Method and device for rapidly solving skull and ultrasound coupling problem in transcranial focused ultrasound

Abstract

The invention relates to the technical field of transcranial focused ultrasound, and discloses a method and a device for quickly solving a skull and ultrasound coupling problem in transcranial focused ultrasound. According to the method, a skull model is constructed based on the Biot theory, and the elastic porous sound absorption characteristic of the skull is considered. Constructing a sound field control equation, and simulating a sound field absorption boundary in the sound field control equation by using a perfect matching layer technology; wherein the perfect matching layer technology has the characteristic of frequency independence, and during frequency sweep calculation, a mass matrix and a stiffness matrix of the perfect matching layer technology only need to be formed once, so that the solving efficiency of sound radiation and sound scattering problems can be improved. And solving the skull structure-sound field coupling equation according to the skull acoustic parameters and frequency to obtain a solving result. Finally, a training data set is generated according to the acoustic parameters and frequency of the skull and the corresponding solving result, and a regression model is obtained through training according to the training data set; the target skull acoustic parameters and the target frequency are input into the regression model, a target solution can be obtained through real-time calculation, and the calculation efficiency is improved.

Description

Technical Field

[0001] This application relates to the technical field of transcranial focused ultrasound, and particularly to a method and device for quickly solving the problem of skull and ultrasound coupling in transcranial focused ultrasound. Background Art

[0002] High-intensity focused ultrasound is a non-invasive and non-invasive focused therapy. Its treatment principle is mainly to use high-energy ultrasonic waves to accurately focus on the lesion area in human tissues. Through the combined effects of the cavitation effect and thermal effect of ultrasonic waves, heat can be focused on the target lesion tissue, resulting in tissue cell necrosis or inactivation of bioactive substances. The efficacy and advantages of high-intensity focused ultrasound have been confirmed in the treatment ablation of various diseases including tumors (such as liver cancer, prostate cancer, breast tumors, uterine fibroids, etc.); furthermore, focused ultrasound technology also has great development potential and broad application prospects for solving medical clinical problems in the brain (such as neural regulation of specific brain regions, opening of the blood-brain barrier, intracranial targeted drug delivery, etc.), and has received extensive attention and research from scholars at home and abroad in recent years.

[0003] However, the skull and surrounding biological soft tissues have strong acoustic parameter inhomogeneity and large acoustic impedance differences (the density and sound velocity change violently at the interface), and the selection of these acoustic parameters is slightly different from that of actual brain tissues, which easily leads to problems such as focus shift, focal region defocus, and overheating burns. At the same time, due to the elastic porous sound absorption characteristics of the skull, it will undergo structural acoustic coupling with high-intensity sound waves, resulting in energy transfer and amplitude attenuation. Therefore, it is necessary to comprehensively analyze the influence of the skull on transcranial focused ultrasound.

[0004] Currently, most of the control equations used in the research of transcranial focused ultrasound are based on the fluid acoustic wave equation, and very few studies consider the influence of shear waves based on the Kelvin-Voigt equation. However, for accurate modeling of the skull, not only its shear wave needs to be considered, but also its porous sound absorption characteristics and coupling with sound waves need to be considered. In addition, the sound velocity, density, attenuation coefficient, etc. in the skull and biological soft tissues are all functions of spatial variation, and there are great differences among individuals. Therefore, it is necessary to establish a theoretical mathematical model for the coupling of the porous elastic structure of the skull and the sound field, consider the influence of the skull material parameters in the modeling and calculation, and evaluate the credibility while giving the model prediction results.

[0005] To accurately capture the wave propagation behavior in the region under study, the relevant governing equations in this region and the infinitely extended region must be solved. However, it is computationally impossible to solve the sound field in an infinite region. Therefore, various strategies must be used to truncate the model to a reasonable size. The transparent boundary is simple to construct, that is, to construct an impedance matching layer \(n\cdot\nabla p + ikp = 0\) (where \(p\) is the sound pressure, \(n\) is the boundary normal vector, and \(k\) is the wave number). However, it often requires a sufficiently large computational domain so that the finally normally incident sound wave dominates, resulting in an increase in computational cost. The Perfectly Matched Layer (PML) technology based on complex coordinate stretching can well attenuate the sound wave incident on the absorbing medium. As Figure 6 shown, (a) is a schematic diagram of a typical structural acoustic wave equation problem, and (b) is a schematic diagram of the perfectly matched layer. \(p\) I is the incident sound wave; \(p\) S is the scattered sound wave; \(p\) R is the radiated sound wave.

[0006] However, the perfectly matched layer technology for handling the infinite domain / semi-infinite domain boundary in the structural acoustic external field coupling problem contains frequency variables. That is, in the swept-frequency analysis of the structural acoustic dynamics system, the mass matrix and stiffness matrix in the perfectly matched layer need to be calculated once for each frequency of interest, resulting in a large amount of computation and cumbersome calculation for the swept-frequency problem. Therefore, the existing perfectly matched layer technology is not yet perfect. Summary of the Invention

[0007] The present application provides a method for quickly solving the problem of skull and ultrasound coupling in transcranial focused ultrasound to solve the problems in the prior art that due to the elastic porous sound absorption characteristics of the skull, it is easy to have structural acoustic coupling with ultrasound, and the swept-frequency problem has a large amount of computation and is cumbersome.

