Moxibustion temperature prediction and optimization method and system based on physical information neural network

Abstract

This invention discloses a method for predicting and optimizing moxibustion temperature based on a physical information neural network, comprising: obtaining the thermophysical parameter formulas of biological tissues; constructing the Pennes biological heat transfer equation within the biological tissue based on the thermophysical parameter formulas; constructing the thermal equilibrium condition of the radiation-convection combined heat transfer boundary on the surface of the biological tissue based on the thermophysical parameter formulas; constructing a physical information neural network, whose input is spatiotemporal coordinates and output is the corresponding temperature value; constructing the loss function of the physical information neural network and optimizing the network based on it, wherein the loss function includes the residual loss term of the Pennes biological heat transfer equation and the loss term of the radiation-convection combined heat transfer boundary thermal equilibrium condition. This invention embeds physical law constraints into the neural network, achieving high-precision prediction of the transient temperature field of skin tissue, overcoming the limitations of traditional experiments and simulations such as high cost, low efficiency, and difficulty in obtaining the internal temperature field.

Description

Technical Field

[0001] This invention belongs to the field of moxibustion therapy technology, specifically relating to a method and system for predicting and optimizing moxibustion temperature based on a physical information neural network. Background Technology

[0002] Mild moxibustion is one of the most commonly used techniques in moxibustion therapy. Its therapeutic effect is highly dependent on the temperature distribution at the moxibustion site, especially the depth of heat penetration into deep tissues. Accurately obtaining the temperature field distribution during mild moxibustion is crucial for optimizing clinical procedures.

[0003] Currently, the main methods for investigating the temperature field distribution of moxibustion include experimental measurement and numerical simulation. In terms of experimental measurement, infrared thermal imagers are typically used to monitor skin surface temperature, or miniature thermocouples are used to measure local temperature. However, these experimental studies are often limited by ethical considerations and current temperature measurement technologies, making it difficult to obtain continuous high-dimensional temperature fields within living tissues. Furthermore, they cannot systematically analyze the thermal evolution patterns under multi-parameter coupling effects, resulting in limitations such as high cost and low efficiency.

[0004] In numerical simulation, traditional numerical methods based on the Pennes biological heat transfer equation (such as the finite element method or the finite difference method) provide an effective way to compensate for the shortcomings of experimental methods. However, these traditional numerical simulation methods have obvious defects in practical applications: First, traditional numerical methods rely heavily on mesh generation. When dealing with abrupt changes in the interfacial parameters of multi-layered biological tissues (such as skin, fat, and muscle), mesh generation is complex and prone to computational divergence or gradient anomalies. Second, the skin surface under moxibustion is a radiation-convection composite heat transfer boundary, containing strongly nonlinear heat flow interactions. Traditional methods incur huge computational costs when iteratively solving such complex boundary conditions. Finally, due to the huge computational burden of mesh generation and iterative calculation, traditional simulations are usually limited to a small number of parameter combination experiments and are difficult to efficiently depict the global nonlinear response surface in multi-parameter space.

[0005] In summary, existing traditional experimental and numerical simulation methods have limitations in exploring the effects of multiple parameters of moxibustion and obtaining the internal continuous temperature field, including high cost, low efficiency, reliance on mesh generation, and difficulty in handling complex composite boundaries. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the above-mentioned defects in the existing moxibustion temperature field prediction methods, thereby providing a moxibustion temperature prediction and optimization method and system based on physical information neural network.

[0007] A method for predicting moxibustion temperature based on a physical information neural network, characterized by comprising: Formulas for obtaining the thermophysical parameters of biological tissues; The Pennes bioheat transfer equation within the biological tissue is constructed based on the aforementioned thermophysical parameter formula. The thermal equilibrium conditions of the radiation-convection combined heat transfer boundary on the surface of the biological tissue are constructed based on the aforementioned thermophysical parameter formulas. Construct a physical information neural network, wherein the input of the physical information neural network is spatiotemporal coordinates and the output is the corresponding temperature value; Construct the loss function of the physical information neural network, and optimize the physical information neural network based on the loss function; The loss function includes the residual loss term of the residual loss of the Pennes biological heat transfer equation and the loss term of the boundary thermal equilibrium condition of the combined radiation-convection heat transfer.

