A computational system for the propagation and scattering process of electromagnetic waves in the abdomen

Abstract

This invention discloses a computational system for the propagation and scattering of electromagnetic waves in the abdomen, belonging to the field of electromagnetic simulation computation technology. This invention constructs a simplified abdominal anatomical model by precisely configuring electromagnetic-physical parameters, tumor parameters, and PML boundary parameters, which is beneficial for adapting to electromagnetic computation models, balancing computational efficiency and anatomical realism. It generates uniform nodes and incorporates respiratory motion parameters to simulate the dynamic changes of the abdomen under real physiological conditions. It selects appropriate kernel functions based on the characteristics of different tissue layers to improve the targeting and accuracy of electromagnetic field calculations. Using an electromagnetic field calculation module combined with Maxwell's equations and the central difference discretization method, it accurately solves for the electromagnetic field distribution of each tissue layer in the abdomen. It quantifies the energy deposition of each tissue and generates visual reports, triggering timely safety warnings. Finally, an EKF dynamic parameter correction module combined with Kalman filtering corrects node characteristics in real time, improving the accuracy and dynamic adaptability of the simplified abdominal anatomical model parameters.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic simulation calculation technology, and in particular to a calculation system for the propagation and scattering process of electromagnetic waves in the abdomen. Background Technology

[0002] In the field of bioelectromagnetic field simulation, numerical techniques such as the finite element method (FEM), finite difference time-domain method (FDTD), and boundary integral equation (BEM) are widely used, but they have significant limitations. When dealing with the complex geometries of biological tissues, mesh generation is difficult, and frequent mesh updates are required in dynamic simulations of multilayered heterogeneous media, leading to low computational efficiency. FDTD also faces mesh generation challenges and often simplifies tissues to homogeneous models, failing to accurately reflect the true electromagnetic response of layered tissues. While BEM can effectively handle unbounded problems, it is limited in terms of problem scale and support for heterogeneity. These shortcomings restrict simulation accuracy and clinical applicability. Summary of the Invention

[0003] The purpose of this invention is to provide a computational system for the propagation and scattering process of electromagnetic waves in the abdomen, so as to improve the above-mentioned technical problems.

[0004] To achieve the above-mentioned objectives, the embodiments of the present invention provide the following technical solutions:

[0005] A computational system for the propagation and scattering process of electromagnetic waves in the abdomen includes:

[0006] The parameter setting module is used to set electromagnetic-physical parameters; acquire three-dimensional medical image data of the abdomen, determine the tumor region, and set tumor region parameters; the electromagnetic-physical parameters include tissue physical properties, PML boundary parameters, and SAR safety threshold; the PML boundary parameters include boundary thickness and boundary absorption coefficient.

[0007] The simplified abdominal anatomy model construction module is used to set the abdominal electromagnetic parameters and construct a simplified abdominal anatomy model based on the distribution pattern of abdominal organs and PML boundary parameters.

[0008] The node-abdominal breathing model construction module is used to generate multiple nodes and distribute them evenly in the simplified abdominal anatomy model; respiratory motion parameters are set and combined with the simplified abdominal anatomy model to construct an initial abdominal breathing model.

[0009] The EKF dynamic parameter correction module is used to set the observation vector and state vector, calculate the observation error covariance, and combine the Kalman filter method to correct the node characteristics in the initial abdominal breathing model to obtain the abdominal breathing model.

[0010] The RBF kernel function adaptation and matrix construction module is used to select the RBF kernel function and set the RBF kernel function parameters based on the distribution characteristics of each tissue layer in the abdominal breathing model, and construct the corresponding RBF matrix.

[0011] The electromagnetic field calculation module is used to generate the complex permittivity and wavenumber based on the labels of each node; and to solve the RBF coefficients based on the RBF matrix, combined with Maxwell's equations and the central difference discretization method, to generate the electromagnetic fields of different tissue layers in the abdominal breathing model.

[0012] The SAR calculation and early warning module is used to calculate the corresponding SAR based on the electromagnetic fields of different tissue layers in the abdominal respiratory model, generate SAR visual reports, and determine whether to issue a warning.

[0013] This system precisely configures multiple parameters through a parameter setting module to construct a simplified abdominal anatomical model, which is conducive to adapting to electromagnetic calculations while balancing computational efficiency and anatomical realism. It generates uniformly distributed nodes and incorporates respiratory motion parameters to simulate the dynamic changes of the abdomen under real physiological conditions. Relying on RBF kernel functions and RBF matrices, and selecting appropriate kernel functions based on the characteristics of different tissue layers, it enhances the targeting and accuracy of electromagnetic field calculations. Using an electromagnetic field calculation module combined with Maxwell's equations and the central difference discretization method, it accurately solves for the electromagnetic field distribution of each tissue layer in the abdomen. It quantifies the energy deposition of each tissue and generates visual reports, triggering timely safety warnings and providing intuitive evidence for radiation safety management. Furthermore, the EKF dynamic parameter correction module, combined with Kalman filtering, corrects node characteristics in real time, further improving the accuracy and dynamic adaptability of model parameters.

[0014] The processing procedure corresponding to the parameter setting module is as follows:

[0015] Define the tissue physical properties of electromagnetic waves propagating in the abdomen, namely, define the speed of light, tissue density, simulation frequency, vacuum permeability, and vacuum permittivity.

[0016] Based on medical standards, healthcare scenarios, and actual needs, establish SAR safety thresholds;

[0017] Set PML boundary parameters;

[0018] Based on three-dimensional abdominal medical images, the tumor region is determined and tumor region parameters are obtained; the tumor region parameters include the tumor location and its radius and tumor-conductivity.

[0019] In the above scheme, the parameter setting module defines physical properties such as the speed of light and tissue density, providing a rigorous basis for subsequent electromagnetic field calculations such as wavenumber solving and Helmholtz equation construction, ensuring that the simulation conforms to real physical laws. SAR safety thresholds are set according to medical standards and medical scenarios, providing quantitative standards for SAR early warning and avoiding excessive electromagnetic energy deposition that could harm the human body. PML boundary parameters are set based on an anatomical model to eliminate boundary electromagnetic wave reflection interference and improve calculation accuracy. The location, radius, and conductivity of the tumor are determined using 3D images, accurately locating and quantifying the tumor, and improving the accuracy of related electromagnetic analysis.

[0020] Furthermore, the simplified abdominal anatomical model includes a stomach-liver-kidney tissue layer, a muscle tissue layer, a skin tissue layer, an adipose tissue layer, and the outermost PML region.

[0021] The processing procedure corresponding to the node-abdominal breathing model construction module is as follows:

[0022] Multiple nodes are generated along the depth direction of the simplified abdominal anatomy model and evenly distributed in the simplified abdominal anatomy model, covering the tissue layers corresponding to the stomach-liver-kidney, muscle, skin, and fat, as well as the PML region;

[0023] The respiratory motion parameters of the abdomen during breathing are set; the respiratory motion parameters include the translational amplitude of the abdomen along the depth direction, the respiratory rate, and the elastic deformation coefficient.

[0024] Physiological signals are acquired through sensors; based on the physiological signals and respiratory motion parameters, the deformation process of each tissue layer, PML region and tumor region during abdominal breathing is simulated using the finite element method, generating rigid body translation values ​​and elastic deformation, and generating the original model of abdominal breathing.

[0025] Based on the position of the nodes in the original abdominal breathing model, node labels are set and the original abdominal breathing model is updated to obtain the initial abdominal breathing model.