[0008] Correspondingly, the present application also provides a device for quickly solving the problem of skull and ultrasound coupling in transcranial focused ultrasound, an electronic device, and a computer-readable storage medium to ensure the implementation and application of the above method.

[0009] To solve the above technical problems, the present application discloses a method for quickly solving the problem of skull and ultrasound coupling in transcranial focused ultrasound, and the method includes:[[]]

[0010] Construct a skull model based on Biot theory;

[0011] Construct a sound field governing equation and use the perfectly matched layer technology to simulate the sound field absorption boundary in the sound field governing equation; the perfectly matched layer technology has the characteristic of being independent of frequency;

[0012] Combine the cranial bone model and the acoustic field control equation to form a cranial bone structure-acoustic field coupling equation, and solve the cranial bone structure-acoustic field coupling equation according to the cranial bone acoustic parameters and frequency to obtain the solution result;

[0013] Generate a training data set according to the cranial bone acoustic parameters, frequency and the corresponding solution result, and train a regression model according to the training data set;

[0014] Input the target cranial bone acoustic parameters and target frequency into the regression model to obtain the target solution.

[0015] This application also discloses a device for quickly solving the coupling problem between the cranial bone and ultrasound in transcranial focused ultrasound. The device includes:

[0016] A cranial bone structure construction module for constructing a cranial bone model based on Biot theory;

[0017] An acoustic field construction module for constructing an acoustic field control equation and using the perfectly matched layer technique to simulate the acoustic field absorption boundary in the acoustic field control equation; The perfectly matched layer technique has the characteristic of being independent of frequency;

[0018] A coupling solution module for combining the cranial bone model and the acoustic field control equation to form a cranial bone structure-acoustic field coupling equation, and solving the cranial bone structure-acoustic field coupling equation according to the cranial bone acoustic parameters and frequency to obtain the solution result;

[0019] A model order reduction solution module for generating a training data set according to the cranial bone acoustic parameters, frequency and the corresponding solution result, and training a regression model according to the training data set;

[0020] The model order reduction solution module is also used to input the target cranial bone acoustic parameters and frequency into the regression model to obtain the target solution.

[0021] This application also discloses an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements one or more of the methods in this application.

[0022] This application also discloses a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements one or more of the methods in this application.

[0023] In this application, a skull model is constructed based on Biot theory, taking into account the elastic porous sound absorption characteristics of the skull. The acoustic field control equation is constructed, and the perfectly matched layer technique is used to simulate the acoustic field absorption boundary in the acoustic field control equation; among them, the perfectly matched layer technique has the characteristic of being independent of frequency. During the swept-frequency calculation, its mass matrix and stiffness matrix only need to be formed once, which can improve the solution efficiency of acoustic radiation and acoustic scattering problems. Then, the skull model and the acoustic field control equation are combined to form the skull structure-acoustic field coupling equation, and the skull structure-acoustic field coupling equation is solved according to the skull acoustic parameters and frequency to obtain the solution results. Finally, a training data set is generated based on the skull acoustic parameters, frequency, and corresponding solution results, and a regression model is trained based on the training data set; by inputting the target skull acoustic parameters and target frequency into the regression model, the target solution can be calculated in real time, improving the calculation efficiency. Therefore, the method in this application provides powerful computing capabilities for the calculation and optimization of transcranial focused ultrasound systems and has broad application prospects.

[0024] Additional aspects and advantages of the present application will be given in the following description section, which will become apparent from the following description or be understood through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The above and / or additional aspects and advantages of the present application will become apparent and be readily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0026] Figure 1 is a flowchart of a fast solution method for the skull-ultrasound coupling problem in transcranial focused ultrasound provided by an embodiment of the present application;

[0027] Figure 2 is a flowchart of the vibro-acoustic coupling analysis provided by an embodiment of the present application;

[0028] Figure 3 is a flowchart of the finite element solution provided by an embodiment of the present application;

[0029] Figure 4 is a technical roadmap of data-driven model reduction provided by an embodiment of the present application;

[0030] Figure 5 is a comparison result diagram of the frequency-independent perfectly matched layer and the matching layer of the commercial software Comsol provided by an embodiment of the present application;

[0031] Figure 6 is a schematic diagram of a typical structural acoustic wave equation problem and a schematic diagram of a perfectly matched layer provided by an embodiment of the present application;

[0032] Figure 7 is a structural schematic diagram of a fast solution device for the skull-ultrasound coupling problem in transcranial focused ultrasound provided by an embodiment of the present application;

[0033] Figure 8 The structural schematic diagram of the electronic device provided by the embodiment of the present application. Detailed implementation manners

[0034] The embodiments of the present application will be described in detail below. The examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions from beginning to end. The embodiments described below by referring to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be construed as a limitation to the present application.

[0035] Those skilled in the art of the present technology can understand that, unless specifically stated otherwise, the singular forms "a", "an", "the" and "said" used herein may also include the plural forms. It should be further understood that the term "including" used in the specification of the present application means the presence of features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their combinations. It should be understood that when we say that an element is "connected" or "coupled" to another element, it can be directly connected or coupled to other elements, or there may also be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or wireless coupling. The phrase "and / or" used herein includes all or any unit and all combinations of one or more related listed items.

