A method for equivalent conversion of detector energy deposition distribution based on Cornish-Fisher expansion

Abstract

The application discloses a kind of Cornish-Fisher expansion-based detector energy deposition distribution equivalent conversion method, the method includes: based on the equivalent conversion method of Cornish-Fisher expansion, according to the correlation between the target matrix of energy deposition distribution in different sizes and medium, the mapping relationship between detector result and target result is established, then the detector measurement result is equivalent conversion according to mapping relationship, and then the energy deposition distribution in target size or target medium is obtained.The energy deposition distribution in specific material detector can be equivalent converted into the energy deposition in target medium (such as water or other tissue equivalent material), the measurement deviation caused by material difference is avoided, and the application is suitable for radiation protection, medical irradiation verification and other scenes;Equivalent energy distribution in target size or target medium is obtained by mathematical calculation, so as to significantly reduce the experimental condition constraint caused by limited equipment selection, and improve the flexibility of measurement.

Description

Technical Field

[0001] This invention relates to the field of radiation detection and data processing technology, and in particular to an equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion. Background Technology

[0002] The distribution of energy deposition in a medium is an important physical quantity in the field of radiation measurement. It characterizes the spatial distribution of the radiation field and the response properties of the measured medium, playing a crucial role in particle physics, radiation protection, and radiotherapy. Currently, conventional measurement methods mainly fall into two categories: (1) Direct measurement method: Measurement is performed in the relevant physical field using detectors such as ionization chambers and semiconductors. However, due to the differences in the materials and sizes of the detectors themselves, detectors of different sizes or materials are often required under different conditions in order to achieve accurate measurement and conversion of energy deposition distribution.

[0003] (2) Monte Carlo simulation method: The deposition energy distribution in the medium is directly calculated by simulating particle transport by computer. Theoretically, the results in any medium material can be obtained, and the calculation results have a high degree of agreement with the experimental results. It is considered the "gold standard". However, this method has a large amount of computation and cannot meet the requirements of real-time or rapid feedback.

[0004] However, the above methods have certain limitations in some application scenarios, such as when the detector size is much larger than the area of ​​interest, and the detector size cannot be further reduced due to manufacturing limitations, or when there is a significant difference between the detector material and the target medium. This is common in the fields of radiation protection and radiotherapy. For example, in radiotherapy plan validation, it is often necessary to obtain the energy deposition distribution in biological tissue (usually approximated by water). However, direct measurement is often limited by detector size and materials, leading to biased results and affecting the assessment of radiotherapy dose.

[0005] Therefore, providing an equivalent conversion technique for detector energy deposition distribution across dimensions and media is a reliable way to solve the current problem. To this end, based on the variation patterns and characteristics of deposition energy distribution in different sizes and media, we propose an equivalent conversion method for detector energy deposition distribution across dimensions and media. Summary of the Invention

[0006] The purpose of this invention is to provide an equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion, which can equivalently convert the energy deposition distribution in a detector made of a specific material to the energy deposition situation in the target medium, avoiding measurement deviations caused by material differences, and is applicable to scenarios such as radiation protection and medical irradiation verification.

[0007] To achieve the above objectives, the present invention provides the following solution: An equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion includes the following steps: S1. Utilize the detector to measure the deposition energy in the target environment and obtain the initial energy deposition dataset; S2. Calculate the statistical moments of the initial energy deposition dataset, including mean, standard deviation, skewness, and excess kurtosis; S3. Calculate the conversion factor between the detector and the target based on the correlation between them; where, when converting across sizes, the conversion factor is the ratio of the detector size to the target size; when converting across media, the conversion factor is the ratio of the mass stopping power of the detector material to that of the target medium. S4. Based on the conversion factor, calculate the target statistical moments of the target energy deposition distribution, including the mean, standard deviation, skewness, and excess kurtosis. S5. Scale the initial energy deposition dataset proportionally according to the conversion factor to obtain the intermediate energy deposition dataset; S6. Based on the intermediate energy deposition dataset and the target statistical moments, the Cornish-Fisher expansion method is performed to obtain the corrected energy deposition dataset; S7. Output the energy deposition dataset as the equivalent energy deposition distribution in the target size or target medium.