[0026] In the above scheme, nodes are generated uniformly along the depth and cover all tissue layers and PML regions to ensure that no region is missed in subsequent electromagnetic field calculations and to guarantee data integrity. Respiratory motion parameters that fit human physiological characteristics are set, and respiratory deformation is simulated by combining sensor physiological signals and finite element methods. This can realistically restore the dynamic changes of various tissues, PML regions and tumors during abdominal breathing, allowing the abdominal breathing model to break away from static limitations and be closer to the real physiological state of the human body. Different regions are distinguished and updated by node labels to obtain the abdominal breathing model. The layer to which each node belongs can be accurately marked, providing a clear regional basis for subsequent RBF kernel function adaptation, electromagnetic field solution and other processes.

[0027] Furthermore, the processing procedure of the RBF kernel function adaptation and matrix construction module is as follows:

[0028] Based on the characteristics of each tissue layer in the abdominal breathing model and the multilayer perceptron, the RBF kernel function was selected and the corresponding RBF kernel function parameters were set.

[0029] When the tissue layer is adipose tissue, a Gaussian RBF kernel function is selected; when the tissue layer is skin / muscle tissue and not located in blood vessels / stomach-liver-kidney tissue layer, a standard thin-plate spline RBF kernel function is selected; when the tissue layer is muscle tissue and located in blood vessels, the standard thin-plate spline RBF kernel function is modified using a multilayer perceptron (MLP). The coupling effect between the blood vessel wall and blood flow is learned through MLP, and the standard thin-plate spline RBF kernel function is modified based on the coupling effect to obtain the modified standard thin-plate spline RBF kernel function.

[0030] Based on the node labels of each node, the Euclidean distance between any two different nodes in the same organizational layer is calculated. Combined with the selected RBF kernel function, the RBF value is calculated and the RBF matrix is ​​constructed. The RBF value of the same node is set to 0.

[0031] In the above scheme, RBF kernel functions are selected specifically according to the characteristics of each tissue layer. For example, Gaussian kernels are used for the fat layer, and standard thin plate splines are used for the skin / muscle / stomach-liver-kidney layers in non-vascular regions. This can accurately match the electromagnetic properties of different tissues and avoid calculation deviations caused by general kernel functions. For the vascular region of the muscle layer, MLP-corrected kernel functions are used to effectively learn the coupling effect between the blood vessel wall and blood flow, and solve the problem of electromagnetic response distortion in this special region. The Euclidean distance of the same layer is calculated based on the node labels and an RBF matrix is ​​constructed (the RBF value of the same node is set to 0) to ensure the rationality and specificity of the matrix construction.

[0032] Furthermore, the processing procedure corresponding to the electromagnetic field calculation module is as follows:

[0033] Based on node labels, the complex permittivity of different tissue layers in the abdominal breathing model is calculated, and the wavenumber of each node is calculated by combining Maxwell's equations.

[0034] Based on the complex permittivity and wavenumber, the Helmholtz equations containing only the electric field are obtained by using Maxwell's equations and through rotation operations; based on the Helmholtz equations, continuous differential equations for different tissue layers in the abdominal breathing model are generated.

[0035] Based on the continuous differential equation and combined with the spatial distribution of nodes in the abdominal breathing model, the second derivative of the electric field is discretized by the central difference method to obtain the second-order sparse differential matrix, coefficient matrix and excitation vector.

[0036] Based on the coefficient matrix and the excitation vector, a system of linear equations is constructed and solved to obtain the RBF coefficients of each node;

[0037] Based on the RBF matrix and RBF coefficients, the electric field amplitude of different nodes is calculated, and the magnetic field amplitude of different nodes is determined by combining the wave impedance of different nodes, thus generating the electromagnetic field of different tissue layers in the abdominal breathing model.

[0038] In the above scheme, calculating the complex permittivity and wavenumber based on node labels allows for precise matching of parameters to the characteristics of each tissue layer. By deriving the Helmholtz equations and continuous differential equations involving the electric field from Maxwell's equations, the complex electromagnetic problem is transformed into a computable mathematical model, simplifying the solution logic. Central difference discretization is used to process the second derivative of the electric field, ensuring computational accuracy while improving computational efficiency by generating a sparse matrix. Solving for the RBF coefficients and combining them with the RBF matrix to calculate the electric and magnetic field amplitudes allows for the accurate generation of the electromagnetic field distribution for each tissue layer, providing reliable electromagnetic data for subsequent SAR calculations and safety early warning modules, ensuring the accuracy of radiation safety management.

[0039] Furthermore, the calculation of the wavenumber of each node includes:

[0040] Perform complex coordinate transformation on the nodes in the PML region, and calculate the mean of the relative permittivity and conductivity around the PML region to generate the complex permittivity of the PML region;

[0041] Based on the node labels of each organizational layer, the corresponding relative permittivity and conductivity are called to generate the complex permittivity of each organizational layer;

[0042] The wavenumber is calculated based on the complex permittivity of each node.

[0043] In the above scheme, the complex coordinate transformation of the PML region nodes and the generation of their complex permittivity by combining the mean of the surrounding medium parameters can accurately meet the functional requirements of PML to eliminate electromagnetic wave reflection at the boundary and avoid the boundary effect from interfering with the electromagnetic field calculation results. The generation of complex permittivity by calling the corresponding parameters of each tissue layer based on the node label can ensure that the complex permittivity is accurately matched with the real electromagnetic properties of different tissue layers such as skin and fat, which meets the requirements of anatomical authenticity.

[0044] Further, obtaining the second-order sparse differential matrix, coefficient matrix, and activation vector includes:

[0045] Based on the spatial distribution of nodes in the abdominal breathing model, the spacing between adjacent nodes is calculated; the average step size is set according to the spacing.

[0046] Based on the spatial distribution characteristics and average step size of the electromagnetic field, the second derivative of each node is discretized using the central difference method to obtain a second-order sparse differential matrix; based on the second-order sparse differential matrix and the wavenumber, the initial coefficient matrix is ​​calculated.

[0047] Set the excitation conditions and select a node as the excitation node; determine the initial excitation vector based on the excitation node, and adjust the initial coefficient matrix and the initial excitation vector in combination with the PML boundary parameters to obtain the coefficient matrix and the excitation vector.

[0048] In the above scheme, the sparsity property is used to significantly reduce data storage and computation, improve computational efficiency, and ensure the computational accuracy of micro-dispersion. The initial coefficient matrix is ​​calculated by combining wavenumber, so that the matrix incorporates the electromagnetic propagation characteristics of each node, which conforms to the real physical laws. The initial excitation vector is determined by selecting excitation nodes and combined with the adjustment of PML boundary parameters, which can simulate the real incident scene of electromagnetic waves, while eliminating boundary reflection interference, ensuring that the final coefficient matrix and excitation vector are both adapted to the dynamic boundary of the model and can accurately reflect the initial conditions of electromagnetic propagation. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a system structure diagram in an embodiment of the present invention;

[0051] Figure 2 This is a schematic cross-sectional view of the distribution of abdominal organs in an embodiment of the present invention;

[0052] Figure 3 This is a structural diagram of a four-layer parallel flat plate medium model in an embodiment of the present invention;

[0053] Figure 4 This is a bar chart showing the SAR peak value and mean value generated at different locations on the human abdomen at a frequency of 433MHz in an embodiment of the present invention.

