A method and system for constructing a prediction model of fluid mechanics flow field velocity
By constructing a PDMNN neural network and combining it with the contrast agent flow and advection diffusion equations, the problem of complex and time-consuming traditional CFD calculations was solved, enabling fast and accurate flow field velocity prediction under different geometric models and boundary conditions, thus improving the adaptability and accuracy of the prediction model.
Patent Information
- Application Number
- CN202411659411.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-19
- Publication Date
- 2025-11-11
- Estimated Expiration
- 2044-11-19
AI Technical Summary
Existing technologies struggle to quickly and accurately predict 3D flow field blood flow velocity under different geometric models and boundary conditions. Traditional CFD calculations are complex and time-consuming, while deep learning methods such as PINN cannot adapt to various geometries.
A PDMNN neural network was constructed to simulate contrast agent flow in a 3D vascular geometry model. By combining the advection diffusion equation and penalty term, and inputting the coronary artery model and contrast agent concentration information through dual paths, the neural network was driven to optimize and predict the flow field velocity.
It enables rapid and accurate flow field velocity prediction under different geometric models and boundary conditions, improves the generalization performance and physical interpretability of the model, and has small errors.
Smart Images
Figure CN119626562B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of artificial intelligence technology, and in particular to a method and system for constructing a predictive model of velocity in a fluid dynamics flow field. Background Technology
[0002] Precise calculation of blood flow velocity plays a crucial role in biomedical engineering and clinical diagnostics. It is essential not only for understanding the pathogenesis of cardiovascular diseases, such as atherosclerosis and thrombosis, but also for evaluating surgical outcomes, guiding interventional treatments, and designing cardiovascular devices. Furthermore, the calculated blood flow velocity can provide a scientific basis for disease prevention, diagnosis, and treatment, thereby improving patient outcomes and quality of life. Therefore, developing highly accurate methods for calculating blood flow velocity is of great value in advancing medical progress and improving public health.
[0003] Computational fluid dynamics (CFD) is a classic numerical simulation method for fluid dynamics, capable of simulating fluid flow in pipes and calculating local pressure and velocity within a three-dimensional (3D) flow field. Applying CFD to hemodynamics in the human body allows for non-invasive calculation of blood pressure and blood flow velocity in blood vessels, providing a technical means for the diagnosis and treatment of clinical cardiovascular diseases. However, traditional CFD calculation methods require quantitatively solving the Navier-Stokes (NS) equations within the 3D flow field, as shown in the following equation:
[0004]
[0005] In the equation, vi is the fluid velocity tensor, ρ is the fluid density, p is the pressure, μ is the fluid kinematic viscosity, and Xi is the volume force. This equation involves solving multiple partial differential equations for various physical quantities, making it very complex and resulting in high computational time costs, which makes it difficult to apply in real-time engineering and clinical settings.
[0006] Current literature reports on rapid solutions for 3D CFD based on deep learning. Li et al. used a dual-channel neural network model to predict the 3D CFD flow field of the aorta and coronary arteries, but used the same and fixed fluid boundary conditions for different models, and essentially predicted the influence of different geometric information on the coronary artery flow field.
[0007] Raissi et al. developed the Physics-informed neural networks (PINN) model to predict the flow field details within intracranial aneurysms by encoding the Navier-Stokes equations into a loss function. However, this algorithm requires separate training for each aneurysm model, meaning it cannot predict 3D flow fields with different geometries and lacks practical application value. The limitation of PINN lies in the excessive complexity of the Navier-Stokes equations, making them difficult to accurately fit with neural network models. Therefore, no research has yet achieved an accurate and fast deep learning prediction method for 3D flow fields with different geometries and boundary conditions. Summary of the Invention
[0008] Based on this, in order to address the above-mentioned technical problems, a method and system for constructing a prediction model for fluid dynamics flow field velocity is provided to solve the problems of slow calculation speed, inability to use different boundary conditions, or inability of the same prediction model to cope with different geometric models in existing technologies.
