Positive problem modeling method and apparatus, electronic device, and computer-readable storage medium

Abstract

The application discloses a kind of positive problem modeling method, device, electronic equipment and computer readable storage medium, wherein, method mainly includes: (1) the physical equation description of electroencephalogram positive problem based on electrode stereoscopic structure boundary condition;(2) with the positive problem finite element construction of electrode stereoscopic structure and head brain structure;(3) conductive matrix calculation.The application proposes the positive problem modeling method based on electrode stereoscopic structure description, while constructing the normal current distribution of electrode coverage area, further constructs the tangential current distribution caused by electrode inner tangential voltage difference, which on the one hand increases the description of tangential current, makes the electric field distribution in electrode more fine, on the one hand, because of the advantage of its stereoscopic structure, can more detailedly, more intuitively describe the distribution of conductivity in electrode, so as to further make the electric field description in electrode more fine.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of physiological signal processing, and in particular to a forward problem modeling method and device, electronic equipment and a computer readable storage medium. BACKGROUND

[0002] Non-invasive electroencephalogram is a means of collecting extracranial electroencephalogram. Because the source of the electroencephalogram signal is located in the intracranial, in scientific research, it is necessary to calculate the electrical activity of the intracranial discharge source based on the extracranial measured electroencephalogram signal. This process is called electroencephalogram source imaging, which is abbreviated as EEG Source Imaging (ESI) in English.

[0003] Source imaging includes forward problem modeling and inverse problem solving. The forward problem modeling refers to that the head-brain model and the intracranial current source discharge distribution and the scalp electrode distribution are known, and the numerical solution of the scalp potential is solved. The inverse problem refers to that the extracranial measured signal and the forward problem model are known, and the distribution of the intracranial current source is solved. As can be seen, the high-precision electroencephalogram forward problem model is an important guarantee for the precision of source imaging, and it is of great significance to improve the precision of forward problem modeling.

[0004] Among them, improving the modeling precision of the head-brain and electrode structure prior can improve the precision of the forward problem modeling. However, in the existing modeling, the description of the electrode structure is simplified to a point structure (such as shown in Figure 1 ) or a surface structure (such as shown in Figure 2 ) on the scalp tissue. From the perspective of electric field distribution, the point structure completely ignores the voltage redistribution effect of the electrode coverage area caused by the existence of the electrode, including the shunt effect caused by the normal current distribution and the voltage redistribution caused by the tangential current flow. The surface structure further considers the normal shunt effect, but ignores the tangential voltage distribution. From the real structure, the point structure ignores the shape and three-dimensional structure of the real electrode, and the surface structure considers the electrode shape, but ignores the three-dimensional structure of the electrode. The model simplification, on the one hand, due to the inherent defects of the model, cannot model the tangential transmission of the electric field, and on the other hand, although the surface structure considers the normal transmission of the electric field, due to the difficulty in modeling the actual conductivity distribution inside the electrode (for example, the uneven conductivity distribution of the electrode-skin contact surface caused by the existence of the paste and the gel), the description of the normal electric field transmission is not accurate enough. SUMMARY

[0005] Therefore, the embodiments of the present application provide a forward problem modeling method, device, electronic equipment and computer readable storage medium to solve the problem that the existing forward problem modeling method is easy to cause model error.

[0006] According to a first aspect, the embodiments of the present application provide a forward problem modeling method, comprising:

[0007] constructing a mathematical equation of electroencephalogram forward problem based on quasi-static Maxwell equation;

[0008] determining a calculation domain, a source domain and a boundary domain of the mathematical equation based on a head structure image, the calculation domain including a head domain and an electrode domain, and the boundary domain including an outer surface of scalp and an outer surface of electrode;

[0009] dividing the head domain into different tissue structures based on segmentation of the head structure image to determine definition domains of different mathematical equations;

[0010] discretizing the head domain based on the segmented tissue structures to obtain a primary head model;

[0011] obtaining a source model based on surface meshing of the cortex, and registering the source model to the primary head model;

[0012] generating electrode meshes corresponding to the electrodes one by one based on the centers and three-dimensional structures of the electrodes, adding structures of the electrode meshes to the primary head model, replacing the outer boundary mesh of the scalp covered by the electrodes in the boundary model with an outer boundary mesh of the electrodes, and forming a secondary head model and a boundary model for final calculation; wherein the boundary model includes two parts: a boundary composed of discretized outer surface of the scalp without electrodes and a boundary composed of discretized outer surface of the electrodes;

[0013] applying the mathematical equation and boundary conditions based on the secondary head model, the source model and the boundary model, and constructing an electroencephalogram forward problem model by using a finite element numerical calculation method.