[0008] Furthermore, the formula for obtaining the thermophysical parameters of biological tissues includes: Biological tissues are divided into multi-layered planar structures, and the initial values ​​of the thermophysical parameters of each layer of the planar structure are obtained. The initial values ​​of the thermal property parameters are processed by the Sigmoid smoothing function to obtain continuously differentiable thermal property parameter formulas; the thermal property parameters include density, specific heat capacity, thermal conductivity and blood perfusion rate.

[0009] Furthermore, the Pennes biological heat transfer equation is specifically expressed as follows: ; in, For tissue density, To organize specific heat capacity, For tissue temperature, For time, Thermal conductivity, For Hamiltonian operators, For blood perfusion rate, Blood density, For the specific heat capacity of blood, For blood temperature, This represents the metabolic heat production rate.

[0010] Furthermore, the specific form of the boundary thermal equilibrium condition for the combined radiation and convection heat transfer is as follows: ; in, Thermal conductivity, For tissue temperature, For depth coordinates, The directional radiant heat flow from the burning moxa sticks. For heat exchange between the skin and the environment, It is a heat flow for long-wave radiation heat exchange between the skin and the environment.

[0011] Furthermore, the structure of the physical information neural network includes: The input layer contains three neurons and is used to input spatiotemporal coordinates. The hidden layers consist of 5 fully connected hidden layers, each containing 64 neurons; The output layer contains one neuron and is used to output the network's original predictions.

[0012] Furthermore, the specific form of the loss function is as follows: ; in, This is the residual loss term in the Pennes biological heat transfer equation. For the initial condition loss term, This represents the loss term under the boundary heat equilibrium condition of combined radiation and convection heat transfer. To organize the bottom isothermal boundary constraint loss term, For axisymmetric boundary constraint loss terms, This is the loss term for convective heat transfer constraint at the side boundary; These are the weighting coefficients for the corresponding loss terms.

[0013] Furthermore, the specific form of the residual loss term in the Pennes biological heat transfer equation is as follows: ; Where F[·] is the differential operator of the Pennes biological heat transfer equation, The temperature field predicted by the physical information neural network. The characteristic normalization scale for PDE residuals, This refers to the number of spatiotemporal configuration points within the organization's internal computing domain.

[0014] Furthermore, the specific form of the loss term in the boundary heat balance condition of the combined radiation and convection heat transfer is as follows: ; in, The characteristic normalization scale for the boundary heat flux residual is... Thermal conductivity, The temperature field predicted by the physical information neural network. For depth coordinates, The directional radiant heat flow from the burning moxa sticks. For heat exchange between the skin and the environment, For long-wave radiation heat exchange between the skin and the environment, The number of spatiotemporal configuration points for the skin surface boundary.

[0015] A method for optimizing moxibustion parameters based on a physical information neural network includes: The evaluation index for optimizing moxibustion parameters is set as the time-area average temperature at a specific depth under the skin. The highest burning temperature of the moxa stick, the diameter of the moxa stick, the moxibustion distance, and the ambient temperature were selected as influencing parameters, and multiple levels were set for each influencing parameter. Based on the physical information neural network, orthogonal experimental simulations were performed on different combinations of the influencing parameters to obtain the evaluation index values ​​under each parameter combination. Based on the evaluation index values, range analysis is performed to calculate the average response value and range value of each influencing parameter at different levels, and the influence weight of each influencing parameter on the deep thermal penetration capability is determined according to the range value. Based on the maximum average response value of each influencing parameter, the optimal combination of moxibustion parameters that balances epidermal safety and deep heat penetration effect is determined.

