A method for optimizing the irreversible electroporation ablation model of cartilage

Abstract

The present invention provides a method for optimizing a cartilage irreversible electroporation ablation model, which relates to the field of data processing technology. The method includes: constructing a cartilage irreversible electroporation ablation model; obtaining an ablation sample data set, the ablation sample data set including multiple ablation samples, and the ablation samples including patient data and ablation parameters; constructing an ablation objective function of the cartilage irreversible electroporation ablation model with the goals of increasing the effective ablation volume, improving the ablation uniformity, and reducing thermal damage; using the ablation sample data set, with the goal of maximizing the ablation objective function, determining optimal model parameters to optimize the cartilage irreversible electroporation ablation model; obtaining patient data of a target patient, and inputting the patient data into the trained and optimized cartilage irreversible electroporation ablation model; and determining the optimal ablation parameters for the target patient by training the optimized cartilage irreversible electroporation ablation model.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and in particular to a method for optimizing a cartilage irreversible electroporation ablation model. Background Art

[0002] Irreversible electroporation (IRE) is a non-thermal ablation technique that uses high-intensity, short-duration electrical pulses to disrupt cell membranes, leading to irreversible cell damage and eventual apoptosis. Cartilage tissue is highly sensitive to temperature. IRE can mitigate the thermal damage associated with traditional thermal ablations (such as radiofrequency ablation and laser ablation), and is gaining increasing attention in cartilage ablation.

[0003] How to determine the optimal ablation parameters for irreversible electroporation technology in the process of cartilage ablation has always been a difficult problem. Currently, it mainly depends on the doctor's clinical experience and the determination of ablation parameters based on previous successful cases.

[0004] However, the empirical parameter method often fails to take into account the differences between individual patients and cannot be adjusted according to the patient's specific cartilage characteristics. As a result, the ablation effect may vary greatly among different patients, making it difficult to achieve personalized treatment and may even cause side effects to patients. Summary of the Invention

[0005] In order to solve the technical problems that the existing empirical parameter methods often fail to take into account the differences between individual patients and cannot be adjusted according to the specific cartilage characteristics of the patients, resulting in large differences in ablation effects among different patients, making it difficult to achieve personalized treatment, and even causing side effects to patients, the present invention provides a method for optimizing the irreversible electroporation ablation model of cartilage.

[0006] The technical solutions provided by the embodiments of the present invention are as follows:

[0007] First aspect

[0008] An embodiment of the present invention provides a method for optimizing a cartilage irreversible electroporation ablation model, the ablation method comprising:

[0009] S1: Construction of irreversible electroporation ablation model of cartilage;

[0010] S2: Acquire an ablation sample data set, where the ablation sample data set includes multiple ablation samples, and the ablation samples include patient data and ablation parameters;

[0011] S3: With the goal of increasing the effective ablation volume, improving ablation uniformity, and reducing thermal damage, an ablation objective function of the irreversible electroporation ablation model of cartilage is constructed;

[0012] S4: using the ablation sample data set, with the goal of maximizing the ablation objective function, determining optimal model parameters to optimize the cartilage irreversible electroporation ablation model;

[0013] S5: Obtain patient data of the target patient and input the patient data into the trained and optimized irreversible electroporation ablation model for cartilage;

[0014] S6: Determine the optimal ablation parameters for the target patient by training the optimized cartilage irreversible electroporation ablation model.

[0015] Furthermore, the S1 specifically includes:

[0016] S101: using the voltage value at the electrode and the temperature value on the cartilage surface as boundary conditions of the irreversible electroporation ablation model of cartilage;

[0017] S102: determining a conductivity equation during ablation;

[0018] S103: Determine the thermal conductivity equation during the ablation process;

[0019] S104: Using Gauss's law, describe the electric field distribution equation of cartilage tissue;

[0020] S105: Considering thermal effects during electroporation and modifying the Pennes biological heat conduction equation;

[0021] S106: Constructing the irreversible electroporation ablation model of cartilage according to the electrical conductivity equation, the thermal conductivity equation, the electric field distribution equation, and the Pennes biological heat conduction equation.

