Radiofrequency ablation rapid simulation method and system based on Monte Carlo method

Abstract

The present invention provides a method and system for rapid simulation of radiofrequency ablation based on the Monte Carlo method, which performs clustering preprocessing on the calculation domain according to image information, constructs a reduced simulation model, reasonably simplifies the electric physical field coupling calculation, uses the finite difference method to calculate the thermal physical field, and iteratively performs rapid thermal / electric physical field coupling calculation; based on CUDA, GPU hardware is used to accelerate the model construction and numerical calculation process in the simulation calculation process. The present invention realizes mixed high- and low-precision voxel grid modeling, alleviates the problem of redundant calculation caused by traditional modeling methods; realizes automatic reduction of symmetrical and equivalent positions, automatically excludes areas that do not need to be calculated from the calculation domain, and reduces the amount of calculation; reasonably simplifies the electric field calculation, combines GPU hardware acceleration, and realizes rapid electric field calculation; realizes accelerated calculation of electric / thermal coupling field, and provides real-time temperature field calculation of the surgical area.

Description

Technical Field

[0001] The present invention relates to the medical field, and in particular to a Monte Carlo-based radiofrequency ablation rapid simulation method and system. Background Art

[0002] In radiofrequency ablation surgery, simulation methods are often used to estimate the ablation area and temperature field distribution, which requires iterative calculation of the electrothermal coupling field. The most commonly used finite element algorithm currently has disadvantages such as high time consumption and high memory usage.

[0003] The invention patent CN111027225A discloses an ablation simulation method based on data fitting, which includes: calculating the measured average values ​​of the short diameter and long diameter data of the ablation boundary under the same ablation power and ablation time, and performing thermal field simulation on the target area, taking the short diameter data as the reference, and taking the long diameter corresponding to the contour line where the temperature threshold is located as the long diameter simulation value; establishing a temperature threshold and ablation power relationship model under low ablation power; establishing a temperature threshold and ablation time relationship model under high ablation power; establishing a correction coefficient and ablation power relationship model; inputting ablation power and ablation time, selecting the temperature threshold and ablation power relationship model or the temperature threshold and ablation time relationship model according to the ablation power, obtaining the temperature threshold, obtaining the corresponding ablation simulation image according to the temperature threshold, and using the correction coefficient and ablation power relationship model to correct the long diameter of the ablation simulation image. However, the above scheme is based on empirical data statistics and lacks adaptation to individual differences; the temperature threshold is difficult to determine and cannot be directly linked to the actual ablation process.

[0004] The finite element steady-state thermal simulation method for tumor phantoms proposed in the article "Numerical Simulation of Radiofrequency Heating Treatment of Tumor Phantoms" published by Tang Rubing can calculate steady-state heat conduction, but lacks adaptability to non-steady-state and non-radio frequency heating scenarios. The boundary-distributed Monte Carlo thermal simulation method proposed in the article "A BOUNDARY-DISPATCH MONTE CARLO (EXODUS) METHOD FOR ANALYSIS OF CONDUCTIVE HEAT TRANSFER PROBLEMS" published by Mohammad HNNaraghi has poor adaptability to irregular boundary conditions and cannot handle internal heat sources. Summary of the invention

[0005] In view of the defects in the prior art, an object of the present invention is to provide a method and system for rapid simulation of radiofrequency ablation based on the Monte Carlo method.

[0006] A Monte Carlo method-based rapid simulation method for radiofrequency ablation provided by the present invention comprises the following steps:

[0007] Basic simulation model construction steps: input CT / MR image data, generate voxel grids based on the image data, and build a basic simulation model;

[0008] Parameter estimation step: input the basic simulation model, refine the model boundary based on the segmentation result of the image data, subdivide the boundary voxels, and estimate the differentiation parameters for each location in the calculation domain of the basic simulation model according to the value of the image data;

[0009] Computational domain reduction step: clustering and reducing the computational domain based on multi-dimensional conditions;

[0010] Electric / thermal physical field coupling calculation steps: use the Monte Carlo method to simplify the electric physical field coupling calculation, use the finite difference method to calculate the thermal physical field, and iterate to perform fast thermal / electric physical field coupling calculation;

[0011] Cell apoptosis calculation step: calculate the cell apoptosis result and judge whether the stop condition is met. If the judgment result is yes, output the ablation area; if the judgment result is no, jump to the calculation domain reduction step.

