CN114117875A - Rapid Monte Carlo simulation method for simulating photon propagation - Google Patents
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Abstract
The invention belongs to the field of optics and discloses a fast Monte Carlo simulation method for simulating photon transmission.
Description
Technical Field
The invention belongs to the field of optics, and relates to a fast Monte Carlo simulation method for simulating photon propagation.
Background
Monte carlo simulation is a method based on repeated random sampling of physical quantities, and is often used to solve problems that are too complex due to the intervention of random variables or that cannot be solved by other mathematical models. Due to its high flexibility and accuracy, monte carlo simulation has become the most common means for simulating photon propagation in complex structured media, and is particularly suitable for simulating photon propagation in biological tissues. In the Monte Carlo simulation process, the random propagation result of each photon is recorded and averaged to obtain an estimated value, so that the Monte Carlo simulation can theoretically achieve any expected simulation accuracy. However, to achieve higher simulation accuracy, a larger number of photons are typically required for simulation, which will result in a doubling of the computational effort. The time efficiency problem of the monte carlo simulation becomes a main limit influencing the simulation precision, and how to improve the simulation speed on the premise of ensuring the simulation precision becomes a critical technical bottleneck to be solved urgently in the field of the monte carlo simulation.
Disclosure of Invention
Aiming at the defects in the existing Monte Carlo simulation technology, the invention provides a rapid Monte Carlo simulation method for simulating photon propagation. According to the method, a photon propagation simulation result is utilized to train a database and a reconstruction model based on a generated countermeasure network, a fine photon propagation simulation result is reconstructed from a rough photon propagation simulation result which only needs to input a small number of photons and consumes less time, and the time consumption of simulation is greatly reduced on the premise of ensuring the quality of the photon propagation simulation result.
The technical scheme of the invention is as follows:
a fast Monte Carlo simulation method for simulating photon transmission, which creates a photon transmission simulation result training database by generating a large number of paired rough and fine photon transmission simulation results; and training a reconstruction model from a rough photon transmission simulation result to a fine photon transmission simulation result by utilizing the training database and the method for generating the confrontation network. In practical application, a rough photon propagation simulation result is obtained based on a small number of photons under the condition of short simulation time, and a fine photon propagation simulation result is reconstructed from the rough photon propagation simulation result by utilizing the trained reconstruction model.
The method comprises the following specific steps:
step one, establishing a photon propagation simulation result training database. Performing classical Monte Carlo simulation based on a small number of photons and a large number of photons respectively by using the same optical parameters to generate a pair of rough and fine photon propagation simulation results; adjusting different optical parameters, repeating the Monte Carlo simulation process to generate a large number of rough and fine photon transmission simulation results in pairs, and establishing a photon transmission simulation result training database.
And step two, training a reconstruction model from the rough photon transmission simulation result to the fine photon transmission simulation result. And (4) training a database to learn a reconstruction model from the photon propagation simulation result obtained in the step one by using a method of generating a confrontation network. The generation countermeasure network comprises a generator and a discriminator, wherein the generator is used for reconstructing a fine photon propagation simulation result from the rough photon propagation simulation result obtained in the step one, and the discriminator is difficult to distinguish the reconstructed fine photon propagation simulation result from the real fine photon propagation simulation result obtained in the step one; the discriminator is used for discriminating the photon propagation simulation result, and discriminating the reconstructed fine photon propagation simulation result and the real fine photon propagation simulation result obtained in the first step as much as possible; and finally obtaining an optimized reconstruction model through the dynamic game process of the generator and the discriminator.
And step three, reconstructing a fine photon transmission simulation result from the rough photon transmission simulation result. Inputting a small amount of photons to perform classical Monte Carlo simulation, and obtaining a rough photon propagation simulation result under the condition of short time consumption; and then, reconstructing a fine photon propagation simulation result from the coarse photon propagation simulation result by using the reconstructed model trained in the second step, wherein the reconstructed photon propagation simulation result is close to the real fine photon propagation simulation result.
The invention has the beneficial effects that the fast Monte Carlo simulation method for simulating photon transmission is provided, and the time consumption of Monte Carlo simulation can be greatly reduced on the premise of ensuring the simulation precision of photon transmission. In addition, the invention has better compatibility, and can be combined with other Monte Carlo simulation acceleration modes, such as a combined Graphic Processor (GPU) parallel operation to further accelerate the simulation speed. Therefore, the method can effectively solve the key bottleneck limiting the practical application of Monte Carlo simulation, and has important application value.
Drawings
FIG. 1 is a schematic view of a tissue model for simulating photon propagation.
FIG. 2 is a flow chart for training a reconstruction model using a pix2pix network.
