JP7761822B2 - Information processing device, recording medium, and program - Google Patents

Description

Application of Article 30, Paragraph 2 of the Patent Act On October 1, 2020, COMMUNICATIONS PHYSICS, Vol. 3, pp. Published in papers 1-8 [Publications, etc.] On October 1, 2020, COMMUNICATIONS PHYSICS, Vol. 3, pp. Published as an abstract of the paper listed in 1-8 [Publications, etc.] Published in the press release of the paper to be published in COMMUNICATIONS PHYSICS on October 1, 2020 [Publications, etc.] Online oral presentation at the 20th University of Tokyo Life Science Symposium on October 30, 2020 [Publications, etc.] Published as an archived video of the presentation at the 20th University of Tokyo Life Science Symposium on November 14, 2020 [Publications, etc.] Published at the Kyoto University Integrated Radiation and Science Research Institute Special Research Group "Positron Science and Its Applications to Science and Engineering" on December 11, 2020 [Publications, etc.] Published in the abstract collection of the Kyoto University Integrated Radiation and Science Research Institute Special Research Group "Positron Science and Its Applications to Science and Engineering" on December 9, 2020 [Publications, etc.] Published in the minutes of the Kyoto University Integrated Radiation and Science Research Institute Special Research Group "Positron Science and Its Applications to Science and Engineering" on March 25, 2021 [Publications, etc.] The Next Generation PET Research Report 2020 was posted on the website and announced on January 18, 2021. [Publications, etc.] Announced at the QST International Research Initiative (IRI) Symposium Next Generation PET Study Group 2021 on January 23, 2021. [Publications, etc.] Announced in the Next Generation PET Research Report 2020 on January 23, 2021. [Publications, etc.] Announced at the 121st Annual Meeting of the Japan Society of Medical Physics on April 17, 2021. [Publications, etc.] Announced at the 121st Annual Meeting of the Japan Society of Medical Physics, held online on April 28, 2021. [Publications, etc.] Announced in the Proceedings of the 121st Annual Meeting of the Japan Society of Medical Physics on April 1, 2021. [Publications, etc.] Announced as an electronic poster at the 121st Annual Meeting of the Japan Society of Medical Physics on April 1, 2021. [Publications, etc.] Published in an article in Physics World on October 13, 2020 [Publications, etc.] Published in a submission to Nature Portfolio Cancer Community on December 7, 2020 [Publications, etc.] Published in the abstract collection of the 58th Symposium on Isotopes and Radiation Research on July 7, 2021

The present invention relates to an information processing device, recording medium, and program for processing information related to PET (Positron Emission Tomography).

In a PET device, a pair of gamma rays is generated through the following process. Specifically, the phenomena occurring in a PET device include a process (β ⁺ decay process) in which a radioisotope, such as ^44Sc , emits a positron (e ⁺ ) and also emits a gamma ray (prompt gamma ray), a process (Ps production process) in which the positron interacts with an electron of a nearby molecule to form a positronium, and a process (annihilation process) in which the positron interacts with an electron of a nearby molecule to generate a pair of gamma rays (annihilation radiation). The pair annihilation process may occur immediately after the beta decay process, or it may occur after the beta decay process, followed by a Ps production process. In the latter case, the time from beta decay to the occurrence of the pair annihilation process is delayed by the lifetime of Ps.

In conventional PET imaging, a pair of gamma rays generated during this annihilation process travels in opposite directions. Detectors positioned on either side of a subject (such as a human body being examined) containing electrons that cause the annihilation process detect this pair of annihilation radiation. The position of the original radioisotope is identified by determining that the positron decay nucleus is located on the line of response (LOR) extending from the positions of the pair of detectors that detected the annihilation radiation. Information about the time of flight (TOF) of the pair of annihilation radiation is also used to limit the range of the identified position. Compton camera technology is also used to detect at least one of the prompt gamma ray and the pair of annihilation radiation to limit the range of the identified position.

Moskal P et al., Feasibility study of the positronium imaging with the J-PET tomograph, Phys. Med. Biol. 64 055017

As such, information about the lifetime of positronium (Ps) has not been used in information processing using the conventional PET devices described above. However, in recent years, attempts have been made to obtain medical information by visualizing the lifetime of this positronium (Non-Patent Document 1).

Under the above circumstances, one of the objects of the present invention is to provide an information processing device, recording medium, and program that performs information processing using information on the lifetime of positronium.