[0012] Preferably, the heat flow conduction direction and relationship between each voxel unit are determined using the differential form of the Pennes bioheat conduction equation.

[0013] Preferably, the computational domain reduction step comprises:

[0014] Determine the tissue type based on the segmentation results of the image data, adjust the calculation domain according to the tissue boundary, and exclude the parts outside the boundary of the target tissue from the calculation domain;

[0015] According to the position of the ablation probe, the area beyond the distance threshold and outside the surgical range is excluded from the calculation domain;

[0016] Based on the intermediate simulation results, respond to parameter changes caused by dynamic processes such as phase transition and apoptosis;

[0017] The model parameters are adjusted for the denatured and burnt areas, and based on the symmetry conditions, the locations with similar calculation conditions of electrical / thermal properties and distance components in the model calculation domain are clustered and reduced.

[0018] Preferably, the differentiated parameters include differentiated thermal conductivity, resistivity, and blood perfusion rate.

[0019] Preferably, using the Monte Carlo method to calculate the electric physical field coupling includes:

[0020] Step S1: Determine the RF emission position as the starting position, generate N simulated particles according to preset parameters, and have a ratio of T b / T hThe particles are high-energy particles, and the rest are low-energy particles. b Represents the target temperature of heating, T h Represents the highest temperature of tissue cells;

[0021] Step S2: Calculate the random walk of the particle. Each time step is run, the simulated particle walks M steps according to the feasible direction of electrical conduction of the model until it reaches the boundary and stops.

[0022] Step S3: After all simulated particles have completed their random walk, the number of high-energy particles and low-energy particles passing through each voxel grid is counted, and the grid electric field strength is estimated to be E i +N h / N×Δe, where E i is the original field strength value, Δe is the unit value of electric field strength;

[0023] Step S4: Calculate Q according to Joule heat formula j = J·E Calculate the heat energy generated by the RF electric field in one time step according to the Pennes equation

[0024]

[0025] In the differential form of the current mesh model, the heat transfer equations are solved using the finite difference method and the results are fed back into the temperature field.

[0026] Preferably, CUDA is used to perform GPU acceleration on the particle wandering process.

[0027] Preferably, CUDA is used to perform parallel hardware acceleration on the heat transfer calculation.

[0028] Preferably, in the cell apoptosis calculation step, the accumulated thermal damage to the cells is calculated according to the temperature field distribution and the Arrhenius equation.

[0029]

[0030] Where A is the ablation damage coefficient, ΔE is the activation energy, R is the universal gas constant, and T is the temperature. When Ω exceeds the threshold, the cells are set to the apoptotic state, and the results of tissue cell apoptosis caused by the ablation thermal effect are calculated to infer the size of the ablation area.

[0031] Preferably, CUDA is used to perform parallel hardware acceleration on the damage calculation.

[0032] A radiofrequency ablation rapid simulation system based on the Monte Carlo method provided by the present invention includes the following modules:

[0033] Basic simulation model building module: input CT / MR image data, generate voxel grids based on the image data, and build a basic simulation model;

[0034] Parameter estimation module: input the basic simulation model, refine the model boundary based on the segmentation results of the image data, subdivide the boundary voxels, and estimate the differentiation parameters for each location in the calculation domain of the basic simulation model according to the value of the image data;

[0035] Computational domain reduction module: clustering and reducing the computational domain based on multi-dimensional conditions;

[0036] Electric / thermal physical field coupling calculation module: uses the Monte Carlo method to simplify the electric physical field coupling calculation, uses the finite difference method to calculate the thermal physical field, and iterates to perform fast thermal / electric physical field coupling calculation;

[0037] Cell apoptosis calculation module: calculates the cell apoptosis results and determines whether the stop condition is met. If the judgment result is yes, the ablation area is output; if the judgment result is no, it jumps to the calculation domain reduction module.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention realizes high- and low-precision mixed voxel grid modeling through parameter estimation, alleviating the problem of redundant calculation caused by traditional modeling methods.

