Small-sample Monte Carlo dose estimation method

Abstract

The invention aims to provide a few-sample Monte Carlo dose estimation method. The method comprises the following steps: setting deposition events to be distributed with a certain width; calculating the width of the distribution according to data obtained by the deposition event; calculating a data calculation specific distribution condition obtained according to the deposition event by adopting an optimization method; and correcting the specific distribution condition according to the medium density. According to the method, a relatively good dose estimation result can be obtained by using a relatively small number of particles, so that the calculation time and the hardware cost are greatly saved, and the application and popularization of the Monte Carlo method in real life are facilitated. Moreover, the method is high in universality, can be used for Monte Carlo for dose calculation, and is also suitable for statistical estimation of other few samples.

Description

Technical Field

[0001] The invention relates to the technical field of scattering simulation, and in particular to a few-sample Monte Carlo dose estimation method. Background Art

[0002] Simulation methods can help scientists better understand the process of particle-matter interaction and the physical mechanism of scattering phenomena. Particle scattering simulation is based on physical laws and mathematical models, and predicts and explains scattering phenomena by calculating particle motion trajectories and energy changes. For example, the Monte Carlo method can be used to simulate the multiple and single scattering processes of particles. This method uses random sampling to approximate the solution of complex physical problems. The Monte Carlo method is a numerical calculation method based on probability and statistical theory, which solves problems through random sampling. The basic idea of ​​the Monte Carlo method is to use random numbers (or pseudo-random numbers) to solve computational problems. Its working principle is to gradually approach the solution of the problem through continuous sampling. The Monte Carlo method simulates the random characteristics of the system by constructing a probability model that is similar to the system performance and conducting random experiments on a digital computer. This method is suitable for computational simulation experiments on discrete systems, and is particularly suitable for dealing with problems that are difficult to solve with traditional mathematical methods. Its advantages include high flexibility and wide application range, but its disadvantages are large amount of calculation and large number of random sampling are required to obtain relatively accurate results.

[0003] In radiotherapy, accurately determining the absorbed dose produced by radiation is one of the foundations for ensuring the effectiveness of radiotherapy. The Monte Carlo method is a computational method that is recognized as the most effective in simulating particle migration and is now widely used in medical physics. However, due to the long calculation time, its application and promotion in clinical treatment plan dose calculation is limited. The Monte Carlo method simulates the transport and reaction of each particle in the medium in detail, but the Monte Carlo method needs to simulate a very large number of particles to meet the accuracy requirements, so the amount of calculation is very large, the calculation time is very long, and the simulation efficiency is very low. Summary of the invention

[0004] The purpose of the present invention is to provide a Monte Carlo dose estimation method for a small number of samples, which can obtain better dose estimation results with a small number of particles, greatly saving calculation time and hardware investment, and is conducive to the application and promotion of the Monte Carlo method in real life. In addition, the method is highly versatile and can be used not only for Monte Carlo dose calculation, but also for other small sample statistical estimates. A few-sample Monte Carlo dose estimation method, comprising: Set the deposition events to a distribution with a certain width; calculating the width of the distribution based on data obtained from the deposition event; Calculating specific distribution conditions based on data obtained from the deposition event using an optimization method; The specific distribution is modified according to the medium density.

[0005] Preferably, calculating the width of the distribution according to the data obtained from the deposition event comprises: The distribution width of the deposition events is calculated based on the energy deposited by the deposition events, the distribution of the deposition events and the shape of the distribution.

[0006] Preferably, setting each event as a distribution with width comprises: ; in is the estimated dose, is the energy deposited by a certain deposition event, The width is The distribution of Indicates sedimentation event, Indicates The coordinates of the deposition event, Indicates the current coordinates.

[0007] Preferably, the step of calculating the distribution width of a deposition event according to the energy deposited by the deposition event, the distribution of the deposition event and the shape of the distribution comprises: Choose One Minimize the following: ; in, It is to seek expectations, is to find the variance, is the dose distribution under ideal conditions, that is, when the number of particles is infinite. is an estimate; Select initial value , calculate ,use approximate , substitute In the expression of , repeat the iteration until convergence.

[0008] Preferably, the use of an optimization method to calculate the specific distribution of data obtained from the deposition event includes: The shape of K of the current sample is calculated using an optimization method, expressed as: ; in, It is to seek expectations, is to find the variance, is the dose distribution under ideal conditions, that is, when the number of particles is infinite. is an estimate.

[0009] Preferably, the correcting the specific distribution condition according to the medium density includes: The ct density is used to correct K, expressed as: ; in, is the density, For the corrected , Indicates sedimentation event, Indicates The coordinates of the deposition event, Indicates the current coordinates.