[0009] Firstly, a method for constructing a predictive model for velocity in a fluid dynamics flow field, the method comprising:
[0010] Acquire a large number of coronary artery CTA images from patients with coronary heart disease, and construct 3D vascular geometric models based on the coronary artery CTA images;
[0011] Blood and contrast agent are added to the 3D vascular geometry model to simulate the flow of contrast agent in the blood. Different inlet flow velocities and physiological pressure boundary conditions are set in different 3D vascular geometry models, and CFD simulations are performed to obtain simulation results. Based on the large number of simulation results obtained, training samples, test samples, and test samples of the PDMNN neural network are constructed. The simulation results include 3D point clouds of contrast agent particle concentration in the flow field and actual flow field velocity.
[0012] The 3D point cloud of contrast agent particle concentration, actual flow field velocity, 3D point cloud of 3D vascular geometry model, and corresponding inlet flow velocity boundary conditions obtained from coronary CTA images of a large number of coronary heart disease patients are input into the PDMNN neural network for learning. The advection diffusion equation is encoded into the loss function and the relationship between contrast agent concentration and fluid velocity is used to drive the PDMNN neural network to calculate convergence, thereby obtaining a predictive model of fluid dynamics flow field velocity.
[0013] Optionally, in the above scheme, the method further includes: encoding a penalty term for the prediction result at the boundary of the 3D vascular geometry model in the loss function.
[0014] In the above scheme, optionally, the penalty term for the prediction result at the boundary of the 3D blood vessel geometry model is:
[0015]
[0016] Among them, v i Let P be the velocity tensor, P be the pressure, x be the point cloud coordinates of the 3D model, ρ be the density, μ be the viscosity, t be the time, and C be the particle concentration in the fluid. Let n be the fluid boundary region and n be the number of model outlets and inlets.
[0017] Optionally, in the above scheme, the method further includes: introducing blood vessel radius information into the PDMNN neural network, so that the PDMNN neural network can correct the initially predicted blood flow velocity based on the blood vessel radius information after making an initial prediction of blood flow velocity.
[0018] Optionally, in the above scheme, the advection diffusion equation is:
[0019]
[0020] Among them, v i Let C be the velocity tensor, C be the particle concentration in the fluid, and t be time.
[0021] Optionally, after acquiring a large number of coronary CTA images from patients with coronary heart disease, the method further includes segmenting the target region of the coronary CTA images.
[0022] Optionally, in the above scheme, after obtaining the simulation results, the large number of simulation results are cleaned, and training samples, test samples and verification samples of the PDMNN neural network are constructed based on the cleaned simulation results.
[0023] Secondly, a system for constructing a prediction model for velocity in a fluid dynamics flow field, the system comprising:
[0024] 3D Vascular Geometry Model Construction Module: Used to acquire a large number of coronary artery CTA images from patients with coronary heart disease, and construct 3D vascular geometry models based on the coronary artery CTA images;
[0025] CFD simulation module: Used to add blood and contrast agent to the 3D vascular geometry model, simulate the flow of contrast agent in the blood, set different inlet flow velocities and physiological pressure boundary conditions in different 3D vascular geometry models, and perform CFD simulation to obtain simulation results. Based on the large number of simulation results obtained, training samples, test samples, and test samples of PDMNN neural network are constructed. The simulation results include 3D point cloud of contrast agent particle concentration in the flow field and actual flow field velocity.
[0026] The prediction model training module is used to input the 3D point cloud of contrast agent particle concentration, actual flow field velocity, 3D point cloud of 3D vascular geometry model, and corresponding inlet flow velocity boundary conditions obtained from a large number of coronary artery CTA images of coronary heart disease patients into the PDMNN neural network for learning; the advection diffusion equation is encoded into the loss function and the relationship between contrast agent concentration and fluid velocity is used to drive the PDMNN neural network to calculate convergence, thereby obtaining the prediction model of fluid dynamics flow field velocity.
