CN109077803B - Modeling method of bleeding simulation model in virtual surgery - Google Patents
Modeling method of bleeding simulation model in virtual surgery Download PDFInfo
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- A61B34/10—Computer-aided planning, simulation or modelling of surgical operations
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- A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
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- A61B2034/101—Computer-aided simulation of surgical operations
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Abstract
The invention discloses a modeling method of a bleeding simulation model in a virtual operation, which comprises the following steps: step one, determining a particle system, and dividing the particle system into grids with the side length of the acting radius of an SPH method; determining a particle i and judging whether the particle i is in the grid, and determining a neighboring particle of the particle i when the particle i is in the grid; and step three, revising the viscosity coefficient and the action radius of the particle i to obtain a revised viscosity coefficient and a revised action radius, and establishing the model according to the stress, the acceleration, the revised viscosity coefficient and the revised action radius of the particle i. According to the modeling method of the bleeding simulation model in the virtual surgery, the efficiency of searching the near point by the SPH method is improved by the grid division method; through the improvement of the physical property of the bleeding model, the smoothness of the bleeding simulation surface is better, the problem of boundary distortion is solved, and the real-time performance and the authenticity of the bleeding simulation are improved; the simulation effect is smoother.
Description
Technical Field
The invention belongs to the technical field of virtual operations in virtual reality, and particularly relates to a modeling method of a bleeding simulation model in a virtual operation.
Background
The virtual reality technology is a virtual world created by computer simulation, and can provide a real feeling for a user. The virtual reality technology comprises computer graphics, artificial intelligence, mechanics and other disciplines, and environment and perception simulation is realized by simulating vision, hearing, touch and the like. The user takes the action of swinging head, lifting hands and the like as input, and the computer processes and responds to the action and feeds back the action to the sense organ of the user. The virtual operation is an important research direction of the virtual reality technology, provides an immersive training platform for surgeons, can cultivate the surgeons more safely and efficiently, reduces the cost, and avoids using animals as research objects and being subject to the responsibility of the animal protection association. In actual surgery, the tissue and organ inevitably needs to be treated as required for treatment, which leads to the necessity of bleeding. If the operator is not well trained, the correct treatment may not be possible in the event of a massive bleeding, with serious consequences. Therefore, the establishment of the virtual operation platform and the simulation of bleeding are important components, so that the sense of reality in the aspect of virtual operation environment vision can be increased, and the capability of treating bleeding conditions for surgeons can be enhanced.
At present, some problems exist in bleeding simulation, the real-time performance of simulation is poor, the real-time performance is a requirement which must be met by a virtual operation, any delay affects the precision of the operation, and the calculated amount is increased along with the increase of the number of particles in the bleeding simulation, so that the real-time performance of the simulation is directly affected; the realism of the simulation with real-time performance requirements is to be improved, including deficiencies in the study of bleeding physics and deficiencies in programming implementation.
Disclosure of Invention
One of the purposes of the invention is to accelerate the efficiency of searching the adjacent point by the SPH method through the grid division method and improve the real-time performance of the bleeding simulation.
The invention aims to revise the particle property parameters through the research on the physical properties of the bleeding, so that the smoothness of the bleeding simulation surface is better, the problem of boundary distortion is solved, and the authenticity of the bleeding simulation is improved.
The technical scheme provided by the invention is as follows:
a modeling method of a bleeding simulation model in virtual surgery comprises the following steps:
step one, determining a particle system and dividing the particle system into grids with the side length of the acting radius of an SPH method;
determining a particle i and judging whether the particle i is in the grid, and determining a neighboring particle of the particle i when the particle i is in the grid; when the particle i is not in the grid, adding more grids in a grading way until the particle i is in the grid;
revising the viscosity coefficient and the action radius of the particle i to obtain a revised viscosity coefficient and a revised action radius, and establishing the model according to the stress, the acceleration, the revised viscosity coefficient and the revised action radius of the particle i;
wherein the revised viscosity coefficient for particle i is:
μ＝bexp(-aPi)；
wherein a and b are coefficients, a is greater than 0 and b is greater than 0; piPlatelet property parameter for particle i;
the revision action radius is:
in the formula, lambda is a constant; m isiIs the mass of particle i; rhoiIs the density of particle i; d is the dimension;
when the particle i is on the bleeding surface, the stress applied to the particle i further comprises the following tension, and the tension applied to the particle i is as follows:
in the formula, C (r)i) Is the tensile field of particle i;
is the unit normal vector of the bleeding surface; is a constant;
acceleration of the particle i due to the tension:
in the formula (f)i tIs the tension to which the particle i is subjected, piIs the density of particle i.