[0010] A few-sample Monte Carlo dose estimation system, comprising: A deposition event processing module, used to set the deposition event to a distribution with a certain width; a distribution width calculation module, used to calculate the width of the distribution based on the data obtained from the deposition event; A distribution shape calculation module, used to calculate the specific distribution situation based on the data obtained from the deposition event using an optimization method; The density correction module is used to correct the specific distribution according to the medium density.

[0011] An electronic device comprises: a chip, a processor and a memory, wherein the memory is used to store computer program code, the computer program code comprises computer instructions, and when the chip executes the computer instructions, the electronic device executes the few-sample Monte Carlo dose estimation method.

[0012] The beneficial effects of the present invention are: 1. The belt width of the present invention is The distribution of the original sample points is replaced by the superposition result, and the superposition result is much smoother, so that a better dose estimation result can be obtained even with a smaller number of particles; 2. The present invention uses an optimization method to determine the width The size of the width makes the simulation result more accurate; 3. The present invention uses an optimization method to determine the specific distribution shape, so that the simulation result is more accurate; 4. The present invention uses CT density information to correct the specific distribution of the width, so that the simulation result is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor. Figure 1 A flow chart of a few-sample Monte Carlo dose estimation method of the present invention; Figure 2 A comparison diagram of simulation results of the present invention and the prior art; Figure 3 The figure is a schematic diagram of the hardware structure of an electronic device of the present invention. DETAILED DESCRIPTION

[0014] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0015] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0016] In addition, the descriptions of "first", "second", etc. in the present invention are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0017] In radiotherapy, accurately determining the absorbed dose produced by radiation is one of the foundations for ensuring the effectiveness of radiotherapy. The Monte Carlo method is a computational method that is recognized as the most effective in simulating particle migration and is now widely used in medical physics. However, due to the long calculation time, its application and promotion in clinical treatment plan dose calculation is limited. The Monte Carlo method simulates the transport and reaction of each particle in the medium in detail, but the Monte Carlo method needs to simulate a very large number of particles to meet the accuracy requirements, so the amount of calculation is very large, the calculation time is very long, and the simulation efficiency is very low.

[0018] The present invention uses the belt width The distribution of replaces the original sample points, the superposition result is much smoother, so that a better dose estimation result can be obtained even with a smaller number of particles; the present invention uses an optimization method to determine the width The size of the width makes the simulation result more accurate; the present invention uses an optimization method to determine the shape of the distribution, so that the simulation result is more accurate; the present invention uses CT density information to correct the specific distribution of the width, so that the simulation result is more accurate.

[0019] Example 1 A few-sample Monte Carlo dose estimation method, characterized in that, referring to Figure 1 ,include: S100, setting the deposition event to a distribution with a certain width; The dose calculated by Monte Carlo simulation consists of a series of energy deposition events. Traditionally, each deposition event is considered as a point (mathematically function), and all points are superimposed to obtain the dose. This approach has a large variance, especially when the number of particles is small. The present invention regards each deposition event as a distribution with a certain width b, so that the superposition result is much smoother, and thus a better dose estimation result can be obtained even with a smaller number of particles. An energy deposition event refers to the interaction between rays and certain objects when they enter the object, transferring energy to the object, and causing a series of reactions. Specifically, energy deposition refers to the deposition of energy carried by an ionized particle or a group of particles and their secondary particles in a specified volume of material when something hits something. The process of energy deposition is to ionize or excite the molecules of the material through the rays themselves or the accompanying secondary particles. For example, in nuclear physics, when rays interact with matter, they transfer energy to the matter, causing the atoms or molecules inside the matter to be ionized or excited, thereby releasing secondary particles.

[0020] S200, calculating the width of the distribution based on the data obtained from the deposition event; Because the present invention regards a deposition event as a distribution, the specific parameters of this distribution must be calculated to estimate the dose. When the number of particles is small, the variance of the dose obtained by superimposing all the points is large, which will cause a large deviation between the estimated result and the actual result. Therefore, the method of treating each deposition event as a point is only applicable to the case where the number of particles is large. For the case where the number of particles is small, the present invention creatively regards each deposition event as a distribution with a certain width. In this way, even if the number of particles is small, the superposition result of the distribution is much smoother than the superposition result of the points. Therefore, even in the case of a small number of particles, the present invention can obtain a better dose estimation result.

[0021] S300, using an optimization method to calculate specific distribution conditions based on data obtained from the deposition event; S400, correcting the specific distribution according to the medium density.

