature of blood at the initial moment, H is room temperature, and alpha is a temperature reduction coefficient in a Newton's cooling law;

(4) calculating the transparency of the blood;

(5) and calculating the normal vector of the grid, and rendering a triangular patch by matching with the illumination model to finally form the bleeding surface.

Compared with the prior art, the invention has the beneficial effects that:

according to the modeling method of the cutting bleeding model in the virtual surgery, provided by the invention, a relatively real cutting surgery simulation effect is obtained by simulating local small deformation of soft tissues before cutting, a cut formed after cutting and a feedback force in the cutting process; by introducing an improved hybrid depth visual rendering method (IMDR), a more realistic bleeding effect is obtained.

Drawings

FIG. 1 is a flow chart of a modeling method for cutting a bleeding model in a virtual surgery according to the present invention.

Fig. 2 is a schematic diagram of establishing an orthogonal plane according to the present invention.

FIG. 3 is a schematic diagram of computing a normal vector of a two-dimensional height field grid node according to the present invention.

FIG. 4 is a 7X 7 GS template according to the present invention.

Fig. 5 is a schematic diagram of a grid center point connection rule according to the present invention.

FIG. 6 is a diagram illustrating a repaired boundary grid according to the present invention.

FIG. 7 is a simulation effect diagram of local small deformation obtained by the modeling method of the cutting bleeding model in the virtual surgery.

FIG. 8 is a diagram of the simulation effect of cutting bleeding obtained by the modeling method of the cutting bleeding model in the virtual surgery according to the present invention.

Detailed Description

The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.

As shown in fig. 1, the present invention provides a modeling method for a cutting bleeding model in a virtual operation, which can obtain a realistic cutting bleeding simulation effect and improve the reality of cutting bleeding simulation in the virtual operation, and the implementation method specifically includes:

first, a maximum tolerance threshold maxforce is set for the soft tissue.

Then, traversing all the point elements, and judging whether the point elements are located in the local extrusion deformation range, wherein the judgment conditions are as follows:

in the formula, l is the extrusion direction vector of the virtual scalpel, P is the coordinate position of the scalpel tip, T is the coordinate position of the point element, and R is the radius of the local extrusion deformation range.

In this example, R has a value of 2.

Then, the displacement of the point element in the local extrusion deformation range is calculated, and the calculation formula is as follows:

where dep is the depth of extrusion along the vector l, l_x、l_y、l_zAs a component of the vector l, n is a constant parameter that determines the degree of deformation, and in this embodiment, n is 4.

And then, calculating the feedback force in the local extrusion deformation process. The formula for calculating the feedback force is:

where k is the hooke's law elastic modulus, and in this example k is about 0.3.

Thereafter, the sliding friction force during the cutting process is calculated when the force exerted by the scalpel on the soft tissue exceeds maxforce. The calculation formula is as follows:

where eta is the coefficient of sliding friction, v_x、v_y、v_zThe component of the cutting movement speed, δ is a non-negative number less than 1.

In this example, η is about 0.1 and δ is about 0.5.

Thereafter, the simulation generated an incision made by the soft tissue. The incision generation is divided into the following 5 steps:

(1) as shown in fig. 2, the tip of the virtual surgical tool is simplified to a proxy ball. And establishing orthogonal planes alpha, beta and gamma with the proxy small ball as the center according to the cutting direction, angle and position of the scalpel.

(2) The offsets of each point element from the three orthogonal planes are calculated separately. The calculation formula is as follows:

in the formula, K_α、K_β、K_γThe offsets of the point elements (x, y, z) from the orthogonal planes α, β, γ, respectively; (x)_tp,y_tp,z_tp) The position coordinates of the proxy small ball are shown, and a, b and c are normal vectors of orthogonal planes alpha, beta and gamma respectively. (a)_x,a_y,a_z),(b_x,b_y,b_z),(c_x,c_y,c_z) Three components of the vectors a, b, c, respectively. And the length of the modulus of the vector a, the length of the modulus of the vector b and the length of the vector c are respectively | a | |, | b | |, and | c |.

(3) Constructing a proper incision shape function and an incision impact field. Then according to K_α、K_β、K_γAnd judging whether the point element is positioned in the cutting influence domain, if so, marking the point element as a point needing to be moved, and if not, skipping until all the point elements are traversed.

Wherein the shape function of the notch is:

in the formula, k₁,k₂To control the constant parameter of the kerf shape, σ is the depth coefficient, which is defined as:

σ＝1+μ₁(μ₂-z_tp)

in the formula, mu₁，μ₂To determine the depth coefficient and the parameters affecting the domain scope.