[0054] Figure 5 This is a bar chart showing the peak and mean SAR values ​​generated at different locations on the human abdomen at a frequency of 1.4 GHz in an embodiment of the present invention. Detailed Implementation

[0055] 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, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0056] Please see Figure 1 This embodiment provides a calculation system for the propagation and scattering process of electromagnetic waves in the abdomen. Figure 1 The system shown can be a software and / or hardware device. The implementing entity of this application can include, but is not limited to, at least one of the following: user equipment, network equipment, etc. User equipment can include, but is not limited to, computers, smartphones, personal digital assistants (PDAs), and the aforementioned electronic devices. Network equipment can include, but is not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of computers or network servers. Cloud computing is a type of distributed computing, consisting of a super virtual computer composed of a group of loosely coupled computers. This embodiment does not impose any limitations on this.

[0057] like Figure 1 As shown, a computational system for the propagation and scattering process of electromagnetic waves in the abdomen includes:

[0058] The parameter setting module is used to set electromagnetic-physical parameters; acquire three-dimensional medical image data of the abdomen, determine the tumor region, and set tumor region parameters; the electromagnetic-physical parameters include tissue physical properties, PML boundary parameters, and SAR safety thresholds; the tumor region parameters include tumor location and its radius, and tumor-conductivity.

[0059] The processing procedure corresponding to the parameter setting module is as follows:

[0060] S11. Define the tissue physical properties of electromagnetic waves propagating in the abdomen, namely, define the speed of light, tissue density, simulation frequency, vacuum permeability, and vacuum dielectric constant.

[0061] S12. Based on medical standards, medical scenarios, and actual needs, establish SAR safety thresholds; when the subsequently calculated SAR exceeds the SAR safety threshold, a safety alarm is triggered.

[0062] S13. Set PML boundary parameters; the PML boundary parameters include boundary thickness and boundary absorption coefficient.

[0063] Specifically, the PML (Perfect Match Layer) boundary parameters are used to eliminate reflections in the simplified abdominal anatomical model, and a perfect match layer is added around the model. Within the perfect match layer, after setting the nodes, the coordinates of the nodes in the absorption layer are calculated according to the PML coordinate transformation formula. The corresponding formula is:

[0064] ;

[0065] ;

[0066] ;

[0067] , , These represent the three-dimensional coordinates of the node in the absorption layer. , , These represent the three-dimensional coordinates of the node in its actual coordinate system. Represents the imaginary unit. , , These represent the boundary absorption coefficients of the corresponding coordinate axes in the actual coordinate system. , , These represent the distances between adjacent nodes in the PML region along the corresponding coordinate axis directions. , These represent the vacuum permittivity and angular frequency, respectively.

[0068] S14. Based on three-dimensional abdominal medical images, determine the tumor region, obtain the tumor location and its radius, and set the tumor-conductivity.

[0069] Specifically, a 3D model is created from the abdominal 3D medical image to determine 3D nodes. The tumor region and its center point are then determined using these 3D nodes, and the tumor location is determined based on a preset tumor radius. In this embodiment, the tumor is located in the liver. Corresponding tumor-conductivity values ​​are assigned to the 3D nodes within the tumor region.

[0070] The abdominal anatomy simplified model construction module is used to set the abdominal electromagnetic parameters and construct a simplified abdominal anatomy model based on the distribution pattern of abdominal organs and PML boundary parameters. The distribution pattern of abdominal organs refers to the positional relationship of organs (biological tissues) such as liver, kidney, muscle, skin and fat in the abdomen.

[0071] Specifically, this involves acquiring three-dimensional medical imaging data of the abdomen and performing three-dimensional imaging to obtain raw data in formats such as DICOM containing organ spatial information; for example... Figure 2 As shown, and combined with the distribution patterns of abdominal organs (e.g., the liver is located in the right upper quadrant, the stomach in the left upper quadrant, etc.), the image is denoised and the target organs are segmented. Redundant details such as microvessels are removed, while the core morphology and positional relationships of the organs are preserved, constructing a four-layer parallel flat plate media model. Then, a perfectly matched layer (PML region) is set based on PML boundary parameters and placed around the four-layer parallel flat plate media model, finally assembling into an initial simplified abdominal anatomical model. The four-layer parallel flat plate media model is divided into four tissue layers, corresponding to the stomach-liver-kidney tissue layer, muscle tissue layer, skin tissue layer, and adipose tissue layer, respectively. Figure 3 As shown, each tissue layer is arranged along the vertical direction (Z-axis) of the media model.

[0072] Based on the electromagnetic response characteristics of biological tissues in electromagnetic fields and combined with relevant data on abdominal organs, the abdominal electromagnetic parameters (basic dielectric constant and interlayer parameters) of various biological tissues in the abdomen were set. According to the basic dielectric constant and interlayer parameters, the initial simplified abdominal anatomical model was adjusted to obtain a simplified abdominal anatomical model. At this point, the simplified abdominal anatomical model not only includes the stomach-liver-kidney tissue layer, muscle tissue layer, skin tissue layer, and adipose tissue layer, but also has an outermost PML region set according to the PML boundary parameters.

[0073] The fundamental dielectric constant includes the relative dielectric constant and permeability for the stomach-liver-kidney, muscle, skin, and fat layers. Interlayer parameters include total layer thickness, interlayer extent, and the layer thickness of each tissue layer; the interlayer extent is:

[0074] ;

[0075] ;

[0076] in, , , , These represent the thicknesses of the stomach-liver-kidney tissue layer, muscle tissue layer, skin tissue layer, and adipose tissue layer, respectively. , , , These represent the coordinates of the tissue layers corresponding to the stomach-liver-kidney tissue layer, muscle tissue layer, skin tissue layer, and adipose tissue layer, respectively. Indicates the total layer thickness.

[0077] According to the formula:

[0078] ;

[0079] ;

[0080] Calculate the relative permittivity and permeability ;in, Indicates the first The real part of the relative permittivity of each tissue layer. Indicates the first The electrical conductivity of each tissue layer Indicates the first The real part of the permeability of each tissue layer Indicates the first The magnetic permeability of each tissue layer is related to its electrical conductivity. Indicates the first The permeability loss related terms of each tissue layer. Among them, The value range is [1, 4], when When the numbers are 1, 2, 3, and 4, the tissue layers are respectively the stomach-liver-kidney tissue layer, muscle tissue layer, skin tissue layer, and adipose tissue layer.

[0081] The node-abdominal breathing model construction module is used to generate multiple nodes and distribute them evenly in the simplified abdominal anatomy model; respiratory motion parameters are set and combined with the simplified abdominal anatomy model to construct an initial abdominal breathing model.

[0082] The processing procedure corresponding to the node-abdominal breathing model construction module is as follows:

[0083] S31. Generate multiple nodes along the depth direction of the simplified abdominal anatomical model. They are evenly distributed throughout the simplified abdominal anatomical model, covering the tissue layers corresponding to the stomach-liver-kidney, muscle, skin, and fat, as well as the PML region; among which, Indicates the first 1 node express Coordinates in a simplified model of abdominal anatomy This represents the total number of nodes.

[0084] S32. Set the respiratory motion parameters of the abdomen during breathing; the respiratory motion parameters include the translational amplitude of the abdomen along the depth direction, the breathing frequency, and the elastic deformation coefficient.

[0085] Specifically, the translational range of the abdomen along the depth direction needs to be determined by referring to the physiological range of abdominal movement during normal human breathing (e.g., approximately 1-3 cm vertical movement during calm breathing and approximately 3-5 cm during deep breathing), combined with simulation scenarios (e.g., routine electromagnetic detection or specific medical procedures), to ensure that the abdominal displacement range under real breathing conditions is covered. Among these:

[0086] For respiratory rate, based on human physiological standards (the resting respiratory rate of an adult is about 12-20 breaths / minute), the middle value of this range (such as 15 breaths / minute) can be directly adopted, or it can be adjusted according to the physiological characteristics of the simulation subjects (such as children and the elderly) to match the real respiratory rhythm.