[0022] Furthermore, the ablation parameters include: pulse number, pulse voltage, pulse duration, pulse period, electrode spacing, and initial temperature.

[0023] Furthermore, the ablation objective function is specifically:

[0024]

[0025] Where f represents the ablation objective function, θ represents the ablation parameter, V eff represents the effective ablation volume, V eff (i) represents the effective ablation volume of the i-th ablation sample, J u represents the ablation uniformity, J u (i) represents the ablation uniformity of the i-th ablation sample, C represents the thermal damage penalty term, C(i) represents the thermal damage penalty term of the i-th ablation sample, λ1 represents the weight coefficient of the effective ablation volume, λ2 represents the weight coefficient of ablation uniformity, and λ3 represents the weight coefficient of the thermal damage penalty term.

[0026] Furthermore, the effective ablation volume is specifically:

[0027]

[0028] Among them, V eff represents the effective ablation volume, Ω represents the model space, H represents the step function, when E(x)-E crit ≥0, the step function value is 1, when E(x)-E crit When <0, the step function value is 0, E represents the electric field intensity, x represents the spatial position, E(x) represents the electric field intensity at the spatial position x, E cirt represents the critical electric field strength that causes irreversible electroporation, and d represents the differential sign.

[0029] Furthermore, the ablation uniformity is specifically:

[0030]

[0031] Among them, J u represents ablation uniformity, Ω represents model space, E represents electric field intensity, x represents spatial position, E(x) represents the electric field intensity at spatial position x, represents the average value of the electric field intensity, and d represents the differential sign.

[0032] Furthermore, the thermal damage penalty term is specifically:

[0033]

[0034] Where C represents the thermal damage penalty term, Ω represents the model space, P represents the penalty function, T represents the temperature, x represents the spatial position, T(x) represents the temperature at the spatial position x, T max represents the damage threshold temperature, and d represents the differential sign.

[0035] Furthermore, the penalty function is specifically:

[0036]

[0037] Among them, α represents the penalty coefficient.

[0038] Furthermore, the S4 is specifically:

[0039] By utilizing the ablation sample data set and aiming to maximize the ablation objective function, the optimal model parameters are determined by the fireworks algorithm to optimize the irreversible electroporation ablation model of cartilage. The beneficial effects of the technical solution provided by the embodiment of the present invention include at least the following:

[0040] In the present invention, by introducing the patient's individual data for optimization, the effective ablation volume is increased, the ablation uniformity is improved, and thermal damage is reduced during the optimization process. At the same time, the ablation parameters can be adjusted according to the specific conditions of the target patient, providing a personalized treatment plan and achieving a more accurate ablation effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0042] Figure 1 A schematic flow chart of a method for optimizing a cartilage irreversible electroporation ablation model provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0044] Reference Manual Figure 1 , showing a flow chart of a method for optimizing a cartilage irreversible electroporation ablation model provided by an embodiment of the present invention.

[0045] An embodiment of the present invention provides a method for optimizing a cartilage irreversible electroporation ablation model. The dual-mode method includes a high-voltage steep pulse ablation mode and a local thermal ablation mode. The method can be implemented by a cartilage irreversible electroporation ablation model optimization device, which can be a terminal or a server. The process flow of the cartilage irreversible electroporation ablation model optimization method can include the following steps:

[0046] S1: Construction of irreversible electroporation ablation model of cartilage.

[0047] In a possible implementation, S1 specifically includes sub-steps S101 to S106:

[0048] S101: The voltage value at the electrode and the temperature value on the cartilage surface are used as boundary conditions of the irreversible electroporation ablation model of the cartilage.

[0049] It should be noted that precise setting of the electrode voltage can better simulate the interaction between the electrode and tissue during actual surgery, thereby improving the reliability of the model. The temperature of the cartilage surface, as a boundary condition, can help control the temperature changes of the tissue during electroporation and ablation, thereby reducing the risk of thermal damage.

[0050] S102: Determine the conductivity equation during ablation:

[0051] σ(T)=σ0[1+β(T-T0)]

[0052] Where σ represents conductivity, T represents temperature, σ(T) represents conductivity at temperature T, σ0 represents conductivity at room temperature, β represents temperature coefficient, and T0 represents reference temperature.