[0014] In some optional embodiments, the generation of the electrode meshes corresponding to the electrodes one by one based on the centers and three-dimensional structures of the electrodes, and the addition of structures of the electrode meshes to the primary head model, and the replacement of the outer boundary mesh of the scalp covered by the electrodes in the boundary model with an outer boundary mesh of the electrodes to form a secondary head model and a boundary model for final calculation, comprises:

[0015] a. for a single electrode, obtaining a boundary element covered by the electrode on the scalp based on the center and structure of the electrode;

[0016] b. expanding the finite element mesh in the outward normal direction of the boundary element;

[0017] c. supplementing node information and element information of the expanded element mesh to mesh information of the primary head model;

[0018] d. updating boundary information corresponding to the original scalp region to electrode boundary information to complete model updating of the single electrode;

[0019] e. Repeat steps a to d above to iterate through all the electrodes and complete the update of the secondary head model.

[0020] In some optional implementations, the boundary conditions are: the normal current over the entire boundary model is 0, and the potential is the same at the individual electrode boundaries, which can be mathematically described as follows:

[0021]

[0022] u l (x)=U l ,on e l (l = 1, 2, ..., L)

[0023] Where σ represents tissue conductivity and u represents electrical potential. Indicates the entire boundary region, on e l u represents the boundary region corresponding to the l-th electrode. l U represents the potential distribution of the l-th electrode. l e represents the potential value of the l-th electrode. l Let L represent the boundary of the l-th electrode, L represent the number of electrodes, and x represent a coordinate point within the computational domain.

[0024] In some optional implementations, the mathematical equations are:

[0025]

[0026] Among them, J p Let Ω represent the initial current, Ω represent the head model, inΩ represent the entire domain of the head model, and x represent a coordinate point within the computational domain.

[0027] In some optional implementations, the step of applying the mathematical equations and boundary conditions based on the quadratic head model, the source model, and the boundary model, and constructing the EEG forward problem model using the finite element numerical calculation method, includes:

[0028] The mathematical equations are weakened and the calculations are simplified by integration by parts, including:

[0029]

[0030] in, The shape function applied to weaken the equation.

[0031] In some optional implementations, the step of applying the mathematical equations and boundary conditions based on the quadratic head model, the source model, and the boundary model, and constructing the EEG forward problem model using the finite element numerical calculation method, further includes:

[0032] The computational domain is discretized using a hexahedron, and the discretization is represented as follows:

[0033]

[0034] Among them, Ω h U represents the discrete computational domain. h (x) represents the voltage of the discrete head domain, P represents the number of vertices in the discrete computational domain, and v j This represents the voltage at the j-th discrete grid vertex. The shape function representing the j-th discrete grid vertex;

[0035] in, It satisfies the following properties:

[0036] x = (x, y, z)

[0037]

[0038] in,

[0039] a j b j c j d j e j f j g j h j The coefficients of the shape function are represented.

[0040] In some optional implementations, the step of applying the mathematical equations and boundary conditions based on the quadratic head model, the source model, and the boundary model, and constructing the EEG forward problem model using the finite element numerical calculation method, further includes:

[0041] Applying the weakened mathematical equations to the discrete computational domain yields the following discrete domain equations:

[0042]

[0043] Where, v = (v1…υ P Let X represent the voltage at the vertices of P discrete grids, S represent the number of intracranial discharge sources, and X = [X1…X2]. S [] represents the coordinates of S intracranial discharge sources;

[0044] In addition, the boundary conditions should also satisfy the following equation:

[0045]

[0046] in, U represents the potential at the m-th vertex in the l-th electrode domain, where M represents the total number of vertices in the l-th electrode. l This represents the potential value of the l-th electrode, on e l This represents the boundary region corresponding to the l-th electrode.

[0047] In some optional implementations, the method further includes:

[0048] The transmission matrix is ​​calculated as follows:

[0049] L = RB T A -1 G

[0050] in, and And it satisfies:

[0051]

[0052]

[0053]

[0054] Where, j k Let x be the shape function of the source model. i This represents the coordinates of the i-th vertex in the quadratic head model. This represents the coordinates of the m-th vertex of the l-th electrode.

[0055] In some optional implementations, the method further includes:

[0056] Use one of the following methods to process the singularities of the source model: subtraction, Saint-Venant's method, Whitney's method, or partial integration.

[0057] According to a second aspect, embodiments of the present invention provide a forward problem modeling apparatus, comprising:

[0058] The first building module is used to construct mathematical equations for the EEG positive problem based on quasi-static Maxwell equations;

[0059] The first determining module is used to determine the computational domain, source domain, and boundary domain of the mathematical equation based on the head structure image. The computational domain includes the head domain and the electrode domain, and the boundary domain includes the outer surface of the scalp and the outer surface of the electrodes.

[0060] The organization segmentation module is used to divide the head domain into different organizational structures based on the segmentation of the head structure image, so as to determine the domain of definition of different mathematical equations;

[0061] The mesh generation module is used to perform mesh generation based on the segmented organizational structure, discretize the head domain, and obtain a primary head model.