[0027] Thirdly, a computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the method for constructing a predictive model of a fluid dynamic flow field velocity as described in the first aspect.
[0028] Fourthly, a computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the method for constructing a predictive model of a fluid dynamic flow field velocity as described in the first aspect.
[0029] This application has at least the following beneficial effects:
[0030] In constructing the prediction model, this application incorporates two fluid materials—blood and contrast agent—into a constructed 3D vascular geometry model to simulate the flow of contrast agent within the blood, thereby providing particle concentration information. Simultaneously, a dual-path input PDMNN network is developed, taking into account the 3D point cloud of the coronary artery model, the actual flow field velocity, and the 3D point cloud of contrast agent particle concentration within the flow field. The 3D point cloud of the coronary artery model provides geometric information, while the 3D point cloud of the contrast agent particle concentration provides physical information, enabling the neural network to simultaneously capture multi-dimensional features and accurately predict flow field velocity. During the prediction model optimization process, a simple advection-diffusion equation is used as the driving force for the neural network model, guiding it to achieve more accurate fitting and thus more precise 3D flow field velocity prediction. Therefore, the prediction model constructed in this manner can achieve more accurate and faster prediction results, and can handle different geometric models and boundary conditions. Attached Figure Description
[0031] Figure 1 This application provides a flowchart illustrating a method for constructing a predictive model for velocity in a fluid dynamics flow field, as an embodiment of the present application.
[0032] Figure 2 A neural network architecture diagram of a prediction model is provided for one embodiment of this application;
[0033] Figure 3 This is a flowchart illustrating the prediction of 3D CFD flow field velocity using a prediction model in one embodiment of this application.
[0034] Figure 4 This is a comparison chart showing the prediction results obtained using the prediction model of this application and the calculation results obtained using traditional CFD. Detailed Implementation
[0035] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0036] In one embodiment, such as Figure 1 As shown, a method for constructing a predictive model for velocity in a fluid dynamics flow field is provided, the method comprising:
[0037] Step S1: Acquire a large number of coronary artery CTA images from patients with coronary heart disease, and construct 3D vascular geometric models based on the coronary artery CTA images;
[0038] Step S2: Add blood and contrast agent to the 3D vascular geometry model to simulate the flow of contrast agent in the blood; set different inlet flow velocities and physiological pressure boundary conditions in different 3D vascular geometry models, and perform CFD simulation to obtain simulation results; construct training samples, test samples, and test samples for the PDMNN neural network based on the large number of simulation results obtained; the simulation results include 3D point cloud of contrast agent particle concentration in the flow field and actual flow field velocity;
[0039] Step S3: The 3D point cloud of contrast agent particle concentration, actual flow field velocity, 3D point cloud of 3D vascular geometry model, and corresponding inlet flow velocity boundary conditions obtained from a large number of coronary artery CTA images of coronary heart disease patients are input into the PDMNN neural network for learning; the advection diffusion equation is encoded into the loss function and the relationship between contrast agent concentration and fluid velocity is used to drive the PDMNN neural network to calculate convergence, thereby obtaining a predictive model of fluid dynamics flow field velocity.
[0040] In this embodiment, addressing the drawback of the complex NS equations in PINN being difficult for neural network models to accurately fit, this invention uses simple velocity-related physical equations to drive the neural network model to capture local features of the 3D flow field, thereby improving model performance. According to the advection-diffusion equation, the velocity tensor vi and the particle concentration C within the fluid satisfy:
[0041]
[0042] In the formula, t represents time. Therefore, the flow velocity can be calculated based on the spatial concentration of particles in the fluid and the gradient of concentration change over time. This invention extracts the particle concentration and flow velocity field within the fluid, improves the PINN algorithm, incorporates the advection-diffusion equation into the loss function, and uses the advection-diffusion equation as the dominant factor, combined with a data-driven method to drive the convergence of the neural network model, forming a physics-data multi-derived neural network (PDMNN). According to the advection transport equation, the flow velocity and particle concentration are closely related as two single variables, unaffected by other physical factors. Therefore, predicting fluid velocity using fluid particle concentration can achieve high accuracy. Compared to the existing PINN neural network, PDMNN incorporates a simpler physical equation into the loss function as a penalty term for the prediction result, resulting in better prediction performance and improved generalization performance and physical interpretability of the neural network model.