[0040] 2. The present invention realizes automatic reduction of symmetrical and equivalent positions by reducing the computational domain, automatically excludes areas that do not need to be calculated from the computational domain, and reduces the amount of calculation.

[0041] 3. The present invention reasonably simplifies the electric field calculation by using the Monte Carlo method and realizes fast electric field calculation by combining with GPU hardware acceleration.

[0042] 4. The present invention uses CUDA to perform GPU acceleration, realizes accelerated calculation of the electrical / thermal coupling field, and provides real-time calculation of the temperature field in the surgical area. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0044] Figure 1 This is an algorithm flow chart of the rapid simulation method of radiofrequency ablation based on the Monte Carlo method.

[0045] Figure 2 Schematic diagram of the Monte Carlo method.

[0046] Figure 3 This is the simulation result diagram of the ablation area.

[0047] Figure 4This is the simulation result diagram of ablation temperature field. DETAILED DESCRIPTION

[0048] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0049] like Figures 1 to 4 As shown, the present invention provides a method and system for rapid simulation of radiofrequency ablation based on the Monte Carlo method, which realizes comprehensive acceleration of radiofrequency ablation simulation from three levels: model construction, numerical calculation, and hardware acceleration, namely: model construction: clustering preprocessing of the calculation domain according to image information, and construction of a reduced simulation model; numerical calculation: using the Monte Carlo method to reasonably simplify the electric physical field coupling calculation, using the faster finite difference method to calculate the thermal physical field, and iteratively performing rapid thermal / electric physical field coupling calculations; hardware acceleration: using GPU hardware based on CUDA to accelerate the model construction and numerical calculation process in the simulation calculation process. Specifically, it includes: inputting image data in the form of CT / MR, generating voxel grids according to the image data, and constructing a basic simulation model; parameter estimation step: inputting the basic simulation model, refining the model boundary based on the segmentation result of the image data, subdividing the boundary voxels, and estimating the differentiated thermal conductivity, resistivity, blood perfusion rate and other parameters according to the numerical value of the image data for each location in the calculation domain of the basic simulation model; calculation domain reduction step: clustering and reducing the calculation domain based on multi-dimensional conditions; electric / thermal physical field coupling calculation step: using the Monte Carlo method to simplify the electric physical field coupling calculation, using the finite difference method to calculate the thermal physical field, and iterating to perform fast thermal / electric physical field coupling calculations; cell apoptosis calculation step: calculating the cell apoptosis result, judging whether the stop condition is met, and if the judgment result is yes, outputting the ablation area; if the judgment result is no, jumping to the calculation domain reduction step.

[0050] Furthermore, the difference form of the Pennes biological heat conduction equation is used between each voxel unit to determine the direction and relationship of heat flow conduction. The calculation domain reduction step includes: determining the tissue type based on the segmentation result of the image data, adjusting the calculation domain according to the tissue boundary, and excluding the parts outside the target tissue boundary from the calculation domain; excluding the areas beyond the distance threshold and not within the surgical range from the calculation domain according to the position of the ablation probe; responding to parameter changes caused by dynamic processes such as phase change and apoptosis based on the simulation intermediate results; adjusting the model parameters for the denatured and burnt areas, and clustering and reducing the locations in the model calculation domain with similar calculation conditions of electrical / thermal properties and distance composition according to the symmetry conditions.

[0051] The Monte Carlo method is used to couple the electric physics to the following calculations:

[0052] Step S1: Determine the RF emission position as the starting position, generate N simulated particles according to preset parameters, and have a ratio of T b / T h The particles are high-energy particles, and the rest are low-energy particles. b Represents the target temperature of heating, T h Represents the highest temperature of tissue cells;

[0053] Step S2: Calculate the random walk of particles. Each time step is run, simulate the particles walking M steps according to the feasible direction of electrical conduction of the model until they reach the boundary and stop. CUDA is used to accelerate the particle walking process with GPU.

