Method for determining a position and / or radioactivity of at least one gamma-emitting source

Abstract

The invention relates to a method for determining the position (zk) or radioactivity of gamma sources (Pk) of an object, wherein: b) interaction data, or 'electron recoils', are acquired with a Compton camera during a movement of the object; c) the electron recoils (REi) are grouped into groups (Gj) relating to a given gamma ray; e) for each group and each possible sequence (Sjk) of electron recoils of the group, a Compton cone (CCjk) is constructed and its intersections (Pjkl) with the axis of the object (z) are calculated; f) for each group, for each possible sequence (Sjk) of electron recoils, a weighted fraction (Rjkl) of gamma rays emitted for each intersection is estimated; g) from the weighted fractions, a radiation curve (CR) representing the activity density of the sources is established; h) their position or their activity is determined from the radiation curve.

Description

[0001] Title: Method for determining the position and / or radioactive activity of at least one gamma-ray emitting source

[0002] TECHNICAL FIELD OF THE INVENTION

[0003]

[0001] The field of the invention is that of methods and systems for evaluating the position and radioactive activity of gamma radiation sources.

[0004] STATE OF THE ART

[0005]

[0002] Compton cameras have been developed for many years to obtain images and thus various information relating to gamma radiation sources (see Ref.1 cited below).

[0006]

[0003] A Compton camera usually consists of two main detectors: a scattering detector: this is the first element that interacts with the incoming gamma ray. The gamma photon undergoes Compton scattering in this detector, transferring some of its energy to an electron and changing direction.

[0007] An absorption detector: after scattering, the gamma photon changes direction and reaches this second detector, where it will be absorbed, usually by the photoelectric effect.

[0008]

[0004] Compton cameras can be used to determine the radioactive element content of a gamma radiation source.

[0009]

[0005] In this case, each source must be positioned within the camera's measurement volume, as is known per se. It follows that if a large number of gamma radiation sources are to be measured, a particularly long measurement time must be anticipated. Therefore, there is a need for a measurement system and method that allows for the rapid measurement of the radioactive compound content of gamma radiation sources.

[0010]

[0006] There is also a need for a system and a measurement method which allows for the rapid measurement of the position of one or more gamma radiation sources integrated within an object.

[0011] References:

[0012]

[0007] Ref.1: Parajuli RK, Sakai M, Parajuli R, Tashiro M. Development and Applications of Compton Camera — A Review. Sensors. 2022; 22(19):7374. https: / / doi.org / 10.3390 / s22197374

[0013] DESCRIPTION OF THE INVENTION

[0014]

[0008] The present invention aims to meet the needs indicated above. To this end, according to this disclosure, a method for determining the position and / or radioactive activity of at least one gamma-ray emitting source is proposed, said at least one source being part of an object under study having an object axis, the method comprising the following steps: b) interaction data are acquired; this interaction data being acquired or having been acquired using a Compton camera during a movement of the object; the object, during this movement, moving along a rectilinear trajectory defining a trajectory axis passing through or alongside a detection chamber of the Compton camera, respecting a trajectory kinematics such that during the movement the object axis follows the trajectory axis;each interaction data, called electron recoil, being a data relating to an interaction in the detection chamber between a gamma ray emitted by the object and an active medium contained in this chamber; each electron recoil comprising an instant and a three-dimensional position of the interaction, and an energy exchanged during the interaction; c) the electron recoil data are grouped into groups, each group being considered as representing a set of interactions generated by the same gamma ray at an instant of emission; e) for each group, for each possible sequence of electron recoil data in the group:;

[0015] - we construct a Compton cone; and

[0016] - zero, one or two possible intersections are determined between the Compton cone constructed for the sequence and the object axis, each intersection being defined for an axial position on the object axis; f) for each group, for each possible sequence of electron recoils and for each intersection determined for it, a weighted fraction of gamma ray emitted at the intersection is estimated, this weighted fraction being representative of a probability that the gamma ray associated with the group was generated at the intersection considered and generated the sequence of electron recoils considered; g) a radiation curve of the object is established having, on the abscissa, the axial positions along the object axis of the object; and on the ordinate, an (axial) activity density, calculated from the weighted fractions of gamma ray estimated for the object;h) the following step h1 is carried out at least once: h1) the position and / or activity of said at least one source is determined from the radiation curve of the object.

[0017]

[0009] It is understood that the method most often begins with an initial step a, during which the object under study is moved along said trajectory, respecting the kinematics of the trajectory.

[0010] The method described above advantageously makes it possible to achieve, for example – depending on the performance required – a positional resolution on the order of centimeters, and to measure the activity of gamma radiation sources with an accuracy of approximately 1%, while allowing the measurement of a large number of sources in a relatively rapid manner.

[0018]

[0011] Radioactive activity, or more simply, activity, here refers to the quantity of gamma rays emitted per unit of time, that is to say, a gamma ray flux. Activity is measured in counts per second, or preferably in becquerels, or even in curies.