[0043] This application collected coronary artery CTA images from 205 patients with coronary heart disease in clinical practice and reconstructed their 3D vascular geometric models. Two fluid materials, blood and contrast agent, were set in the flow field to simulate the flow of contrast agent in blood, providing particle concentration information. Eleven different inlet flow velocities and physiological pressure boundary conditions were applied to different models, resulting in 2255 CFD simulations, which served as training and testing samples for the deep learning model. Figure 2 As shown, a dual-path input PDMNN neural network was designed. The two paths of the network are respectively input to the 3D point cloud of the coronary artery model and the 3D point cloud of the contrast agent particle concentration in the flow field; the advection diffusion equation is encoded in the network's loss function, and the relationship between contrast agent concentration and fluid velocity is used to drive the neural network to converge.
[0044] Therefore, as Figure 3 As shown, the prediction model, by inputting 3D blood vessel point clouds and contrast agent particle concentration point clouds, enables the extraction of features from both datasets and the integration of these features for blood flow velocity prediction. Specifically, in practice, the contrast agent particle concentration point cloud is used to extract concentration information from the image through image processing methods.
[0045] In the aforementioned method for constructing a predictive model for fluid dynamics flow field velocity, the 3D vascular geometry model incorporates both blood and contrast agent as fluid materials to simulate the flow of contrast agent within the blood, thus providing particle concentration information. Simultaneously, a dual-path input PDMNN network is developed, taking into account the 3D point cloud of the coronary artery model, the actual flow field velocity, and the 3D point cloud of contrast agent particle concentration within the flow field. The 3D point cloud of the coronary artery model provides geometric information, while the 3D point cloud of the contrast agent particle concentration provides physical information, enabling the neural network to simultaneously capture multi-dimensional features and accurately predict flow field velocity. During the optimization of the predictive model, a simple advection-diffusion equation is used as the driving force for the neural network model, guiding it to achieve a more accurate fit and thus a more precise 3D flow field velocity prediction effect. Therefore, the predictive model constructed in this way can achieve more accurate and faster prediction results, and can handle different geometric models and boundary conditions.
[0046] In one embodiment, the method further includes encoding a penalty term for the prediction result at the boundary of the 3D vascular geometry model in the loss function.
[0047] In one embodiment, the penalty term for the prediction result at the boundary of the 3D blood vessel geometry model is:
[0048]
[0049] Among them, v i Let P be the velocity tensor, P be the pressure, x be the point cloud coordinates of the 3D model, ρ be the density, μ be the viscosity, t be the time, and C be the particle concentration in the fluid. Let n be the fluid boundary region and n be the number of model outlets and inlets.
[0050] In this embodiment, a penalty is applied separately to the boundary prediction results at the 3D model boundary, forming a physics- and data-driven neural network model. This ensures that the model can provide more accurate prediction results at the boundaries of the 3D blood vessel model, i.e., the region where the blood vessel contacts the surrounding tissue. This is because in actual fluid dynamics, the flow characteristics at the boundary are often complex, such as changes in flow velocity and pressure distribution, making accurate predictions in these areas crucial. By adding a penalty term to the loss function, the model pays more attention to the prediction errors in these boundary regions during training, thereby optimizing the model's performance in these critical areas.
[0051] In one embodiment, the method further includes: introducing blood vessel radius information into the PDMNN neural network, so that the PDMNN neural network can correct the initially predicted blood flow velocity based on the blood vessel radius information after making an initial prediction of blood flow velocity.
