KR20220063031A - System, method and program for fluid simulation based on 3d image - Google Patents

Abstract

A three-dimensional image-based fluid simulation method is provided. The three-dimensional image-based fluid simulation method performed by an electronic device according to one aspect of the present invention includes the steps of: dividing, by the electronic device, a 3D image into a fluid area and a surrounding area using a shading function f having a shading value from 0 to 1; and analyzing, by the electronic device, the fluid flow in the fluid area using the Navier-Stokes equation represented by Equation 1 and Equation 2 below.

Description

3D image-based fluid simulation method, device and program {SYSTEM, METHOD AND PROGRAM FOR FLUID SIMULATION BASED ON 3D IMAGE}

The present invention relates to a method, apparatus and program for simulating a fluid in a 3D image, and more particularly, to a method, apparatus and program for quickly and easily obtaining a simulation result of a fluid included in a 3D image.

Conventional fluid simulation (eg, blood flow simulation) segments a fluid passage (eg, blood vessel) from a three-dimensional image (eg, a 3D medical image of a patient) and ultimately creates a fluid passage (eg, blood vessel) In order to express it, a fluid passage surface triangulation is created through finite element modeling, etc., and flow analysis is performed on it. For example, as shown in FIG. 1 , (a) medical imaging, (b) blood vessel separation and grid generation, and (c) CFD (Computational Fluid Dynamics) simulation may be performed.

The biggest problem that this execution process cannot be automated is the division of the fluid passage and the surface grid step, and the need for a technology to increase the processing speed of fluid simulation by automating these steps is increasing.

KR 10-1373563 KR 10-1703564 US 2013-0243294

The problem to be solved by the present invention is that when it is displayed only as 0/1 (or shaded value) whether a pixel of a three-dimensional image is inside a fluid passage or not, an explicit shape for a pixel displayed above 1 or a threshold value It is to provide a method to automatically perform fluid flow analysis through the solution of the Navier-Stokes equation without the need for a reconstruction process.

The problems to be solved by the present invention are not limited to the problems mentioned above, and other problems not mentioned will be clearly understood by those skilled in the art from the following description.

In a fluid simulation method of a 3D image performed by an electronic device according to an aspect of the present invention for solving the above problems, the electronic device uses a shading function f having a shading value from 0 to 1 for the 3D image. dividing the fluid region into a fluid region and a peripheral region; and analyzing, by the electronic device, the fluid flow in the fluid region using a Navier-Stokes equation expressed by Equations 1 and 2 below.

[Equation 　1]

[Equation 　2]

where ρ is the density of the fluid, μ is the viscosity coefficient of the fluid, g is the acceleration due to gravity, u is the velocity of the fluid, and p is the pressure of the fluid.

Other specific details of the invention are included in the detailed description and drawings.

According to the present invention as described above, it has various effects as follows.

According to the present invention, the analysis processing speed of fluid simulation can be rapidly increased.

In addition, according to the present invention, various blood flow simulations such as brain and cardiovascular system tailored to a specific patient that can be performed based on existing medical images (CT, MRI), etc. can be dramatically improved and accelerated.

In addition, according to the present invention, it is possible to quantitatively check blood pressure and blood flow velocity on the blood vessel wall through automatic blood flow analysis immediately after taking an MRI without going through a separate blood vessel shape reconstruction step.

In addition, according to the present invention, hemodynamic information (pressure, frictional force, flow velocity, etc.) that can be helpful in the diagnosis of vascular disease (e.g. cerebrovascular disease) can be provided.

In addition, according to the present invention, the therapeutic effect of vascular disease (e.g. coil embolization) can be predicted through simulation before the actual operation.

In addition, according to the present invention, it is possible to quickly predict the process of drug delivery through blood vessels.

In addition, according to the present invention, it is possible to predict the pattern of hemodynamic changes through follow-up of a specific patient.

Effects of the present invention are not limited to the effects mentioned above, and other effects not mentioned will be clearly understood by those skilled in the art from the following description.

1 is an exemplary diagram illustrating a conventional blood flow simulation method.
2 is a flowchart illustrating a fluid simulation method of a 3D image according to an embodiment of the present invention.
3 to 20 are exemplary views for explaining a fluid simulation method of a 3D image according to an embodiment of the present invention.

Advantages and features of the present invention and methods of achieving them will become apparent with reference to the embodiments described below in detail in conjunction with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but may be implemented in various different forms, and only the present embodiments allow the disclosure of the present invention to be complete, and those of ordinary skill in the art to which the present invention pertains. It is provided to fully understand the scope of the present invention to those skilled in the art, and the present invention is only defined by the scope of the claims.