Fig. 3 is a schematic structural diagram of a pix2pix network used in training a reconstruction model.
Fig. 4 is a graph comparing photon absorption profiles. Wherein: (a) inputting a rough photon absorption distribution diagram of 10000 photons; (b) a fine photon absorption profile reconstructed based on the coarse photon absorption profile; (c) a fine photon absorption profile of 1000000 photons in number was input.
Detailed Description
The following uses a conventional photon propagation simulation, i.e. the absorption profile of photons in a single-layer biological tissue model, and the detailed description of the embodiments of the present invention is made with reference to the accompanying drawings.
Example 1
In this example, a single layer biological tissue model embedded with a spherical tumor, as shown in fig. 1, was used and the absorption profile of photons in the biological tissue model was simulated. More specifically, all photons are incident vertically into the biological tissue model at the X-axis center position; for the surrounding tissue, the absorption coefficient μ a, the scattering coefficient μ s, the anisotropy factor g, and the refractive index n were set to 2cm, respectively-1、100cm-10.8 and 1.4; the anisotropy factor g and refractive index n for the embedded tumor were the same as for the surrounding tissue, with an absorption coefficient of 5cm-1To 14cm-1With a step length of 3cm-1Scattering coefficient of 100cm-1To 400cm-1With a step length of 100cm-1(ii) a The position of the tumor varies from 0.5mm to 0.8mm along the X-axis with a step size of 0.1mm and from 0.2mm to 0.8mm along the Z-axis with a step size of 0.2 mm; the radius of the tumor varies between 0.1mm and 0.2mm in steps of 0.05 mm. Thus, a total of 768 different combinations of parameters can be obtained, combining the possibilities of all the above parameters. Based on the parameter combination, 10000 photons are used as input to obtain a rough photon absorption distribution graph; obtaining a fine photon absorption profile using 1000000 photons as input; 768 pairs of coarse and fine lights can be obtained in totalThe sub-absorption profile. Randomly dividing the 768 pair photon absorption distribution graph into a training set, a verification set and a test set according to the proportion of about 3:1: 1; the training set and the verification set are used for training the reconstruction model, and the test set is used for testing the trained reconstruction model. An improved generative countermeasure network, the pix2pix network, will be employed in training the reconstructed model. And aiming at the simulation precision of the reconstructed photon absorption distribution diagram, evaluating the peak signal-to-noise ratio and the power coupling efficiency percentage difference after five-fold cross test.
The specific implementation steps are as follows:
step one, establishing a photon absorption distribution map training database. Classical monte carlo simulations were performed based on 10000 photons and 1000000 photons, respectively, using the 768 optical parameter combinations described above, to generate 768 pairs of coarse and fine photon absorption profiles. Randomly dividing the 768 pair photon absorption distribution graph into a training set, a verification set and a test set according to the proportion of about 3:1: 1; wherein 460 is used as a training set for the photon absorption distribution map, 154 is used as a verification set for the photon absorption distribution map, 154 is used as a test set for the rough photon absorption distribution map, and 154 is used as a standard for evaluating the reconstructed photon absorption distribution map.
And step two, training a reconstruction model from the rough photon absorption distribution map to the fine photon absorption distribution map. And (3) learning the reconstructed model from the training set obtained in the step one by utilizing an improved generation countermeasure network, namely a pix2pix network, wherein the specific process of training the reconstructed model is shown in FIG. 2. The pix2pix network comprises a generator and a discriminator, the generator being configured to reconstruct a fine photon absorption profile from a coarse photon absorption profile, the discriminator being configured to be unable to distinguish between the reconstructed and true fine photon absorption profiles; the discriminator is used for discriminating the photon absorption distribution map and discriminating the reconstructed and real fine photon absorption distribution map as far as possible; and optimizing the comprehensive loss function to continuously optimize the reconstruction model through the dynamic game process of the generator and the discriminator. The formula of the synthetic loss function is as follows:
wherein: g is a generator; d is a discriminator; e is the desired output; x is the coarse photon absorption profile; y is the fine photon absorption profile; λ is a fixed weight of 100; l iscGAN(G, D) is loss of antagonism; l isL1(G) Is an L1 loss; argminGmaxDA dynamic gaming process of a finger generator and a discriminator.
The concrete structure of the pix2pix network is shown in fig. 3, the generator is a 15-layer U-Net structure, and the discriminator is a 4-layer PatchGAN structure. The hyperparameters used were a probability of neuronal inactivation of 50%, a slope of the leakage activation function of 0.2, all convolutions with a convolution kernel of 4 × 4 and a step size of 2.