[0016] A moxibustion temperature prediction and optimization system based on physical information neural network includes: The parameter acquisition module is used to obtain the formulas for the thermophysical parameters of biological tissues. The equation construction module is used to construct the Pennes biological heat transfer equation inside the biological tissue based on the thermophysical parameter formula, and to construct the thermal equilibrium condition of the radiation-convection combined heat transfer boundary on the surface of the biological tissue. A network construction module is used to construct a physical information neural network, wherein the input of the physical information neural network is spatiotemporal coordinates and the output is the corresponding temperature value; The loss function construction and optimization module is used to construct the loss function of the physical information neural network and optimize the physical information neural network based on the loss function; the loss function includes the residual loss term of the Pennes biological heat transfer equation and the loss term of the boundary thermal equilibrium condition of the radiation-convection combined heat transfer. The parameter optimization module is used to perform orthogonal experimental simulations based on the optimized physical information neural network. The time-area double average temperature at a specific subcutaneous depth is used as the evaluation index. By performing range analysis on the orthogonal experimental results, the influence weight of each moxibustion parameter and the optimal combination of moxibustion parameters are determined.

[0017] Beneficial effects: The present invention provides a moxibustion temperature prediction method based on physical information neural network. It adopts physical information neural network and directly maps spatiotemporal coordinates as input to temperature value. It does not rely on the cumbersome mesh generation process in traditional finite element or finite difference methods, completely gets rid of mesh constraints, greatly reduces the complexity and time cost of pre-processing, and avoids the problem of decreased solution accuracy due to poor mesh quality.

[0018] This method achieves model training and solution driven by purely physical laws by embedding the Pennes biological heat transfer equation and radiation-convection composite boundary conditions into the loss function of a neural network in the form of residuals. It can accurately predict the transient temperature field of skin tissue without relying on difficult-to-obtain measured temperature data inside living tissue as supervision, overcoming the limitations of traditional experimental measurements which are constrained by ethical factors and temperature measurement techniques, making it difficult to obtain continuous high-dimensional internal temperature fields.

[0019] To address the complex radiation-convection combined heat transfer boundary conditions on the skin surface under moxibustion, this method constructs a corresponding boundary loss term in the loss function for strict constraint, overcoming the shortcomings of traditional numerical methods in dealing with such strongly nonlinear boundaries, which have large computational overhead and are prone to divergence in iterative solutions. This ensures the global convergence and numerical stability of temperature field prediction under complex boundary conditions. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a schematic diagram of the main method steps of the present invention; Figure 2 This is a schematic diagram of the physical information neural network of the present invention. Detailed Implementation

[0022] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0023] Example 1: This embodiment establishes a geometric model in a two-dimensional cylindrical coordinate system (r, z) based on the axisymmetric characteristics of gentle moxibustion. Here, r represents the radial coordinate, and z represents the tissue depth coordinate. In this embodiment, biological tissue is simplified into a three-layered planar structure: skin, fat, and muscle. As a preferred embodiment, the thickness and thermophysical parameters of each layer are set according to references and classical theories of biological heat transfer, as shown in Table 1. The computational domain is set as follows: radial r ∈ [0, 0.04 m], depth z ∈ [0, 0.025 m], and time t ∈ [0, 1200 s], corresponding to a 20-minute moxibustion duration.

[0024] In this embodiment, the moxibustion temperature prediction and optimization method based on physical information neural networks is applied to gentle moxibustion. As another implementation of this embodiment, the corresponding method can also be applied to other moxibustion techniques.

[0025] Table 1. Thermophysical properties of biological tissues

[0026] Reference Figure 1 As shown, this embodiment provides a method for predicting moxibustion temperature based on a physical information neural network, including: Formulas for obtaining the thermophysical parameters of biological tissues; The Pennes bioheat transfer equation within the biological tissue is constructed based on the aforementioned thermophysical parameter formula. The thermal equilibrium conditions of the radiation-convection combined heat transfer boundary on the surface of the biological tissue are constructed based on the aforementioned thermophysical parameter formulas. Construct a physical information neural network, wherein the input of the physical information neural network is spatiotemporal coordinates and the output is the corresponding temperature value; Construct the loss function of the physical information neural network, and optimize the physical information neural network based on the loss function; The loss function includes the residual loss term of the residual loss of the Pennes biological heat transfer equation and the loss term of the boundary thermal equilibrium condition of the combined radiation-convection heat transfer.