[0036] Those skilled in the art can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless specifically defined as here.

[0037] The solution provided by the embodiment of the present application can be executed by any electronic device. For example, it can be a terminal device or a server. Among them, the server can be an independent physical server, a server cluster or a distributed system composed of multiple physical servers, or a cloud server providing cloud computing services. The terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, etc., but is not limited thereto. The terminal and the server can be directly or indirectly connected through wired or wireless communication methods, and the present application does not limit this. For the technical problems existing in the prior art, the method and device for quickly solving the skull and ultrasound coupling problem in transcranial focused ultrasound provided by the present application are intended to solve at least one of the technical problems of the prior art.

[0038] The following uses specific embodiments to elaborate in detail on the technical solution of this application and how the technical solution of this application solves the above technical problems. The following several specific embodiments can be combined with each other, and for the same or similar concepts or processes, they may not be repeated in some embodiments. The embodiments of this application will be described below in conjunction with the accompanying drawings.

[0039] An embodiment of this application provides a possible implementation manner. As Figure 1 shown, a flowchart of a method for quickly solving the problem of skull-ultrasound coupling in transcranial focused ultrasound is provided. This solution can be executed by any electronic device. Optionally, it can be executed on the server side or the terminal device.

[0040] As Figure 1 shown in, this method may include the following steps:

[0041] Step 101, construct a skull model based on Biot theory.

[0042] Biot theory takes into account the elasticity and porous sound absorption characteristics of the skull, and models its structural and acoustic properties at the same time. Therefore, it can make the numerical simulation of transcranial focused ultrasound more accurate. As Figure 2 shown, in the embodiment of this application, in terms of structure, the elastic porous sound absorption characteristics of the skull are modeled based on Biot theory.

[0043] Step 102, construct a sound field control equation, and use the perfectly matched layer technique to simulate the sound field absorption boundary in the sound field control equation; the perfectly matched layer technique has the characteristic of being independent of frequency.

[0044] In the existing method, when performing a swept-frequency analysis of a structural-acoustic dynamics system, the mass matrix and stiffness matrix in the perfectly matched layer need to be calculated once for each frequency of interest, resulting in a large amount of calculation and cumbersome calculation for the swept-frequency problem. In the embodiment of this application, a new perfectly matched layer technique is proposed. This perfectly matched layer technique has the characteristic of being independent of frequency. During swept-frequency calculation, its mass matrix and stiffness matrix only need to be formed once, which can improve the solution efficiency of sound radiation and sound scattering problems. As Figure 2 shown, in terms of ultrasound, in the embodiment of this application, the perfectly matched layer technique independent of frequency is used to model the external sound field absorption boundary.

[0045] Step 103, combine the skull model and the sound field control equation to form a skull structure-sound field coupling equation, and solve the skull structure-sound field coupling equation according to the skull acoustic parameters and frequency to obtain the solution result.

[0046] In the embodiment of this application, by solving the skull structure-sound field coupling equation, that is Figure 2 shown in the vibro-acoustic coupling analysis, the corresponding solution result can be obtained, such as the sound pressure distribution of the sound field.

[0047] In the embodiments of the present application, a finite element algorithm is used to solve the skull structure-acoustic field coupling equation under different skull acoustic parameters and frequencies. The specific process is as follows Figure 3 As shown, first, simulation variables such as sound speed, density, absorption coefficient, etc. are configured through the configuration file of the main program, and the simulation variables are stored in the main program; then the main program calls the mesh file of the subroutine to perform mesh division on the skull structure and the acoustic field to obtain mesh data, and a set of algebraic equations with finite dimensions is determined based on the mesh data; finally, the algebraic equations are solved by finite element method, and the results are output; and the results are visualized through post-processing.

[0048] Step 104, generate a training dataset according to the skull acoustic parameters, frequencies and the corresponding solution results, and train a regression model according to the training dataset.

[0049] In the embodiments of the present application, the skull structure-acoustic field coupling equation is solved for different skull acoustic parameters and different frequencies, and the solution results under different skull acoustic parameters and frequencies can be obtained. Considering that the amount of data is too large, in the embodiments of the present application, multiple groups of skull acoustic parameters and corresponding multiple frequencies can be obtained as samples, and the corresponding solution results are used as label data to construct a training dataset. By training a preset network with the training dataset, a trained regression model can be obtained.

[0050] Step 105, input the target skull acoustic parameters and the target frequency into the regression model to obtain the target solution.

[0051] In the embodiments of the present application, a skull model is constructed based on the Biot theory, considering the elastic porous sound absorption characteristics of the skull. The acoustic field control equation is constructed, and the perfectly matched layer technique is used to simulate the acoustic field absorption boundary in the acoustic field control equation; among them, the perfectly matched layer technique has the characteristic of being independent of frequency. During the swept-frequency calculation, its mass matrix and stiffness matrix only need to be formed once, which can improve the solution efficiency of the acoustic radiation and acoustic scattering problems. Then, the skull model and the acoustic field control equation are combined to form the skull structure-acoustic field coupling equation, and the skull structure-acoustic field coupling equation is solved according to the skull acoustic parameters and frequencies to obtain the solution results. Finally, a training dataset is generated according to the skull acoustic parameters, frequencies and the corresponding solution results, and a regression model is trained according to the training dataset; inputting the target skull acoustic parameters and the target frequency into the regression model can calculate the target solution in real time, improving the calculation efficiency. Therefore, the method in the embodiments of the present application provides powerful computing capabilities for the calculation and optimization of transcranial focused ultrasound systems and has broad application prospects.