[0053] It should be noted that during the ablation process, rising temperature causes changes in the electrical conductivity of cartilage tissue, which directly affects the electric field distribution. Therefore, incorporating temperature into the conductivity equation allows the model to more realistically reflect the electrical behavior during ablation.

[0054] S103: Determine the thermal conductivity equation during ablation:

[0055]

[0056] Wherein, k represents thermal conductivity, k(T) represents thermal conductivity at temperature T, k0 represents the initial thermal conductivity of cartilage, a, b, α represent heat conduction parameters, and e represents a natural constant.

[0057] It should be noted that the thermal conductivity equation takes into account the nonlinear effect of temperature and can more accurately predict the changes in heat conduction during ablation, especially under high temperature conditions, which is very important for avoiding overheating damage.

[0058] S104: Using Gauss's law, describe the electric field distribution equation of cartilage tissue:

[0059]

[0060] Where E represents the electric field strength, represents the gradient operation, and U represents the input voltage.

[0061] It should be noted that the electric field distribution equation can simulate the electric field intensity distribution between the electrode and the cartilage tissue, ensuring the precise positioning of the ablation area and thus maximizing the effective ablation volume.

[0062] S105: Considering the thermal effect during electroporation, the Pennes biological heat conduction equation is modified:

[0063]

[0064] Where ρ represents the density of cartilage tissue, c represents the specific heat capacity, represents partial derivative operation, t represents time, Q j represents the heat caused by electroporation, Q m Represents metabolic heat.

[0065]

[0066] Where τ represents the pulse duration and p represents the pulse period.

[0067] It should be noted that the Pennes biological heat conduction equation is a classic model for tissue temperature distribution, accounting for factors such as heat conduction within the tissue and the heat dissipation effect of blood flow. During IRE, the thermal effect primarily comes from Joule heating (generated by the electrical pulse) and metabolic heat in the tissue. By modifying the Pennes equation, we can accurately describe the contributions of these heat sources, ensuring the accuracy of the temperature distribution in the model.

[0068] S106: Based on the electrical conductivity equation, thermal conductivity equation, electric field distribution equation and Pennes biological heat conduction equation, a cartilage irreversible electroporation ablation model was constructed.

[0069] Furthermore, the irreversible electroporation ablation model for cartilage is also used to determine the mapping relationship between patient data and ablation parameters, which can be accomplished using convolutional neural networks and artificial neural networks. The optimization of the irreversible electroporation ablation model for cartilage is mainly to find the best model parameters so that the corresponding best ablation parameters can be determined based on different patient data. Convolutional neural networks and artificial neural networks can identify complex relationships in different patient data, provide more accurate parameter adjustments, and ensure that the best ablation parameter combination can be found in different patients. Convolutional neural networks and artificial neural networks are already relatively mature existing technologies, and the present invention will not elaborate on them.

[0070] S2: Acquire an ablation sample dataset, where the ablation sample dataset includes multiple ablation samples, and the ablation samples include patient data and ablation parameters.

[0071] Optionally, the ablation parameters include: pulse number, pulse voltage, pulse duration, pulse period, electrode spacing, and initial temperature.

[0072] S3: With the goal of increasing the effective ablation volume, improving ablation uniformity, and reducing thermal damage, an ablation objective function of the irreversible electroporation ablation model for cartilage was constructed.

[0073] Optionally, the ablation objective function is specifically:

[0074]

[0075] Where f represents the ablation objective function, θ represents the ablation parameter, V eff represents the effective ablation volume, V eff (i) represents the effective ablation volume of the i-th ablation sample, J u represents the ablation uniformity, J u(i) represents the ablation uniformity of the i-th ablation sample, C represents the thermal damage penalty term, C(i) represents the thermal damage penalty term of the i-th ablation sample, λ1 represents the weight coefficient of the effective ablation volume, λ2 represents the weight coefficient of ablation uniformity, and λ3 represents the weight coefficient of the thermal damage penalty term.

[0076] Among them, those skilled in the art can set the weight coefficient λ1 of the effective ablation volume, the weight coefficient λ2 of the ablation uniformity, and the weight coefficient λ3 of the thermal damage penalty term according to actual conditions, and the present invention does not limit them.