[0027] Specifically, the formulas for obtaining the thermophysical parameters of biological tissues include: Biological tissues were divided into multi-layer planar hierarchical structures, and the initial values ​​of the thermophysical parameters of each layer of the planar hierarchical structure were obtained. The method of dividing the multi-layer planar hierarchical structure and the initial values ​​of the obtained thermophysical parameters are shown in Table 1. The initial values ​​of the thermal property parameters are processed by the Sigmoid smoothing function to obtain continuously differentiable thermal property parameter formulas; the thermal property parameters include density, specific heat capacity, thermal conductivity and blood perfusion rate.

[0028] In this embodiment, the Sigmoid smoothing process is described as follows: ; in The depth of the skin-fat interface. denoted as the fat-muscle interface depth, and 2000 as the interface steepness coefficient, achieving continuous differentiability while ensuring the stratified physical properties.

[0029] The smoothed density is expressed as: ; in, , , These represent the densities of skin, fat, and muscle, respectively. As a preferred embodiment, other thermophysical parameters, including specific heat capacity, thermal conductivity, and blood perfusion coefficient, are all smoothed using the same method.

[0030] By using the Sigmoid smoothing operation, a continuous transition of the physical property parameters of the three-layer tissue is achieved at the interface. This ensures that the automatic differentiation of the physical information neural network meets the requirement of the continuity of the physical field and avoids gradient anomalies and training non-convergence caused by abrupt changes in physical property parameters.

[0031] In this embodiment, the Pennes biological heat transfer equation is specifically expressed as follows: ; in, For tissue density, To organize specific heat capacity, For tissue temperature, For time, Thermal conductivity, For Hamiltonian operators, For blood perfusion rate, Blood density, For the specific heat capacity of blood, For blood temperature, This represents the metabolic heat production rate.

[0032] In this embodiment, the burning moxa stick is used as an external heat flow, acting directly on the skin surface boundary, and is not repeatedly calculated as an internal heat source term in the governing equation. The specific form of the boundary thermal equilibrium condition for the combined radiation and convection heat transfer is as follows: ; in, Thermal conductivity, For tissue temperature, For depth coordinates, The directional radiative heat flux of the burning moxa stick is calculated using the Stefan-Boltzmann law, taking into account the angular coefficient, distance attenuation, and radial Gaussian distribution. For heat exchange between the skin and the environment, For long-wave radiation heat exchange between the skin and the environment, among which The convective heat transfer coefficient is... For ambient temperature, Skin surface temperature For emission rate, is the Stefan-Boltzmann constant.

[0033] As a preferred embodiment, the temperature at the burning end of the moxa stick is... Taking into account the periodic fluctuations of combustion: the base temperature adopts a cosine wave model with a period of 500s, and the highest temperature is... The fluctuation range is 200°C; ensuring the combustion temperature is always higher than the ignition point of the moxa wool (180°C), the mathematical expression of which is: ; ; As a preferred embodiment of this method, in order to ignore the ash removal operation of the moxa stick and thus focus on the influence of the core moxibustion parameters, in some other embodiments of this method, the effective radiation coefficient of the moxa stick is temporarily increased by 10% during the ash removal period (ash removal every 60s for 5s), and then returns to normal after 5s, thereby simulating real clinical operation.

[0034] In this embodiment, the following boundary conditions are also set: Axisymmetric boundary (r=0): Radial temperature gradient is 0, i.e. ; Side boundary ( ): Convective heat transfer boundary, i.e. ; Bottom boundary ( ): The core isothermal boundary of the human body, i.e. .

[0035] Reference Figure 2 As shown, in this embodiment, the constructed Physical Information Neural Network (PINN) is a supervised learning framework based on a feedforward neural network and constrained by the residuals of physical equations. The network has approximately 17,000 trainable parameters, and the structure of the Physical Information Neural Network includes: The input layer contains three neurons and is used to input spatiotemporal coordinates. The hidden layers consist of 5 fully connected hidden layers, each containing 64 neurons; The output layer contains one neuron and is used to output the network's original predictions.

[0036] As a preferred embodiment, the network uses a Xavier normal distribution to initialize the weights and initializes the bias term to 0, thereby improving training stability.