[0054] Step S3: After all simulated particles have completed their random walk, the number of high-energy particles and low-energy particles passing through each voxel grid is counted, and the grid electric field strength is estimated to be E i +N h / N×Δe, where E i is the original field strength value, Δe is the unit value of electric field strength;

[0055] Step S4: Calculate Q according to Joule heat formula j = J·E Calculate the heat energy generated by the RF electric field in one time step according to the Pennes equation

[0056]

[0057] The heat transfer equation is solved using the finite difference method in the differential form of the current grid model, and the results are fed back into the temperature field. CUDA is used to parallelize the heat transfer calculations for hardware acceleration.

[0058] In the cell apoptosis calculation step, the accumulated thermal damage to the cells is calculated according to the temperature field distribution and the Arrhenius equation.

[0059]

[0060] Where A is the ablation damage coefficient, ΔE is the activation energy, R is the universal gas constant, and T is the temperature. When Ω exceeds the threshold, the cells are set to apoptotic state, and the apoptosis results of tissue cells caused by the ablation thermal effect are calculated to estimate the size of the ablation area. CUDA is used to parallelize the damage calculation for hardware acceleration.

[0061] In more detail, the Monte Carlo method-based rapid simulation method for radiofrequency ablation provided by the present invention includes:

[0062] S1: Construction of basic simulation model. Input CT / MR image data, generate voxel grids based on the image data, use the differential form of Pennes biological heat conduction equation to determine the heat flow conduction direction and relationship between each voxel unit, and build a low-precision basic simulation model. After the low-precision basic simulation model is built, initialize the properties of each position in the area, and the initialization parameters are determined according to the preset basic parameters of the tissue.

[0063] S2: Parameter estimation. Input the basic simulation model, refine the model boundary based on the segmentation results of the image data, and further subdivide the boundary voxels to match the shape of the organ. For each location in the simulation model calculation domain, estimate the differential thermal conductivity, resistivity, blood perfusion rate and other parameters based on the values ​​of the image data.

[0064] S3: Computational domain reduction. The tissue type is determined based on the segmentation results of the image data, and the computational domain is adjusted according to the tissue boundary, excluding the parts outside the target tissue boundary from the computational domain; according to the position of the ablation probe, the areas beyond the distance threshold and outside the surgical range are excluded from the computational domain; based on the intermediate simulation results, the parameter changes caused by dynamic processes such as phase change and apoptosis are responded to, and the model parameters are adjusted for the denatured and burnt areas. According to the symmetry conditions, the locations in the model computational domain with similar electrical / thermal properties and distance composition computational conditions are clustered and reduced.

[0065] After S2 and S3, we can obtain the refined simulation model, and the next step is the numerical calculation part.

[0066] S4: Electric / thermal physical field coupling calculation. The finite difference method and Monte Carlo method are used to perform coupled calculations of the electric field and temperature field. The Monte Carlo method's particle dispatching algorithm is used to accelerate the calculation of the electric field distribution. Each iteration will calculate the changes in the temperature field distribution caused by radio frequency heating and human body heat transfer under the current conditions.

[0067] The specific steps of calculating RF heating by Monte Carlo method in S4 include:

[0068] S4-MC1: Determine the RF emission position (e.g., the notch on the RF probe) as the starting position, and generate N simulated particles according to the preset parameters, with a ratio of T b / T h The particles are high-energy particles, and the rest are low-energy particles. b Represents the target temperature of heating, T h Represents the highest temperature of tissue cells.

[0069] S4-MC2: Calculate the random walk of particles. Each time step, simulate the particles walking M steps according to the feasible direction of electrical conduction of the model until they reach the boundary and stop. Since the movement between particles in this part is independent of each other, CUDA is used to accelerate the particle walking process with GPU.

[0070] S4-MC3: After all simulated particles have completed random walks, the number of high-energy particles and low-energy particles passing through each voxel grid is counted, and the grid electric field strength can be estimated as E i +N h / N×Δe, where E i is the original field strength value, and Δe is the unit value of the electric field strength.

[0071] S4-MC4: Calculate Q based on Joule heat formula j = J·E calculates the heat energy generated by the RF electric field in one time step, and then according to the Pennes equation

[0072]

[0073] In the differential form of the current grid model, the finite difference method is used to solve the heat transfer equation and the result is fed back to the temperature field. Since the solutions of the heat transfer equations at various locations in this part are independent of each other, CUDA is used to parallelize the heat transfer calculations and accelerate them.