Preferably, the second step further comprises: and if the peripheral grid of the grid where the particle i is located exists, calculating the distance between the particle in the peripheral grid and the particle i, and finding out a point located in the action radius range of the particle i as a neighboring particle of the particle i.
Preferably, the number of meshes per increment is 1.
Preferably, in the second step, the method of determining whether or not the particle i is on the surface of bleeding includes:
calculating the tension field of the particle i:
wherein if there is a neighboring particle j around the particle i, Aj1, otherwise Aj＝0；mjThe mass of a neighboring particle j that is a particle i; rhojIs the density of particle i; w (r)i-rjH) is a kernel function; r isiIs the radius of particle i; r isjIs the radius of particle j; h is the action radius of the particle i;
if C (r)i) When 0, particle i is not on the bleeding surface; if C (r)i) Not equal to 0, the particle i is on the bleeding surface.
Preferably, the platelet property parameter P is also included in the step threeiThe values vary with time:
wherein k is a transmission coefficient; m isjThe mass of a neighboring particle j that is a particle i; piPlatelet property parameter for particle i; pjA platelet property parameter of a neighboring particle j that is particle i; w (r)i-rjH) is a kernel function; r isiIs the radius of particle i; r isjIs the radius of particle j; h is the radius of action of the particle i.
Preferably, in the third step, the value of a is 200, and the value of b is 0.5.
The invention has the beneficial effects that:
according to the modeling method of the blood flow simulation model in the virtual surgery, provided by the invention, through the research on the physical properties of the blood flow, a Navier-Stokes (N-S) equation for simulating fluid and an SPH method for solving the Navier-Stokes (N-S) equation are improved, and the efficiency of searching for an adjacent point by the SPH method is accelerated by a meshing method; through the improvement of the physical property of the bleeding model, the smoothness of the bleeding simulation surface is better, the problem of boundary distortion is solved, and the real-time performance and the authenticity of the bleeding simulation are improved; the simulation effect is smoother.
Drawings
FIG. 1 is a grid division diagram according to the present invention.
FIG. 2 is a comparison of FPS using the method of searching for a proximity point according to the present invention and FPS traversing a particle proximity point.
FIG. 3 is a diagram showing the effect of bleeding simulation using the modeling method of the present invention.
Fig. 4 is a graph showing the effect of bleeding simulation without introducing the tension to which the particles are subjected.
Fig. 5 is a graph showing the effect of bleeding simulation on the viscosity coefficient of the platelet property-free calculation particles.
Fig. 6 is a graph of the simulation effect without revising the action radius in the SPH as a function of particle density.
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.
The invention provides a modeling method of a bleeding simulation model in a virtual operation, which can improve the real-time performance and the authenticity of the bleeding simulation in the virtual operation and comprises the following steps:
first, a method of dividing a grid is used to search for a point near the particle i.
As shown in FIG. 1, the invention divides the particle system into grids with the SPH method action radius as the side length, improves the efficiency of searching the near point in the SPH method by the method of dividing the grids, and improves the computational efficiency of the bleeding simulation. The method for dividing the grid into regions is determined according to the positions of the particles i which need to be calculated in the programming process, so that unnecessary grids are reduced, and the memory is saved. The method specifically comprises the following steps: firstly, determining a particle system, dividing the particle system into grids with the action radius of an SPH method as the side length, and judging whether a particle i is in the grids; if the particle i is in the grid, finding out other particles in the grid where the particle i is as the adjacent particles (adjacent points) of the particle i; if particle i is not in the grid, adding more grids until particle i is in the grid; to save memory, the grid is increased multiple times, each time by 1 grid (capable of holding 200 particles) until the particle i is in the grid. And then, judging whether a peripheral grid of the grid where the particle i is located exists or not, if so, calculating the distance between the particle in the peripheral grid and the particle i, and finding out a point located in the action radius range of the particle i as a near particle (a near point) of the particle i.