[0008] Preferably, in S4, the target statistical moments of the target energy deposition distribution are calculated, including the mean. Standard deviation skewness and excess kurtosis The formula is as follows:

[0009] Where n is the conversion factor. These represent the mean, standard deviation, skewness, and excess kurtosis of the initial energy deposition dataset, respectively.

[0010] Preferably, in step S5, the initial energy deposition dataset is scaled proportionally according to a conversion factor to obtain an intermediate energy deposition dataset, as shown in the following formula:

[0011] in, W For intermediate energy deposition datasets, Y This is the initial energy deposition dataset.

[0012] Preferably, in S6, the Cornish-Fisher expansion method is performed to obtain the corrected energy deposition dataset, specifically including: The intermediate energy deposition dataset W is sorted and the data volume is statistically analyzed. Then, an empirical quantile p is constructed based on the data volume, and the empirical quantile is converted into a standard normal quantile u. The Cornish-Fisher polynomial is applied to u to correct for skewness and kurtosis, resulting in the corrected variable z0. The mean μ0 and standard deviation σ0 of the corrected variable z0 are calculated, and then standardized to obtain the variable z1. The variable z1 is linearly scaled to the target mean. with standard deviation The corrected energy deposition dataset Z is obtained.

[0013] Preferably, in S6, the Cornish-Fisher polynomial is applied to correct the skewness and kurtosis of u, resulting in the correction variable z0, as shown in the following formula: .

[0014] Preferably, in step S6, the mean μ0 and standard deviation σ0 of the modified variable z0 are calculated, and then standardized to obtain the variable z1, as shown in the following formula: .

[0015] Preferably, in S6, the corrected energy deposition dataset Z is calculated as follows: .

[0016] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements an equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion as described above.

[0017] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: (1) This invention can convert the measurement results of large-size detectors into equivalent results of small-size detectors based on the variation law of energy deposition distribution in different detector sizes. Even when it is difficult to further reduce the size of the detector, it can still obtain an energy deposition distribution that is closer to the actual small-scale region. At the same time, this invention can equivalently convert the energy deposition distribution in a detector made of a specific material into the energy deposition situation in the target medium (e.g., water or other tissue equivalent materials), avoiding measurement deviations caused by material differences, and is applicable to scenarios such as radiation protection and medical irradiation verification; (2) In the conversion process, the present invention can maintain the spatial variation trend and detailed structure of energy deposition distribution to a large extent, ensuring that the converted energy deposition distribution strictly conforms to the physical non-negativity and statistical law of radiation energy deposition, and there will be no distortion of the distribution shape, thus ensuring the accuracy and reliability of the conversion results. (3) The cross-size and cross-medium equivalent conversion method proposed in this invention can obtain the equivalent energy distribution in the target size or target medium through mathematical calculation without changing the detector material or reducing the detector size, thereby significantly reducing the experimental condition constraints caused by limited equipment selection and improving the flexibility of measurement. (4) The method proposed in this invention is applicable to both dose conversion from ionization chamber / semiconductor detector to water equivalent tissue in radiotherapy and energy deposition assessment from monitoring detector to key human organs in radiation protection. Equivalent conversion can be performed simply by setting the equivalent conversion coefficient and the moment parameter of the target result according to the measurement scenario, avoiding the repetitive work of developing correction algorithms separately for different detectors and different media. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating the equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion provided by this invention. Figure 2 [100 μm] is the [100 μm] in Method 1 of this embodiment of the invention. 3 The deposition energy distribution in large and small diamond detectors is oriented towards [75 μm]. 3 The result of equivalent conversion between large and small diamond detectors; Figure 3 [100 μm] is the [100 μm] in Method 1 of this embodiment of the invention. 3 The energy distribution of deposited particles in large and small diamond detectors is oriented towards [50 μm]. 3 The result of equivalent conversion between large and small diamond detectors; Figure 4 [100 μm] is the [100 μm] in Method 1 of this embodiment of the invention. 3 The energy distribution of deposited particles in large and small diamond detectors is directed towards [100 μm]. 3 A diagram showing the results of equivalent conversion between large and small biological tissues; Figure 5 [75 μm] is the [75 μm] in Method 1 of this embodiment of the invention. 3 The deposition energy distribution in large and small diamond detectors is oriented towards [75 μm]. 3 A diagram showing the results of equivalent conversion between large and small biological tissues. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] like Figure 1 As shown, the present invention provides an equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion, comprising the following steps: S1. Utilize the detector to measure the deposition energy in the target environment and obtain the initial energy deposition dataset; S2. Calculate the statistical moments of the initial energy deposition dataset, including mean, standard deviation, skewness, and excess kurtosis; S3. Calculate the conversion factor between the detector and the target based on the correlation between them; where, when converting across sizes, the conversion factor is the ratio of the detector size to the target size; when converting across media, the conversion factor is the ratio of the mass stopping power of the detector material to that of the target medium. S4. Based on the conversion factor, calculate the target statistical moments of the target energy deposition distribution, including the mean, standard deviation, skewness, and excess kurtosis. S5. Scale the initial energy deposition dataset proportionally according to the conversion factor to obtain the intermediate energy deposition dataset; S6. Based on the intermediate energy deposition dataset and the target statistical moments, the Cornish-Fisher expansion method is performed to obtain the corrected energy deposition dataset; S7. Output the energy deposition dataset as the equivalent energy deposition distribution in the target size or target medium.