[0087] For the elastic deformation coefficient, the biomechanical properties of different tissue layers in the abdomen (such as skin, fat, muscle, and internal organs) can be used as a basis. For example, the elastic coefficient of skin is approximately 1-2 MPa, and that of fat is approximately 0.1-0.5 MPa. Since the elastic differences between different tissues (such as muscle and fat) directly affect the degree of deformation during respiration, basic elastic parameters for each layer are obtained from medical literature or biological tissue mechanics databases. These parameters are then combined with the laws governing the coordinated deformation of tissues during respiration to set the corresponding elastic deformation coefficient for each region. This ensures the simulation of the deformation differences of different tissues during respiration. Therefore, by setting the elastic deformation coefficient according to the biomechanical properties of different tissues, the model accurately simulates the dynamic changes of biological tissues.

[0088] Respiratory motion parameters need to closely match the normal physiological characteristics of human respiration (such as frequency and displacement amplitude) to avoid model distortion due to deviations from the actual physiological range, ensuring that the simulation results reflect the electromagnetic wave conduction and scattering patterns in the actual human body. Parameter details should be adjusted according to the simulated medical scenario (such as electromagnetic tumor therapy or radiation safety assessment) (e.g., parameters under deep breathing conditions may need to be considered in treatment scenarios) to ensure that parameter settings are consistent with actual application requirements and enhance the clinical reference value of the simulation results.

[0089] S33. Obtain physiological signals through sensors; based on the physiological signals and respiratory motion parameters, simulate the deformation process of each tissue layer, PML region and tumor region during abdominal breathing using the finite element method, generate rigid body translation values ​​and elastic deformation, and generate the original model of abdominal breathing.

[0090] Specifically, physiological signals during abdominal breathing are acquired through sensors (such as pressure sensors for monitoring respiratory movements, and electrocardiogram / respiratory sensors for recording physiological rhythms). These signals can directly reflect the dynamic activity characteristics of the abdomen during breathing.

[0091] Physiological signals are correlated and matched with pre-set respiratory motion parameters to clarify the intensity, rhythm, and basic deformation properties of different tissues. The physiological signals are filtered, denoised, and feature-extracted to obtain key features such as signal amplitude and period. These features are then correlated and matched with the pre-set respiratory motion parameters. The respiratory motion intensity (serving as a benchmark for the overall rigid body translational displacement) is determined by the correspondence between signal amplitude and pre-set respiratory displacement amplitude parameters. The respiratory rhythm is clarified by the correspondence between signal period and respiratory frequency parameters. Simultaneously, based on the pre-set basic deformation properties of different tissues and the respiratory state reflected by the current respiratory physiological signals, the basic degree of elastic deformation of each tissue layer under this respiratory state is quantified. This provides a precise quantitative basis for subsequent finite element simulations of the rigid body translational values ​​and elastic deformation of each region.

[0092] Based on the fundamental properties and degree of deformation, the finite element method (FEM) was used to simulate the respiratory deformation process of each tissue layer (stomach-liver-kidney layer, muscle layer, skin layer, and adipose tissue layer), PML region, and tumor region in a simplified abdominal anatomical model. By dividing the model into finite element meshes, the motion state of each mesh element under respiratory force was calculated, thereby generating rigid body translational values ​​(overall displacement) and elastic deformation (local deformation degree) for each region. Integrating the rigid body translational values ​​and elastic deformation of each region, the structural morphology of the simplified abdominal anatomical model was updated, resulting in an original abdominal respiratory model that reflects the dynamic changes of respiration, ensuring the accuracy of the computational basis. By driving deformation simulation with real physiological signals, the original abdominal respiratory model can reproduce the actual dynamic changes of various tissues (including tumors) during human respiration, avoiding deviations between the static model and the actual physiological state. This provides a model basis that closely matches the human body for subsequent electromagnetic field calculations, reducing electromagnetic calculation errors caused by model distortion.

[0093] Therefore, this invention can accurately recreate the dynamic electromagnetic environment and improve calculation accuracy. Respiration causes changes in the position, shape, and relative relationships of abdominal tissues, which in turn affects the propagation and scattering paths of electromagnetic waves in the abdomen. The original abdominal breathing model can simulate respiratory deformation to recreate the electromagnetic propagation environment under respiratory conditions, enabling subsequent electromagnetic field calculations (such as electromagnetic field distribution in each tissue layer and SAR value calculation) to accurately match the electromagnetic characteristics under real physiological scenarios, thereby improving the reliability of the calculation results.

[0094] Furthermore, this invention covers key areas to ensure computational integrity. The simulation process of the original abdominal breathing model encompasses the deformation of each tissue layer, the PML region, and the tumor region (the core area of ​​concern). This ensures that during subsequent electromagnetic calculations, the dynamic characteristics of the main tissue medium for electromagnetic wave propagation, the PML region used to eliminate boundary reflections, and the tumor region of clinical focus are all included in the calculation scope. This avoids computational loopholes caused by missing deformation in key areas, thus guaranteeing the integrity and comprehensiveness of electromagnetic calculations.

[0095] S34. Based on the position of the node in the original abdominal breathing model, set the node label and update the original abdominal breathing model to obtain the initial abdominal breathing model.

[0096] Specifically, the PML is divided into an upper PML region and a lower PML region. A node in the lower PML region has a label of 0; a node in the upper PML region has a label of 1. A node in the skin tissue layer has a label of 2. A node in the adipose tissue layer has a label of 3. A node in the muscle tissue layer but not in a blood vessel has a label of 4. A node in the stomach-liver-kidney tissue layer but not within a tumor region has a label of 5. A node in the stomach-liver-kidney tissue layer and within a tumor region has a label of 6. A node in the muscle tissue layer and within a blood vessel has a label of 7.

[0097] The EKF dynamic parameter correction module is used to set the observation vector and state vector, calculate the observation error covariance, and correct the nodal characteristics in the initial abdominal breathing model using the Kalman filtering method.

[0098] The processing procedure of the EKF dynamic parameter correction module is as follows:

[0099] S41. Determine the simulation parameters and acquire multi-source sensor data, which will be used as the state vector and observation vector, respectively. Specifically, the relative permittivity and conductivity of each tissue layer in the initial abdominal breathing model will be used as the state vector. The corresponding expression is:

[0100] ;

[0101] Indicates the current moment. , These represent the relative permittivity and conductivity of the skin tissue layer, respectively. , Representing the relative permittivity and conductivity of the adipose tissue layer, respectively. , These represent the relative permittivity and conductivity of the muscle tissue layer, respectively. , These represent the relative permittivity and conductivity of the stomach-liver-kidney tissue layers, respectively. This represents the transpose of the matrix.

[0102] Multi-source sensor data, including wave time markers, ultrasonic morphological characteristic values, real-time temperature, and measurement impedance, are set as observation vectors. The corresponding expression is:

[0103] ;

[0104] Indicates the wave time marker, Indicates the morphological characteristic value of ultrasound. Indicates real-time temperature. This indicates the measured impedance.

[0105] S42. Based on the correlation between the dielectric properties of the state vector and multi-source sensor data (physiological signals), establish a nonlinear transition model and calculate the state vector and prediction error covariance at the next moment.

[0106] The formula corresponding to the nonlinear transfer model is:

[0107] ;

[0108] in, Represents a nonlinear transfer function. This represents the state vector at the next moment. This represents the state vector from the previous time step. This represents the control quantity at the previous moment.