Comparing the FPS of the simulation result with the FPS traversing the particle near point by using the method for searching the near point provided by the present invention, as shown in fig. 2, it can be seen that the near point searched by the method for searching the near point provided by the present invention can basically cover all the actual near points of the particle i by comparing in the figure.
And then revising the viscosity coefficient and the acting radius of the particle i to obtain a revised viscosity coefficient and a revised acting radius, and establishing the model according to the stress, the acceleration, the revised viscosity coefficient and the revised acting radius of the particle i. The method specifically comprises the following steps:
when the stress of the particle i is calculated, whether the particle i is on the surface of bleeding is judged firstly, and when the particle i is on the surface of bleeding, the tension applied to the particle i is introduced.
The method for judging whether the particle i is on the surface of bleeding comprises the following steps:
calculating the tension field of the particle i:
wherein if there is a neighboring particle j around the particle i, Aj1, otherwise Aj＝0；mjThe mass of a neighboring particle j that is a particle i; rhojIs the density of particle i; w (r)i-rjH) is a kernel function; r isiIs the radius of particle i; r isjIs the radius of particle j; h is the action radius of the particle i;
if C (r)i) When 0, particle i is not on the bleeding surface; if C (r)i) Not equal to 0, the particle i is on the bleeding surface.
When the particle i is on the bleeding surface, the tension to which the particle i is subjected is calculated:
wherein κ is the surface curvature of the particle;
the unit normal vector of the bleeding surface is a constant and is used for normalized calculation;
further calculating the surface curvature of the particle
I.e. the tension to which the particle i is subjected
Thereafter, the acceleration of the particle i due to the tension is calculated:
wherein f isi tIs the tension to which the particle i is subjected, piIs the density of particle i.
The platelet properties were introduced and the viscosity coefficient of particle i was revised. Because blood contains platelets, blood gradually coagulates under the action of the platelets. The particles are subjected to an increasing viscosity force with time, and therefore platelet-related properties P are introduced, the effect of which directly affects the viscosity coefficient μ.
First, P is calculated according to the SPH methodiThe values vary with time:
wherein k is a transfer coefficient,
namely, it is
Wherein k is a transmission coefficient; m isjThe mass of a neighboring particle j that is a particle i; piPlatelet property parameter for particle i; pjA platelet property parameter of a neighboring particle j that is particle i; w (r)i-rjH) is a kernel function; r isiIs the radius of particle i; r isjIs the radius of particle j; h is the radius of action of the particle i.
Viscosity coefficient of revised particle i: mu-bexp (-aP)i)。
Wherein a and b are coefficients, a is more than 0, and b is more than 0; piIs the platelet nature of particle i.
In this embodiment, when P is 200 for a and 0.5 for biAs the value decreases, the viscosity coefficient μ increases.
Since the density of the particles becomes relatively small as the distance between the particles increases during the movement of the particles. This results in that when the acting radius in the conventional SPH method is used for the force calculation in the modeling, the viscous force and pressure between particles approach zero when the distance between particles approaches the acting radius, which is not in accordance with the actual situation.
Therefore, the action radius in SPH is revised as a function of particle density, and the revised action radius is:
wherein λ is a constant; m isiIs the mass of particle i; rhoiIs the density of particle i; d is the dimension.
And then, establishing a bleeding simulation model by adopting the revised parameters.
By adopting the modeling method of the bleeding simulation model in the virtual surgery, the influence of the tension and the platelet on the viscous coefficient of viscous force is introduced into the traditional Navier-Stokes (N-S) equation, and the constant action radius in the SPH method is revised as the function of the particle density, and the result of the bleeding simulation is shown in figure 3. The bleeding simulation effect without introducing the tension to which the particle i is subjected (not including step two) is shown in fig. 4. The bleeding simulation effect of the viscosity coefficient of particle i (not including step three) was calculated without introducing platelet properties, as shown in fig. 5. The action radius in SPH was not revised to the simulated effect of the particle density function (step four not included), as shown in fig. 6. As can be seen from comparison of FIGS. 4-6 with FIG. 3, respectively, the method provided by the present invention improves the physical properties of the bleeding model, so that the smoothness of the bleeding simulation surface is better, and the problem of boundary distortion is solved.