[0062] The registration module is used to obtain a source model based on the surface mesh division of the cortex, and to register the source model to the primary head model;

[0063] The second construction module is used to generate electrode meshes corresponding to the electrodes one by one based on the center and three-dimensional structure of the electrodes, add the structure of the electrode meshes to the primary head model, and replace the outer boundary mesh of the scalp covered by the electrodes in the boundary model with the outer boundary mesh of the electrodes to form the final secondary head model and boundary model for calculation; wherein, the boundary model includes two parts: the boundary composed of the discretized outer surface of the scalp without electrodes and the boundary composed of the discretized outer surface of the electrodes.

[0064] The third construction module is used to construct the EEG positive problem model by applying the mathematical equations and boundary conditions based on the quadratic head model, the source model, and the boundary model, and using the finite element numerical calculation method.

[0065] According to a third aspect, embodiments of the present invention provide an electronic device, comprising:

[0066] The memory and the processor are interconnected, the memory is used to store a computer program, and when the computer program is executed by the processor, it implements any of the positive problem modeling methods described in the first aspect above.

[0067] According to a fourth aspect, embodiments of the present invention provide a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements any of the forward problem modeling methods described in the first aspect.

[0068] This invention proposes a forward problem modeling method based on the description of the three-dimensional structure of electrodes, which mainly includes: (1) description of the physical equation of the forward problem of EEG based on the boundary conditions of the three-dimensional structure of electrodes; (2) finite element construction of the forward problem with the three-dimensional structure of electrodes and the structure of the head; (3) calculation of the conduction matrix. The difference between the forward problem modeling method provided by this invention and the traditional forward problem modeling method that assumes that the electrodes are point structures is that the electrodes are no longer simply described as a point, but are given a specific structure, thereby more accurately describing the electrical signal transmission between the electrodes and the head; the difference between the forward problem modeling method that further optimizes the assumption that the electrodes are surface structures is that the electrodes not only exist as boundary conditions, but are given a specific structure. While constructing the normal current distribution in the electrode coverage area, the tangential current distribution caused by the tangential voltage difference inside the electrodes is further constructed. On the one hand, the model increases the description of the tangential current, making the electric field distribution inside the electrodes more refined. On the other hand, due to the advantage of its three-dimensional structure, it can describe the distribution of conductivity inside the electrodes in more detail and more intuitively, thereby further refining the description of the electric field inside the electrodes. In other words, this forward problem model can describe the conductivity distribution more intuitively and in more detail, and thus can more precisely model a three-dimensional electrode model that can describe the tangential electric field distribution. Furthermore, by incorporating the finite element mesh describing the electrode into the computational domain, it not only improves accuracy but also simplifies the calculation. Attached Figure Description

[0069] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0070] Figure 1 A schematic diagram illustrating the point structure of electrodes in modeling the positive problem of electroencephalography (EEG).

[0071] Figure 2 A schematic diagram illustrating the surface structure of electrodes in modeling the positive problem of electroencephalography (EEG).

[0072] Figure 3 A flowchart illustrating a forward problem modeling method provided in an embodiment of the present invention;

[0073] Figure 4 A schematic diagram illustrating the three-dimensional structure of electrodes in the positive EEG problem modeling provided in this embodiment of the invention;

[0074] Figure 5 This is a schematic diagram of the structure of a forward problem modeling device provided in an embodiment of the present invention;

[0075] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] It should be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. In the following descriptions of embodiments, "a plurality of" means two or more, unless otherwise expressly specified.

[0078] Definition of the noun:

[0079]

[0080]

[0081] Please see Figure 3 This invention provides a method for modeling positive problems, including:

[0082] S101: Constructing mathematical equations for the EEG positive problem based on quasi-static Maxwell equations;

[0083] In this embodiment of the invention, the quasi-static Maxwell equation is used to describe the relationship between intracranial neurogenic discharge and external electromagnetic field;

[0084] S102: Determine the computational domain (i.e., quadratic head domain), source domain, and boundary domain of the mathematical equation based on the head structure image. The computational domain includes the head domain (i.e., primary head domain) and the electrode domain. The boundary domain includes the outer surface of the scalp and the outer surface of the electrodes.

[0085] S103: Based on the segmentation of the head structure image, the head domain is divided into different tissue structures to determine the domain of the different mathematical equations;

[0086] S104: Based on the segmented tissue structure, perform mesh generation, discretize the head domain, and obtain a primary head model;

[0087] In this embodiment of the invention, the head domain is discretized for subsequent numerical solutions. For example, a hexahedral or tetrahedral mesh is used to divide the head domain, forming the head model required for numerical calculation. Since a three-dimensional structure of electrodes needs to be added to the computational domain later, this head model (or head mesh model) is referred to here as a primary head model.