[0037] As a further improvement to this embodiment, the input spatiotemporal coordinates are independently dimensionless, and t, r, z are normalized to the interval [0,1], as follows: , , ; Meanwhile, this embodiment introduces a hard constraint structure at the output end, mapping the original network output u to physical temperature, thereby strictly satisfying the initial temperature condition at t=0, i.e., the human body's basal body temperature of 37°C, expressed as: ; in, , This ensures that the network output is always 37°C at t=0 during any iteration, eliminating the need for additional initial condition loss during training and greatly simplifying the optimization objective.

[0038] In this embodiment, the loss function of the physical information neural network is composed of a weighted average of the PDE loss, the initial condition loss, and the losses of each boundary condition, specifically in the following form: ; in, This is the residual loss term in the Pennes biological heat transfer equation. For the initial condition loss term, This represents the loss term under the boundary heat equilibrium condition of combined radiation and convection heat transfer. To organize the bottom isothermal boundary constraint loss term, For axisymmetric boundary constraint loss terms, This is the loss term for convective heat transfer constraint at the side boundary; These are the weighting coefficients for the corresponding loss terms.

[0039] Specifically, the residual loss term of the Pennes biological heat transfer equation Latin hypercube sampling is used to generate within the computational domain of the tissue. This allows for the allocation of spatiotemporal points, thereby reducing sample stacking and improving global variability capture when solving high-dimensional partial differential equations using a physical information neural network. The first and second derivatives of temperature with respect to spatiotemporal coordinates are calculated and substituted into the Pennes equation to obtain the residuals. The loss term is expressed as the mean squared error after residual normalization: ; Where F[·] is the differential operator of the Pennes biological heat transfer equation, The temperature field predicted by the physical information neural network. This is the feature normalization scale for the PDE residuals, used to balance the magnitude differences between different loss terms and prevent gradient updates from being dominated by loss terms with larger magnitudes. This refers to the number of spatiotemporal configuration points within the organization's internal computing domain.

[0040] PDE control equation loss The residual loss of the Pennes biological heat transfer equation is used to constrain the temperature field of the computational domain within the tissue to satisfy the physical laws of heat transfer.

[0041] Initial condition loss The initial temperature constraint loss is used to force the tissue's global temperature at t=0 to be the human body's basal body temperature of 37.0°C. If, as mentioned above, a hard constraint on the initial condition is introduced at the neural network output to ensure that the predicted temperature at t=0 remains constant at 37.0°C during any iteration, the initial condition has been analytically satisfied. Therefore, the weight coefficient of this term is set during training. No additional training is required. The expression for this term is: ; in, The number of sampling points at the initial time.

[0042] The loss term of the boundary heat equilibrium condition for combined radiation and convection heat transfer is expressed as: The skin surface boundary loss is the radiation-convection combined boundary constraint loss of the skin surface (z=0), used to force the heat flow balance of the skin surface to satisfy the radiation-convection combined heat transfer boundary thermal equilibrium condition. Sampling is performed on the z=0 surface. For each spatiotemporal configuration point, the normalized mean square error of the boundary heat flux residual is calculated, expressed as: ; in, The characteristic normalization scale for the boundary heat flux residual is... Thermal conductivity, The temperature field predicted by the physical information neural network. For depth coordinates, The directional radiant heat flow from the burning moxa sticks. For heat exchange between the skin and the environment, For long-wave radiation heat exchange between the skin and the environment, The number of spatiotemporal configuration points for the skin surface boundary.

[0043] Organizational bottom boundary loss For the bottom of the organization ( The isothermal boundary constraint loss is used to force the temperature of deep human tissues to maintain the core body temperature at 37.0°C. Bottom boundary sampling For each spatiotemporal location point, the mean square error between the predicted temperature and 37.0°C is calculated and expressed as: ; Axisymmetric boundary loss The boundary constraint loss is applied along the axis of symmetry (r=0) to force the radial temperature gradient to be zero under axisymmetric conditions, conforming to the axisymmetric characteristics of the temperature field. Sampling is performed on the axis of symmetry (r=0). For each spatiotemporal location point, the normalized mean square error of the radial temperature gradient is calculated, expressed as: ; in, This is the characteristic normalization scale for the temperature gradient.