And step three, reconstructing a fine photon absorption distribution map from the rough photon absorption distribution map. And (3) reconstructing a fine photon absorption distribution map from the rough photon absorption distribution map in the test set by using the test set obtained in the step one and the reconstruction model trained in the step two, wherein a representative reconstruction result is shown in fig. 4.
After five-fold cross inspection, the simulation precision of the reconstructed photon absorption distribution graph is evaluated by utilizing the peak signal-to-noise ratio and the percentage difference of the power coupling efficiency, the average peak signal-to-noise ratio is 35.5dB, and the percentage difference of the power coupling efficiency is 0.97%, so that the reconstructed photon absorption distribution graph has high simulation precision and is close to a real fine photon absorption distribution graph. In addition, the method is tested for the improvement of Monte Carlo simulation speed on a windows10 environment, a Central Processing Unit (CPU) of a 16GB RAM and a computer of a Graphic Processing Unit (GPU) of an 8GB RAM; more specifically, the average calculation time for simulating a fine photon absorption profile with an input of 1000000 photons is 1874 seconds, while the average calculation time for simulating a coarse photon absorption profile with an input of 10000 photons is only 18.3 seconds, and the average time for reconstructing a fine photon absorption profile from a coarse photon absorption profile is only 0.06 seconds; therefore, the method can improve the simulation speed of Monte Carlo by about 102 times in the embodiment.
Claims (7)
1. A fast Monte Carlo simulation method for simulating photon transmission is characterized in that a small number of photons are input to carry out Monte Carlo simulation, and a rough photon transmission simulation result is obtained; then, reconstructing a fine photon propagation simulation result from the coarse photon propagation simulation result by using the trained reconstruction model, wherein the reconstructed photon propagation simulation result is close to a real fine photon propagation simulation result;
the training process obtained by the reconstruction model is as follows:
(1) generating a pair of coarse and fine photon propagation simulation results based on a small number of photons and a large number of photons, respectively, using the same optical parameters; generating a large number of photon transmission simulation results in pairs by adjusting different optical parameters, and establishing a photon transmission simulation result training database; training a reconstruction model from a rough photon transmission simulation result to a fine photon transmission simulation result by utilizing the training database and a supervised learning algorithm;
(2) training a database to learn a reconstruction model from the photon propagation simulation result by using the generated countermeasure network; the generation countermeasure network comprises a generator and a discriminator, wherein the generator is used for reconstructing a fine photon propagation simulation result from a coarse photon propagation simulation result, so that the discriminator is difficult to distinguish the reconstructed fine photon propagation simulation result from a real fine photon propagation simulation result; the discriminator is used for discriminating the photon propagation simulation result and discriminating a reconstructed and real fine photon propagation simulation result as much as possible; and finally obtaining an optimized reconstruction model through the dynamic game process of the generator and the discriminator.
2. The fast Monte Carlo simulation method for simulating photon propagation according to claim 1, wherein the generation countermeasure network is a pix2pix network, and the specific structure of the pix2pix network is as follows: the generator is a 15-layer U-Net structure, and the discriminator is a 4-layer PatchGAN structure; all convolutions use a convolution kernel of 4 x 4 and a step size of 2.
3. The fast monte carlo simulation method for simulating photon propagation according to claim 1, wherein the dynamic game process of the generator and the discriminator continuously optimizes the reconstruction model by optimizing a synthetic loss function, the formula of which is as follows:
wherein: g is a generator; d is a discriminator; e is the desired output; x is the coarse photon absorption profile; y is the fine photon absorption profile; λ is a fixed weight; l iscGAN(G, D) is loss of antagonism; l isL1(G) Is an L1 loss; arg minG maxDA dynamic gaming process of a finger generator and a discriminator.
4. The fast monte carlo simulation method for simulating photon propagation according to claim 2, wherein the dynamic game process of the generator and the discriminator continuously optimizes the reconstruction model by optimizing a synthetic loss function, the formula of which is as follows:
wherein: g is a generator; d is a discriminator; e is the desired output; x is the coarse photon absorption profile; y is the fine photon absorption profile; λ is a fixed weight; l iscGAN(G, D) is loss of antagonism; l isL1(G) Is an L1 loss; arg minG maxDA dynamic gaming process of a finger generator and a discriminator.
5. The fast monte carlo simulation method for simulating photon propagation according to claim 1, wherein the accuracy of the reconstructed photon propagation simulation result is evaluated using a five-fold cross-test.
6. The fast monte carlo simulation method for simulating photon propagation according to claim 2, wherein the accuracy of the reconstructed photon propagation simulation result is evaluated using a five-fold cross-test.
7. The fast Monte Carlo simulation method for simulating photon propagation according to claim 3, wherein the accuracy of the reconstructed photon propagation simulation result is evaluated using a five-fold cross-test.
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