[0052] In an alternative embodiment, the skull model is:

[0053]

[0054] Wherein, is the stress tensor; ω is the angular frequency; and is the equivalent density, which takes into account the viscous and inertial energy dissipation caused by the relative motion of the solid and the fluid; u s (r) is the displacement; p f (r) is the sound pressure; φ is the porosity; γ is the specific heat capacity; is related to the equivalent bulk modulus.

[0055] According to Equation (1), it is obvious that the Biot theory takes into account both the solid elasticity and the fluid acoustic characteristics, which is convenient for coupling with the ultrasonic field. Compared with the traditional skull modeling that only considers longitudinal waves, the skull model in the embodiments of the present application takes into account the effects of both longitudinal waves and transverse waves.

[0056] In an alternative embodiment, the acoustic field control equation is:

[0057]

[0058] where r is the point position vector, ω is the angular frequency, c(r) is the inhomogeneous sound speed, p(r) is the sound pressure, is the source term.

[0059] In an alternative embodiment, the complex mapping of the perfectly matched layer technique in one dimension is:

[0060]

[0061] where the real coordinate x is transformed into the complex coordinate x* through the above formula, and σ(x) is the absorption function; ω mid is the specified frequency in the frequency range.

[0062] The complex mapping of the traditional perfectly matched layer technique in one dimension is:

[0063]

[0064] It should be noted that due to the presence of 1 / ω in Equation (4), in the swept-frequency analysis of the structural acoustic dynamics system, the mass matrix and the stiffness matrix in the perfectly matched layer need to be calculated once for each frequency of interest. To avoid this cumbersome process, 1 / ω is replaced with a constant 1 / ω mid , to obtain the frequency-independent perfectly matched layer technique corresponding to the embodiments of the present application, that is, Equation (3), where ω mid is the specified frequency in the frequency range, such as the middle frequency. In the swept-frequency calculation, for the entire frequency range considered in the embodiments of the present application, the integral calculation only needs to be performed once, thus improving the calculation efficiency.

[0065] In an alternative embodiment, the absorption function is:

[0066]

[0067] where c is the speed of sound; C / c is a dimensionless factor and C is greater than c; x ext and x int are the points corresponding to the outer boundary and the inner boundary of the real coordinate x in the perfectly matched layer, respectively; ζ is a dimensionless variable related to the distance, which is 0 when x = x int and is 1 when x = x ext .

[0068] The effective critical frequency in the absorption function is: f cri = f mid / (C / c). If f cri is greater than the minimum value f mid in the frequency range, then C / c needs to be increased; if f cri is less than the minimum value f mid in the frequency range, it means that the value of C / c is effective throughout the considered frequency range.

[0069] Replacing 1 / ω in Equation (4) with a constant 1 / ω mid avoids the need to continuously calculate the mass matrix and the stiffness matrix during the frequency sweep process, but the low-frequency accuracy is reduced. Therefore, a new absorption function, namely Equation (5), is proposed in the embodiments of the present application to enable good absorption of the incident wave at low frequencies.

[0070] For the rigid sphere acoustic scattering problem, with the same mesh in the computational domain and the perfectly matched layer, the low-frequency absorption effect is better than that of commercial software. The perfectly matched layer technology proposed in the embodiments of the present application has high accuracy, and due to its frequency-independent characteristics, during the frequency sweep calculation, its mass matrix and stiffness matrix only need to be formed once, thus improving the solution efficiency of acoustic radiation and acoustic scattering problems.

[0071] In an alternative embodiment, the acoustic parameters of the skull may include the skull density, the speed of sound, and the absorption attenuation coefficient.

[0072] The acoustic parameters of the skull have strong non-uniformity. A three-dimensional skull model is reconstructed by using magnetic resonance imaging or computed tomography images. According to the Hounsfield unit HU in the scanned images, the porosity φ of the skull medium can be calculated (φ = 1 - HU / 1000). Then, the skull density ρ, the speed of sound c, and the absorption attenuation coefficient α at different positions can be obtained by interpolation:

[0073] ρ = φ × ρ f + (1 - φ) × ρ s , c = φ × c f + (1 - φ) × c s , α = α f + φ β × (α s - αf ), (6)

[0074] where the subscripts f and s are the acoustic parameters related to the fluid and the solid respectively, and β is a constant of 0.5.