[0109] Prediction error covariance The corresponding formula is:

[0110] ;

[0111] in, , Let Jacobian matrix and transpose of the transition function be represented respectively. This represents the error covariance at the previous time step. This represents the process noise covariance; in practical applications, it is set based on sensor accuracy. .

[0112] S43. Based on the observation vector, prediction error covariance, and the state vector at the next time step, calculate the observation vector and observation error covariance at the next time step using the observation function.

[0113] Specifically, according to the formula:

[0114] ;

[0115] Calculate the Jacobian matrix of the observation function. . This represents the matrix of first-order partial derivatives of the observation function at the predicted state. This represents the state vector.

[0116] In this embodiment, The dimensions are observation vector dimension m1 × state vector dimension n1. m1=4 (4 observation components), n1=8 (dielectric constant and conductivity of skin / fat / muscle / stomach-liver-kidney, a total of 4 layers × 2 parameters).

[0117] The observation vector at the next moment The corresponding formula is:

[0118] ;

[0119] in, This represents the observation function.

[0120] Observation error covariance The corresponding formula is:

[0121] ;

[0122] in, , Let Jacobian matrix and its transpose represent the observation function, respectively. This represents the observation noise covariance.

[0123] S44. Based on the observation vector and observation error covariance at the next time step, calculate the Kalman gain, update the state vector and prediction error covariance at the next time step, and use the updated state vector at the next time step as the optimal state vector.

[0124] Kalman gain The corresponding formula is:

[0125] .

[0126] The formulas for updating the state vector and prediction error covariance at the next time step are:

[0127] ;

[0128] ;

[0129] in, This represents the updated prediction error covariance. This represents the updated state vector for the next time step. Represents the identity matrix.

[0130] S45. Determine whether there are outliers in the observation vector at the next time step through residual test. If there are outliers, remove them to obtain the updated observation vector at the next time step, which will be used for the next update of the state vector.

[0131] The expression for the residual test is:

[0132] ;

[0133] in, , Let them represent the residual matrix and its transpose, respectively. Degrees of freedom are represented by the dimension of the observation vector. The chi-square distribution.

[0134] S46. Based on the optimal state vector and combined with Maxwell's equations, establish the temperature response model of each tissue layer in the initial abdominal breathing model, and adjust the nodal characteristics (relative permittivity and conductivity) of each tissue layer in the initial abdominal breathing model.

[0135] Specifically, relevant literature was collected, and a temperature response model was constructed based on the optimal state vector. Taking muscle and stomach-liver-kidney as examples, the corresponding temperature response model is as follows:

[0136] ;

[0137] ;

[0138] ;

[0139] ;

[0140] in, The real-time temperature is collected by a fiber optic sensor. , Let represent the relative permittivity of the muscle tissue layer at real-time temperature and the relative permittivity of the optimal state vector, respectively. , Let represent the electrical conductivity of the muscle tissue layer at real-time temperature and the electrical conductivity of the optimal state vector, respectively. , Let represent the conductivity of the stomach-liver-kidney tissue layer at real-time temperature and the conductivity of the optimal state vector, respectively. , Let represent the relative permittivity of the stomach-liver-kidney tissue layers at real-time temperature and the relative permittivity of the optimal state vector, respectively.

[0141] The real-time temperature is measured by a fiber optic sensor and input into the corresponding temperature response model. The electromagnetic field distribution of Maxwell's equations is solved using the collocation method of local radial basis functions. The influence of the electromagnetic field distribution is analyzed by adjusting the relative permittivity and conductivity of each tissue layer.

[0142] The tissue state of each tissue layer is acquired, and the relative permittivity and conductivity of the corresponding tissue layer are adjusted accordingly. For example, if the tissue state of the stomach-liver-kidney tissue layer is that the stomach is full, ultrasound is used to determine whether there is fluid in the stomach. If so, the corresponding dielectric parameter group is switched; otherwise, the original relative permittivity and conductivity are retained. If the tissue state of the tumor area is that of tumor necrosis, the current temperature of the tumor area is detected. If the current temperature is >50°C and the duration is >10s, the relative permittivity and conductivity of the tumor area are reduced by 30%–50% (reducing ion concentration) to avoid overestimating energy absorption.

[0143] The adjusted node characteristics output by the EKF dynamic parameter correction module are applied to the initial abdominal breathing model to obtain the abdominal breathing model, which is beneficial for subsequent electromagnetic field calculations.

[0144] The RBF kernel function adaptation and matrix construction module is used to select the RBF kernel function and set the RBF kernel function parameters based on the distribution characteristics of each tissue layer in the abdominal breathing model, and construct the corresponding RBF matrix.

[0145] The processing procedure of the RBF kernel function adaptation and matrix construction module is as follows:

[0146] S51. Based on the characteristics of each tissue layer in the abdominal breathing model and the multilayer perceptron, select the RBF kernel function and set the corresponding RBF kernel function parameters.

[0147] Specifically, the RBF kernel function is a distance-based interpolation or approximation function. Its core idea is to construct global or local basis functions using the spatial distance between nodes. When the tissue layer is adipose tissue, it is a region with low dielectric constant, and the smoothing properties of the Gaussian RBF kernel function are suitable for this region; therefore, the Gaussian RBF kernel function is chosen. The formula for the Gaussian RBF kernel function is:

[0148] ;

[0149] in, This represents a Gaussian RBF kernel function. Represents the natural constant. , These represent the shape parameter and the Euclidean distance, respectively.

[0150] When the tissue layer is the skin or muscle tissue layer and is not located within blood vessels or the stomach-liver-kidney tissue layer, the standard thin-plate spline RBF kernel function is selected. The standard thin-plate spline (RBF) kernel function balances global smoothness with local interpolation accuracy. It can smoothly reflect the gradual changes in electromagnetic parameters (such as dielectric constant and conductivity) within tissue layers through global correlation, while capturing subtle differences in electromagnetic response within tissue layers through local interpolation. The skin, muscle (non-vascular), and stomach-liver-kidney tissue layers belong to regions in abdominal anatomy where "electromagnetic properties are relatively uniform and gradually changing, without significant local abrupt changes" (avoiding drastic fluctuations in local dielectric constant caused by blood vessels). These regions precisely meet the requirement of a kernel function that simultaneously satisfies global smooth fitting and local detail preservation. The characteristics of the standard thin-plate spline kernel function perfectly match this requirement, thus the standard thin-plate spline (RBF) kernel function was chosen.

[0151] When the tissue layer is muscle tissue and located within a blood vessel, a multilayer perceptron (MLP) is used to correct the standard thin-plate spline RBF kernel function. Because the electromagnetic properties of the vascular region differ fundamentally from those of ordinary muscle tissue, the standard thin-plate spline RBF kernel function cannot accurately characterize this difference. The core reason for this is:

[0152] Because the dielectric constant and conductivity of ordinary muscle tissue exhibit a continuous and gradual change, while the vascular region contains two media—the vessel wall (high dielectric, low conductivity) and the blood flow (low dielectric, high conductivity)—the electromagnetic parameters of these two media differ significantly. This leads to unique responses in the vascular region, such as enhanced reflection and refraction and abrupt energy loss, resulting in drastic local abrupt changes in the electromagnetic properties of the vascular region. However, the "global smooth fitting" characteristic of the standard thin-plate spline kernel function cannot capture these drastic local changes, easily leading to distortion in electromagnetic field calculations.