The terminology used herein is for the purpose of describing the embodiments and is not intended to limit the present invention. In this specification, the singular also includes the plural unless specifically stated otherwise in the phrase. As used herein, “comprises” and/or “comprising” does not exclude the presence or addition of one or more other components in addition to the stated components. Like reference numerals refer to like elements throughout, and "and/or" includes each and every combination of one or more of the recited elements. Although "first", "second", etc. are used to describe various elements, these elements are not limited by these terms, of course. These terms are only used to distinguish one component from another. Accordingly, it goes without saying that the first component mentioned below may be the second component within the spirit of the present invention.

Unless otherwise defined, all terms (including technical and scientific terms) used herein will have the meaning commonly understood by those of ordinary skill in the art to which this invention belongs. In addition, terms defined in a commonly used dictionary are not to be interpreted ideally or excessively unless specifically defined explicitly.

Spatially relative terms "below", "beneath", "lower", "above", "upper", etc. It can be used to easily describe the correlation between a component and other components. Spatially relative terms should be understood as terms including different directions of components during use or operation in addition to the directions shown in the drawings. For example, when a component shown in the drawing is turned over, a component described as “beneath” or “beneath” of another component may be placed “above” of the other component. can Accordingly, the exemplary term “below” may include both directions below and above. Components may also be oriented in other orientations, and thus spatially relative terms may be interpreted according to orientation.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The content of the fluid analysis of the present invention is partially described in the paper "A geometric multigrid accelerated incompressible ow simulation over complex geometries" Gwangsoo GO and Hyung Taek AHN [COMPUTERS & FLUIDS, Volume 197, 30 January 2020, Article number 104350], The above article may be incorporated herein by reference to the extent that there is no conflict between the statements and drawings mentioned herein.

2 is a flowchart illustrating a fluid simulation method of a 3D image according to an embodiment of the present invention. 3 to 20 are exemplary views for explaining a fluid simulation method of a 3D image according to an embodiment of the present invention.

Meanwhile, the present invention is a method for analyzing a fluid region included in a 3D image, and the 3D image and the fluid region are not limited to a specific type. However, for convenience of explanation, a blood vessel of a medical image will be described below as an example.

Meanwhile, although not shown in the drawings, the electronic device for executing the method for simulating the fluid of a 3D image according to an embodiment of the present invention includes a control unit controlling overall fluid simulation-related operations, 3D image, fluid analysis result data, and the like. It may include a database to store it.

In an embodiment, the control unit 110 may control various operations of generating learning data (eg, a defective product image) in general, and the database 120 may store a good product image, a foreign material image, a defective product image, foreign material image information, and the like. can be saved

2 to 20 , according to an embodiment, the electronic device may divide a 3D image into a fluid region and a peripheral region using a shading function f having shading values ranging from 0 to 1. That is, a region may be segmented by defining a shade value for each pixel of the 3D image, subdividing it into a plurality of sub-pixels, and interpolating the function f.

More specifically, in operations S21 to S24, the Voxel including the boundary region between 0 and 1 is subdivided into a selective lattice region (S21), the shading function value of the subdivided lattice region is interpolated (S22), and the set The non-vascular and vascular regions are divided into 0 and 1 based on the threshold shading function value (S23), and the vascular region divided by 1 can be analyzed using the Navier-Stokes equation (S24). The specific details are as follows.

In an embodiment, as shown in FIG. 3 , the electronic device may define a shading value for each pixel to determine the presence or absence of a fluid region in a given medical image. Accordingly, as shown in FIG. 4 , it can be identified as a value of f of a scalar function (having a value between 0 and 1) indicating a shadow. For example, if f=1 at a specific location (x, y, z), it may be perfect black (100% blood vessels), and if f=0, it may be perfect white (0% blood vessels). In this case, the f function can be understood as a probability density function that not only represents a shadow but also probabilistically represents whether or not it is a blood vessel region.

In an embodiment, the electronic device may generate a high-resolution floating voxel by subdividing each pixel included in the 3D image into a plurality of sub-pixels based on initial shadow information of the 3D image.

Specifically, since the resolution of a normal medical image may not provide a high enough resolution for flow analysis, the inside of one pixel is subdivided into several detailed pixels as shown in FIG. 5 based on the initial shading information. Therefore, it is necessary to create a high-resolution flow grid that can perform blood flow analysis with sufficient resolution. In this case, the density of high-resolution floating voxels can be subdivided into arbitrary resolutions according to computer performance and user selection. Where Nx, Ny, and Nz represent the number of subdivided cells in each direction, a different number of cells may be used in each direction if necessary.