[0022] In the embodiment of the present invention, if you want to estimate the simulation results more accurately, you can choose to optimize the shape of the distribution. Common distributions include the following types: Normal distribution: Also known as Gaussian distribution, it is a continuous probability distribution with a bell-shaped curve shape. The data is most concentrated at the mean. The farther away from the mean, the sparser the distribution. The characteristics of normal distribution are symmetry and the mean and standard deviation can fully describe the distribution. Exponential distribution: It is suitable for describing the time interval between independent and continuous events. Its distribution density function presents a single peak right skewness and a long tail. For example, calculate the interval time between two events in a continuous time. Poisson distribution: It is suitable for describing the number of events in a certain time period, such as the number of telephone calls received and the number of traffic accidents. Its distribution presents a narrow peak and a long tail. After confirming the width of the distribution, the embodiment of the present invention finds the shape of the distribution that best suits the current sample. The distribution shape suitable for the current sample is conducive to more accurate simulation of particle scattering, thereby obtaining more accurate simulation results.

[0023] Preferably, S100, setting the deposition event to a distribution with a certain width includes: S110, setting each event to a distribution with width; The Monte Carlo method simulates the transport and reaction of each particle in the medium in great detail. At the same time, a very large number of particles need to be simulated to meet the accuracy requirements. Therefore, the amount of calculation is extremely large and the calculation time is very long. Then how to shorten the simulation time of the Monte Carlo method has become a technical problem that needs to be solved urgently. The main influencing factor of the long simulation time of the Monte Carlo method is that there are too many particles and the amount of calculation is too large, which leads to a long calculation time and low simulation efficiency. Therefore, if the number of particles in the Monte Carlo simulation is reduced, it is obvious that the calculation time can be greatly reduced and the simulation efficiency can be improved. However, simply reducing the number of particles in the Monte Carlo simulation will lead to inaccurate simulation results due to insufficient number of simulated samples. Because in the prior art, the dose calculated by the Monte Carlo simulation consists of a series of energy deposition events. The prior art regards each deposition event as a point (mathematically, Function), all points are superimposed to get the dose. This approach is acceptable when there are a large number of samples. However, due to the reduction of simulated particles in order to reduce simulation time, this approach will result in a large variance and inaccurate simulation results.

[0024] In the embodiment of the present invention, each deposition time is set as a distribution with a certain width, and then in the simulation, each distribution is superimposed to obtain the simulation result, and the Monte Carlo result with a small number of particles is used to estimate the dose with high accuracy. And this method is not sensitive to the number of particles, refer to Figure 2 , that is, the processing result with a small number of particles is close to that with a large number of particles, which has strong robustness. Figure 2 In the figure, the first row of four figures are the results of the original method, and the number of particles increases 10 times from left to right. The second row is the result after processing with the method of the present invention. It can be seen that for different numbers of particles, their processing results are similar. That is, we can make a very good estimate of the dose with a sample number of 1 / 1000.

[0025] S120, superimposing each distribution calculation dose estimation result.

[0026] ‌Distribution superposition‌ refers to the process of adding multiple distribution functions to obtain a new distribution function. The present invention changes the sedimentation events originally represented by points into distributions with a certain width, which can reduce variance and has a high accuracy.

[0027] Preferably, S200, calculating the width of the distribution according to data obtained from the deposition event includes: The distribution width of the deposition events is calculated based on the energy deposited by the deposition events, the estimated dose and the shape of the distribution.

[0028] ‌The energy deposited by a particle deposition event refers to the energy lost by high-speed charged particles when they interact with the atoms of the material when passing through it. This lost energy is called deposited energy because it is "deposited" into the material when passing through it and is absorbed or scattered, affecting the material.‌ There are two main mechanisms for particle energy deposition: collision loss‌, where electrons lose energy by interacting with orbital electrons in the medium, causing atomic excitation or ionization. This mechanism of energy loss is called "collision loss"‌. Radiation loss‌, where light charged particles emit electromagnetic radiation when their acceleration changes, and this radiation is called bremsstrahlung. The energy loss of bremsstrahlung is related to the kinetic energy and atomic number of the electron‌.

[0029] The shape of the distribution refers to the morphological characteristics of the probability distribution, which mainly includes indicators such as symmetry, skewness and kurtosis. In the embodiment of the present invention, Gaussian distribution (normal distribution) is selected as the distribution model of each deposition event, and its probability density function presents a bell-shaped curve, with small ends and a large middle, and is symmetrical about the mean.

[0030] The estimated dose is the absorbed dose estimated by the Monte Carlo method for particle simulation.

[0031] Preferably, setting each event to a distribution having a width comprises: ; in is the estimated dose, is the energy deposited by a certain deposition event, The width is The distribution of Indicates sedimentation event, Indicates The coordinates of the deposition event, Indicates the current coordinates.