[0075] In an alternative embodiment, a training dataset is generated based on the cranial acoustic parameters, frequencies, and corresponding solution results, and a regression model is obtained by training based on the training dataset, including:

[0076] Using a preset sampling method to obtain multiple sets of cranial acoustic parameters, multiple different frequencies, and corresponding multiple solution results, and constructing a training dataset;

[0077] As Figure 4 shown, in the embodiment of the present application, a preset sampling method is used to optimize the sampling process to obtain corresponding sample parameters (i.e., cranial acoustic parameters and frequencies), and the corresponding solution results are obtained by solving the cranial structure-acoustic field coupling equations for multiple sets of cranial acoustic parameters and different frequencies. Furthermore, a training dataset is constructed based on the sample parameters and the corresponding solutions.

[0078] Frequency f and parameter μ samples:

[0079]

[0080] Solutions y at different frequencies and parameter values a Formed a tensor grid:

[0081]

[0082] Using low-rank singular value decomposition (SVD) to perform tensor decomposition on the training dataset for parameter variables and frequency variables, and obtaining the principal components with the data energy proportion of the solution results for the parameter terms and frequency terms greater than a threshold; usually, the singular values decrease rapidly, and truncating and compressing them can reduce the dimension while extracting the most important characteristics of the matrix.

[0083] Based on the principal components of the solution results corresponding to the sample points of the parameter terms and frequency terms, using a preset neural network to obtain the mapping relationship between the projection coefficients corresponding to the parameter terms and frequency terms; among them, the preset neural network can be Gaussian process regression, deep feedforward neural network, and other neural networks, which are not specifically limited in the embodiment of the present application.

[0084] For the mapping relationship between the projection coefficients corresponding to the parameter terms and frequency terms, a regression function is obtained through linear combination of tensor products, and a regression model is obtained.

[0085] Since the dimension of the regression model after model order reduction according to the above method is very small, the large-scale transcranial focused ultrasound problem can be directly solved, and the calculation time is predictable.

[0086] In an optional embodiment, a preset sampling method is used to obtain multiple sets of cranial acoustic parameters, multiple different frequencies, and corresponding multiple solution results, and a training data set is constructed, including:

[0087] The Sobol low-discrepancy sequence or sparse grid collocation method is used to obtain multiple sets of cranial acoustic parameters and multiple different frequencies, obtaining a sample parameter database and a sample frequency database, and based on the finite element method, the cranial structure-acoustic field coupling equation is solved to obtain the solution results under the corresponding cranial acoustic parameters and frequency samples, obtaining a solution result database;

[0088] The sample parameter database, the sample frequency database, and the solution result database are compressed by the proper orthogonal decomposition method to obtain a training data set.

[0089] In the embodiment of the present application, the Sobol low-discrepancy sequence or sparse grid collocation method is used to optimize the sampling process, and high-precision calculation results can be obtained with as few sample points as possible. After obtaining the sample parameter database, it is compressed by the proper orthogonal decomposition method (Proper Orthogonal Decomposition: POD) to obtain a training data set (the solution of the full-order model serves as both the snapshot set of POD and the input of the preset training model. At this time, POD can construct a reduced-order subspace), which can further reduce the amount of calculation data and improve the calculation efficiency.

[0090] The specific algorithm for obtaining multiple sets of cranial acoustic parameters, multiple different frequencies, and corresponding multiple solution results to generate a training data set and training a regression model based on the training data set can be called a data-driven model reduction algorithm in the embodiment of the present application. This algorithm accelerates the calculation of a large-scale transcranial focused ultrasound system. In the offline stage, a sample database is constructed by solving the solutions under different cranial acoustic parameters and frequencies to train the regression model; in the online stage, the constructed regression model can be used to quickly interpolate and extrapolate the solutions of the transcranial focused ultrasound system under new parameter or frequency variables, that is Figure 4 the predicted results shown. It can be seen that the offline and online processes are completely decoupled, facilitating online real-time calculation and capable of handling multi-parameter change problems. At the same time, the tensor decomposition based on the frequency quantity and the parameter quantity is simpler than directly performing global Gaussian process regression, and the data-driven training process has more hyperparameters to make the prediction more flexible.

[0091] In the embodiment of the present application, the regression model reduction process, that is, the offline training model and online calculation, is as follows:

[0092]

[0093] In the formula, is the original response y aThe approximation, that is, the output of the prediction result through the trained regression model;

[0094] Tensor product:

[0095]

[0096] In the formula, and are the l-th order discrete frequency and parameter-related components, and σ l is the l-th order singular value;

[0097] Two radial basis neural networks, one for frequency training and the other for parameter training;

[0098]

[0099] In the formula, f is the frequency, μ is the skull acoustic parameter, and are the l-th order continuous frequency and skull acoustic parameter-related components, is the database related to the frequency; is the database related to the skull acoustic parameter;

[0100] Then, a low-dimensional surrogate model is assembled through the tensor product:

[0101]

[0102] As Figure 4 shown, in the embodiment of the present application, after predicting the result under the new parameter or frequency variable through the regression model, it is judged whether the error of the result meets the requirement. If not, new simulation results or experimental data are obtained, and the preset neural network (such as Gaussian process regression) is adjusted through the regression model and the data to obtain a more accurate regression model.

[0103] In the black box machine learning method, it is often required that there be enough training data to generate an accurate regression model. However, the idea of combining the physical model and the data model proposed in the embodiment of the present application reduces the requirement for training data.