[0088] S105: Obtain the source model based on the surface mesh generation of the cortex, and register the source model to the primary head model;

[0089] In this embodiment of the invention, for finer cortical mesh division, registration with the template coordinate system is involved, and the divided source model should be re-registered to the primary head model;

[0090] S106: Based on the center and three-dimensional structure of the electrodes, generate electrode meshes corresponding to each electrode one by one. Add the structure of the electrode meshes to the primary head model, and replace the outer boundary mesh of the scalp covered by the electrodes in the boundary model with the outer boundary mesh of the electrodes, forming the final secondary head model and boundary model for calculation; wherein, the boundary model includes two parts: a boundary composed of discretized electrode-free scalp outer surface and a boundary composed of discretized electrode outer surfaces; see also Figure 4 A schematic diagram illustrating the three-dimensional structure of the electrodes shown.

[0091] S107: Based on the quadratic head model, the source model, and the boundary model, apply the mathematical equations and boundary conditions, and construct the EEG positive problem model using the finite element numerical calculation method.

[0092] EEG positive problem modeling is based on structural priors such as a real geometric brain model, an intracranial neural source model, and electrode location and model. It constructs a model that infers the distribution of extracranial scalp potentials from intracranial cortical discharges and is an important prerequisite for high spatiotemporal resolution source imaging. This invention proposes a forward problem modeling method based on the description of the three-dimensional structure of electrodes, which mainly includes: (1) mathematical equation description of the EEG forward problem based on the boundary conditions of the three-dimensional structure of electrodes; (2) finite element construction of the forward problem with the three-dimensional structure of electrodes and the structure of the head; (3) calculation of the conduction matrix. The difference between the forward problem modeling method provided by this invention and the traditional point electrode forward problem modeling method is that the electrode is no longer simply described as a point, but is given a specific structure, thereby describing the electrical signal transmission between the electrode and the head. The difference between the forward problem modeling method that further optimizes the assumption that the electrode is a surface structure is that the electrode not only exists as a boundary condition, but is given a specific structure. While constructing the normal current distribution in the electrode coverage area, the tangential current distribution caused by the tangential voltage difference inside the electrode is further constructed. On the one hand, the model increases the description of the tangential current, making the electric field distribution inside the electrode more refined. On the other hand, due to the advantage of its three-dimensional structure, it can describe the distribution of conductivity inside the electrode in more detail and more intuitively, thereby further refining the description of the electric field inside the electrode. In other words, this forward problem model can describe the conductivity distribution more intuitively and in more detail, and thus can more precisely model a three-dimensional electrode model that can describe the tangential electric field distribution. By incorporating the electrode mesh into the computational domain, it not only improves accuracy but also simplifies computation.

[0093] In some specific implementations, the prior construction of brain structure, namely the construction of brain structure model, can be based on brain structure images such as MRI, to segment brain tissue and obtain personalized brain structure and corresponding conductivity.

[0094] In some specific implementations, the electrode mesh corresponding to the center and three-dimensional structure of the electrodes is determined one by one, and the structure of the electrode mesh is added to the primary head model. The outer boundary mesh of the scalp covered by the electrodes in the boundary model is replaced with the outer boundary mesh of the electrodes, forming the final secondary head model and boundary model used for calculation, including:

[0095] a. For a single electrode, obtain the boundary unit covered by the electrode on the scalp based on the center and structure of the electrode (e.g., the radius of the electrode);

[0096] b. Expand the finite element mesh outwards along the normal direction based on the boundary element;

[0097] For example, columnar units can be added outwards by 2mm based on the coverage area;

[0098] c. Add the node and cell information of the expanded cell mesh to the mesh information of the primary head model;

[0099] d. Update the boundary information corresponding to the original scalp region to the electrode boundary information to complete the model update of a single electrode;

[0100] e. Repeat steps a to d above to iterate through all the electrodes and complete the update of the secondary head model.

[0101] In this embodiment of the invention, the electrode model is incorporated into the computational domain and meshed to directly obtain its internal potential distribution in numerical calculations. This process is called secondary head model update. The secondary head model includes: discretized gray matter domain, white matter domain, cerebrospinal fluid domain, skull domain, scalp domain, and electrode domain.

[0102] The boundary domain also changes due to the reconstruction of the computational domain. This boundary domain reconstruction occurs concurrently with the computational domain reconstruction process, as described in step d above. The reconstructed boundary domain is the scalp surface excluding the electrode coverage area and the outer surface of the electrodes.

[0103] The prior construction of the three-dimensional electrode structure is as follows:

[0104] 1) Determine the bottom mesh of the electrode based on the corresponding position and shape of the center of the electrode model, as well as the mesh of the head surface covered by the electrode;

[0105] 2) Construct an electrode thickness matrix based on prior empirical values ​​of electrode thickness. The matrix size depends on the length and width of the outer rectangle of the electrode and the resolution of the head grid. Specifically, the calculation is: length / resolution, width / resolution.

[0106] 3) Construct the electrode mesh based on the bottom surface mesh and thickness matrix. The specific shape of the electrode depends on the shape of the bottom surface mesh and the thickness matrix.