[0074] S5: Calculation of cell apoptosis. Based on the temperature field distribution, the cumulative thermal damage received by the cells is calculated according to the Arrhenius equation.

[0075]

[0076] Where A is the ablation damage coefficient, ΔE is the activation energy, R is the universal gas constant, T is the temperature, and when Ω exceeds the threshold (the default value is 1), the cell is set to apoptotic state. The apoptosis results of tissue cells caused by the ablation thermal effect are calculated to infer the size of the ablation area. Since the damage accumulation at each position in this part is independent of each other, CUDA is used to parallelize the damage calculation for hardware acceleration.

[0077] If the stopping condition is not met (the operation time threshold, core temperature threshold, ablation lesion size threshold, etc. can be used), jump to step 3 and perform the next round of iteration; if it is met, the final ablation area is output, including the short diameter, long diameter and specific shape of the ablation area.

[0078] The simulation performance comparison of different acceleration modes in a voxel grid with 125,000 voxels using this algorithm yields the following results:

[0079]

[0080] The CPU uses unaccelerated computing, CPU multithreading is implemented using the C++ thread library, and GPU acceleration is implemented using CUDA.

[0081] According to the present invention, a rapid simulation system for radiofrequency ablation based on the Monte Carlo method includes a basic simulation model construction module: inputting image data in the form of CT / MR, generating a voxel grid according to the image data, and constructing a basic simulation model; a parameter estimation module: inputting the basic simulation model, refining the model boundary based on the segmentation result of the image data, subdividing the boundary voxels, and estimating the differential parameters for each location in the calculation domain of the basic simulation model according to the numerical value of the image data; a calculation domain reduction module: clustering and reducing the calculation domain based on multi-dimensional conditions; an electric / thermal physical field coupling calculation module: using the Monte Carlo method to simplify the electric physical field coupling calculation, using the finite difference method to calculate the thermal physical field, and iteratively performing rapid thermal / electric physical field coupling calculations; a cell apoptosis calculation module: calculating the cell apoptosis result, judging whether the stop condition is met, and if the judgment result is yes, outputting the ablation area; if the judgment result is no, jumping to the calculation domain reduction module.

[0082] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A rapid simulation method for radiofrequency ablation based on Monte Carlo method, characterized in that: The steps include: Basic simulation model construction steps: input CT / MR image data, generate voxel grids based on the image data, and build a basic simulation model; Parameter estimation step: input the basic simulation model, refine the model boundary based on the segmentation result of the image data, subdivide the boundary voxels, and estimate the differentiation parameters for each location in the calculation domain of the basic simulation model according to the value of the image data; Computational domain reduction step: clustering and reducing the computational domain based on multi-dimensional conditions; Electric / thermal physical field coupling calculation steps: use the Monte Carlo method to simplify the electric physical field coupling calculation, use the finite difference method to calculate the thermal physical field, and iterate to perform fast thermal / electric physical field coupling calculation; Cell apoptosis calculation step: calculate the cell apoptosis result, determine whether the stop condition is met, and if the determination result is yes, output the ablation area; If the judgment result is no, jump to the computational domain reduction step; The Monte Carlo method is used to couple the electric physics to the following calculations: Step S1: Determine the RF emission position as the starting position, generate N simulated particles according to preset parameters, and have a ratio of T b / T h The particles are high-energy particles, and the rest are low-energy particles. b Represents the target temperature of heating, T h Represents the highest temperature of tissue cells; Step S2: Calculate the random walk of the particle. Each time step is run, the simulated particle walks M steps according to the feasible direction of electrical conduction of the model until it reaches the boundary and stops. Step S3: After all simulated particles have completed their random walk, the number of high-energy particles and low-energy particles passing through each voxel grid is counted, and the grid electric field strength is estimated to be E i +N h / N×Δe, where E i is the original field strength value, Δe is the unit value of electric field strength; Step S4: Calculate Q according to Joule heat formula j = J·E Calculate the heat energy generated by the RF electric field in one time step according to the Pennes equation In the differential form of the current mesh model, the heat transfer equations are solved using the finite difference method and the results are fed back into the temperature field.