In an embodiment, the electronic device may interpolate the shadow function f using a numerical interpolation method. For example, a shading value between 0 and 1 should be defined for each of the subdivided flow voxels, where a numerical interpolation method can be used. Shading function f value of flowing voxel subdivided by a relatively simple linear function (Bi-linear in 2D, Trilinear in 3D) interpolation, but more accurate Cubic spline (Bi-cubic in 2D, Tri-cubic in 3D) function can be defined. For example, the shading function f is interpolated using Catmull-Rom Cubic Spline. In this case, it has the advantage of being able to express between pixels with a smooth and continuous (C ¹ continuous) shading function, which results in subdivision. If the blood vessel passing through the flow voxel is smooth, it may mean that it is continuously expressed.

In an embodiment, the electronic device may set a threshold value indicating a boundary that can distinguish the fluid region from the surrounding region, and define the shade value of the high-resolution flow voxel using the interpolated shade function f and the threshold value. For example, defining the boundary of the blood vessel from the shade information of the 3D image may be automatically defined as the boundary value of the shade is defined. That is, the boundary value may be a threshold value. For example, if the threshold value is defined as f=0.5, all regions with f > 0.5 are classified as inside the blood vessel (fluid region) and the rest into the outside of the vessel (or non-fluid region). can

On the other hand, the shadow image of the 3D image may be used as an auxiliary form of filtering or image processing if necessary.

After operation 21 is completed, a shading function having a value of 0 to 1 is defined everywhere in the 3D image space (vertex, plane, element center, etc. of Voxcel), and based on this, preprocessing for blood flow analysis This can be done.

In an embodiment, in operation S24, the electronic device may analyze the fluid flow in the fluid region using a Navier-Stokes equation expressed by Equations 1 and 2 below. there is.

Specifically, for the analysis of blood flow, numerical analysis of the governing equations describing the behavior of a fluid having a viscosity, that is, the Navier-Stokes equations, should be performed. In the case of a flow with a constant density, such as blood flow, in which compressibility of a fluid is not allowed, the Navier-Stokes equation is expressed by Equations 1 and 2 below, where Equation 1 is derived from the law of conservation of momentum of the fluid, Equation 2 is expressed as a second constraint expression derived from the mass conservation of the fluid.

where ρ is the density of the fluid, μ is the viscosity coefficient of the fluid, g is the acceleration due to gravity, u is the velocity of the fluid, and p is the pressure of the fluid.

Equations 1 and 2 above are impossible to solve analytically with respect to a general shape, so only a numerical solution using a computer is possible. .

For example, the velocity and pressure, which are unknowns in the equation, may be set as shown in FIG. 6 in all flow voxels. Numerical solutions of Equations 1 and 2 are basically about a method of obtaining a speed field and a pressure field at a future time point from the past speed field and pressure field already known at the present time point.

In an embodiment, in the step of analyzing the fluid flow in the fluid region, the electronic device may calculate Equation 3 below by discretizing Equation 1 from the velocity and pressure of the current time and the past time, and the fluid region and the surrounding area The velocity boundary condition at the boundary can be set so that the velocity non-slip condition is satisfied at the boundary of , and the temporary velocity field u* can be calculated by interpreting Equation 3 below to satisfy the velocity boundary condition.

는 시간에 대하여 차분된 항이고,

은 현재와 과거의 속도장부터 정의되는 비선형 대류항이고,

는 현재의 압력장으로부터 정의되는 압력의 공간 변화율이고,

은 선형 점성항이다.here

is the time-differentiated term,

is a nonlinear convection term defined from the present and past velocity fields,

is the spatial rate of change of pressure defined from the current pressure field,

is a linear viscous term.

Specifically, in the discrete momentum equation as in Equation 3, a temporary velocity field may be calculated by applying a non-slip condition on the vessel wall to an arbitrary three-dimensional space image expressed as 0/1. The numerical method used for the spatial difference may be a finite difference method, a finite volume method, or a finite element method. For example, when the finite difference method is used, for example, the velocity boundary condition at the vessel wall is And, as shown in FIG. 8, it is possible to set the velocity adhesion condition to be satisfied at a point where the value of the shadow function f interpolated by the cubic spline function has a threshold value (e.g. f=0.5).