[0019]

[0012] The activity density used in step g to establish the radiation curve of the object under study is an axial activity density per unit length along the object axis. It can be calculated, in particular, by summing the weighted fractions over successive intervals along the object axis, or by any equivalent calculation. In some cases, this density is calculated discretely over the intervals used to calculate it. In particular, it is often possible to calculate only one density value per source.

[0020]

[0013] The activity of a source is then calculated by integrating the activity density of the source's radiation curve over its axial extent. This calculation amounts to summing the density value(s) over the axial extent of the source, if the density has been calculated at discrete points.

[0021]

[0014] The method is particularly applicable to the determination of the radioactive activity of sources whose positions are already known.

[0022]

[0015] In this document, the term 'source' should be understood as meaning 'source of gamma radiation'.

[0023]

[0016] Furthermore, to simplify the description, it is not systematically specified in this document for each characteristic whether it is applicable indifferently to one source or to several sources. Consequently, any reference to 'a source' or 'sources' should be interpreted, unless otherwise indicated or technically impossible, as meaning 'one or more sources' or 'at least one source'.

[0024]

[0017] For the same purpose, in this document, the terms 'activity' or 'radioactivity' should be understood as possibly referring, if the context permits, to 'a quantity of gamma radiation emitted', and in particular 'emitted per unit of time' or 'emitted over a certain period' (in particular, during step a). A determination of the radioactivity of a source thus includes, in particular, the determination of the quantity of gamma radiation emitted by that source, especially during step a.

[0025]

[0018] The method can be implemented particularly for determining the properties of sources of heavy radioactive elements.

[0019] Thus, in certain embodiments at least one source has a density greater than 5 g / cm3, or even greater than 8 g / cm3, or even greater than 10 g / cm3.

[0026]

[0020] In certain embodiments, the determination process further includes a step d preceding step e, during which the groups are filtered so as to retain only those whose total energy is greater than a predetermined value.

[0027]

[0021] In certain embodiments, at a step h1, the position and / or activity of a source is determined using information contained only in an axial range of the studied radiation curve defined with respect to an axial extent of the source, and optionally with respect to the axial extent of the source or sources adjacent to the source considered.

[0028]

[0022] In certain embodiments, for at least one source studied, an axial activity density of a first gamma ray source during a displacement of the latter along the trajectory axis respecting the kinematics of traversing the trajectory is modeled in the form of a pre-calculated radiation curve of the first source, associated with the source studied; said first source being either the source studied, or a reference gamma ray source placed at the same axial position as the source studied; the pre-calculated radiation curve comprising, in abscissa, axial positions along the object axis of the source considered, and in ordinate, the activity density of said at least one first source;and at a considered step h1, the position and / or activity of said at least one source studied within the object is determined as a function of the pre-calculated radiation curve(s) associated with said at least one source studied.

[0029]

[0023] In certain embodiments, at the considered step h1, the position and / or activity of said at least one source under study is determined by minimizing a difference between a radiation curve representing an activity density of said at least one source under study and the pre-calculated radiation curve(s) associated with said at least one source under study.

[0030]

[0024] In certain embodiments, the object comprises a plurality of sources rigidly fixed to one another; at least one of said sources is a gamma ray source said to be occulted; and the considered step h1 comprises the following steps: h11) a cleaned radiation curve is calculated by subtracting from the object's radiation curve one or more pre-calculated radiation curve(s) associated with said at least one radiation source to be occulted; h12) the position and / or activity of at least one source other than the source(s) to be occulted is determined from said cleaned radiation curve.

[0025] In certain embodiments, step h includes the performance of at least one preliminary step h1 followed by a subsequent step h1; and during step h11 of the subsequent step h1, the pre-calculated radiation curve(s) associated with said at least one radiation source to be occulted used to calculate the purified radiation curve is or are calculated taking into account the position and / or activity of said at least one source to be occulted as calculated in step h12 of the preliminary step h1.

[0031]

[0026] In certain embodiments of the determination method, at the considered step h1, the position and / or activity of a source under study within the object is determined as a function of at least a pre-calculated reference radiation curve attributed to a reference source disposed at a predetermined axial position on the object under study, in particular a known or estimated axial position of the source under study.

[0032]

[0027] The reference source is typically located at the same axial position known in advance as the source under study.

[0033]

[0028] In certain variants of this latter embodiment, at the stage h1 considered, where appropriate at the stage h12, the position and / or activity of the source under study is determined as a function of a ratio between a value, for example an area under a predetermined curve interval, calculated from a radiation curve representative of an activity density of the source under study, and a corresponding value calculated from said pre-calculated reference radiation curve.

[0034]

[0029] Any suitable value that allows the calculation of the position and / or activity of the source under study can be used. Typically, a position and / or activity of the source under study is determined by comparison (typically, as a function of a ratio) between the area under the radiation curve (of the object, or the cleaned curve) and the area under the corresponding pre-calculated reference radiation curve, i.e. the reference radiation curve positioned at (for example, centered on) the location of the source under study.