[0153] Furthermore, the blood vessel wall and blood flow are not independent entities; rather, they are subject to an electromagnetic-fluid coupling effect (the dynamic flow of blood slightly alters the dielectric properties of the blood vessel wall), and the electromagnetic response of the blood vessel wall also affects the charge distribution in the blood flow. This coupling effect further alters the local electromagnetic field distribution. However, standard thin-plate spline kernel functions are fixed-form mathematical functions and cannot adaptively learn this dynamic and complex coupling relationship. Therefore, the learning capabilities of MLPs are needed to model this coupling effect.

[0154] The coupling effect between the vessel wall and blood flow is learned through MLP, and the standard thin-plate spline RBF kernel function is modified based on this coupling effect. Therefore, the modified standard thin-plate spline RBF kernel function... This can improve the accuracy of local field distribution; the corresponding formula is:

[0155] ;

[0156] in, This indicates MLP.

[0157] The MLP correction process is divided into three core stages: "data preparation - model training - kernel function correction". The specific steps are as follows:

[0158] First, construct the training dataset (input data and label data). The input data consists of two parts: one is the basic information of the nodes in the vascular region (such as the Euclidean distance between nodes). Corresponding standard thin plate spline kernel function value Secondly, the actual physical characteristics of the vascular region (such as vessel diameter, blood flow velocity, and dielectric constant and conductivity of the vessel wall / blood flow). Label data is obtained through high-precision electromagnetic simulation tools (such as COMSOL) or clinical testing equipment, capturing the actual electromagnetic field distribution data of the vascular region (such as nodal electric field amplitude and magnetic field amplitude), which serves as the "target label" for MLP training—that is, the ideal electromagnetic response that the kernel function should match after MLP correction.

[0159] Secondly, the MLP is trained on a training dataset, enabling it to learn coupling effects. An MLP architecture (input layer - hidden layer - output layer) is constructed, with the input layer receiving... The hidden layers consist of 2-3 layers (16-32 neurons per layer) to fit nonlinear coupling relationships. The output layer outputs preliminary results, such as correction coefficients or corrected kernel function values. The training dataset is divided into training and validation sets. The error (e.g., mean square error, MSE) between the electromagnetic field distribution corresponding to the kernel function output by the MLP and the true label (measured / high-precision simulated electromagnetic field distribution) is used as the loss function. The weights and biases of the MLP are iteratively optimized using the backpropagation algorithm.

[0160] During training, the MLP autonomously captures patterns (coupling effects) such as "changes in blood flow velocity → alterations in the dielectric properties of the blood vessel wall → enhanced electromagnetic field reflection" and "increased blood vessel diameter → expanded coupling effect range → shift in local field strength peak." These coupling effects are then transformed into weight parameters within the MLP model, achieving implicit modeling of the coupling relationships.

[0161] Finally, the kernel function is modified using MLP to generate a kernel function adapted to the vascular region. In actual electromagnetic calculations, when encountering a node in the muscle tissue layer that is located within a blood vessel, the Euclidean distance between that node and its neighboring nodes is first calculated. Substituting into the standard thin-plate spline kernel function yields MLP output correction results: The MLP is trained by inputting real-time physical parameters of the blood vessel region (such as current blood flow velocity, which can be obtained through sensors), and the MLP outputs the corrected kernel function value. Incorporate into subsequent calculations: using the formula:

[0162] ;

[0163] Calculate the mean relative permittivity of the tissue surrounding the PML region. It is used to replace the standard kernel function value and participate in the construction of the RBF matrix of the vascular region. In the subsequent electromagnetic field solution, it accurately reflects the coupling effect between the blood vessel wall and blood flow, improves the calculation accuracy of the electric and magnetic field distribution in the region, and ultimately ensures the accuracy of the SAR value calculation. Indicates the first The volume of adjacent tissue units, Indicates electrical conductivity. Represents the complex permittivity. This represents the real part of the relative permittivity. This indicates the total number of adjacent organizational units.

[0164] S52. Based on the node labels of each node, calculate the Euclidean distance between any two different nodes in the same organizational layer, combine the selected RBF kernel function to calculate the RBF value, and construct the RBF matrix; wherein, the RBF value of the same node is set to 0.

[0165] For example, when both nodes are located in the adipose tissue layer, the RBF value is calculated using a Gaussian RBF kernel function. If both nodes are located in the skin tissue layer, the RBF value is calculated using a standard thin-plate spline RBF kernel function. This ensures that the RBF kernel function calculates RBF values ​​between different tissue layers in the abdominal breathing model, and calculating RBF values ​​by region is beneficial for accurate SAR value calculation. It should be noted that in S52, the processing object is nodes located in the same tissue layer.

[0166] The electromagnetic field calculation module is used to generate the complex permittivity and wavenumber based on the labels of each node; and to solve the RBF coefficients based on the RBF matrix, combined with Maxwell's equations and the central difference discretization method, to generate the electromagnetic fields of different tissue layers in the abdominal breathing model.

[0167] The processing procedure corresponding to the electromagnetic field calculation module is as follows:

[0168] S61. Based on node labels, calculate the complex permittivity of different tissue layers in the abdominal breathing model, and combine Maxwell's equations to calculate the wavenumber of each node.

[0169] S61 includes:

[0170] S61-1. Perform complex coordinate transformation on the nodes in the PML region, and calculate the mean of the relative permittivity and conductivity around the PML region to generate the complex permittivity of the PML region.

[0171] Specifically, according to the PML coordinate transformation formula, a complex coordinate transformation is performed on the nodes within the PML region. This involves introducing an imaginary number into the depth coordinates of the nodes within the PML region to obtain their complex coordinates. Using the complex coordinates of the PML nodes, the volume of adjacent tissue units is calculated. Then, the average relative permittivity and conductivity around the PML region are calculated according to the formula:

[0172] ;

[0173] ;

[0174] The mean dielectric constant was obtained. and mean conductivity And it serves as the dielectric constant and conductivity of the PML region. , They represent the first The conductivity and relative permittivity of adjacent tissue units.

[0175] Calculate the complex permittivity of the PML region based on the mean dielectric constant and mean conductivity of the PML region. The corresponding formula is:

[0176] .

[0177] S61-2. Based on the node labels of each tissue layer, call the corresponding relative permittivity and conductivity to generate the complex permittivity of each tissue layer.

[0178] Specifically, based on the node label (e.g., skin, fat, muscle, etc.), the relative permittivity and conductivity of the corresponding tissue layer at the current frequency are retrieved. The corresponding relative permittivity and conductivity are then combined with the current frequency to generate the complex permittivity of the nodes in each tissue layer. The corresponding formula is:

[0179] ;

[0180] Indicates the first The real part of the relative permittivity of each tissue layer. Indicates the first The electrical conductivity of each tissue layer.

[0181] Since the nodes in each organizational layer can directly reflect the actual energy storage and consumption characteristics, there is no need to perform complex coordinate transformation.

[0182] S61-3. Calculate the corresponding wavenumber based on the complex permittivity of each node. The corresponding formula is:

[0183] .

[0184] When the node is in the organizational layer for When a node is in a PML region, for .in, It represents the vacuum permeability.

[0185] Specifically, wavenumber is used to quantify the “speed” of electromagnetic wave propagation and the rate of energy decay at that node. For example, propagation is faster and decays less in fat, while propagation is slower and decays more in muscle.

[0186] For the PML region, the fundamental wavenumber is first calculated using the complex permittivity and vacuum permeability of the nodes in the PML region. Since the PML undergoes a complex coordinate transformation, the fundamental wavenumber is corrected by the ratio of the original coordinates to the transformed coordinates, so that the wavenumber can truly reflect the attenuation behavior in the complex coordinates. This yields the wavenumber corresponding to each node in the PML region, ensuring that the wave is absorbed and not reflected when it reaches the PML.