In an embodiment, when a temporary velocity field is defined in a three-dimensional space through the analysis of Equation 3, in the step of analyzing the fluid flow in the fluid region, the electronic device performs the Poisson equation and multiple The temporary pressure field ϕ can be calculated using a multigrid method.

where ρ is the density of the fluid, f is the shadow function, φ is the temporary pressure field, and u* is the temporary velocity field.

Specifically, a temporary pressure field in a space expressed by an arbitrary 0/1 can be obtained through Equation (4). Equation 4 is a Poisson equation for an unknown temporary pressure field, which is a step that takes 99% or more of CPU time in fluid simulation. For the discretization of Equation 4, f, which is a shading function expressed by interpolation with lattice subdivision and cubic spline, can be directly used. For a quick solution of Equation 4, the present invention uses a multigrid method applicable to an arbitrary spatial region expressed by 0/1, which will be described in detail later as follows.

Optimal convergence acceleration using the multigrid method for the region marked 0/1

In one embodiment, an efficient solution of the Poisson equation expressed in Equation 4 is absolutely essential for a quick solution of the fluid flow. In the general multigrid method, in order to obtain a numerical solution on a dense grid at the top, an error is estimated on a series of sparse grids (restriction), and it is repeatedly reflected (prolongation) to the solution on the dense grid at the top. It is driven by doing this, and this operation is called Multigrid V-cycle. Among the methods developed so far, the fastest method for problems with general boundary conditions is known as the multigrid method. The method of its application was not known.

Accordingly, in the present invention, if the 3D space is displayed as 0/1 on the basis of an equally spaced Uniform Cartesian Grid, an arbitrary region can be efficiently displayed, and 0/ on the dense grid of the top level The paper "A geometric multigrid accelerated incompressible ow simulation over complex geometries" published that it is possible to implement the optimal Multigrid algorithm for an arbitrary 3D area by reflecting the information indicated by 1 on the coarse grid at the bottom level (this process is called Restriction) " Gwangsoo GO and Hyung Taek AHN [COMPUTERS & FLUIDS, Volume 197, 30 January 2020, Article number 104350], which is incorporated herein by reference to the extent that there is no conflict between the statements and drawings mentioned herein. may be included herein.

The area display value of 0/1 used here can be substituted with the shading function f described above, and the shading function value is separately selected on the coarse grid for each step necessary for the implementation of the multigrid technique on the subdivided grid. It can be easily obtained from the already interpolated and expressed shade function values without calculation.

In this patent, as a multigrid method that extends the concept disclosed in the above paper, the multigrid method for arbitrary shapes that operates on a grid selectively refined in a three-dimensional space is schematically described as shown in FIG. can be

Using the multi-grid method of the present invention, it is possible to selectively subdivide a part requiring arbitrary fluid flow in a three-dimensional space, and to reversely use the information of this subdivided area (interpolated 0/1 shadow function f information), thereby providing an efficient multigrid A solution may be implemented. In addition, if additional convergence acceleration is required, another multigrid restriction can be performed on arbitrary shapes expressed as 0 and 1 on the bottom most level, that is, the Uniform Cartesian grid. do.

In this series of processes, any explicit blood vessel-shaped surface is not required, and all fluid regions are expressed only by the value of the shade function f expressed as 0/1, and the fluid flow is analyzed for that region. will become

Then, in the step of analyzing the fluid flow in the fluid region, the electronic device uses the temporary velocity field u*, the temporary pressure field φ, and the following Equations 5 and 6 to the velocity field and pressure of the next time in the fluid region field can be calculated.

는 임시 압력장으로부터 정의되는 압력의 공간 변화율이고, pⁿ⁺¹은 다음 시점의 압력장이고, pⁿ은 현재 시점의 압력장이다.where u ⁿ⁺¹ is the velocity field at the next time, u ⁿ is the velocity field at the current time,

is the spatial rate of change of pressure defined from the temporary pressure field, p ⁿ⁺¹ is the pressure field at the next point in time, and p ⁿ is the pressure field at the current point in time.

Accordingly, according to the present invention, it is possible to easily analyze the fluid through shadow information as soon as the image is acquired without the need to acquire the 3D shape of the fluid region included in the 3D image.

On the other hand, the multi-lattice method will be briefly described as follows. The content of the multi-lattice method is as described above in the content of the paper.

1. Multigrid method

The geometric multigrid (MG) algorithm using edge/face-wise heaviside function restriction is simple to implement, can be easily parallelized, and can be applied to irregular domain problems.

1.1. Standard multigrid method

The multi-grid (hereinafter referred to as MG) method can solve a linear system (Ax = b) using an iterative-limited extension loop (V-cycle) as shown in FIG. 10 .