[0023] Furthermore, in S4, the target statistical moments of the target energy deposition distribution are calculated, including the mean. Standard deviation skewness and excess kurtosis The formula is as follows:

[0024] Where n is the conversion factor. These represent the mean, standard deviation, skewness, and excess kurtosis of the initial energy deposition dataset, respectively.

[0025] Furthermore, in S5, the initial energy deposition dataset is scaled proportionally according to a conversion factor to obtain an intermediate energy deposition dataset, as shown in the following formula:

[0026] in, W For intermediate energy deposition datasets, Y This is the initial energy deposition dataset.

[0027] Furthermore, in S6, the Cornish-Fisher expansion method is executed to obtain the corrected energy deposition dataset, which specifically includes: The intermediate energy deposition dataset W is sorted and the data volume is counted. Then, an empirical quantile p is constructed based on the data volume, and the empirical quantile is converted into a standard normal quantile u. Applying Cornish-Fisher polynomials to correct the skewness and kurtosis of u, the correction variable z0 is obtained, as shown in the following formula:

[0028] Calculate the mean μ0 and standard deviation σ0 of the corrected variable z0, and then standardize it to obtain the variable z1, as shown in the following formula:

[0029] The variable z1 is linearly scaled to the target mean. with standard deviation The corrected energy deposition dataset Z is obtained, as shown in the following formula: .

[0030] Example 1 This embodiment uses two application scenarios as examples: equivalent conversion of the deposition energy distribution in a large-size diamond detector to a small-size diamond detector under 30 MeV proton irradiation, and equivalent conversion of the deposition energy distribution in a diamond detector to biological tissue of the same size. These examples illustrate the application effect of the proposed method in cross-size and cross-medium equivalent conversion of diamond detectors. The specific implementation steps are as follows: S1: Place the diamond detector under 30 MeV proton irradiation to obtain the energy deposition dataset Y; S2: Calculate the mean of the detector deposition energy dataset Y. Standard deviation skewness and excess kurtosis ; S3: Based on the correlation between the detector and the target, derive and calculate the conversion factor n between them; for the deposition energy distribution in a large-size diamond detector, perform an equivalent conversion to a small-size diamond detector, with the conversion factor being the size ratio of the two; for the deposition energy distribution in a diamond detector, perform an equivalent conversion to biological tissue of the same size, with the conversion factor being the mass stopping power ratio of the two.

[0031] S4: Calculate the mean value of energy deposition X in the target detector or target medium based on the conversion factor n. Standard deviation skewness and excess kurtosis ; The calculation formula is: ; S5: Scale the dataset Y proportionally according to the conversion factor n to obtain the dataset W; Right now:

[0032] S6: Sort the dataset W and count the data volume, then construct the empirical quantile p based on the data volume, and convert the empirical quantile into the standard normal quantile u; S7: Apply Cornish-Fisher polynomials to modify u, and obtain the modified variable. ; Specifically:

[0033] S8: Calculate the mean μ0 and standard deviation σ0 of the corrected variable z0, and then standardize it to obtain the variable z1, as shown in the following formula:

[0034] S9: Linearly scale variable z1 to the target mean. with standard deviation The corrected energy deposition dataset Z is obtained, as shown in the following formula: .