Wherein the range of the cleavage impact domain is:

in this example, k is taken₁、k₂100/9, 25/36, u₁、 μ ₂1, 1/4.

(4) And calculating the displacement of each point element needing to be moved, and performing displacement operation.

Wherein, the calculation formula of the displacement amount of each point element needing to be moved is as follows:

in the formula eta₁、η₂、η₃Is a parameter for controlling the displacement. In this example take η₁、η₂、η₃Respectively 0.06, 0.1 and 0.1. (5) And constructing a two-dimensional height field grid rendering cut surface. The method comprises the following specific steps:

firstly, establishing uniform two-dimensional height field grids for a soft tissue cutting area, and setting an initial height threshold value for all the grids;

traversing all point elements, and calculating the grid position of each point according to the position coordinates of the point elements;

if the height of the point element exceeds the threshold of the grid where the point is located, updating the threshold by using the height of the point element; otherwise, not updating;

performing smoothing treatment on the height of each grid (generally taking the average value of 7 multiplied by 7 grids adjacent to the periphery) to reduce the height difference between the adjacent grids and improve the smoothness of the cutting mark surface;

and fifthly, calculating the normal vector of each grid node (as shown in figure 3), and normalizing to facilitate rendering under the illumination model.

In step 5, the normal vector at mesh node (i, j) is:

in the formula, vector P_A、P_B、P_C、P_DThe calculation process of (2) is as follows:

in the formula, vectors a, B, C, D respectively represent four vectors pointing to mesh nodes (i, j), and their calculation process is as follows:

where Pos (i, j) represents the position coordinates of the mesh node (i, j).

In this embodiment, the RGB value of blood is selected to be (0.8,0,0) to render the color of the incision.

Thereafter, the maximum flow volume (i.e., the maximum particle generation number) is set according to the cutting situation. In the present embodiment, 3000 is set.

Then, the blood flow in real time (the number of particles generated per unit time) is calculated, and particles are generated at the bleeding site.

Wherein, the calculation formula of the blood flow is as follows:

in the formula, λ₁、λ₂、λ₃Constant for controlling blood flow, t₀To create a bleeding time. In this embodiment, let λ₁、λ₂、λ₃Respectively 100, -0.01 and 2.

Thereafter, the bleeding surface is rendered using an improved hybrid depth visual rendering (IMDR) method. The IMDR method is specifically divided into the following 5 steps:

(1) a smooth height field is established. The establishment process is as follows:

establishing a uniform two-dimensional height field grid for a blood flowing area, and setting an initial height threshold value for all grids;

secondly, carrying out stress analysis (pressure, viscous force and surface tension) on the particles, and calculating position coordinates of the particles;

determining the grid position of the particle according to the coordinate of the particle;

if the height value of the particle exceeds the threshold value of the grid where the particle is located, updating the threshold value of the grid by using the height value of the particle; otherwise, updating is not carried out;

carrying out smoothing treatment on the threshold values of all grids, wherein the treatment process is as follows:

in the formula, Height_i,jAs threshold for grid (i, j), HEIGHT_i,jThe height value of grid (i, j) after smoothing processing, the 7 × 7 GS template is shown in fig. 4;

sixthly, connecting the central points of each grid according to the rule of the figure 5, wherein the height of the central point is the height of the grid;

(2) and repairing the boundary grid. If the situation in the grid as shown in fig. 6(a) and 6(c) occurs (the height of the top left/bottom right corner vertex of the grid is lower than the height of the soft tissue surface, and the remaining vertices are higher than the height of the soft tissue surface), the connection is performed according to the connection rule of fig. 6(b) and 6 (d).

(3) RGB values of the blood color are calculated. The calculation formula is as follows:

in the formula (C)_R,C_G,C_B) RGB value corresponding to blood color at time t, (C)_R0,C_G0,C_B0) At an initial time t ═ t₀The RGB values corresponding to the color of the blood,

are respectively control C_R,C_G,C_BConstants of rates of change of three component values, T₀The temperature of blood at the initial moment, H is room temperature, and alpha is the temperature reduction coefficient in Newton's law of cooling.

In this example, (C) is taken_R0,C_G0,C_B0) Has a value of (159,10,7),

has a value of 60,2,2, T₀38.5 deg.C, H25 deg.C, t₀The value of α is 0.15.

(4) The transparency of the blood was calculated. The calculation formula is as follows:

alpha in the formula_i,jIs a grid cell grid_i,jTransparency, num_i,jGrid for grid cell_i,jThe number of the particles in (a) is,

is a constant parameter that controls transparency.