A surprising property of the MG method is that the total number of cycles required for convergence is almost constant regardless of the grid resolution, and can represent an optimal performance of O(N). where N is the total number of cells.

The Gauss-Seidel iterative solver can be used more smoothly in the current MG method. The number of pre-smoothing for the limit is 10, and the number of post-smoothing for the extension is 2. Regardless of the highest mesh resolution, the coarsest grid for the constraint can be set in a 2×2 2D square domain and a 2×2×2 3D cube domain.

The cell centroid method is currently used in the pressure Poisson equation, where the unknown can be sampled at the cell centroid. The two-dimensional constraint and extension procedure for the cell-centric manner can be performed simply as shown in FIG. 11 .

In the constraint process, the source term (b2h) of the coarse grid may be defined by averaging residuals (rh) of the fine grid. In the case of extension, the solution of the coarse grid (x2h) may be equally applied to the solution of the fine grid (xh).

11 , the constraint and extend procedure can be expressed as b2h = Rrh and xh = xh + Px2h, where R and P represent the constraint and extend operators, respectively. These two operators satisfy the variable property, P= cRT, where c is a constant real value. This means that extension and constraint operators transpose each other into constants.

1.2. Multigrid method for an irregular domain

Current pressure Poisson equations for irregular domains can be solved as in the case of normal domains because domain irregularities are automatically expressed as Heaviside functions included in Poisson's equations. Based on this fact, the standard MG algorithm can be similarly applied to the present Poisson equation if the Heaviside function is defined consistently on a continuously coarsened grid.

When the spatial discretization of the pressure Poisson equation is considered, the system matrix (A) of the Poisson equation may include a Heaviside function. Therefore, in the constraint process, A must be continuously reconstructed from a coarsened grid. Here, an edge/face-wise constraint algorithm is used. Based on this algorithm, the Heaviside function for the edge/face of a coarse grid can be defined by averaging the Heaviside function for the fine grid edge/face. The procedure for the two-division dimension is shown in FIG. 12 .

The Heaviside function constraint algorithm can be extended to 3D cases in a similar way. Instead of edgewise averaging of the Heaviside function in 2D, face-wise averaging is applied to the limits of the Heaviside function in 3D. More specifically, the Heaviside function on the cell surface of a coarse grid can be simply defined by averaging the Heaviside function on the corresponding four sides of the corresponding fine grid.

The current edge/face-wise constraint algorithm for the Heaviside function is strongly recommended for the following reasons: First, using the precomputed Heaviside function can eliminate redundant calculations of the Heaviside function, thereby saving computation time and memory. Second, geometric information can easily be lost during the constraint procedure if the Heaviside function is recalculated on each coarse grid.

When the Heaviside function constraint algorithm is used, the MG algorithm can be implemented recursively as in Algorithm 1 shown in FIG. 13 .

In this algorithm, a recursive function "multigrid_v_cycle" is defined. The sub-functions marked "pre_smooth" and "post_smooth" are implemented by the red-black Gauss-Seidel algorithm. The subfunction "system_matrix" follows the discretization of the pressure Poisson equation. The remaining sub-functions, ie, “restrict_cell_center”, “prolongate” and “restrict_cell_edgeface”, correspond to FIGS. 11-(a), 11-(b) and 12, respectively. The Heaviside function constraint can be extended to the 3D case in a similar way.

1.3. Verication study

으로 표현되며,

는 알 수 없으며

는 하기 수학식 7과 같이 정의된 소스 벡터이다.To demonstrate the validity and performance of the current MG algorithm using Heaviside function constraints, an analytically defined Poisson problem for the irregular domain is considered. The irregular domain (shown in Fig. 13) is {(x, y) | Defined as sin x sin y ≥ 0.2 and 0 ≤ x, y ≤ π}, the Poisson equation with irregular boundaries is

is expressed as

is unknown

is a source vector defined as in Equation 7 below.

)이 불규칙한 경계에 적용될 수 있고, 포아송 방정식의 분석적 해법은

로 표현될 수 있다.In the above problem, the Neumann boundary condition (Neumann boundary condition, ie

) can be applied to irregular boundaries, and the analytic solution of the Poisson equation is

can be expressed as

The results of the current MG method using the Heaviside function constraint are provided along with the results of the standard CG (conjugate gradient) method. First, the residual history is considered. 14 depicts the L2-norm of the residual versus the number of cycles (MG) or repetitions (CG). In the present MG method, the solutions of each grid system converge within an almost fixed number of cycles. Conversely, the number of iterations of the CG method for convergence increases as the problem size increases. This result means that the current MG method performs optimally in an irregular region, and this behavior is characteristic of the MG method. Next, the actual calculation time is displayed using a linear and logarithmic scale as shown in FIG. 16 .