[0044] Lateral boundary convection loss The outermost radial direction of the computational domain ( The convective heat transfer boundary constraint loss is used to simulate the convective heat transfer between the tissue side boundary and the surrounding environment, avoiding simulation errors caused by artificial adiabatic boundaries. Side boundary sampling For each spatiotemporal configuration point, the normalized mean square error of the convective boundary heat flux residual is calculated, expressed as: ; in, The convective heat transfer coefficient at the side boundary is... This is the characteristic normalization scale for the lateral boundary residuals.

[0045] As a preferred embodiment, to ensure the preferential convergence of the strongly nonlinear radiation-convection boundary and to address the imbalance in the magnitude of the multiphysics loss terms, this embodiment employs an asymmetric static weighting strategy, with the specific weight settings as follows: ; The skin surface boundary loss weight is set to the highest value of 30.0 because the core driver of heat transfer in moxibustion comes from surface radiative heat flow, and the prediction accuracy of this boundary directly determines the accuracy of the entire temperature field solution. The bottom isothermal boundary has a high correlation with internal tissue heat transfer, and its weight is set to 10.0. The axisymmetric and lateral boundaries are auxiliary constraints, and their weights are set to 5.0. This weighting strategy can effectively balance the contributions of each constraint, significantly improving the model's convergence speed and solution accuracy.

[0046] This embodiment also provides a specific example of a physical information neural network training method, implemented based on the PyTorch deep learning framework. The training hardware is a workstation equipped with an NVIDIA RTX 5060 graphics card. The complete training configuration is as follows: The optimizer is the Adam optimizer, with an initial learning rate of... Configure a StepLR learning rate decay strategy, where the learning rate decays to 0.5 times its original value every 5000 epochs.

[0047] The iteration is set to a total of 20,000 epochs, and a mini-batch training strategy is adopted. In each round, 10,000 PDE placement points and 1,000 boundary placement points are randomly sampled to calculate the loss.

[0048] The training stabilization strategy employs gradient clipping (maximum norm 1.0) to avoid gradient explosion, and refreshes the global configuration point pool every 2000 epochs through Latin hypercube sampling to prevent the model from overfitting at fixed points.

[0049] The sampling method involves generating all configuration points using Latin hypercube sampling to ensure that the samples are uniformly distributed within the spatiotemporal computational domain.

[0050] Example 2: This embodiment also provides a method for optimizing moxibustion parameters based on a physical information neural network, including: The evaluation index for optimizing moxibustion parameters is set as the time-area dual average temperature at a specific subcutaneous depth. Specifically, this embodiment uses the time-area dual average temperature at a subcutaneous depth of 5mm, a circular area with a radius of 5mm, and during the last 500 seconds of moxibustion (i.e., from the 700th to the 1200th second) as the evaluation index, thereby comprehensively reflecting the deep heat penetration effect in the steady-state phase and avoiding the result deviation caused by transient fluctuations and single-point sampling. Meanwhile, the area averaging adopts... The radial sampling method achieves natural area weighting, ensuring that the sampling results are consistent with the true average value of the region.

[0051] The highest burning temperature of the moxa stick, the diameter of the moxa stick, the moxibustion distance, and the ambient temperature were selected as influencing parameters, and multiple levels were set for each parameter; specifically, three levels were set for each parameter, and the design... Orthogonal experiment.

[0052] Based on the physical information neural network obtained in Example 1, orthogonal experimental simulations were performed on different combinations of the influencing parameters to obtain the evaluation index values ​​for each parameter combination. The evaluation index values ​​obtained in this example are shown in Table 2 below. Table 2. Orthogonal experimental design and results

[0053] Range analysis was performed based on the evaluation index values ​​to calculate the average response value and range value of each influencing parameter at different levels. The influence weight of each influencing parameter on the deep heat penetration capability was determined according to the magnitude of the range value. In this embodiment, the range analysis results show that the influence weight of each parameter on the deep heat penetration capability is as follows: moxa stick diameter (R=5.46) > moxibustion distance (R=3.56) > ambient temperature (R=2.41) > moxa stick combustion temperature (R=2.31). The results indicate that compared to increasing the combustion intensity of the moxa stick itself, changing the geometric structure (diameter) and spatial layout (moxibustion distance) is a more efficient way to improve the deep heat effect.