One aspect of the present invention that solves the problems of the above-mentioned conventional examples is an information processing device that includes signal receiving means for receiving a signal indicating that a pair of annihilation radiation rays emitted in opposite directions has been detected in a subject; change amount analysis means for acquiring, based on the received signal, information on the change amount in the number of annihilation radiation rays detected over time related to the lifetime of positrons emitted in the subject; and estimation means for estimating the dissolved concentration of radicals near the source of the annihilation radiation rays based on the acquired change amount information.

Another aspect of the present invention is an information processing device that includes: signal receiving means for receiving a signal indicating that a pair of annihilation radiation rays emitted in opposite directions has been detected in a subject; change amount analysis means for acquiring, based on the received signal, information on the change in the number of annihilation radiation rays detected in a time series relating to the lifetime of positrons emitted in the subject, for each position where the pair of annihilation radiation rays is generated; and component analysis means for applying an inverse Laplace transform to the acquired change amount information, and acquiring information representing the proportion of the number of detections for each annihilation radiation wave whose change amount over time differs from each other.

This invention makes it possible to perform information processing using information on the lifetime of positronium.

1 is a block diagram illustrating an example of the configuration of an information processing device according to an embodiment of the present invention. FIG. 1 is an explanatory diagram showing the relationship between the dissolved concentration of radical molecules and the amount of annihilation radiation generated. 1 is a functional block diagram of an information processing device according to an embodiment of the present invention; FIG. 2 is an explanatory diagram illustrating an example of information acquired by an information processing device according to an embodiment of the present invention. FIG. 10 is a functional block diagram of another aspect of the information processing device according to the embodiment of the present invention. 1 is an explanatory diagram illustrating an example of information output by an information processing device according to an embodiment of the present invention.

Embodiments of the present invention will be described with reference to the drawings. As shown in FIG. 1, an information processing device 1 according to an embodiment of the present invention includes a control unit 11, a memory unit 12, an operation unit 13, an output unit 14, and an interface unit 15. In one example of this embodiment, the information processing device 1 is realized as a PET (Positron Emission Tomography) device and is connected to a detector 20.

That is, this information processing device 1 functions as a general PET device, and detects a pair of gamma rays (hereinafter referred to as annihilation radiation) generated when a radioisotope such as ^Sc , for example, undergoes β ⁺ decay in a subject such as a human body, releases a positron (e ⁺ ), and then emits a prompt gamma ray using the detector 20. The information processing device 1 then obtains, from the positions where the pair of annihilation radiations are detected and information on the time of flight (TOF) of each of the pair of annihilation radiations, the coordinates of the generation positions of the annihilation radiations (information representing the position of a voxel containing the generation position of the pair of annihilation radiations when the space including the subject is divided into virtual cubic voxels), or information on the line segment (LOR) connecting the two detection positions of the pair of annihilation radiations, or information on the LOR narrowed down by the TOF. Alternatively, if prompt gamma rays or annihilation radiations undergo Compton scattering in the detector, the direction from which the prompt gamma rays or annihilation radiations originate can be detected from the scattering angle using a Compton camera. In this case, too, it is possible to obtain narrowed-down position information (information specifying the position of a voxel or an LOR) by any combination of information on one or more directions and an LOR. Such a method using a Compton camera and a method using TOF may be used simultaneously.

Furthermore, a pair of annihilation radiation can be generated when a positron emitted in β ⁺ decay interacts with an electron, etc. of a nearby molecule to form a positronium (Ps production process), and a positron in the formed positronium interacts with an electron, etc. of a nearby molecule, or when a positron generated in β ⁺ decay directly interacts with an electron, etc. of a nearby molecule. Below, a pair of annihilation radiation generated in these cases is called an annihilation radiation pair.

Experiments have shown that the amount of annihilation radiation generated without going through the Ps production process is the largest, and that it is generated relatively quickly after β ⁺ decay (i.e., after prompt gamma ray emission). However, if the Ps production process is performed, it takes time for the annihilation radiation to interact with electrons of nearby molecules after β ⁺ decay, so the time until the annihilation radiation is generated is relatively delayed.