[0104] In the embodiment of the present application, the coupling mechanism between the skull and the sound wave is studied, and the energy transfer law and attenuation mechanism therein are revealed, providing a theoretical and methodological basis for the functional evaluation of transcranial ultrasound therapy and the formulation of personalized surgical plans, and is expected to further promote the development of multiple disciplines such as computational mechanics, computational ultrasonics, biomedicine, and brain science.

[0105] For the rigid sphere sound scattering problem, as Figure 5As shown, when the grids of the computational domain and the perfectly matched layer are the same, the simulation results of the method in the embodiments of the present application (present) show that the low-frequency absorption effect is better than that of the commercial software Comsol. Therefore, the method in the embodiments of the present application has been proven feasible through numerical simulation. When running example simulations on a personal computer and comparing with the analytical solution, the calculation accuracy of the proposed method is verified; compared with other perfectly matched layer techniques, the calculation speed is faster; compared with the results in Comsol software, the calculation efficiency is verified.

[0106] Based on the same principle as the method provided in the embodiments of the present application, the embodiments of the present application also provide a device for quickly solving the problem of coupling between the skull and ultrasound in transcranial focused ultrasound, as Figure 7 shown, the device includes:

[0107] A skull structure construction module 701 for constructing a skull model based on the Biot theory;

[0108] An acoustic field construction module 702 for constructing an acoustic field control equation and using the perfectly matched layer technique to simulate the acoustic field absorption boundary in the acoustic field control equation; the perfectly matched layer technique has the characteristic of being independent of frequency;

[0109] A coupling solution module 703 for jointly forming a skull structure-acoustic field coupling equation with the skull model and the acoustic field control equation, and solving the skull structure-acoustic field coupling equation according to the skull acoustic parameters and frequency to obtain a solution result;

[0110] A model order reduction solution module 704 for generating a training data set according to the skull acoustic parameters, frequency and the corresponding solution result, and training to obtain a regression model according to the training data set;

[0111] The model order reduction solution module 704 is also used to input the target skull acoustic parameters and the target frequency into the regression model to obtain a target solution.

[0112] In the embodiments of the present application, a skull model is constructed based on Biot theory, taking into account the elastic porous sound absorption characteristics of the skull. The sound field control equation is constructed, and the perfectly matched layer technique is used to simulate the sound field absorption boundary in the sound field control equation; among them, the perfectly matched layer technique has the characteristic of being independent of frequency. During the swept-frequency calculation, its mass matrix and stiffness matrix only need to be formed once, which can improve the solution efficiency of sound radiation and sound scattering problems. Then, the skull model and the sound field control equation are combined to form a skull structure-sound field coupling equation, and the skull structure-sound field coupling equation is solved according to the skull acoustic parameters and frequency to obtain the solution result. Finally, a training dataset is generated according to the skull acoustic parameters, frequency, and the corresponding solution result, and a regression model is trained according to the training dataset; the target skull acoustic parameters and target frequency are input into the regression model, and the target solution can be calculated in real time, improving the calculation efficiency. Therefore, the method in the embodiments of the present application provides powerful computing capabilities for the calculation and optimization of transcranial focused ultrasound systems and has broad application prospects.

[0113] The fast solution device for the skull-ultrasound coupling problem in transcranial focused ultrasound provided by the embodiments of the present application can implement Figures 1 to 4 each process implemented in the method embodiments. To avoid repetition, it will not be elaborated here.

[0114] The fast solution device for the skull-ultrasound coupling problem in transcranial focused ultrasound in the embodiments of the present application can execute the fast solution method for the skull-ultrasound coupling problem in transcranial focused ultrasound provided by the embodiments of the present application. Their implementation principles are similar. The actions performed by each module and unit in the fast solution device for the skull-ultrasound coupling problem in transcranial focused ultrasound in each embodiment of the present application correspond to the steps in the fast solution method for the skull-ultrasound coupling problem in transcranial focused ultrasound in each embodiment of the present application. For the detailed function descriptions of each module of the fast solution device for the skull-ultrasound coupling problem in transcranial focused ultrasound, reference can specifically be made to the descriptions in the corresponding fast solution method for the skull-ultrasound coupling problem in transcranial focused ultrasound shown above. It will not be elaborated here.

[0115] Based on the same principle as the method shown in the embodiments of the present application, the embodiments of the present application also provide an electronic device, which may include, but is not limited to: a processor and a memory; the memory is used to store a computer program; the processor is used to execute the method for quickly solving the skull-ultrasound coupling problem in transcranial focused ultrasound shown in any optional embodiment of the present application by calling the computer program. Compared with the prior art, the method for quickly solving the skull-ultrasound coupling problem in transcranial focused ultrasound provided by the present application constructs a skull model based on the Biot theory and takes into account the elastic porous sound absorption characteristics of the skull. The acoustic field control equation is constructed, and the perfectly matched layer technology is used to simulate the acoustic field absorption boundary in the acoustic field control equation; among them, the perfectly matched layer technology has the characteristic of being independent of frequency. During the swept-frequency calculation, its mass matrix and stiffness matrix only need to be formed once, which can improve the solution efficiency of the acoustic radiation and acoustic scattering problems. Then, the skull structure-acoustic field coupling equation is formed by combining the skull model and the acoustic field control equation, and the skull structure-acoustic field coupling equation is solved according to the skull acoustic parameters and frequency to obtain the solution result. Finally, a training data set is generated according to the skull acoustic parameters, frequency, and the corresponding solution result, and a regression model is obtained by training according to the training data set; the target skull acoustic parameters and target frequency are input into the regression model, and the target solution can be calculated in real time, improving the calculation efficiency. Therefore, the method in the embodiments of the present application provides powerful computing capabilities for the calculation and optimization of the transcranial focused ultrasound system and has broad application prospects.