[0077] It's important to note that optimizing the effective ablation volume ensures maximum coverage of diseased tissue, enhancing the thoroughness of treatment. Optimizing ablation uniformity prevents overablation of certain areas, minimizing damage to surrounding healthy tissue. By penalizing thermal damage, temperatures are kept within a reasonable range, minimizing damage to surrounding cartilage or joint tissue, and protecting healthy tissue.

[0078] Optionally, the effective ablation volume is specifically:

[0079]

[0080] Among them, V eff represents the effective ablation volume, Ω represents the model space, H represents the step function, when E(x)-E crit ≥0, the step function value is 1, when E(x)-E crit When <0, the step function value is 0, E represents the electric field intensity, x represents the spatial position, E(x) represents the electric field intensity at the spatial position x, E cirt represents the critical electric field strength that causes irreversible electroporation, and d represents the differential sign.

[0081] Optionally, the ablation uniformity is specifically:

[0082]

[0083] Among them, J u represents ablation uniformity, Ω represents model space, E represents electric field intensity, x represents spatial position, E(x) represents the electric field intensity at spatial position x, represents the average value of the electric field intensity, and d represents the differential sign.

[0084] Optionally, the thermal damage penalty term is specifically:

[0085]

[0086] Where C represents the thermal damage penalty term, Ω represents the model space, P represents the penalty function, T represents the temperature, x represents the spatial position, T(x) represents the temperature at the spatial position x, T max represents the damage threshold temperature, and d represents the differential sign.

[0087] Optionally, the penalty function is specifically:

[0088]

[0089] Among them, α represents the penalty coefficient.

[0090] S4: Using the ablation sample dataset, the optimal model parameters are determined with the goal of maximizing the ablation objective function to optimize the irreversible electroporation ablation model of cartilage.

[0091] In a possible implementation, S4 specifically includes: utilizing the ablation sample data set, taking maximizing the ablation objective function as the goal, and determining optimal model parameters through a fireworks algorithm to optimize the irreversible electroporation ablation model of cartilage.

[0092] Among them, the Fireworks Algorithm (FWA) is a global optimization algorithm with powerful global search capabilities and can explore complex and multi-dimensional parameter spaces.

[0093] Specifically, the ablation objective function is used as the fitness function of the fireworks algorithm.

[0094] Initialize the firework individual. Each firework individual consists of multiple dimensional components. Each firework individual represents a feasible set of model parameters, and each component represents a model parameter.

[0095] Perform explosion operations on each individual firework:

[0096]

[0097] Among them, A i represents the explosion radius of the i-th firework individual, x i represents the i-th firework individual, f represents the fitness function, N represents the total number of firework individuals, min represents the minimum value, ε represents the hyperparameter to avoid division by zero, C A Indicates the explosion radius adjustment coefficient, S i represents the number of explosion sparks of the i-th firework individual, max represents the maximum value, C S Indicates the explosion spark number adjustment coefficient.

[0098] It should be noted that the explosion radius is dynamically adjusted through the fitness function. Individuals with higher fitness values ​​have smaller explosion radius, and vice versa. This adaptive adjustment mechanism ensures a balance between global search and local optimization among individuals with different fitness levels. High-fitness individuals focus on detailed search in local areas, while low-fitness individuals conduct global exploration to avoid being trapped in local optima.

[0099] Furthermore, the number of explosion sparks is also determined by the fitness function. Individuals with low fitness generate more sparks, while individuals with high fitness generate fewer sparks. By adjusting the number of sparks, the algorithm can effectively allocate computing resources. Individuals with high fitness use fewer sparks during local searches, conserving resources; while individuals with low fitness generate more sparks for global searches, exploring new areas.

[0100] Limit the number of explosion sparks generated by explosion operations:

[0101]

[0102] in, S represents the number of explosion sparks of the i-th firework after restriction processing, max Indicates the maximum number of explosion sparks, S min Indicates the minimum number of explosion sparks.

[0103] Among them, those skilled in the art can set the maximum number of explosion sparks and the minimum number of explosion sparks according to actual conditions, and the present invention does not limit this.