The control unit 11 is a program-controlled device such as a CPU, and operates according to a program stored in the memory unit 12. In this embodiment, the control unit 11 receives signals from the detector 20 indicating the time and position at which annihilation radiation pairs emitted in opposite directions were detected. The control unit 11 then generates the position at which the annihilation radiation pairs were generated (information specifying the voxel position or LOR).

The control unit 11 also executes processing to acquire information on time- series changes in the number of detections of annihilation radiation pairs for each voxel or LOR. The control unit 11 may then perform processing to estimate the dissolved concentration of radicals near the source of generation of annihilation radiation pairs based on the acquired information on time-series changes . In another example, the control unit 11 may apply an inverse Laplace transform to the acquired information on time-series changes to acquire information representing the ratio of the number of detections of annihilation radiation pairs that change over time differently from each other, and perform processing using the acquired information. The details of the processing performed by the control unit 11 will be described later.

The storage unit 12 is a memory device, disk device, etc., and stores the program executed by the control unit 11. This program may be provided stored on a computer-readable, non-transitory recording medium and stored in the storage unit 12. The storage unit 12 also stores various data necessary for the processing of the control unit 11, and also functions as a work memory for the control unit 11.

The operation unit 13 includes a mouse, keyboard, etc., accepts user instructions, and outputs the content of those instructions to the control unit 11. The output unit 14 is a display device, etc., and outputs information according to instructions input from the control unit 11.

The interface unit 15 is connected to the detector 20 and receives from the detector 20 signals indicating the detection of prompt gamma rays and signals indicating the time and position at which an annihilation radiation pair was detected, and outputs the received signals to the control unit 11.

[Insights into the interaction between positronium and nearby molecules]
The inventors, through experiments using a larger number of positronium atoms than in conventional experiments, have found that positronium atoms easily interact with radicals, and that the rate at which this interaction occurs is proportional to the concentration (dissolved concentration) of the radicals in the vicinity.

FIG. 2 is an explanatory diagram showing the results of measurements by the inventors of the amount of annihilation radiation pairs generated per microsecond (positronium annihilation rate) when the abundance ratio of nitrogen _N2 , which is a non-radical molecule, to oxygen _O2, which is a radical molecule, is changed.

As shown in FIG. 2, when the abundance ratio of oxygen _O2 is represented by partial pressure _pO2 on the horizontal axis and the number of annihilation radiation pairs generated per microsecond is measured and plotted for the cases of nitrogen _N2 only, air ( _N2 : _O2 = approximately 8:2), and oxygen _O2 only, it can be seen that the number of annihilation radiation pairs generated per microsecond is proportional to the abundance ratio of oxygen _O2 .

In other words, if the dissolved concentration of oxygen _O2 is expressed as p and the amount of annihilation radiation pairs generated, that is, the annihilation rate of positronium (described later) is expressed as 1/τ, then the following relationship exists between them:
Here, the coefficients a and b are determined experimentally and vary depending on the type of radical and the environment in which it exists (inside the human body, inside an animal other than the human body, and other environmental differences such as temperature).

[First example of operation of control unit]
Based on the above findings, the control unit 11 according to one example of this embodiment executes a program stored in the memory unit 12, thereby realizing a configuration that functionally includes a signal receiving unit 21, a change amount analysis unit 22, an estimation unit 23, and an output unit 24, as illustrated in FIG. 3.

Here, the signal receiving unit 21 receives signals indicating the detection of prompt gamma rays and signals indicating the time and position at which annihilation radiation was detected from the detector 20 connected via the interface unit 15. The signal receiving unit 21 also generates information indicating the position at which annihilation radiation pairs were generated using processing similar to that of a typical PET device, and counts and records the number of times annihilation radiation pairs were detected for each specified time and for each position at which annihilation radiation pairs were generated (voxel or LOR).

Specifically, the signal receiving unit 21 sets the time t, determined by a predetermined method, as t = 0, and counts and records the number of annihilation radiation pairs detected for each predetermined time period Δt from time t = 0 onwards, for each position (voxel or LOR) at which annihilation radiation pairs are generated. As a result, as shown in the example in Figure 4, for each position (P) at which annihilation radiation pairs are generated, count values are recorded such as the total number of annihilation radiation pairs detected from t = 0 to t = Δt, the total number of annihilation radiation pairs detected from time t = Δt to t = 2Δt, etc.

Here, the method for determining time t=0 may be to set the time when a prompt gamma ray is detected as time t=0.