[0107] 4) Incorporate the electrode mesh as a new tissue mesh into the primary head model, apply conductivity, and construct a secondary head model;

[0108] 5) Modify the boundary corresponding to the electrode model.

[0109] In some specific implementations, the boundary conditions are: the normal current over the entire boundary model is 0, and the potential is the same at the individual electrode boundaries. The corresponding mathematical description is:

[0110]

[0111] u l (x)=U l ,on e l (l = 1, 2, ..., L)

[0112] Where σ represents tissue conductivity and u represents electrical potential. Indicates the entire boundary region, on e l u represents the boundary region corresponding to the l-th electrode. l U represents the potential distribution of the l-th electrode. l e represents the potential value of the l-th electrode (a constant for a single electrode). l Let L represent the boundary of the l-th electrode, L represent the number of electrodes, x represent a coordinate point within the computational domain (the entire boundary region), and n represent the outward normal vector perpendicular to the surface.

[0113] In this embodiment of the invention, to describe the three-dimensional structure of the electrode, the boundary is divided as follows: Figure 4 The two parts shown are: 1) the scalp boundary without electrodes ( Figure 4 (dotted lines in the middle); 2) Electrode boundaries ( Figure 4 (Solid lines in the diagram). Since the three-dimensional electrode is a conductor with extremely excellent conductivity, such as silver / gold, its resistivity is negligible. Therefore, the potential at each node on the electrode boundary is the same.

[0114] In some specific implementations, the mathematical equations are:

[0115]

[0116] Among them, J p Let Ω represent the initial current, Ω represent the head model, inΩ represent the entire domain of the head model, and x represent a coordinate point within the computational domain.

[0117] In some specific implementations, the step of constructing an EEG forward problem model based on the quadratic head model, the source model, and the boundary model, applying the mathematical equations and boundary conditions, and using the finite element numerical calculation method includes:

[0118] The mathematical equations are weakened and the calculations are simplified by integration by parts, including:

[0119]

[0120] in, The shape function applied to weaken the equation.

[0121] In some specific implementations, the step of constructing the EEG forward problem model using the finite element numerical calculation method based on the quadratic head model, the source model, and the boundary model, applying the mathematical equations and boundary conditions, further includes:

[0122] The computational domain is discretized using a hexahedron, and the discretization is represented as follows:

[0123]

[0124] Among them, Ω h U represents the discrete computational domain. h (x) represents the voltage of the discrete head domain, P represents the number of vertices in the discrete computational domain, and v j This represents the voltage at the j-th discrete grid vertex. Let represent the shape function of the j-th discrete grid vertex.

[0125] in It satisfies the following properties:

[0126] x = (x, y, z)

[0127]

[0128] in,

[0129] a j b j c j d j e j f j g j h j The coefficients of the shape function are represented by...

[0130] To solve this problem.

[0131] In some specific implementations, the step of constructing the EEG forward problem model using the finite element numerical calculation method based on the quadratic head model, the source model, and the boundary model, applying the mathematical equations and boundary conditions, further includes:

[0132] Applying the weakened mathematical equations to the discrete computational domain yields the following discrete domain equations:

[0133]

[0134] Where P represents the number of vertices in the discrete computational domain, and v = (v1…υ) P X represents the voltage at the vertices of P discrete grids, S represents the number of intracranial discharge sources (the number of vertices in the discrete source domain), and X = [X1…X2]. s [] represents the coordinates of S intracranial discharge sources;

[0135] In addition, the boundary conditions should also satisfy the following equation:

[0136]

[0137] in, U represents the potential at the m-th vertex in the l-th electrode domain, where M represents the total number of vertices in the l-th electrode (note that M varies slightly depending on the electrode). l This represents the potential value of the l-th electrode, on e l This represents the boundary region corresponding to the l-th electrode.

[0138] In some specific implementations, the step of constructing the EEG forward problem model using the finite element numerical calculation method based on the quadratic head model, the source model, and the boundary model, applying the mathematical equations and boundary conditions, further includes:

[0139] The transmission matrix is ​​calculated as follows:

[0140] L = RB T A -1 G

[0141] in, Head And it satisfies:

[0142]

[0143]

[0144]

[0145] Where, j k Let x be the shape function of the source model. i This represents the coordinates of the i-th vertex in the quadratic head model. This represents the coordinates of the m-th vertex of the l-th electrode.

[0146] In some specific implementations, during the process of constructing the EEG positive problem model using the finite element numerical calculation method based on the quadratic head model, the source model, and the boundary model, applying the mathematical equations and boundary conditions, in order to solve the singularities caused by the infinite potential in the source domain, one of the subtraction method, the Saint-Venant method, the Whitney method, and the partial integration method is used to process the singularities of the source model.

[0147] Of course, the methods for eliminating singularities are not limited to the ones mentioned above.