[0104] It should be noted that limiting the range of the number of explosion sparks can effectively control the amount of calculation and avoid excessively high calculation costs due to too many sparks.

[0105] Randomly select some fireworks individuals, generate a random number, and determine whether the random number is less than the mutation probability. If so, perform Gaussian mutation operation:

[0106]

[0107] in, represents the jth dimension component of the i-th firework individual after Gaussian mutation, x ij represents the j-th dimension component in the i-th firework individual, and e represents a random number that satisfies the Gaussian distribution with mean 1 and variance 1.

[0108] It's important to note that Gaussian mutation allows for slight random changes in the dimensional components of each individual firework, increasing the diversity of solutions. This randomness can help the algorithm escape local optima. Especially when stuck in a local optimum, mutation can explore new solution spaces and increase the chances of finding a global optimum.

[0109] Perform mapping operations on each individual firework:

[0110] x′ ij =L j +|x ij |%(U j -L j )

[0111] Where x′ ij represents the j-th dimension component in the i-th firework individual after the mapping operation, L j Indicates the lower limit of the j-th dimension, U j Indicates the upper limit of the j-th dimension, and % indicates the modulo operation.

[0112] It's important to note that the mapping operation ensures that each dimension of the solution does not exceed feasible upper and lower limits, preventing the algorithm from generating invalid solutions. For example, parameters in irreversible electroporation (IRE) ablation of cartilage (such as voltage and pulse frequency) are physically limited, and exceeding reasonable limits can lead to invalid or dangerous solutions.

[0113] Perform a selection operation on each firework individual, and the probability of each firework individual being selected is:

[0114]

[0115] Among them, P(x i ) represents the current individual x i The probability of being selected, D(x i ) represents the current individual x i The sum of the distances to other individuals except itself, d represents the Euclidean distance between two individuals, x u Represents the u-th firework individual.

[0116] It should be noted that determining the selection probability based on the distance between individuals can effectively prevent the population from being overly concentrated in a certain area and increase the diversity of solutions. Selecting individuals with larger distances (i.e., individuals that are farther away from other individuals) can help maintain population diversity and ensure that the optimization process does not prematurely converge on a local optimal solution.

[0117] Check whether the current iteration count has reached the maximum number of iterations. If so, output the firework representative with the highest fitness. Otherwise, return to continue iteration.

[0118] In this paper, the Fireworks algorithm is used for optimization in the irreversible electroporation ablation model for cartilage. This algorithm can determine optimal ablation parameters based on efficient, accurate, and global search. The Fireworks algorithm's global search capabilities, adaptability to high-dimensional problems, rapid convergence, and robustness make it particularly well-suited for complex multi-objective optimization problems, ensuring an optimal balance between multiple objectives, such as increasing the effective ablation volume, optimizing ablation uniformity, and minimizing thermal damage.

[0119] S5: Obtain patient data of the target patient and input the patient data into the trained and optimized irreversible electroporation ablation model for cartilage.

[0120] S6: Determine the optimal ablation parameters for the target patient by training the optimized cartilage irreversible electroporation ablation model.

[0121] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0122] In the present invention, by introducing the patient's individual data for optimization, the effective ablation volume is increased, the ablation uniformity is improved, and thermal damage is reduced during the optimization process. At the same time, the ablation parameters can be adjusted according to the specific conditions of the target patient, providing a personalized treatment plan and achieving a more accurate ablation effect.

[0123] The present invention further provides a cartilage irreversible electroporation ablation model optimization system 20, which is applied to the above-mentioned cartilage irreversible electroporation ablation model optimization method, comprising:

[0124] Processor 201.

[0125] The memory 202 stores computer-readable instructions. When the computer-readable instructions are executed by the processor 201 , the method for optimizing the irreversible electroporation ablation model of cartilage in the method embodiment is implemented.

[0126] The cartilage irreversible electroporation ablation model optimization system 20 provided by the present invention can execute the above-mentioned cartilage irreversible electroporation ablation model optimization method and achieve the same or similar technical effects. To avoid repetition, the present invention will not elaborate on it.