The change amount analyzing unit 22 refers to the count value of the number of times annihilation radiation pairs are detected in each of the above periods for each position at which annihilation radiation pairs are generated, and acquires information on the change in the number of times annihilation radiation pairs are detected in time series for each position at which annihilation radiation pairs are generated. In this way, the change in the number of times annihilation radiation pairs are detected in time series is related to the lifetime of positronium generated in the subject.

Specifically, the change amount analysis unit 22 calculates the change in the count value of the number of times annihilation radiation pairs are detected in each of the above periods for each position where annihilation radiation pairs are generated, using a kind of exponential function.
The annihilation rate 1/τ is calculated by fitting with the following equation. Here, I is the number of positronium generated, and C is a background term that takes noise into consideration. In this example, the annihilation rate 1/τ corresponds to the information on the amount of change in the number of times annihilation radiation pairs are detected over time, which is the information of the present invention.

The estimation unit 23 substitutes the calculated annihilation rate 1/τ into equation (1) to calculate an estimated value of the dissolved concentration p of, for example, oxygen _O2 , a radical. The output unit 24 outputs the calculated estimated value p and presents it to the user as the dissolved concentration of the radical (here, oxygen _O2 ) near the source of the annihilation radiation pair.

[Second example of operation of control unit]
Furthermore, the distribution of radicals near the location where positronium is generated within the subject may not be uniform. For example, if there are normal cells and cancerous cells within a human organ, the dissolved concentrations of oxygen, which is a radical, within each cell will differ. In such cases, it may not be appropriate to fit the change in the count value of the number of times annihilation radiation pairs are detected with a single exponential function. That is, in such cases, instead of fitting function (2), it may be appropriate to use the sum of multiple types of exponential functions with different annihilation rates 1/τi (i=1, 2, ...) for the change in the count value of the number of times annihilation radiation pairs are detected. For example,
It is appropriate to do so.

Here, the necessary information is the value τ relating to the annihilation rate and the number Ii of positronium that reacts with radicals and annihilates at an annihilation rate of 1/τi.
The inverse Laplace transform with image function:
By utilizing the relationship above and equation (3), the number Ii of positronium that reacts with radicals and annihilates at an annihilation rate of 1/τi can be calculated.

Accordingly, the control unit 11 according to another example of this embodiment executes a program stored in the memory unit 12 to realize a configuration that functionally includes a signal reception unit 21, a change amount analysis unit 22', a component analysis unit 31, and a component information processing unit 32, as illustrated in FIG. 5. Here, components that are similar to those in the example of FIG. 3 are assigned the same reference numerals, and repeated explanations will be omitted.

The change amount analysis unit 22′ acquires the count value S(t) of the number of times annihilation radiation pairs are detected in each of the above periods for each position of generation of annihilation radiation pairs output by the signal reception unit 21 as information on the change in the number of times annihilation radiation pairs are detected in time series for each position of generation of annihilation radiation pairs, and outputs this information to the component analysis unit 31.

The component analysis unit 31 numerically applies an inverse Laplace transform to the information on the change in the number of annihilation radiation pair detections in a time series output by the change amount analysis unit 22'. Specifically, this numerical inverse Laplace transform can be performed using the widely known CONTIN method, which uses Tikhonov regularization. Since the CONTIN method is widely known, a detailed description of its details will be omitted.

That is, the component analysis unit 31
The predetermined range of τ, τmin<τ≦τmax, is divided into n parts, and τi is determined as τi=(τmax−τmin)×(i/n)+τmin (i=1, 2, . . . n).

Then, the component analysis unit 31 uses the CONTIN method to find Ii corresponding to τi that minimizes the following J through successive iterative calculations:
where α is the regularization parameter,
is a matrix with n rows and m columns, and the i-th row and j-th column are
It is as follows.
is an n-dimensional vector, the i-th component of which is
Furthermore,
is an m-dimensional vector, the j-th component of which is
It is what it is.

The component analysis unit 31 uses the above-mentioned iterative calculation to find Ii (i = 1, 2..., n) that minimizes J, and outputs this together with the corresponding τi to the component information processing unit 32. In this example, the component analysis unit 31 numerically performed the inverse Laplace transform using the CONTIN method, which uses iterative calculations, but as long as it can obtain Ii and τi that minimize J, the component analysis unit 31 can use any method to process the inverse Laplace transform, whether it is an analytical method or a numerical solution method other than the CONTIN method.