[0032] The shape can be high in the middle and low on both sides, such as a Gaussian distribution. In an embodiment of the present invention, the distribution width of each deposition event is specifically studied, and the energy deposited by the deposition event, the estimated dose and the specific relationship between the shape of the distribution and the distribution width are obtained through simulation experiments. Then, the distribution width of each deposition event is calculated. The width after distribution superposition usually refers to the width of the result after the superposition of two or more distribution functions. Distribution superposition refers to the superposition of the probability distribution functions of two or more random variables to calculate their joint distribution. This superimposed width reflects the degree of discreteness of the distribution after superposition. In an embodiment of the present invention, each deposition event is converted into a distribution form, and then superimposed on multiple distributions to reflect a better dose estimation result.

[0033] Preferably, calculating the distribution width of a deposition event according to the energy deposited by the deposition event, the distribution of the deposition event and the shape of the distribution comprises: Choose One Minimize the following: ; in, It is to seek expectations, is to find the variance, is the dose distribution under ideal conditions, that is, when the number of particles is infinite. is an estimate; Select initial value , calculate ,use approximate , substitute In the expression of , repeat the iteration until convergence.

[0034] In an embodiment of the present invention, The simulation results So for different numbers of particles, we can calculate the corresponding ,result Will be close to the same , that is, the processing results with different numbers of particles are close, which shows that the method has strong robustness. It also verifies from the side that the present invention can obtain the same simulation results as the simulation with many particles without using a lot of particles for simulation, and the number of particles simulated by the present invention is less, thereby greatly reducing the simulation time of Monte Carlo, improving the simulation efficiency, and also ensuring a higher result accuracy.

[0035] Preferably, the specific distribution of data obtained from the deposition event is calculated using an optimization method, including: The shape of K of the current sample is calculated using an optimization method, expressed as: ; in, It is to seek expectations, is to find the variance, is the dose distribution under ideal conditions, that is, when the number of particles is infinite. is an estimate.

[0036] Furthermore, the present invention uses an optimization method to calculate the most suitable sample shape, that is, Also used as an optimization parameter, the estimated result is It will be better if you don't calculate shape, you can It can be regarded as a Gaussian distribution with a high middle and low sides. It can also obtain better dose estimation results and reduce the amount of calculation. If higher accuracy is required for the dose estimation results, Also used as an optimization parameter to find the most suitable one for the current sample The shape of the particle makes the superposition result of each deposition event more accurate and the estimated dose more precise.

[0037] Preferably, correcting the specific distribution according to the medium density includes: Using ct density correction , expressed as: ; in, is the density, For the corrected , Indicates sedimentation event, Indicates The coordinates of the deposition event, Indicates the current coordinates.

[0038] Furthermore, the above approach It is invariant to spatial translation, but the actual human body is not like this. Therefore, the present invention can also use CT density correction , so that the results are better. CT density can reflect the density of an object, and the range of CT values ​​is generally from -1000HU to +1000HU. CT value is a reflection of the density of human tissue, and is generally expressed in HU. The CT value of air is the lowest, close to -1000HU; the density of fat is between -70HU and -90HU; the density of water is next, which is about 0HU; the density of soft tissue is generally around 30-50HU; the density of cerebral hemorrhage is generally around 50-90HU; the density of calcification and bone is getting higher and higher, and the highest can reach +1000HU; the CT value of metal-like substances is higher, such as the steel plate implanted in the body, the CT value can reach 2000-3000HU. CT value is a numerical value used to express tissue density, which mainly reflects the absorption coefficient of tissue to X-rays. The higher the CT value, the greater the density of tissues and organs, and the high-density shadows are shown on CT images; the lower the CT value, the smaller the density of tissues and organs, and the low-density shadows are shown on CT images. Different diseases can present different CT densities. In the embodiment of the present invention, the K value is corrected according to the CT value of the human body, so that the result of the Monte Carlo method simulation is more accurate.

[0039] Example 2 A few-sample Monte Carlo dose estimation system, comprising: A deposition event processing module, used to set the deposition event to a distribution with a certain width; A distribution width calculation module, used to calculate the width of the distribution according to the parameters of the deposition event; A distribution shape calculation module is used to calculate the specific distribution based on the data obtained from the deposition event using an optimization method; The density correction module is used to correct the specific distribution according to the medium density.

[0040] Example 3 An electronic device includes: a chip, a processor and a memory, the memory is used to store computer program code, the computer program code includes computer instructions, and when the chip executes the computer instructions, the electronic device executes a few-sample Monte Chi dose estimation method.