[0054] Based on the level with the highest average response value of each influencing parameter, the optimal combination of moxibustion parameters that balances epidermal safety and deep heat penetration is determined. Based on orthogonal range analysis theory, the optimal level of each factor corresponds to the level with the highest average response value (K value). Through screening the global parameter space, this embodiment determines a globally optimal parameter combination that maximizes deep heat penetration: moxa stick diameter 18mm, moxibustion distance 25mm, ambient temperature 32°C, and moxa stick combustion temperature 650°C.

[0055] Example 3: This embodiment provides a moxibustion temperature prediction and optimization system based on a physical information neural network, used to implement the method of Embodiment 1 or Embodiment 2, including: The parameter acquisition module is used to obtain the formulas for the thermophysical parameters of biological tissues. The equation construction module is used to construct the Pennes biological heat transfer equation inside the biological tissue based on the thermophysical parameter formula, and to construct the thermal equilibrium condition of the radiation-convection combined heat transfer boundary on the surface of the biological tissue. A network construction module is used to construct a physical information neural network, wherein the input of the physical information neural network is spatiotemporal coordinates and the output is the corresponding temperature value; The loss function construction and optimization module is used to construct the loss function of the physical information neural network and optimize the physical information neural network based on the loss function; the loss function includes the residual loss term of the Pennes biological heat transfer equation and the loss term of the boundary thermal equilibrium condition of the radiation-convection combined heat transfer. The parameter optimization module is used to perform orthogonal experimental simulations based on the optimized physical information neural network. The time-area double average temperature at a specific subcutaneous depth is used as the evaluation index. By performing range analysis on the orthogonal experimental results, the influence weight of each moxibustion parameter and the optimal combination of moxibustion parameters are determined.

[0056] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0057] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for predicting moxibustion temperature based on a physical information neural network, characterized in that, include: Formulas for obtaining the thermophysical parameters of biological tissues; The Pennes bioheat transfer equation within the biological tissue is constructed based on the aforementioned thermophysical parameter formula. Based on the aforementioned thermophysical property parameter formulas, the thermal equilibrium conditions of the radiation-convection combined heat transfer boundary on the surface of the biological tissue are constructed; a physical information neural network is constructed, wherein the input of the physical information neural network is spatiotemporal coordinates and the output is the corresponding temperature value; a loss function of the physical information neural network is constructed, and the physical information neural network is optimized based on the loss function; the loss function includes the residual loss term of the residual loss of the Pennes biological heat transfer equation and the loss term of the radiation-convection combined heat transfer boundary thermal equilibrium conditions.

2. The method for predicting moxibustion temperature based on a physical information neural network according to claim 1, characterized in that, The method for obtaining the thermophysical parameters of biological tissue includes: dividing the biological tissue into multiple planar layered structures and obtaining initial values ​​of thermophysical parameters for each layer of the planar layered structure; performing continuous transition processing on the interface of the initial values ​​of the thermophysical parameters based on the Sigmoid smoothing function to obtain continuously differentiable thermophysical parameter formulas; the thermophysical parameters include density, specific heat capacity, thermal conductivity and blood perfusion rate.

3. The method for predicting moxibustion temperature based on a physical information neural network according to claim 1, characterized in that, The Pennes biological heat transfer equation is specifically expressed as follows: ； in, For tissue density, To organize specific heat capacity, For tissue temperature, For time, Thermal conductivity, For Hamiltonian operators, For blood perfusion rate, Blood density, For the specific heat capacity of blood, For blood temperature, This represents the metabolic heat production rate.