[0187] For each tissue layer, the wavenumber is calculated using the complex permittivity and free permeability of each tissue layer.

[0188] S62. Based on the complex permittivity and wavenumber, the Helmholtz equation containing only the electric field is obtained by using Maxwell's equations and through rotation operations; based on the Helmholtz equation, the continuous differential equations of different tissue layers in the abdominal breathing model are generated.

[0189] S63. Based on the continuous differential equation and combined with the spatial distribution of nodes in the abdominal breathing model, the second derivative of the electric field is discretized by the central difference method to obtain the second-order sparse differential matrix, coefficient matrix and excitation vector.

[0190] S63 includes:

[0191] S63-1. Based on the spatial distribution of nodes (coordinates of each node) in the abdominal breathing model, calculate the spacing between adjacent nodes; set the average step size according to the spacing.

[0192] S63-2. Based on the spatial distribution characteristics and average step size of the electromagnetic field, the second derivative of each node is discretized by the central difference method to obtain the second-order sparse differential matrix; based on the second-order sparse differential matrix and wavenumber, the initial coefficient matrix is ​​calculated.

[0193] S63-3. Set the excitation conditions and select a node as the excitation node; determine the initial excitation vector based on the excitation node, and adjust the initial coefficient matrix and the initial excitation vector in combination with the PML boundary parameters to obtain the coefficient matrix and the excitation vector.

[0194] Specifically, the excitation conditions need to simulate the physical scenario of electromagnetic waves incident from outside the body to the abdomen. Typically, the excitation electric field value (e.g., 1 V / m) is set at nodes close to the body surface (e.g., nodes near the boundary between the skin layer and the outside world, or nodes adjacent to the skin layer in the lower PML region; nodes deep within the body should be avoided to conform to the laws of electromagnetic wave propagation). Nodes on the body surface (close to the human body surface) in the abdominal breathing model can be used as excitation nodes, with priority given to nodes in the superficial skin layer or at the edge of the lower PML region to ensure effective propagation of the excitation to all tissue layers within the body.

[0195] When obtaining the initial excitation vector, the vector dimension is consistent with the number of nodes, and only the positions corresponding to the excitation nodes are assigned the set excitation electric field value (the rest of the nodes are 0). During the adjustment process, the wavenumber characteristics of the PML region are incorporated into the initial coefficient matrix in combination with PML boundary parameters (such as boundary absorption coefficient and complex coordinate transformation results) (the absorption effect of PML is reflected by correcting the diagonal elements of the wavenumber). At the same time, the 0 value state of non-excitation nodes in the PML region in the excitation vector is maintained. Finally, a coefficient matrix and excitation vector that are adapted to the PML boundary and contain excitation source information are obtained.

[0196] S64. Based on the coefficient matrix and excitation vector, construct a system of linear equations and solve them to obtain the RBF coefficients of each node;

[0197] S65. Based on the RBF matrix and RBF coefficients, calculate the electric field amplitude of different nodes, and combine the wave impedance of different nodes to determine the magnetic field amplitude of different nodes, thereby generating the electromagnetic field of different tissue layers in the abdominal breathing model.

[0198] Specifically, based on the RBF matrix and RBF coefficients, the complex amplitude of the electric field at each node is obtained through matrix multiplication. This complex amplitude contains both amplitude and phase information, reflecting the spatial distribution characteristics of the electric field. The magnitude of the complex amplitude is taken to obtain the electric field amplitude at each node, reflecting the intensity and energy attenuation law of electromagnetic waves in different tissue layers. Combining the complex wave impedance of the tissue layer where each node is located, the electric field amplitude is divided by the absolute value of the wave impedance to calculate the magnetic field amplitude, while retaining the phase information to reflect the hysteresis characteristics of the magnetic field relative to the electric field. Finally, the electromagnetic field distribution of different tissue layers in the abdominal breathing model is obtained, including the amplitude, phase, and energy attenuation characteristics of the electric and magnetic fields, providing accurate input data for subsequent SAR analysis and dynamic parameter correction.

[0199] The SAR calculation and early warning module is used to calculate the corresponding SAR based on the electromagnetic fields of different tissue layers in the abdominal breathing model, generate SAR visual reports, and determine whether to issue a warning.

[0200] Specifically, SAR is the rate at which electromagnetic field energy is absorbed by tissue, and the corresponding formula is:

[0201] ;

[0202] in, Indicates tissue density, Indicates electrical conductivity. , These represent the electric field strength and absolute value, respectively.

[0203] In this embodiment, based on the electromagnetic fields of different tissue layers in the abdominal breathing model output by the electromagnetic field calculation module, and combined with the SAR formula, the SAR of different tissue layers in the abdominal breathing model is calculated, and a SAR visual report is generated. Electric field strength. Need to pass through electric potential The gradient is calculated (as can be seen from Maxwell's equations). Due to electric potential This is obtained by solving the continuous differential equations of electromagnetic wave propagation using the radial basis function (RBF) method. However, solving continuous differential equations in a computer requires discretization of the derivatives. First, the spatial partial derivatives of the RBF expression are calculated, transforming the continuous gradient calculation into discrete numerical computation, i.e.:

[0204] ;

[0205] Thus, the electric field strength at each node is obtained. . Represents the norm, Indicates the first The coefficients of the RBF kernel function corresponding to each node. , Represent the spatial location of the electric field to be calculated and its first position, respectively. One portion, Represents the RBF kernel function. This indicates finding the partial derivative. Indicates the first The position coordinates of each node Represents the gradient operator. Represents electric potential In spatial location Along the first Each component The partial derivatives of .

[0206] Subsequently, by combining the SAR formula and substituting the conductivity and tissue density corresponding to different tissue layers in the abdominal breathing model, the SAR of each tissue layer is calculated, and a SAR visual report is generated.

[0207] Determine whether the SAR of the tumor area exceeds the preset SAR safety threshold; if so, send a warning to the display screen that "the SAR of the tumor area exceeds the SAR safety threshold, and the transmission power needs to be reduced" to remind the system to adjust the transmission power.

[0208] The system was simulated at frequencies of 433MHz and 1.4GHz, respectively, and SAR visibility reports were obtained. Based on the data in the SAR visibility reports, SAR histograms for different tissue layers were plotted. Figure 4 and Figure 5 As shown, the liver and fat remained SAR hotspots at both frequencies, and the SAR distribution patterns across different tissue layers remained consistent, demonstrating good frequency adaptability. The SAR values ​​of the liver were relatively stable at 433 MHz and 1.4 GHz, effectively avoiding excessively high local electromagnetic energy absorption.

[0209] In summary, this system precisely configures electromagnetic-physical parameters, tumor parameters, and PML boundary parameters through a parameter setting module to construct a simplified abdominal anatomical model, which is conducive to adapting to electromagnetic calculations while balancing computational efficiency and anatomical realism. It generates uniformly distributed nodes and incorporates respiratory motion parameters, enabling the model to simulate the dynamic changes of the abdomen under real physiological conditions. Relying on RBF kernel functions and RBF matrices, and selecting appropriate kernel functions based on the characteristics of different tissue layers, it improves the targeting and accuracy of electromagnetic field calculations. Using an electromagnetic field calculation module combined with Maxwell's equations and the central difference discretization method, it accurately solves for the electromagnetic field distribution of each tissue layer in the abdomen. It quantifies the energy deposition of each tissue and generates visual reports, triggering timely safety warnings and providing intuitive evidence for radiation safety management. Furthermore, the EKF dynamic parameter correction module, combined with Kalman filtering, corrects node characteristics in real time, further improving the accuracy and dynamic adaptability of model parameters.