Here, the computation time of each grid system is normalized by dividing the computation time of the MG method in the coarsest system (64 × 64). In this figure, the superiority of the MG method is clearly confirmed, and the optimal performance with complexity O(N) is clearly demonstrated. Finally, Fig. 17 shows the convergence history of errors using a logarithmic scale.

The numerical error of the Poisson equation is completely dependent on the discretization scheme. Therefore, the results of both methods are identical and converge to an analytical solution accompanied by the desired quadratic ratio. A rigorous validation study confirmed that using the Heaviside function constraint algorithm, the MG method can perform optimally and correctly for Poisson's equations in the irregular domain.

1.4. Parallel multigrid method

In actual calculations, the most time-consuming part of the projection method is solving the pressure Poisson equation. For this reason, the parallel scalability of flow simulation greatly depends on the performance of the MG method in parallel computation. In this subsection, a parallelization strategy for the current MG algorithm using the Heaviside function constraint is presented.

In the current MG algorithm, the convergence speed can be improved because the final grid of the constraint procedure is as coarse as possible. For this reason, the coarsest grid for the constraint is set to 2x2 in the 2D square domain, and 2x2x2 in the 3D cube domain, regardless of the mesh resolution, which is the most accurate in the current study. Considering the case where MPI parallelization is applied, if the computational domain is divided into np×np MPI processes in 2D, the constraint procedure is performed until there is a 2×2 grid in each MPI process, so the coarsest grid of the entire computational domain is 2np×2np becomes For this reason, the convergence speed may decrease as the number of MPI processes increases in parallel computation.

In order to overcome these shortcomings in parallel computation, a multi-step algorithm should be applied. An example of a multi-level algorithm is shown in FIG. 18 . In Fig. 18, the computational area composed of the 4nx4n grid is divided into 4x4 MPI processes. Based on Fig. 18, the multi-level algorithm for a single V-cycle can be summarized as follows.

1. The limiting procedure (n×n → 2×2) is performed in each MPI process

2. In each MPI process, information from the coarsest grid is collected in a single process

3. The series V-cycle procedure (8x8 → 2x2 → 8x8) is performed in a single process

4. Results of series V-cycles are scattered across the corresponding MPI process

5. The extension procedure (2x2 → nxn) is performed in each MPI process.

Through this process, the MG method can be applied to parallel operation without any disadvantages due to parallelization. This algorithm can be similarly applied to 3D problems. The multi-step algorithm can be easily applied to the current multi-grid algorithm. Compared to applying the multi-step algorithm to the standard MG method in the general domain, the only difference is to collect the Heaviside function in the aggregation process.

Meanwhile, the electronic device may include a graphic processing unit that processes shadow information of subdivided high-resolution floating voxels and a processor (CPU) that processes initial shadow information.

The method proposed by the present invention is very suitable for parallelization. In particular, parallelization using a graphic processing unit is suitable for a subdivided lattice, and parallelization using a processor is executed for the first Level-0 lattice (a lattice with the same density as the resolution of the first medical image) before subdivision, as shown in Figure 19 and 20, it is possible to efficiently implement parallel operations that are used at the same time.

Meanwhile, according to another embodiment of the present disclosure, the electronic device may divide the 3D image into a fluid region and a peripheral region by defining 0 or 1 for each pixel based on the brightness value of the 3D image. That is, in the above embodiment, all other methods are the same, but only a method of dividing a region may be applied differently. For example, the brightness value per pixel is obtained instead of dividing the area through the shading value, and 1 is assigned to a pixel having a brightness value corresponding to the fluid area by comparing it with the general brightness values of the pre-stored fluid area and surrounding area; The region can be divided in such a way that 0 is assigned to pixels having a brightness value corresponding to the surrounding region.

In the fluid simulation method of a 3D image performed by an electronic device according to an aspect of the present invention, the electronic device converts the 3D image into a fluid region and a peripheral region using a shading function f having shading values ranging from 0 to 1. dividing; and analyzing, by the electronic device, the fluid flow in the fluid region using the Navier-Stokes equation expressed by Equation 1 and Equation 2 below.