[0052] In this embodiment, vessel radius information is introduced before the network output to further correct the prediction results. The radius of the vessel is a crucial factor affecting hemodynamic characteristics, especially when calculating blood flow velocity and pressure distribution. By introducing vessel radius information before the model outputs the prediction results, the prediction results can be further corrected and optimized. This correction takes into account the geometric characteristics of the vessel, making the prediction results more consistent with actual physical conditions and improving the accuracy and reliability of the predictions.
[0053] In one embodiment, after acquiring a large number of coronary artery CTA images from patients with coronary heart disease, the method further includes: segmenting the target region of the coronary artery CTA images.
[0054] In one embodiment, after obtaining the simulation results, the large number of simulation results are cleaned, and training samples, test samples, and validation samples of the PDMNN neural network are constructed based on the cleaned simulation results.
[0055] In this embodiment, erroneous data in the simulation results are deleted or replaced to ensure the accuracy of the data.
[0056] like Figure 4 The figure shows a comparison between the prediction results of the flow velocity using traditional CFD calculation process speed and the prediction results of the 3D flow velocity using the prediction model of this application. In a test set of 100 cases, the normalized mean square error between the flow velocity of each node in the flow field predicted by the PDMNN of this application and the actual CFD calculation results is 0.0309, indicating that the error between the two is small.
[0057] In one embodiment, a system for constructing a predictive model for velocity in a fluid dynamics flow field is provided, the system comprising:
[0058] 3D Vascular Geometry Model Construction Module: Used to acquire a large number of coronary artery CTA images from patients with coronary heart disease, and construct 3D vascular geometry models based on the coronary artery CTA images;
[0059] The CFD simulation module is used to add blood and contrast agent to the 3D vascular geometry model to simulate the flow of contrast agent in the blood; different inlet flow velocities and physiological pressure boundary conditions are set in different 3D vascular geometry models, and CFD simulations are performed to obtain simulation results. Based on the large number of simulation results obtained, training samples, test samples, and test samples of the PDMNN neural network are constructed; the simulation results include 3D point clouds of contrast agent particle concentration in the flow field and the actual flow field velocity.
[0060] The prediction model training module is used to input the 3D point cloud of contrast agent particle concentration, actual flow field velocity, 3D point cloud of 3D vascular geometry model, and corresponding inlet flow velocity boundary conditions obtained from a large number of coronary artery CTA images of coronary heart disease patients into the PDMNN neural network for learning; the advection diffusion equation is encoded into the loss function and the relationship between contrast agent concentration and fluid velocity is used to drive the PDMNN neural network to calculate convergence, thereby obtaining the prediction model of fluid dynamics flow field velocity.
[0061] Specific limitations regarding the system for constructing a predictive model for velocity in a fluid dynamics flow field can be found in the limitations of the method for constructing a predictive model for velocity in a fluid dynamics flow field described above, and will not be repeated here. Each module in the aforementioned system for constructing a predictive model for velocity in a fluid dynamics flow field can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.
[0062] In one embodiment, a computer device, which may be a server, is provided. The computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage medium. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements the aforementioned method for constructing a predictive model for fluid dynamics flow field velocity.
[0063] In one embodiment, a computer program product is also provided, including a computer program / instructions that, when executed by a processor, relate to all or part of the processes in the methods of the above embodiments.
[0064] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.
[0065] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0066] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.