4. The method for predicting moxibustion temperature based on a physical information neural network according to claim 1, characterized in that, The specific form of the boundary thermal equilibrium condition for the combined radiation and convection heat transfer is as follows: ； in, Thermal conductivity, For tissue temperature, For depth coordinates, The directional radiant heat flow from the burning moxa sticks. For heat exchange between the skin and the environment, It is a heat flow for long-wave radiation heat exchange between the skin and the environment.

5. The method for predicting moxibustion temperature based on a physical information neural network according to claim 1, characterized in that, The structure of the physical information neural network includes: The input layer contains three neurons and is used to input spatiotemporal coordinates. The hidden layers consist of 5 fully connected hidden layers, each containing 64 neurons; The output layer contains one neuron and is used to output the network's original predictions.

6. The method for predicting moxibustion temperature based on a physical information neural network according to claim 1, characterized in that, The specific form of the loss function is as follows: ； in, This is the residual loss term in the Pennes biological heat transfer equation. For the initial condition loss term, This represents the loss term under the boundary heat equilibrium condition of combined radiation and convection heat transfer. To organize the bottom isothermal boundary constraint loss term, For axisymmetric boundary constraint loss terms, This is the loss term for convective heat transfer constraint at the side boundary; These are the weighting coefficients for the corresponding loss terms.

7. The method for predicting moxibustion temperature based on a physical information neural network according to claim 1, characterized in that, The specific form of the residual loss term in the Penns biological heat transfer equation is as follows: ； Where F[·] is the differential operator of the Pennes biological heat transfer equation, The temperature field predicted by the physical information neural network. The characteristic normalization scale for PDE residuals, This refers to the number of spatiotemporal configuration points within the organization's internal computing domain.

8. The method for predicting moxibustion temperature based on a physical information neural network according to claim 1, characterized in that, The specific form of the loss term in the boundary heat balance condition for the combined radiation and convection heat transfer is as follows: ； in, The characteristic normalization scale for the boundary heat flux residual is... Thermal conductivity, The temperature field predicted by the physical information neural network. For depth coordinates, The directional radiant heat flow from the burning moxa sticks. For heat exchange between the skin and the environment, For long-wave radiation heat exchange between the skin and the environment, The number of spatiotemporal configuration points for the skin surface boundary.

9. A method for optimizing moxibustion parameters based on a physical information neural network, characterized in that, include: The evaluation index for optimizing moxibustion parameters is set as the time-area average temperature at a specific depth under the skin. The highest burning temperature of the moxa stick, the diameter of the moxa stick, the moxibustion distance, and the ambient temperature were selected as influencing parameters, and multiple levels were set for each influencing parameter. Based on the physical information neural network, orthogonal experimental simulations were performed on different combinations of the influencing parameters to obtain the evaluation index values ​​under each parameter combination. Based on the evaluation index values, range analysis is performed to calculate the average response value and range value of each influencing parameter at different levels, and the influence weight of each influencing parameter on the deep thermal penetration capability is determined according to the range value. Based on the maximum average response value of each influencing parameter, the optimal combination of moxibustion parameters that balances epidermal safety and deep heat penetration effect is determined.

10. A moxibustion temperature prediction and optimization system based on physical information neural networks, characterized in that, include: The parameter acquisition module is used to obtain the formulas for the thermophysical parameters of biological tissues. The equation construction module is used to construct the Pennes biological heat transfer equation inside the biological tissue based on the thermophysical parameter formula, and to construct the thermal equilibrium condition of the radiation-convection combined heat transfer boundary on the surface of the biological tissue. A network construction module is used to construct a physical information neural network, wherein the input of the physical information neural network is spatiotemporal coordinates and the output is the corresponding temperature value; The loss function construction and optimization module is used to construct the loss function of the physical information neural network and optimize the physical information neural network based on the loss function; the loss function includes the residual loss term of the Pennes biological heat transfer equation and the loss term of the boundary thermal equilibrium condition of the combined radiation and convection heat transfer. The parameter optimization module is used to perform orthogonal experimental simulations based on the optimized physical information neural network. The time-area double average temperature at a specific depth under the skin is used as the evaluation index. By performing range analysis on the orthogonal experimental results, the influence weight of each moxibustion parameter and the optimal combination of moxibustion parameters are determined.

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