According to various embodiments of the present disclosure, the dividing into the fluid region and the surrounding region may include, by the electronic device, subdividing each pixel included in the 3D image into a plurality of sub-pixels based on initial shadow information of the 3D image. generating a high-resolution flow voxel by doing; interpolating, by the electronic device, the shadow function f using a numerical interpolation method; setting, by the electronic device, a threshold value indicating a boundary by which the fluid region and the peripheral region can be distinguished; and defining a shadow value of the high-resolution floating voxel using the interpolated shadow function f and the threshold value.

According to various embodiments of the present disclosure, the analyzing of the fluid flow in the fluid region may include: calculating, by the electronic device, Equation (3) by discretizing Equation 1 from the velocity and pressure of a current time and a past time; setting, by the electronic device, a velocity boundary condition at the boundary such that a non-slip condition is satisfied at the boundary between the fluid region and the peripheral region; and calculating, by the electronic device, a temporary velocity field u* by analyzing Equation 3 above to satisfy the set velocity boundary condition.

According to various embodiments, in the analyzing of the fluid flow in the fluid region, the electronic device calculates the temporary pressure field φ using the Poisson equation and the multigrid method expressed by Equation 4 above. Calculating; may include.

According to various embodiments, in the analyzing of the fluid flow in the fluid region, the electronic device uses the temporary velocity field u*, the temporary pressure field φ, and the above-described Equations 5 and 6 in the fluid region It may include; calculating the velocity field and the pressure field of the next time in

In a fluid simulation method of a 3D image performed by an electronic device according to an aspect of the present invention, the electronic device converts the 3D image into a fluid by defining 0 or 1 for each pixel based on a brightness value of the 3D image. dividing into a region and a peripheral region; and analyzing, by the electronic device, the fluid flow in the fluid region using the Navier-Stokes equation expressed by Equations 1 and 2 described above.

An electronic device for performing fluid simulation of a 3D image according to an aspect of the present invention divides a 3D image into a fluid region and a peripheral region using a shading function f having shading values ranging from 0 to 1, and performs the above-described math The fluid flow in the fluid region may be analyzed using the Navier-Stokes equation expressed by Equation 1 and Equation 2.

According to various embodiments, the electronic device generates a high-resolution floating voxel (volxel) by subdividing each pixel included in the 3D image into a plurality of sub-pixels based on initial shadow information of the 3D image, Interpolating the shadow function f using a numerical interpolation method, setting a threshold value indicating a boundary that can distinguish the fluid region from the surrounding region, and using the interpolated shadow function f and the threshold value The shadow value of the high-resolution flow voxel is defined, Equation 1 is discretized from the velocity and pressure of the current time and the past time to calculate Equation 3 below, and the velocity adhesion (Non) at the boundary between the fluid region and the peripheral region -slip), a velocity boundary condition at the boundary is set so that the condition is satisfied, and a temporary velocity field u* can be calculated by analyzing Equation 3 above to satisfy the set velocity boundary condition.

According to various embodiments of the present disclosure, the electronic device may include a graphic processing unit that processes shadow information of the subdivided high-resolution floating voxel and a processor that processes the initial shadow information.

The fluid simulation program of the three-dimensional image may be stored in a medium in order to execute the method of any one of claims 1 to 5 by being combined with a computer which is hardware.

The steps of a method or algorithm described in relation to an embodiment of the present invention may be implemented directly in hardware, as a software module executed by hardware, or by a combination thereof. A software module may contain random access memory (RAM), read only memory (ROM), erasable programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, hard disk, removable disk, CD-ROM, or It may reside in any type of computer-readable recording medium well known in the art to which the present invention pertains.

As mentioned above, although embodiments of the present invention have been described with reference to the accompanying drawings, those skilled in the art to which the present invention pertains know that the present invention may be embodied in other specific forms without changing the technical spirit or essential features thereof. you will be able to understand Therefore, it should be understood that the embodiments described above are illustrative in all respects and not restrictive.

Claims (10)

In the fluid simulation method of a 3D image performed by an electronic device,
dividing, by the electronic device, the 3D image into a fluid region and a peripheral region using a shading function f having shading values ranging from 0 to 1; and
Analyzing, by the electronic device, the fluid flow in the fluid region using the Navier-Stokes equation expressed by Equation 1 and Equation 2 below; A method of fluid simulation of images.
[Equation 1]