The component information processing unit 32 substitutes the extinction rate 1/τi (i = 1, 2, ..., n) calculated from a predetermined τi or by a predetermined calculation that minimizes J into equation (1) to calculate an estimated value of the dissolved concentration pi of the radical (e.g., oxygen _O2 ) corresponding to τi. Here, τi is determined as an ordered number in an arithmetic (or geometric) progression, so if the numbers are arranged in order of magnitude, the values of the dissolved concentration pi proportional to 1/τi will also be ordered numbers and can be arranged in order of magnitude.

The component information processing unit 32 plots the magnitude of the corresponding Ii (Ii corresponding to τi used to estimate pi) with the dissolved concentration pi on the horizontal axis, and outputs the plot. The results of this plot vary depending on the part of the subject (i.e., the location where the annihilation radiation pair was generated), and represent the distribution of dissolved oxygen concentration for each location where the annihilation radiation pair was generated, as shown in Figures 6(a) and 6(b).

The component information processing unit 32 outputs and presents to the user a distribution of dissolved oxygen concentrations, such as the example shown in Figure 6, based on the pair of Ii and τi determined for each position where annihilation radiation pairs are generated.

As an example, if the subject is a human body, the area to the left of point X in Figure 6 (the side with a lower dissolved oxygen concentration) indicates that the tissue surrounding the location where the annihilation radiation pair was generated is hypoxic. For example, since cancerous cells are more susceptible to hypoxia than normal cells, the distribution of cancerous cells is shown by the above output.

[Modification]
The component analysis unit 31 modifies the second term of equation (4) to:
may be employed to implement the CONTIN method.

[Background]
It is widely known that when the number of prompt gamma rays or annihilation radiation pairs detected by the detector 20 becomes large, non-constant background noise occurs (e.g., Coleman PG, et al., “A method of improving the statistical accuracy in measurements on positrons annihilating in gases”, J. Phys., E5, 376-378, 1972).

That is, when a prompt gamma ray is detected at t = 0 and an attempt is made to obtain the time t at which the annihilation radiation pair resulting from the β ⁺ decay that produced the prompt gamma ray (i.e., the corresponding annihilation radiation pair) is detected, if the number of detected prompt gamma rays and annihilation radiation pairs is large, it may not be possible to associate the prompt gamma ray representing time t = 0 with the corresponding annihilation radiation pair. Therefore, the detection rate η of annihilation radiation pairs per unit time is used. In this case, the probability of detecting an annihilation radiation pair within a certain time ΔT (where ΔT is sufficiently short so that 0≦ηΔT<<1) is ηΔT, and the probability of not detecting an annihilation radiation pair is 1−ηΔT.

Therefore, the rate at which annihilation radiation pairs are detected by a certain time t1 (the magnitude of the background noise) is
This approximation holds when ΔT is sufficiently small.

Therefore, using this result, the non-constant background noise is taken into consideration and equation (3) is modified as follows:
That is, the background noise is approximately represented as something that depends on time, more specifically, something that decays at a constant rate depending on time. Note that the value of η may be experimentally determined as a default value in advance, but since the value of η varies depending on the shape of the subject (such as the body shape in the case of a human body) and other circumstances, it is preferable to determine the value for each measurement. For example, the value of η is determined based on the measurement rate per unit time (the coincidence rate of annihilation radiation) of annihilation radiation pairs detected by the detector 20 (i.e., all annihilation radiation pairs regardless of their generation positions).

Furthermore, when equation (5) is used instead of equation (3), equations (4) and (4') become
is transformed into:

In this example, the component analysis unit 31 executes a sequential iterative calculation (modified CONTIN method) similar to the CONTIN method using equation (6) instead of equations (4) and (4'), and obtains a set of Ii, τi (i = 1, 2..., n) that minimizes J. Note that in the first term of equation (6),
The division by takes into consideration that the measurement of annihilation radiation pairs is performed by counting, and is intended to normalize the reliability of the data by the uncertainty due to the counting measurement.

REFERENCE SIGNS LIST 1 information processing device, 11 control unit, 12 storage unit, 13 operation unit, 14 output unit, 15 interface unit, 20 detector, 21 signal receiving unit, 22, 22' change amount analysis unit, 23 estimation unit, 24 output unit, 31 component analysis unit, 32 component information processing unit.