2. The method for rapid simulation of radiofrequency ablation based on Monte Carlo method according to claim 1, characterized in that: The difference form of Pennes's bioheat conduction equation is used to determine the direction and relationship of heat flow between each voxel unit.

3. The Monte Carlo method-based rapid simulation method for radiofrequency ablation according to claim 1, characterized in that: The computational domain reduction step comprises: Determine the tissue type based on the segmentation results of the image data, adjust the calculation domain according to the tissue boundary, and exclude the parts outside the boundary of the target tissue from the calculation domain; According to the position of the ablation probe, the area beyond the distance threshold and outside the surgical range is excluded from the calculation domain; Based on the intermediate simulation results, respond to parameter changes caused by dynamic processes such as phase transition and apoptosis; The model parameters are adjusted for the denatured and burnt areas, and based on the symmetry conditions, the locations with similar calculation conditions of electrical / thermal properties and distance components in the model calculation domain are clustered and reduced.

4. The Monte Carlo method-based rapid simulation method for radiofrequency ablation according to claim 1, characterized in that: The differential parameters include differentiated thermal conductivity, resistivity, and blood perfusion rate.

5. The Monte Carlo method-based rapid simulation method for radiofrequency ablation according to claim 1, characterized in that: CUDA is used to accelerate the particle movement process using GPU.

6. The Monte Carlo method-based rapid simulation method for radiofrequency ablation according to claim 1, characterized in that: Use CUDA to parallelize the heat transfer calculations and perform hardware acceleration.

7. The Monte Carlo method-based rapid simulation method for radiofrequency ablation according to claim 1, characterized in that: In the cell apoptosis calculation step, the accumulated thermal damage to the cells is calculated according to the temperature field distribution and the Arrhenius equation. Where A is the ablation damage coefficient, ΔE is the activation energy, R is the universal gas constant, and T is the temperature. When Ω exceeds the threshold, the cells are set to the apoptotic state, and the results of tissue cell apoptosis caused by the ablation thermal effect are calculated to infer the size of the ablation area.

8. The Monte Carlo method-based rapid simulation method for radiofrequency ablation according to claim 7, characterized in that: The damage calculation is parallelized and hardware accelerated using CUDA.

9. A rapid simulation system for radiofrequency ablation based on Monte Carlo method, characterized in that: Includes the following modules: Basic simulation model building module: input CT / MR image data, generate voxel grids based on the image data, and build a basic simulation model; Parameter estimation module: input the basic simulation model, refine the model boundary based on the segmentation results of the image data, subdivide the boundary voxels, and estimate the differentiation parameters for each location in the calculation domain of the basic simulation model according to the value of the image data; Computational domain reduction module: clustering and reducing the computational domain based on multi-dimensional conditions; Electric / thermal physical field coupling calculation module: uses the Monte Carlo method to simplify the electric physical field coupling calculation, uses the finite difference method to calculate the thermal physical field, and iterates to perform fast thermal / electric physical field coupling calculation; Cell apoptosis calculation module: calculates the cell apoptosis results and determines whether the stop condition is met. If the judgment result is yes, the ablation area is output; If the judgment result is no, jump to the computational domain reduction module; The Monte Carlo method is used to couple the electric physics to the following calculations: Step S1: Determine the RF emission position as the starting position, generate N simulated particles according to preset parameters, and have a ratio of T b / T h The particles are high-energy particles, and the rest are low-energy particles. b Represents the target temperature of heating, T h Represents the highest temperature of tissue cells; Step S2: Calculate the random walk of the particle. Each time step is run, the simulated particle walks M steps according to the feasible direction of electrical conduction of the model until it reaches the boundary and stops. Step S3: After all simulated particles have completed their random walk, the number of high-energy particles and low-energy particles passing through each voxel grid is counted, and the grid electric field strength is estimated to be E i +N h / N×Δe, where E i is the original field strength value, Δe is the unit value of electric field strength; Step S4: Calculate Q according to Joule heat formula j = J·E Calculate the heat energy generated by the RF electric field in one time step according to the Pennes equation In the differential form of the current mesh model, the heat transfer equations are solved using the finite difference method and the results are fed back into the temperature field.

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