[0148] In addition, to address the problem of large errors caused by insufficient surface smoothness, nodal displacement methods can be used to smooth the nodes on the skin surface and the skull surface; to address the problem of skull current leakage caused by the thin skull layer, nodal displacement, discontinuous Galerkin finite element method and hybrid finite element method can be used for improvement.

[0149] In this embodiment of the invention, since the stiffness matrix A has typical sparsity, symmetry, and positive definiteness, it can be inverted using a direct method or an iterative method. This completes the solution for the transmission matrix.

[0150] The forward problem modeling method provided in this invention can be applied to both adults and infants, greatly improving modeling accuracy.

[0151] Accordingly, please refer to Figure 5 This invention provides a positive problem modeling apparatus, which includes:

[0152] The first building module 601 is used to construct mathematical equations for the EEG positive problem based on quasi-static Maxwell equations;

[0153] The first determining module 602 is used to determine the computational domain, source domain, and boundary domain of the mathematical equation based on the head structure image. The computational domain includes the head domain and the electrode domain, and the boundary domain includes the outer surface of the scalp and the outer surface of the electrodes.

[0154] The organization segmentation module 603 is used to divide the head domain into different organizational structures based on the segmentation of the head structure image, so as to determine the domain of definition of different mathematical equations;

[0155] Mesh generation module 604 is used to perform mesh generation based on the segmented organizational structure, discretize the head domain, and obtain a primary head model;

[0156] Registration module 605 is used to obtain a source model based on surface mesh division of the cortex, and to register the source model to the primary head model;

[0157] The second construction module 606 is used to generate electrode meshes corresponding to the electrodes one by one based on the center and three-dimensional structure of the electrodes, add the structure of the electrode meshes to the primary head model, and replace the outer boundary mesh of the scalp covered by the electrodes in the boundary model with the outer boundary mesh of the electrodes to form the final secondary head model and boundary model for calculation; wherein, the boundary model includes two parts: the boundary composed of the discretized outer surface of the scalp without electrodes and the boundary composed of the discretized outer surface of the electrodes.

[0158] The third construction module 607 is used to construct the EEG positive problem model by applying the mathematical equations and boundary conditions based on the quadratic head model, the source model and the boundary model, and using the finite element numerical calculation method.

[0159] In some alternative implementations, the second building module 606 includes:

[0160] An acquisition unit is configured to, for a single electrode, acquire the boundary unit covered by the electrode on the scalp based on the center and structure of the electrode;

[0161] An expansion unit is used to expand the finite element mesh outwards along the normal direction based on the boundary unit.

[0162] The supplementary unit is used to supplement the node information and cell information of the expanded cell mesh into the mesh information of the primary head model;

[0163] The update unit updates the boundary information corresponding to the original scalp region to the electrode boundary information, thus completing the model update of a single electrode.

[0164] In some optional implementations, the boundary conditions are: the normal current over the entire boundary model is 0, and the potential is the same at the individual electrode boundaries, which can be mathematically described as follows:

[0165]

[0166] u l (x)=U l ,on e l (l=1, 2, ..., L)

[0167] Where σ represents tissue conductivity and u represents electrical potential. Indicates the entire boundary region, on e l u represents the boundary region corresponding to the l-th electrode. l U represents the potential distribution of the l-th electrode. l e represents the potential value of the l-th electrode. l Let L represent the boundary of the l-th electrode, L represent the number of electrodes, and x represent a coordinate point within the computational domain.

[0168] In some optional implementations, the mathematical equations are:

[0169]

[0170] Among them, J p Let Ω represent the initial current, Ω represent the head model, inΩ represent the entire domain of the head model, and x represent a coordinate point within the computational domain.

[0171] In some alternative implementations, the third building module 607 includes:

[0172] A weakening unit, used to weaken the mathematical equations and simplify the calculations through integration by parts, includes:

[0173]

[0174] in, The shape function applied to weaken the equation.

[0175] In some optional implementations, the third building module 607 further includes:

[0176] Discretization unit, used to discretize the computational domain using a hexahedron, wherein the discretization is represented as:

[0177]

[0178] Among them, Ω h U represents the discrete computational domain. h (x) represents the voltage of the discrete head domain, P represents the number of vertices in the discrete computational domain, and v j This represents the voltage at the j-th discrete grid vertex. The shape function representing the j-th discrete grid vertex;

[0179] in, It satisfies the following properties:

[0180] x = (x, y, z)

[0181]

[0182] in,

[0183] a j b j c j d j e j f j g j h j The coefficients of the shape function are represented.

[0184] In some optional implementations, the third building module 607 further includes:

[0185] An application unit is used to apply the weakened mathematical equations to the discrete computational domain, resulting in the following discrete domain equations:

[0186]

[0187] Where, v = (v1…υ P Let X represent the voltage at the vertices of P discrete grids, S represent the number of intracranial discharge sources, and X = [X1…X2]. S [] represents the coordinates of S intracranial discharge sources;

[0188] In addition, the boundary conditions should also satisfy the following equation:

[0189]

[0190] in, U represents the potential at the m-th vertex in the l-th electrode domain, where M represents the total number of vertices in the l-th electrode. l This represents the potential value of the l-th electrode, on e l This represents the boundary region corresponding to the l-th electrode.