According to the modeling method of the blood flow simulation model in the virtual surgery, provided by the invention, through the research on the physical properties of the blood flow, a Navier-Stokes (N-S) equation for simulating fluid and an SPH method for solving the Navier-Stokes (N-S) equation are improved, and the efficiency of searching for an adjacent point by the SPH method is accelerated by a meshing method; through the improvement of the physical property of the bleeding model, the smoothness of the bleeding simulation surface is better, the problem of boundary distortion is solved, and the real-time performance and the authenticity of the bleeding simulation are improved; the simulation effect is smoother.
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 of a bleeding simulation model in a virtual surgery is characterized by comprising the following steps:
step one, determining a particle system and dividing the particle system into grids with the side length of the acting radius of an SPH method;
determining a particle i and judging whether the particle i is in the grid, and determining a neighboring particle of the particle i when the particle i is in the grid; when the particle i is not in the grid, adding more grids in a grading way until the particle i is in the grid;
revising the viscosity coefficient and the action radius of the particle i to obtain a revised viscosity coefficient and a revised action radius, and establishing the model according to the stress, the acceleration, the revised viscosity coefficient and the revised action radius of the particle i;
wherein the revised viscosity coefficient for particle i is:
μ＝bexp(-aPi)；
wherein a and b are coefficients, a is greater than 0 and b is greater than 0; piPlatelet property parameter for particle i;
the revision action radius is:
in the formula, lambda is a constant; m isiIs the mass of particle i; rhoiIs the density of particle i; d is the dimension;
when the particle i is on the bleeding surface, the stress applied to the particle i further comprises the following tension, and the tension applied to the particle i is as follows:
in the formula, C (r)i) Is the tensile field of particle i;
is the unit normal vector of the bleeding surface; is a constant;
acceleration of the particle i due to the tension:
in the formula (f)i tIs the tension to which the particle i is subjected, piIs the density of particle i;
in the third step, the value of a is 200, and the value of b is 0.5.
2. The method for modeling a virtual intra-operative bleeding simulation model according to claim 1, wherein the second step further comprises: and if the peripheral grid of the grid where the particle i is located exists, calculating the distance between the particle in the peripheral grid and the particle i, and finding out a point located in the action radius range of the particle i as a neighboring particle of the particle i.
3. The method of claim 2, wherein the number of meshes to be added at a time is 1.
4. The method for modeling a virtual intra-operative bleeding simulation model according to claim 1 or 3, wherein in the second step, the method for determining whether or not the particle i is on the bleeding surface is:
calculating the tension field of the particle i:
wherein if there is a neighboring particle j around the particle i, Aj1, otherwise Aj＝0；mjThe mass of a neighboring particle j that is a particle i; rhojIs the density of particle i; w (r)i-rjH) is a kernel function; r isiIs the radius of particle i; r isjIs the radius of particle j; h is the action radius of the particle i;
if C (r)i) When 0, particle i is not on the bleeding surface; if C (r)i) Not equal to 0, the particle i is on the bleeding surface.
5. The method for modeling a simulation model of bleeding during virtual surgery according to claim 4, further comprising, in the third step, the platelet property parameter PiThe values vary with time:
wherein k is a transmission coefficient; m isjThe mass of a neighboring particle j that is a particle i; piPlatelet property parameter for particle i; pjA platelet property parameter of a neighboring particle j that is particle i; w (r)i-rjH) is a kernel function; r isiIs the radius of particle i; r isjIs the radius of particle j; h is the radius of action of the particle i.
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| Virtual surgical bleeding simulation with navier-stokes equation and modified smooth particle hydrodynamics method;Shi, W. 等;《 IEEE International Conference on Information and Automation 》;20170630;第276-281页 * |
| 基于GPU 加速的粒子流体动力学流血模拟算法;罗中粟等;《计算机应用与软件》;20180228;第35卷(第2期);第242-247页，图1 * |
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