[0116] In an optional embodiment, an electronic device is further provided, as Figure 8 shown, Figure 8 the electronic device 800 shown may be a server, including: a processor 801 and a memory 803. Among them, the processor 801 and the memory 803 are connected, such as by a bus 802. Optionally, the electronic device 800 may further include a transceiver 804. It should be noted that in actual applications, the transceiver 804 is not limited to one, and the structure of the electronic device 800 does not constitute a limitation to the embodiments of the present application.

[0117] The processor 801 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute various exemplary logical blocks, modules, and circuits described in connection with the disclosure of this application. The processor 801 may also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0118] The bus 802 may include a path for transmitting information between the above components. The bus 802 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The bus 802 may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 8 only a thick line is used to represent it in the figure, but it does not mean that there is only one bus or one type of bus.

[0119] The memory 803 may be a ROM (Read Only Memory) or other type of static storage device that can store static information and instructions, a RAM (Random Access Memory) or other type of dynamic storage device that can store information and instructions, or it may also be an EEPROM (Electrically Erasable Programmable Read Only Memory), a CD-ROM (Compact Disc Read Only Memory), or other optical disc storage, optical disc storage (including compact discs, laser discs, optical discs, digital versatile discs, Blu-ray discs, etc.), magnetic storage media, or other magnetic storage devices, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto.

[0120] The memory 803 is used to store the application program code for executing the solution of this application, and is controlled by the processor 801 for execution. The processor 801 is used to execute the application program code stored in the memory 803 to implement the content shown in the foregoing method embodiments.

[0121] Among them, the electronic device includes but is not limited to: mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Tablet Computers), PMPs (Portable Multimedia Players), in-vehicle terminals (such as in-vehicle navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Figure 8 The electronic device shown is only an example and should not impose any limitations on the functions and usage scope of the embodiments of this application.

[0122] The server provided by this application can be an independent physical server, or a server cluster or distributed system composed of multiple physical servers. It can also be a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, as well as big data and artificial intelligence platforms. The terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, etc., but is not limited thereto. The terminal and the server can be directly or indirectly connected through wired or wireless communication methods, and this application does not make any restrictions here.

[0123] The embodiments of this application provide a computer-readable storage medium, on which a computer program is stored. When it runs on a computer, it enables the computer to execute the corresponding content in the foregoing method embodiments.

[0124] It should be understood that although the steps in the flowchart of the accompanying drawings are shown in sequence according to the indication of the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless there is a clear indication in this article, the execution of these steps has no strict order restriction, and they can be executed in other orders. Moreover, at least a part of the steps in the flowchart of the accompanying drawings may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0125] It should be noted that the above-mentioned computer-readable storage medium in the present application can also be a computer-readable signal medium or a combination of a computer-readable storage medium and a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of the computer-readable storage medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, the computer-readable storage medium can be any tangible medium that contains or stores a program, and this program can be used by or in combination with an instruction execution system, apparatus, or device. And in the present application, the computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, in which computer-readable program code is carried. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The computer-readable signal medium can also be any computer-readable medium other than the computer-readable storage medium, and this computer-readable signal medium can send, propagate, or transmit a program for use by or in combination with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted by any appropriate medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination of the above.

[0126] The above-mentioned computer-readable medium can be included in the above-mentioned electronic device; or it can exist separately and not be assembled into the electronic device.

[0127] The above-mentioned computer-readable medium carries one or more programs, and when the above-mentioned one or more programs are executed by the electronic device, the electronic device is caused to execute the method shown in the above-mentioned embodiments.

[0128] According to one aspect of the present application, there is provided a computer program product or a computer program, and the computer program product or the computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the method and device for quickly solving the problem of skull and ultrasound coupling in transcranial focused ultrasound provided in the above various optional implementation manners.

[0129] Computer program code for performing the operations of this application can be written in one or more programming languages or combinations thereof. The above-mentioned programming languages include object-oriented programming languages such as Java, Smalltalk, C++, and also include conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any kind of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (for example, by using an Internet service provider to connect through the Internet).

[0130] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in the flowchart or block diagram can represent a module, a program segment, or a part of code that contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks can occur in a different order than that marked in the accompanying drawings. For example, two consecutive blocks shown can actually be executed substantially in parallel, and they can sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0131] The modules described in the embodiments of this application can be implemented in software or in hardware. Among them, the name of the module does not constitute a limitation on the module itself in some cases. For example, the skull structure construction module can also be described as "the skull structure construction module for constructing a skull model based on the Biot theory".