[0191] In some optional implementations, the third building module 607 further includes:

[0192] The computational unit is used to calculate the transmission matrix as follows:

[0193] L = RB T A -1 G

[0194] in, Head And it satisfies:

[0195]

[0196]

[0197]

[0198] Where, j k Let x be the shape function of the source model. i This represents the coordinates of the i-th vertex in the quadratic head model. This represents the coordinates of the m-th vertex of the l-th electrode.

[0199] In some optional implementations, the third building module 607 further includes:

[0200] Use one of the following methods to process the singularities of the source model: subtraction, Saint-Venant's method, Whitney's method, or partial integration.

[0201] The embodiments of the present invention are device embodiments based on the same inventive concept as the method embodiments described above. Therefore, for specific technical details and corresponding technical effects, please refer to the method embodiments described above, and they will not be repeated here.

[0202] This invention also provides an electronic device, such as... Figure 6 As shown, the electronic device may include a processor 71 and a memory 72, wherein the processor 71 and the memory 72 can communicate with each other via a bus or other means. Figure 6 Taking the example of a connection between China and Israel via a bus.

[0203] Processor 71 can be a central processing unit (CPU). Processor 71 can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or combinations of the above types of chips.

[0204] Memory 72, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs, and modules, such as the program instructions / modules corresponding to the positive problem modeling method in this embodiment of the invention (e.g., Figure 5 The first building module 601, the first determining module 602, the organization and partitioning module 603, the mesh partitioning module 604, the registration module 605, the second building module 606, and the third building module 607 are shown. The processor 71 executes various functional applications and data processing by running non-transitory software programs, instructions, and modules stored in the memory 72, thereby realizing the forward problem modeling method in the above method embodiments.

[0205] The memory 72 may include a program storage area and a data storage area. The program storage area may store the operating system and applications required for at least one function; the data storage area may store data created by the processor 71, etc. Furthermore, the memory 72 may include high-speed random access memory and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory 72 may optionally include memory remotely located relative to the processor 71, and these remote memories may be connected to the processor 71 via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0206] The one or more modules are stored in the memory 72, and when executed by the processor 71, they perform the following: Figures 3-4 The positive problem modeling method in the illustrated embodiment.

[0207] For specific details regarding the aforementioned electronic devices, please refer to the relevant documentation. Figures 3 to 4 The relevant descriptions and effects in the illustrated embodiments are for understanding purposes only and will not be repeated here.

[0208] Accordingly, this embodiment of the invention also provides a computer-readable storage medium for storing a computer program. When the computer program is executed by a processor, it implements the various processes of the above-described positive problem modeling method embodiment and achieves the same technical effect. To avoid repetition, it will not be described again here.

[0209] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0210] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the apparatus embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0211] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A forward problem modeling method, characterized in that, include: Constructing mathematical equations for the positive EEG problem based on quasi-static Maxwell's equations; The computational domain, source domain, and boundary domain of the mathematical equations are determined based on head structure images. The computational domain includes the head domain and the electrode domain, and the boundary domain includes the outer surface of the scalp and the outer surface of the electrodes. Based on the segmentation of the head structure image, the head domain is divided into different tissue structures to determine the domain of the different mathematical equations; Based on the segmented organizational structure, a mesh is generated, and the head domain is discretized to obtain a primary head model. The source model is obtained by meshing the surface of the cortex, and the source model is registered to the primary head model. Based on the center and three-dimensional structure of the electrodes, the electrode mesh corresponding to each electrode is generated one by one. The structure of the electrode mesh is added to the primary head model, and the outer boundary mesh of the scalp covered by the electrodes in the boundary model is replaced with the outer boundary mesh of the electrodes, forming the final secondary head model and boundary model used for calculation. The boundary model includes two parts: the boundary composed of the discretized outer surface of the scalp without electrodes and the boundary composed of the discretized outer surface of the electrodes. Based on the quadratic head model, the source model, and the boundary model, the mathematical equations and boundary conditions are applied, and the EEG positive problem model is constructed using the finite element numerical calculation method.

2. The method according to claim 1, characterized in that, The electrode-based center and three-dimensional structure are determined one by one, and their corresponding electrode meshes are added to the primary head model. The outer boundary mesh of the scalp covered by the electrodes in the boundary model is replaced with the outer boundary mesh of the electrodes, forming the final secondary head model and boundary model used for calculation, including: a. For a single electrode, based on the center and structure of the electrode, obtain the boundary unit covered by the electrode on the scalp; b. Expand the finite element mesh outwards along the normal direction based on the boundary elements; c. Add the node and cell information of the expanded cell mesh to the mesh information of the primary head model; d. Update the boundary information corresponding to the original scalp region to the electrode boundary information to complete the model update of a single electrode; e. Repeat steps a to d above to iterate through all the electrodes and complete the update of the secondary head model.