[0041] refer to Figure 3, the electronic device 2 includes a processor 21, a memory 22, an input device 23, and an output device 24. The processor 21, the memory 22, the input device 23, and the output device 24 are coupled via a connector, and the connector includes various interfaces, transmission lines, or buses, etc., which are not limited in the embodiments of the present invention. It should be understood that in various embodiments of the present invention, coupling refers to mutual connection in a specific manner, including direct connection or indirect connection through other devices, for example, through various interfaces, transmission lines, buses, etc.

[0042] The processor 21 may be one or more graphics processing units (GPUs). When the processor 21 is a GPU, the GPU may be a single-core GPU or a multi-core GPU. Optionally, the processor 21 may be a processor group consisting of multiple GPUs, and the multiple processors are coupled to each other via one or more buses. Optionally, the processor may also be other types of processors, etc., which are not limited in the embodiments of the present invention.

[0043] The memory 22 can be used to store computer program instructions and various computer program codes including program codes for executing the scheme of the present invention. Optionally, the memory includes but is not limited to random access memory (RAM), read-only memory (ROM), erasable programmable read only memory (EPROM), or portable read only memory (CD-ROM), which is used for related instructions and data.

[0044] The input device 23 is used to input data and / or signals, and the output device 24 is used to output data and / or signals. The output device 24 and the input device 23 may be independent devices or an integrated device.

[0045] The present invention uses the belt width The distribution of replaces the original sample points, the superposition result is much smoother, so that a better dose estimation result can be obtained even with a smaller number of particles; the present invention uses an optimization method to determine the width The size of the width makes the simulation result more accurate; the present invention uses an optimization method to determine the shape of the distribution, so that the simulation result is more accurate; the present invention uses CT density information to correct the specific distribution of the width, so that the simulation result is more accurate.

[0046] The foregoing is merely a specific embodiment of the present invention, which enables those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A few-sample Monte Carlo dose estimation method, characterized in that: include: Set the deposition events to a distribution with a certain width; calculating the width of the distribution based on data obtained from the deposition event; Calculating specific distribution conditions based on data obtained from the deposition event using an optimization method; The specific distribution is modified according to the medium density.

2. The few-sample Monte Carlo dose estimation method according to claim 1, characterized in that: Calculating the width of the distribution according to the data obtained from the deposition event includes: The distribution width of the deposition events is calculated based on the energy deposited by the deposition events, the distribution of the deposition events and the shape of the distribution.

3. The few-sample Monte Carlo dose estimation method according to claim 2, characterized in that: The step of setting each event to a distribution having a width includes: ； in is the estimated dose, is the energy deposited by a certain deposition event, The width is The distribution of Indicates sedimentation event, Indicates The coordinates of the deposition event, Indicates the current coordinates.

4. The few-sample Monte Carlo dose estimation method according to claim 3, characterized in that: The step of calculating the distribution width of a deposition event according to the energy deposited by the deposition event, the distribution of the deposition event and the shape of the distribution comprises: Choose One Minimize the following: ； in, It is to seek expectations, is to find the variance, is the dose distribution under ideal conditions, that is, when the number of particles is infinite. is an estimate; Select initial value , calculate ,use approximate , substitute In the expression of , repeat the iteration until convergence.

5. The few-sample Monte Carlo dose estimation method according to claim 3, characterized in that: The specific distribution of the data obtained from the deposition event using the optimization method includes: The shape of K of the current sample is calculated using an optimization method, expressed as: ； in, It is to seek expectations, is to find the variance, is the dose distribution under ideal conditions, that is, when the number of particles is infinite. is an estimate.

6. The few-sample Monte Carlo dose estimation method according to claim 5, characterized in that: The correcting of the specific distribution according to the medium density comprises: The ct density is used to correct K, expressed as: ； in, is the density, For the corrected , Indicates sedimentation event, Indicates The coordinates of the deposition event, Indicates the current coordinates.

7. A few-sample Monte Carlo dose estimation system, characterized in that: include: A deposition event processing module, used to set the deposition event to a distribution with a certain width; a distribution width calculation module, used to calculate the width of the distribution based on the data obtained from the deposition event; A distribution shape calculation module, used to calculate the specific distribution situation based on the data obtained from the deposition event using an optimization method; The density correction module is used to correct the specific distribution according to the medium density.

8. An electronic device, characterized in that: include: A chip, a processor and a memory, wherein the memory is used to store computer program code, the computer program code includes computer instructions, and when the chip executes the computer instructions, the electronic device executes a few-sample Monte Carlo dose estimation method as described in any one of claims 1 to 6.

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