[Equation 2]

where ρ is the density of the fluid, μ is the viscosity coefficient of the fluid, g is the acceleration due to gravity, u is the velocity of the fluid, and p is the pressure of the fluid. The method of claim 1, wherein the dividing into a fluid region and a peripheral region comprises:
generating, by the electronic device, high-resolution floating voxels (volxels) by subdividing each pixel included in the 3D image into a plurality of sub-pixels based on initial shadow information of the 3D image;
interpolating, by the electronic device, the shadow function f using a numerical interpolation method;
setting, by the electronic device, a threshold value indicating a boundary by which the fluid region and the peripheral region can be distinguished; and
and defining a shadow value of the high-resolution fluid voxel using the interpolated shadow function f and the threshold value. The method of claim 1 , wherein analyzing the fluid flow in the fluid domain comprises:
calculating, by the electronic device, Equation 3 below by discretizing Equation 1 from the velocity and pressure of the current time and the past time;
setting, by the electronic device, a velocity boundary condition at the boundary such that a non-slip condition is satisfied at the boundary between the fluid region and the peripheral region; and
and calculating, by the electronic device, a temporary velocity field u* by interpreting Equation 3 below to satisfy the set velocity boundary condition.
[Equation 3]

here

is the time-differentiated term,

is a nonlinear convection term defined from the present and past velocity fields,

is the spatial rate of change of pressure defined from the current pressure field,

is a linear viscous term. 4. The method of claim 3, wherein analyzing the fluid flow in the fluid domain comprises:
and calculating, by the electronic device, a temporary pressure field φ using a Poisson equation and a multigrid method expressed by Equation 4 below.
[Equation 4]

where ρ is the density of the fluid, f is the shadow function, φ is the temporary pressure field, and u* is the temporary velocity field. 5. The method of claim 4, wherein analyzing the fluid flow in the fluid domain comprises:
calculating, by the electronic device, the velocity field and the pressure field at the next time point in the fluid region using the temporary velocity field u*, the temporary pressure field φ, and Equations 5 and 6 below 3D image fluid simulation method, characterized in that.
[Equation 5]

[Equation 6]

where u ⁿ⁺¹ is the velocity field at the next time, u ⁿ is the velocity field at the current time,

is the spatial rate of change of pressure defined from the temporary pressure field, p ⁿ⁺¹ is the pressure field at the next point in time, and p ⁿ is the pressure field at the current point in time. In the fluid simulation method of a 3D image performed by an electronic device,
dividing the 3D image into a fluid region and a peripheral region according to the electronic device defining 0 or 1 for each pixel based on a brightness value of the 3D image; and
Analyzing, by the electronic device, the fluid flow in the fluid region using the Navier-Stokes equation expressed by Equation 1 and Equation 2 below; A method of fluid simulation of images.
[Equation 1]

[Equation 2]

where ρ is the density of the fluid, μ is the viscosity coefficient of the fluid, g is the acceleration due to gravity, u is the velocity of the fluid, and p is the pressure of the fluid. An electronic device for performing fluid simulation of a three-dimensional image, the electronic device comprising:
The electronic device is
The 3D image is divided into a fluid region and a surrounding region using a shading function f having shading values from 0 to 1,
A fluid simulation electronic device of a three-dimensional image, characterized in that the fluid flow in the fluid region is analyzed using the Navier-Stokes equation expressed by Equation 1 and Equation 2 below.
[Equation 1]

[Equation 2]

where ρ is the density of the fluid, μ is the viscosity coefficient of the fluid, g is the acceleration due to gravity, u is the velocity of the fluid, and p is the pressure of the fluid. The method of claim 7, wherein the electronic device comprises:
generating high-resolution floating voxels by subdividing each pixel included in the 3D image into a plurality of sub-pixels based on the initial shading information of the 3D image;
Interpolating the shadow function f using a numerical interpolation method,
setting a threshold value indicating a boundary that can distinguish the fluid region from the surrounding region,
using the interpolated shading function f and the threshold value to define a shading value of the high-resolution floating voxel,
By discretizing Equation 1 from the velocity and pressure of the current time and the past time, the following Equation 3 is calculated,
setting a velocity boundary condition at the boundary such that a non-slip condition is satisfied at the boundary between the fluid region and the peripheral region,
A fluid simulation electronic device for a three-dimensional image, characterized in that the temporary velocity field u* is calculated by interpreting Equation 3 below to satisfy the set velocity boundary condition.
[Equation 3]

here

is the time-differentiated term,

is a nonlinear convection term defined from the present and past velocity fields,

is the spatial rate of change of pressure defined from the current pressure field,

is a linear viscous term. 8. The method of claim 7,
and the electronic device includes a graphic processing unit that processes shadow information of the subdivided high-resolution fluid voxel and a processor that processes the initial shadow information. A fluid simulation program of a three-dimensional image, which is combined with a computer as hardware and stored in a medium to execute the method of any one of claims 1 to 5.

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