3. The method according to claim 2, characterized in that, The boundary conditions are: the normal current over the entire boundary model is 0, and the potential is the same at the individual electrode boundaries. The corresponding mathematical description is: in, , Indicates tissue conductivity. Represents electric potential, Indicates the entire boundary area. Indicates the first The boundary regions corresponding to the electrodes. Indicates the first The potential distribution of the electrodes, Indicates the first The potential value of each of the electrodes, Indicates the first The boundary of each electrode, where L represents the number of electrodes. x This represents a coordinate point within the computational domain.

4. The method according to claim 3, characterized in that, The mathematical equation is: in, Indicates the initial current. Ω This refers to the head model. inΩ This refers to the entire domain of the head model. x This represents a coordinate point within the computational domain.

5. The method according to claim 4, characterized in that, The method of constructing a forward EEG problem model based on the quadratic head model, the source model, and the boundary model, by applying the mathematical equations and boundary conditions and using the finite element numerical calculation method, includes: The mathematical equations are weakened and the calculations are simplified by integration by parts, including: in, The shape function applied to weaken the equation.

6. The method according to claim 5, characterized in that, The method of constructing an EEG forward problem model based on the quadratic head model, the source model, and the boundary model, applying the mathematical equations and boundary conditions, and using the finite element numerical calculation method, further includes: The computational domain is discretized using a hexahedron, and the discretization is represented as follows: in, Represents a discrete computational domain. Let P represent the voltage of the discrete computational domain, and let P represent the number of vertices in the discrete computational domain. Indicates the first Voltage at each discrete grid vertex Indicates the first Shape functions of discrete mesh vertices; in, It satisfies the following properties: , , , , , , , The coefficients of the shape function are represented.

7. The method according to claim 6, characterized in that, The method of constructing an EEG forward problem model based on the quadratic head model, the source model, and the boundary model, applying the mathematical equations and boundary conditions, and using the finite element numerical calculation method, further includes: Applying the weakened mathematical equations to the discrete computational domain yields the following discrete domain equations: in, Let S represent the voltage at the vertices of P discrete grids, and let S represent the number of intracranial discharge sources. Represents the coordinates of S intracranial discharge sources; In addition, the boundary conditions should also satisfy the following equation: in, Indicates the first The potential at the m-th vertex in the n-th electrode domain, M represents the potential at the m-th vertex. Each electrode comprises a total of M vertices. Indicates the first The potential value of each of the electrodes, Indicates the first The boundary regions corresponding to the electrodes.

8. The method according to claim 7, characterized in that, Also includes: The transmission matrix is ​​calculated as follows: in, ,and , i =1,2… L , k =1,2… L ; And satisfy: in, For the shape function of the source model, Represents the second head in the quadratic head model vertex coordinates Indicates the first The first electrode m The coordinates of each vertex.

9. The method according to claim 8, characterized in that, Also includes: Use one of the following methods to process the singularities of the source model: subtraction, Saint-Venant's method, Whitney's method, or partial integration.

10. A forward problem modeling apparatus, characterized in that, include: The first building module is used to construct mathematical equations for the EEG positive problem based on quasi-static Maxwell equations; The first determining module is used to determine the computational domain, source domain, and boundary domain of the mathematical equation based on the head structure image. The computational domain includes the head domain and the electrode domain, and the boundary domain includes the outer surface of the scalp and the outer surface of the electrodes. The organization segmentation module is used to divide the head domain into different organizational structures based on the segmentation of the head structure image, so as to determine the domain of definition of different mathematical equations; The mesh generation module is used to perform mesh generation based on the segmented organizational structure, discretize the head domain, and obtain a primary head model. The registration module is used to obtain a source model based on the surface mesh division of the cortex, and to register the source model to the primary head model; The second construction module is used to generate electrode meshes corresponding to the electrodes one by one based on the center and three-dimensional structure of the electrodes, add the structure of the electrode meshes to the primary head model, and replace the outer boundary mesh of the scalp covered by the electrodes in the boundary model with the outer boundary mesh of the electrodes to form the final secondary head model and boundary model for calculation; wherein, the boundary model includes two parts: the boundary composed of the discretized outer surface of the scalp without electrodes and the boundary composed of the discretized outer surface of the electrodes. The third construction module is used to construct the EEG positive problem model by applying the mathematical equations and boundary conditions based on the quadratic head model, the source model, and the boundary model, and using the finite element numerical calculation method.

11. An electronic device, characterized in that, include: A memory and a processor are interconnected, the memory being used to store a computer program, which, when executed by the processor, implements the forward problem modeling method according to any one of claims 1 to 9.

12. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program, which, when executed by a processor, implements the forward problem modeling method according to any one of claims 1 to 9.

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