Claims
1. A method for constructing a predictive model for velocity in a fluid dynamics flow field, characterized in that, The method includes: Acquire a large number of coronary artery CTA images from patients with coronary heart disease, and construct 3D vascular geometric models based on the coronary artery CTA images; Blood and contrast agent are added to the 3D vascular geometry model to simulate the flow of contrast agent in the blood. Different inlet flow velocities and physiological pressure boundary conditions are set in different 3D vascular geometry models, and CFD simulations are performed to obtain simulation results. Based on the large number of simulation results obtained, training samples, test samples, and validation samples of the PDMNN neural network are constructed. The simulation results include 3D point clouds of contrast agent particle concentration in the flow field and actual flow field velocity. The 3D point cloud of contrast agent particle concentration, actual flow field velocity, 3D point cloud of 3D vascular geometry model, and corresponding inlet flow velocity boundary conditions obtained from coronary CTA images of a large number of coronary heart disease patients are input into the PDMNN neural network for learning; the advection diffusion equation is encoded into the loss function and the relationship between contrast agent concentration and fluid velocity is used to drive the PDMNN neural network to calculate convergence, thereby obtaining a predictive model of fluid dynamics flow field velocity; The method further includes: encoding a penalty term for the prediction result at the boundary of the 3D vascular geometry model in the loss function; The penalty term for the prediction result at the boundary of the 3D blood vessel geometry model is: ， in, For the velocity tensor, For pressure, Point cloud coordinates for the 3D model. For density, Where t is viscosity and t is time. Let n be the fluid boundary region, and n be the number of model outlets and inlets. The method further includes: introducing blood vessel radius information into the PDMNN neural network, so that the PDMNN neural network can make a preliminary prediction of blood flow velocity and then correct the preliminary prediction of blood flow velocity based on the blood vessel radius information; The advection diffusion equation is: ， in, For the velocity tensor, The concentration of particles within the fluid. For time.
2. The method for constructing a prediction model for fluid dynamics flow field velocity according to claim 1, characterized in that, After acquiring a large number of coronary artery CTA images from patients with coronary heart disease, the method further includes: segmenting the target region of the coronary artery CTA images.
3. The method for constructing a prediction model for the velocity of a fluid dynamics flow field according to claim 1, characterized in that, After obtaining the simulation results, the large number of simulation results are cleaned, and training samples, test samples and validation samples of the PDMNN neural network are constructed based on the cleaned simulation results.
4. A system for constructing a predictive model for velocity in a fluid dynamics flow field, characterized in that, The system includes: 3D Vascular Geometry Model Construction Module: Used to acquire a large number of coronary artery CTA images from patients with coronary heart disease, and construct 3D vascular geometry models based on the coronary artery CTA images; The CFD simulation module is used to add blood and contrast agent to the 3D vascular geometry model to simulate the flow of contrast agent in the blood; different inlet flow velocities and physiological pressure boundary conditions are set in different 3D vascular geometry models, and CFD simulations are performed to obtain simulation results. Based on the large number of simulation results obtained, training samples, test samples, and test samples of the PDMNN neural network are constructed; the simulation results include 3D point clouds of contrast agent particle concentration in the flow field and the actual flow field velocity. The prediction model training module is used to input the 3D point cloud of contrast agent particle concentration, actual flow field velocity, 3D point cloud of 3D vascular geometry model, and corresponding inlet flow velocity boundary conditions obtained from a large number of coronary artery CTA images of coronary heart disease patients into the PDMNN neural network for learning; the advection diffusion equation is encoded into the loss function to drive the PDMNN neural network to converge by utilizing the relationship between contrast agent concentration and fluid velocity; the loss function encodes the penalty term of the prediction result at the boundary of the 3D vascular geometry model; and the vascular radius information is introduced into the PDMNN neural network so that after the PDMNN neural network makes an initial prediction of blood flow velocity, it corrects the initial prediction of blood flow velocity based on the vascular radius information to obtain a prediction model of fluid dynamic flow field velocity; The penalty term for the prediction result at the boundary of the 3D blood vessel geometry model is: ， in, For the velocity tensor, For pressure, Point cloud coordinates for the 3D model. For density, Where t is viscosity and t is time. Let n be the fluid boundary region, and n be the number of model outlets and inlets. The advection diffusion equation is: ， in, For the velocity tensor, The concentration of particles within the fluid. For time.
5. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 3.
6. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1 to 3.