[0035] Thus, the obtained modified variable Z has mean, standard deviation, skewness, and excess kurtosis results that are similar to those of the target X.

[0036] S10: To verify the equivalent conversion effect of the method of the present invention, the deposition energy distribution of protons in detectors of different cubic shapes (side lengths of 100μm, 75μm, and 50μm) was obtained, as well as the deposition energy distribution of protons in biological tissues of the same size (usually approximated by water, side lengths of 100μm and 75μm) under the same conditions. The method proposed in this invention was then used for equivalent conversion calculation, and the comparison between the conversion results and the actual distributions was performed. Figure 2-5 As shown.

[0037] Figure 2-5 The horizontal axis represents the energy deposited in the medium, and the vertical axis represents the probability distribution of the deposited energy. According to... Figure 2-5 It can be seen that the results obtained by performing equivalent conversions across size and medium in the detector using the method of the present invention have a high degree of agreement with the measured results under the same conditions. That is, the method of the present invention can achieve accurate equivalent conversions of the deposition energy distribution measured by the detector across size and medium, and can provide a technical means with a wide range of applications and flexible measurement for accurate measurement of energy deposition distribution in the medium.

[0038] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements an equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion as described above.

[0039] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0040] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for equivalent conversion of detector energy deposition distribution based on Cornish-Fisher expansion, characterized in that, Includes the following steps: S1. Utilize the detector to measure the deposition energy in the target environment and obtain the initial energy deposition dataset; S2. Calculate the statistical moments of the initial energy deposition dataset, including mean, standard deviation, skewness, and excess kurtosis; S3. Calculate the conversion factor between the detector and the target based on the correlation between them; where, when converting across sizes, the conversion factor is the ratio of the detector size to the target size; when converting across media, the conversion factor is the ratio of the mass stopping power of the detector material to that of the target medium. S4. Based on the conversion factor, calculate the target statistical moments of the target energy deposition distribution, including the mean, standard deviation, skewness, and excess kurtosis. S5. Scale the initial energy deposition dataset proportionally according to the conversion factor to obtain the intermediate energy deposition dataset; S6. Based on the intermediate energy deposition dataset and the target statistical moments, the Cornish-Fisher expansion method is performed to obtain the corrected energy deposition dataset; S7. Output the energy deposition dataset as the equivalent energy deposition distribution in the target size or target medium.

2. The equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion according to claim 1, characterized in that, In step S4, the target statistical moments of the target energy deposition distribution are calculated, including the mean. Standard deviation skewness and excess kurtosis The formula is as follows: Where n is the conversion factor. These represent the mean, standard deviation, skewness, and excess kurtosis of the initial energy deposition dataset, respectively.

3. The equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion according to claim 2, characterized in that, In step S5, the initial energy deposition dataset is scaled proportionally according to a conversion factor to obtain an intermediate energy deposition dataset, as shown in the following formula: in, W For intermediate energy deposition datasets, Y This is the initial energy deposition dataset.

4. The equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion according to claim 3, characterized in that, In step S6, the Cornish-Fisher expansion method is executed to obtain the corrected energy deposition dataset, which specifically includes: The intermediate energy deposition dataset W is sorted and the data volume is statistically analyzed. Then, an empirical quantile p is constructed based on the data volume, and the empirical quantile is converted into a standard normal quantile u. The Cornish-Fisher polynomial is applied to u to correct for skewness and kurtosis, resulting in the corrected variable z0. The mean μ0 and standard deviation σ0 of the corrected variable z0 are calculated, and then standardized to obtain the variable z1. The variable z1 is linearly scaled to the target mean. with standard deviation The corrected energy deposition dataset Z is obtained.

5. The equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion according to claim 4, characterized in that, In step S6, Cornish-Fisher polynomials are applied to correct the skewness and kurtosis of u, resulting in the correction variable z0, as shown in the following formula: 。 6. The equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion according to claim 5, characterized in that, In step S6, the mean μ0 and standard deviation σ0 of the modified variable z0 are calculated, and then standardized to obtain the variable z1, as shown in the following formula: 。 7. The equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion according to claim 6, characterized in that, In S6, the corrected energy deposition dataset Z is defined as follows: 。 8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the equivalent conversion method for detector energy deposition distribution based on Cornish-Fisher expansion as described in any one of claims 1-7.

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