[0210] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.

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

[0212] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A computational system for the propagation and scattering process of electromagnetic waves in the abdomen, characterized in that, include: The parameter setting module is used to set electromagnetic and physical parameters; Acquire three-dimensional medical imaging data of the abdomen, determine the tumor region, and set tumor region parameters; the electromagnetic-physical parameters include tissue physical properties, PML boundary parameters, and SAR safety threshold; the PML boundary parameters include boundary thickness and boundary absorption coefficient. The simplified abdominal anatomy model construction module is used to set the abdominal electromagnetic parameters and construct a simplified abdominal anatomy model based on the distribution pattern of abdominal organs and PML boundary parameters. The node-abdominal breathing model construction module is used to generate multiple nodes and distribute them evenly in the simplified abdominal anatomy model; respiratory motion parameters are set and combined with the simplified abdominal anatomy model to construct an initial abdominal breathing model. The EKF dynamic parameter correction module is used to set the observation vector and state vector, calculate the observation error covariance, and combine the Kalman filter method to correct the node characteristics in the initial abdominal breathing model to obtain the abdominal breathing model. The RBF kernel function adaptation and matrix construction module is used to select the RBF kernel function and set the RBF kernel function parameters based on the distribution characteristics of each tissue layer in the abdominal breathing model, and construct the corresponding RBF matrix. The electromagnetic field calculation module is used to generate the complex permittivity and wavenumber based on the labels of each node; and to solve the RBF coefficients based on the RBF matrix, combined with Maxwell's equations and the central difference discretization method, to generate the electromagnetic fields of different tissue layers in the abdominal breathing model. The SAR calculation and early warning module is used to calculate the corresponding SAR based on the electromagnetic fields of different tissue layers in the abdominal respiratory model, generate SAR visual reports, and determine whether to issue a warning.

2. The calculation system for the propagation and scattering process of electromagnetic waves in the abdomen according to claim 1, characterized in that, The processing procedure corresponding to the parameter setting module is as follows: Define the tissue physical properties of electromagnetic waves propagating in the abdomen, namely, define the speed of light, tissue density, simulation frequency, vacuum permeability, and vacuum permittivity. Based on medical standards, healthcare scenarios, and actual needs, establish SAR safety thresholds; Set PML boundary parameters; Based on three-dimensional abdominal medical images, the tumor region is determined and tumor region parameters are obtained; the tumor region parameters include the tumor location and its radius and tumor-conductivity.

3. The calculation system for the propagation and scattering process of electromagnetic waves in the abdomen according to claim 1, characterized in that, The simplified abdominal anatomical model includes the stomach-liver-kidney tissue layer, muscle tissue layer, skin tissue layer, adipose tissue layer, and the outermost PML region.

4. The calculation system for the propagation and scattering process of electromagnetic waves in the abdomen according to claim 3, characterized in that, The processing procedure corresponding to the node-abdominal breathing model construction module is as follows: Multiple nodes are generated along the depth direction of the simplified abdominal anatomy model and evenly distributed in the simplified abdominal anatomy model, covering the tissue layers corresponding to the stomach-liver-kidney, muscle, skin, and fat, as well as the PML region; The respiratory motion parameters of the abdomen during breathing are set; the respiratory motion parameters include the translational amplitude of the abdomen along the depth direction, the respiratory rate, and the elastic deformation coefficient. Physiological signals are acquired through sensors; Based on physiological signals and respiratory motion parameters, the deformation process of each tissue layer, PML region and tumor region during abdominal breathing is simulated by the finite element method to generate rigid body translation values ​​and elastic deformation, thus generating the original model of abdominal breathing. Based on the position of the nodes in the original abdominal breathing model, node labels are set and the original abdominal breathing model is updated to obtain the initial abdominal breathing model.

5. The calculation system for the propagation and scattering process of electromagnetic waves in the abdomen according to claim 3, characterized in that, The processing procedure of the RBF kernel function adaptation and matrix construction module is as follows: Based on the characteristics of each tissue layer in the abdominal breathing model and the multilayer perceptron, the RBF kernel function was selected and the corresponding RBF kernel function parameters were set. When the tissue layer is adipose tissue, select the Gaussian RBF kernel function; When the tissue layer is the skin / muscle tissue layer and not located in a blood vessel / stomach-liver-kidney tissue layer, the standard thin-plate spline RBF kernel function is selected; when the tissue layer is the muscle tissue layer and located in a blood vessel, the standard thin-plate spline RBF kernel function is modified using a multilayer perceptron. The coupling effect between the blood vessel wall and blood flow is learned through MLP, and the standard thin-plate spline RBF kernel function is modified based on the coupling effect to obtain the modified standard thin-plate spline RBF kernel function. Based on the node labels of each node, the Euclidean distance between any two different nodes in the same organizational layer is calculated. Combined with the selected RBF kernel function, the RBF value is calculated and the RBF matrix is ​​constructed. The RBF value of the same node is set to 0.

6. The calculation system for the propagation and scattering process of electromagnetic waves in the abdomen according to claim 4, characterized in that, The processing procedure corresponding to the electromagnetic field calculation module is as follows: Based on node labels, the complex permittivity of different tissue layers in the abdominal breathing model is calculated, and the wavenumber of each node is calculated by combining Maxwell's equations. Based on the complex permittivity and wavenumber, the Helmholtz equations containing only the electric field are obtained by using Maxwell's equations and through rotation operations; based on the Helmholtz equations, continuous differential equations for different tissue layers in the abdominal breathing model are generated. Based on the continuous differential equation and combined with the spatial distribution of nodes in the abdominal breathing model, the second derivative of the electric field is discretized by the central difference method to obtain the second-order sparse differential matrix, coefficient matrix and excitation vector. Based on the coefficient matrix and the excitation vector, a system of linear equations is constructed and solved to obtain the RBF coefficients of each node; Based on the RBF matrix and RBF coefficients, the electric field amplitude of different nodes is calculated, and the magnetic field amplitude of different nodes is determined by combining the wave impedance of different nodes, thus generating the electromagnetic field of different tissue layers in the abdominal breathing model.

7. The calculation system for the propagation and scattering process of electromagnetic waves in the abdomen according to claim 6, characterized in that, The calculation of the wavenumber at each node includes: Perform complex coordinate transformation on the nodes in the PML region, and calculate the mean of the relative permittivity and conductivity around the PML region to generate the complex permittivity of the PML region; Based on the node labels of each organizational layer, the corresponding relative permittivity and conductivity are called to generate the complex permittivity of each organizational layer; The wavenumber is calculated based on the complex permittivity of each node.

8. The calculation system for the propagation and scattering process of electromagnetic waves in the abdomen according to claim 6, characterized in that, The process of obtaining the second-order sparse differential matrix, coefficient matrix, and activation vector includes: Based on the spatial distribution of nodes in the abdominal breathing model, the spacing between adjacent nodes is calculated; the average step size is set according to the spacing. Based on the spatial distribution characteristics and average step size of the electromagnetic field, the second derivative of each node is discretized using the central difference method to obtain a second-order sparse differential matrix; based on the second-order sparse differential matrix and the wavenumber, the initial coefficient matrix is ​​calculated. Set the excitation conditions and select a node as the excitation node; determine the initial excitation vector based on the excitation node, and adjust the initial coefficient matrix and the initial excitation vector in combination with the PML boundary parameters to obtain the coefficient matrix and the excitation vector.

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