[0132] The above description is only a preferred embodiment of this application and an explanation of the applied technical principles. Those skilled in the art should understand that the scope of disclosure involved in this application is not limited to the technical solutions formed by the specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosure concept. For example, technical solutions formed by mutually replacing the above features with other technical features having similar functions disclosed in this application (but not limited to).

Claims

1. A method for quickly solving the skull-ultrasound coupling problem in transcranial focused ultrasound, characterized in that: The method comprises: Construct a skull model based on Biot's theory; Constructing an acoustic field control equation and using a perfect matching layer technology to simulate an acoustic field absorption boundary in the acoustic field control equation; the perfect matching layer technology has a frequency-independent characteristic; Combining the skull model with the sound field control equation to form a skull structure-sound field coupling equation, and solving the skull structure-sound field coupling equation according to skull acoustic parameters and frequency to obtain a solution result; Generate a training data set according to the skull acoustic parameters, the frequency and the corresponding solution results, and obtain a regression model by training according to the training data set; The target skull acoustic parameters and the target frequency are input into the regression model to obtain the target solution.

2. The method for rapidly solving the skull-ultrasound coupling problem in transcranial focused ultrasound according to claim 1, characterized in that: The skull model is: in, is the stress tensor; ω is the angular frequency; and is the equivalent density, which takes into account the viscous and inertial energy dissipation caused by the mutual motion of solid and fluid; u s (r) is the displacement; p f (r) is the sound pressure; φ is the porosity; γ is the specific heat capacity; Related to the equivalent bulk modulus.

3. The method for rapidly solving the skull-ultrasound coupling problem in transcranial focused ultrasound according to claim 1, characterized in that: The complex mapping of the perfect matching layer technology in one dimension is: Among them, the real coordinate x is transformed into the complex coordinate x* through the above formula, σ(x) is the absorption function; ω mid The specified frequency for the frequency interval.

4. The method for rapidly solving the skull-ultrasound coupling problem in transcranial focused ultrasound according to claim 3, characterized in that: The absorption function is: Where c is the speed of sound; C / c is a dimensionless factor and C is greater than c; x ext and x int are the points corresponding to the outer and inner boundaries of the perfect matching layer with real coordinate x respectively; The effective critical frequency in the absorption function is: f cri =f mid / (C / c), if f cri Greater than the minimum value f in the frequency interval mid , then C / c needs to be increased; if f cri Less than the minimum value f in the frequency interval mid , which means that the C / c value is valid in the entire frequency range considered.

5. The method for rapidly solving the skull-ultrasound coupling problem in transcranial focused ultrasound according to claim 1, characterized in that: The skull acoustic parameters include skull density, sound velocity and absorption attenuation coefficient.

6. The method for rapidly solving the skull-ultrasound coupling problem in transcranial focused ultrasound according to claim 1, characterized in that: Generating a training data set according to the skull acoustic parameters, the frequency and the corresponding solution results, and obtaining a regression model through training according to the training data set, comprises: Using a preset sampling method to obtain multiple groups of skull acoustic parameters, multiple different frequencies, and corresponding multiple solution results, to construct a training data set; Using low-rank singular value decomposition to perform tensor decomposition of parameter variables and frequency variables on the training data set, and obtaining principal components whose data energy proportion of solution results for parameter terms and frequency terms is greater than a threshold; Based on the principal components of the solution results corresponding to the parameter items and the frequency items, a mapping relationship between the projection coefficients corresponding to the parameter items and the frequency items is obtained using a preset neural network; According to the mapping relationship between the parameter item and the projection coefficient corresponding to the frequency item, a regression function is obtained by linear combination tensor product, and the regression model is obtained.

7. The method for rapidly solving the skull-ultrasound coupling problem in transcranial focused ultrasound according to claim 6, characterized in that: The method of using a preset sampling method to obtain multiple groups of skull acoustic parameters, multiple different frequencies, and corresponding multiple solution results to construct a training data set includes: A Sobol low-discrepancy sequence or a sparse grid point collocation method is used to obtain multiple groups of skull acoustic parameters and multiple different frequencies, and a sample parameter database and a sample frequency database are obtained. The skull structure-acoustic field coupling equation is solved based on the finite element method to obtain the solution results corresponding to the skull acoustic parameters and frequency samples, and a solution result database is obtained. The training data set is obtained by compressing the sample parameter database, the sample frequency database and the solution result database using the eigenorthogonal decomposition method.

8. A device for quickly solving the skull-ultrasound coupling problem in transcranial focused ultrasound, characterized in that: The device comprises: Skull structure building module, used to build skull models based on Biot theory; An acoustic field construction module, used to construct an acoustic field control equation and simulate an acoustic field absorption boundary in the acoustic field control equation using a perfect matching layer technology; the perfect matching layer technology has a frequency-independent characteristic; A coupling solution module, used to combine the skull model and the sound field control equation to form a skull structure-sound field coupling equation, and solve the skull structure-sound field coupling equation according to skull acoustic parameters and frequency to obtain a solution result; A model reduction solution module, used to generate a training data set according to the skull acoustic parameters, the frequency and the corresponding solution results, and to obtain a regression model through training according to the training data set; The model reduction solution module is also used to input the target skull acoustic parameters and target frequency into the regression model to obtain the target solution.

9. An electronic device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

Images