In this embodiment, take

Is 134.

(5) And (3) calculating a normal vector of the grid (the same as the method for rendering the algorithm vector of the notch timing), and rendering a triangular patch by matching with an illumination model to finally form the bleeding surface.

By adopting the modeling method of the cutting bleeding model in the virtual operation, provided by the invention, the vivid cutting bleeding simulation effect is realized by fusing the local small deformation of the soft tissue before cutting, the cut formed after cutting, the real-time feedback force of the cutting process and the bleeding.

As can be seen from FIG. 7, the method provided by the invention realizes a vivid simulation effect of local small deformation, and conforms to a real cutting and extruding process. As can be seen from the graph 8, the method provided by the invention realizes vivid cutting bleeding simulation and accords with the real soft tissue cutting bleeding effect.

While embodiments of the invention have been described above, it is not limited to the applications set forth in the description and the embodiments, which are fully applicable in various fields of endeavor to which the invention pertains, and further modifications may readily be made by those skilled in the art, it being understood that the invention is not limited to the details shown and described herein without departing from the general concept defined by the appended claims and their equivalents.

Claims (5)

1. A modeling method for a cutting bleeding model in a virtual surgery is characterized by comprising the following steps:

step one, setting a maximum bearing force threshold maxforce for soft tissues;

step two, generating local small deformation according to the position, the angle and the direction of the soft tissue extruded by the virtual scalpel, and calculating a feedback force;

step three, when the acting force of the scalpel on the soft tissue exceeds maxforce, calculating the sliding friction force in the cutting process, and rendering a cut;

step four, setting the maximum bleeding volume, namely the maximum particle generation quantity according to the cutting condition, and introducing a mathematical function to calculate the real-time blood flow volume, namely the particle quantity generated in unit time;

and step five, adopting an improved mixed depth vision rendering method IMDR to render the blood surface.

2. The modeling method of the incision bleeding model in the virtual surgery as set forth in claim 1, wherein the method for generating the local small deformation in the second step comprises the following two processes:

(1) traversing all the point elements, judging whether the point elements are positioned in the deformation range, wherein the judgment conditions are as follows:

in the formula, l is the extrusion direction vector of the virtual scalpel, P is the coordinate position of the scalpel tip, T is the coordinate position of any point element, and R is the radius of the deformation range;

(2) and calculating the displacement of the point element in the deformation range according to the following calculation formula:

where dep is the depth of extrusion along the vector l, l_x、l_y、l_zFor the components of the vector l, n is a constant parameter that determines the degree of deformation.

3. The modeling method for the incision bleeding model in the virtual surgery as set forth in claim 2, wherein the formula for calculating the sliding friction force of the incision process in the third step is as follows:

where eta is the coefficient of sliding friction, v_x、v_y、v_zFor the component of the cutting movement velocity, δ is a non-negative number less than 1, and k is the hooke's law elastic coefficient.

4. The modeling method of the virtual intraoperative incision flow model according to claim 1, characterized in that the function of calculating the real-time blood flow in the fourth step is:

in the formula, λ₁、λ₂、λ₃Constant parameter for controlling blood flow, t₀To create a bleeding time.

5. The modeling method of the virtual intraoperative incision bleeding model according to claim 1, wherein the IMDR method in the fifth step specifically comprises the following steps:

(1) establishing a smooth height field; the establishment process is as follows:

establishing a uniform two-dimensional height field grid for a blood flowing area, and setting an initial height threshold value for all grids;

secondly, carrying out stress analysis on the particles, including pressure, viscous force and surface tension, and calculating position coordinates of the particles;

determining the grid position of the particle according to the coordinate of the particle;

if the height value of the particle exceeds the threshold value of the grid where the particle is located, updating the threshold value of the grid by using the height value of the particle; otherwise, updating is not carried out;

smoothing the threshold values of all the grids;

sixthly, connecting the central points of each grid, wherein the height of the central point is the height of the grid;

(2) repairing the boundary grid;

(3) calculating RGB values of blood colors; the calculation formula is as follows:

in the formula (C)_R,C_G,C_B) RGB value corresponding to blood color at time t, (C)_R0,C_G0,C_B0) At an initial time t ═ t₀The RGB values corresponding to the color of the blood,

are respectively control C_R,C_G,C_BConstants of rates of change of three component values, T₀The temperature of blood at the initial moment, H is room temperature, and alpha is a temperature reduction coefficient in a Newton's cooling law;

(4) calculating the transparency of the blood;

(5) and calculating the normal vector of the grid, and rendering a triangular patch by matching with the illumination model to finally form the bleeding surface.

Images