Claims (10)

signal receiving means for receiving a signal indicating that a pair of annihilation radiation beams emitted in opposite directions have been detected in the subject;
an annihilation rate analysis means for acquiring information on the annihilation rate of positronium from the number of detections of time-series annihilation radiation emitted in the subject based on the received signal;
an estimation means for estimating a dissolved concentration of radicals in the vicinity of a source of the annihilation radiation based on the acquired information on the annihilation rate of positronium ;
An information processing device comprising: 2. The information processing device according to claim 1,
the annihilation rate analysis means acquires information about the annihilation rate of the positronium by fitting at least one type of exponential function to a change in the time series of detected annihilation radiation emitted in the subject ;
The estimation means is an information processing device that estimates the dissolved concentration of radicals in the vicinity of the source of the annihilation radiation as an amount proportional to information on the annihilation rate of the positronium . 3. The information processing device according to claim 1,
The radical is an oxygen molecule. signal receiving means for receiving a signal indicating that a pair of annihilation radiation beams emitted in opposite directions have been detected in the subject;
an annihilation rate analysis means for acquiring information on the annihilation rate of positronium from the number of detections of the time-series annihilation radiations emitted in the subject for each generation position of the pair of annihilation radiations based on the received signal;
a component analysis means for applying an inverse Laplace transform to the acquired information on the annihilation rate of positronium , and acquiring information representing the ratio of the number of times each annihilation radiation is detected, for each annihilation radiation having a different annihilation rate with respect to time;
An information processing device comprising: 5. The information processing device according to claim 4,
an information processing device that estimates the dissolved concentration of radicals in the vicinity of a source of generation of the annihilation radiation as an amount proportional to the annihilation rate of positronium with respect to the time, based on information obtained by the component analysis means that indicates the ratio of the number of times that the annihilation radiation is detected to the dissolved concentration of the radical, and obtains and outputs information that indicates, for each generation position of the pair of annihilation radiations, the ratio of the number of times that the annihilation radiation is detected to the dissolved concentration of the radical. 6. The information processing device according to claim 4,
The component analysis means is an information processing device that performs a calculation by applying an inverse Laplace transform to the received signal, assuming time-dependent background noise. Computer,
signal receiving means for receiving a signal indicating that a pair of annihilation radiation beams emitted in opposite directions have been detected in the subject;
an annihilation rate analysis means for acquiring information on the annihilation rate of positronium from the number of detections of time-series annihilation radiation emitted in the subject based on the received signal;
an estimation means for estimating a dissolved concentration of radicals near a source of the annihilation radiation based on the acquired information on the annihilation rate ;
A computer-readable recording medium storing a program that functions as a Computer,
signal receiving means for receiving a signal indicating that a pair of annihilation radiation beams emitted in opposite directions have been detected in the subject;
an annihilation rate analysis means for acquiring information on the annihilation rate of positronium from the number of detections of the time-series annihilation radiations emitted in the subject for each generation position of the pair of annihilation radiations based on the received signal ;
a component analysis means for applying an inverse Laplace transform to the acquired information on the annihilation rate of the positronium , and acquiring information representing the ratio of the number of times each annihilation radiation is detected, for each annihilation radiation having a different annihilation rate of the positronium with respect to time;
A computer-readable recording medium storing a program that functions as a Computer,
signal receiving means for receiving a signal indicating that a pair of annihilation radiation beams emitted in opposite directions have been detected in the subject;
an annihilation rate analysis means for acquiring information on the annihilation rate of positronium from the number of detections of time-series annihilation radiation emitted in the subject based on the received signal;
an estimation means for estimating a dissolved concentration of radicals in the vicinity of a source of the annihilation radiation based on the acquired information on the annihilation rate of positronium ;
A program that functions as a Computer,
signal receiving means for receiving a signal indicating that a pair of annihilation radiation beams emitted in opposite directions have been detected in the subject;
an annihilation rate analysis means for acquiring information on the annihilation rate of positronium from the number of detections of the time-series annihilation radiations emitted in the subject for each generation position of the pair of annihilation radiations based on the received signal ;
a component analysis means for applying an inverse Laplace transform to the acquired information on the annihilation rate of the positronium , and acquiring information representing the ratio of the number of times each annihilation radiation is detected, for each annihilation radiation having a different annihilation rate of the positronium with respect to time;
A program that functions as a