[0127] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0128] In the present invention, by introducing the patient's individual data for optimization, the effective ablation volume is increased, the ablation uniformity is improved, and thermal damage is reduced during the optimization process. At the same time, the ablation parameters can be adjusted according to the specific conditions of the target patient, providing a personalized treatment plan and achieving a more accurate ablation effect.

[0129] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for optimizing a cartilage irreversible electroporation ablation model, characterized in that: include: S1: Construction of irreversible electroporation ablation model of cartilage; S2: Acquire an ablation sample data set, where the ablation sample data set includes multiple ablation samples, and the ablation samples include patient data and ablation parameters; S3: With the goal of increasing the effective ablation volume, improving ablation uniformity, and reducing thermal damage, an ablation objective function of the irreversible electroporation ablation model of cartilage is constructed; S4: using the ablation sample data set, with the goal of maximizing the ablation objective function, determining optimal model parameters to optimize the cartilage irreversible electroporation ablation model; S5: Obtain patient data of the target patient and input the patient data into the trained and optimized irreversible electroporation ablation model for cartilage; S6: Determine optimal ablation parameters for the target patient by training the optimized irreversible electroporation ablation model for cartilage; The ablation objective function is specifically: ； Where f represents the ablation objective function, θ represents the ablation parameter, V eff represents the effective ablation volume, V eff (i) represents the effective ablation volume of the i-th ablation sample, J u represents the ablation uniformity, J u (i) represents the ablation uniformity of the i-th ablation sample, C represents the thermal damage penalty term, C(i) represents the thermal damage penalty term of the i-th ablation sample, λ1 represents the weight coefficient of the effective ablation volume, λ2 represents the weight coefficient of the ablation uniformity, and λ3 represents the weight coefficient of the thermal damage penalty term; The S4 is specifically: The ablation sample data set is used to maximize the ablation objective function and determine optimal model parameters through a fireworks algorithm to optimize the cartilage irreversible electroporation ablation model.

2. The method for optimizing the irreversible electroporation ablation model of cartilage according to claim 1, characterized in that: Said S1 specifically includes: S101: using the voltage value at the electrode and the temperature value on the cartilage surface as boundary conditions of the irreversible electroporation ablation model of cartilage; S102: determining a conductivity equation during ablation; S103: Determine the thermal conductivity equation during the ablation process; S104: Using Gauss's law, describe the electric field distribution equation of cartilage tissue; S105: Considering thermal effects during electroporation and modifying the Pennes biological heat conduction equation; S106: Constructing the irreversible electroporation ablation model of cartilage according to the electrical conductivity equation, the thermal conductivity equation, the electric field distribution equation, and the Pennes biological heat conduction equation.

3. The method for optimizing the cartilage irreversible electroporation ablation model according to claim 1, characterized in that: The ablation parameters include: pulse number, pulse voltage, pulse duration, pulse period, electrode spacing, and initial temperature.

4. The method for optimizing the irreversible electroporation ablation model of cartilage according to claim 1, characterized in that: The effective ablation volume is specifically: ； Among them, V eff represents the effective ablation volume, Ω represents the model space, H represents the step function, when When , the step function value is 1, when When the step function value is 0, E represents the electric field strength, x represents the spatial position, E(x) represents the electric field strength at the spatial position x, and E cirt represents the critical electric field strength that causes irreversible electroporation, and d represents the differential sign.

5. The method for optimizing the irreversible electroporation ablation model of cartilage according to claim 1, characterized in that: The ablation uniformity is specifically: ； Among them, J u represents ablation uniformity, Ω represents model space, E represents electric field intensity, x represents spatial position, E(x) represents the electric field intensity at spatial position x, represents the average value of the electric field intensity, and d represents the differential sign.

6. The method for optimizing the cartilage irreversible electroporation ablation model according to claim 1, characterized in that: The thermal damage penalty term is specifically: ； Where C represents the thermal damage penalty term, Ω represents the model space, P represents the penalty function, T represents the temperature, x represents the spatial position, T(x) represents the temperature at the spatial position x, T max represents the damage threshold temperature, and d represents the differential sign.

7. The method for optimizing the irreversible electroporation ablation model of cartilage according to claim 6, characterized in that: The penalty function is specifically: ； Among them, α represents the penalty coefficient.

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