[0035]

[0030] In certain implementations, at the stage h1 considered,

[0036] - the pre-calculated radiation curve(s) associated with said at least one source studied is or are one or more parametric curve(s);

[0037] - a value is determined for the parameter(s) of the pre-calculated parametric radiation curve(s) that minimizes the difference between a radiation curve of the object or a refined curve relating to at least one source under study and the parametric radiation curve associated with the source under study, or the sum of the parametric radiation curves associated with the sources under study; and

[0038] - the position and / or activity of said at least one source under study is determined from the parameter value(s) thus determined.

[0031] By extension, this disclosure also relates to a method for determining the radioactive element content of an object under study whose radioactive element composition is known. This method includes determining the activity of a gamma-ray emitting source forming part of an object, by implementing the determination method defined above, and determining the radioactive element content of said at least one gamma-ray source from its activity determined during step A.

[0039]

[0032] Each of the processes according to this disclosure may include, in particular, a computer-implemented process, the term 'computer' herein covering any data processing system, in particular distributed or non-distributed.

[0040]

[0033] In a particular embodiment, the different steps of the process for determining the position or radioactivity of gamma ray sources are determined by computer program instructions.

[0041]

[0034] Accordingly, the present disclosure also relates to a computer program comprising instructions which cause at least steps g and h of the process described above to be executed when said program is executed by a computer.

[0042]

[0035] This program may use any programming language, and be in the form of source code, object code, or intermediate code between source code and object code, such as in a partially compiled form, or in any other desirable form.

[0043]

[0036] This disclosure also relates to a non-volatile storage medium readable by at least one processor and on which a computer program as described above is stored. The information medium can be any entity or device capable of storing the program. For example, the medium can include a storage means, such as a ROM, for example a CD-ROM or a microelectronic circuit ROM, or a magnetic recording means, for example a floppy disk or a hard disk drive. Alternatively, the information medium can be an integrated circuit in which the program is incorporated, the circuit being adapted to execute or to be used in the execution of the process in question.

[0044]

[0037] By extension, this disclosure also relates to a determination device comprising at least one processor and at least one recording medium as defined above.

[0045]

[0038] Finally, the present disclosure also includes a determination system comprising a Compton camera and a determination device as defined above.

[0046] BRIEF DESCRIPTION OF FIGURES

[0039] Other advantages, purposes and particular features of the present invention will become apparent from the following non-limiting description of at least one particular embodiment of the devices and methods of the present invention, with reference to the accompanying drawings, in which: Fig. 1 is a schematic perspective view of a determination system according to this disclosure; Fig. 2 is a schematic view representing the passage of a nuclear fuel rod through the detection chamber of the Compton camera of the system shown in Fig. 1; Fig. 3 is a block diagram representing the steps of an implementation of a method for determining radioactivity according to this disclosure; Fig.Fig. 4 is a block diagram representing the steps of an implementation method for determining the position and / or radioactivity of gamma ray source(s) according to this disclosure; Fig. 5 is a block diagram representing a variant of step h1 of the radioactivity determination method shown in Fig. 4; Fig. 6A is a diagram representing a radiation curve of an object under study, obtained by a method for determining the position and / or radioactivity of gamma ray source(s) according to this disclosure; Fig. 6B is a diagram representing a radiation curve emitted from a reference source used in a method for determining the position and / or radioactivity of gamma ray source(s) according to this disclosure; Fig.Figure 6C is a diagram comparatively representing a cleaned radiation curve and an emitted radiation curve from a reference source used in a method for determining the position and / or radioactivity of gamma ray source(s) according to this disclosure; Figure 7 is a figure schematically representing the relative positions of sources integrated into an object under study.

[0047] DETAILED DESCRIPTION OF THE INVENTION

[0048]

[0040] Various embodiments of devices and methods according to this disclosure will now be presented in relation to the figures, by way of non-limiting examples of embodiments.

[0049]

[0041] These examples are given in the case of determining the radioactivity of pellets in a nuclear fuel rod, namely an assembly of nuclear fuel pellets, which is the subject of study within the meaning of this disclosure. Each pellet in the rod thus constitutes an example of a gamma radiation source.

[0042] Therefore, in this document, any reference to a pellet should be interpreted more generally as meaning 'a gamma radiation source'.

[0050]

[0043] Fig. 1 schematically represents a gamma radioactivity determination system 10, enabling the implementation of processes according to this disclosure.

[0044] This system 10 comprises a Compton camera 100 and a post-processing computer 200, the latter constituting a gamma radioactivity determination device within the meaning of this disclosure.

[0051]

[0045] The determination device 200 has the hardware architecture of a computer, as schematically illustrated in Figure 1. Generally, any data processing device comprising at least one memory capable of storing data and the program that will be described later, and one or more processors capable of executing this program, can be used. The data processing device can be located near the Compton camera 100, or, conversely, remotely, and for example, accessible via a network such as the internet.

[0052]

[0046] In this embodiment, the determination device 200 includes, in particular, a processor 202, a non-volatile flash memory 204, and other elements not shown (RAM, communication means, etc.). The determination device 200 is connected to the Compton camera 100, which it controls and from which it receives information acquired by the camera.

[0053]

[0047] The non-volatile memory 204 of the determination device 200 constitutes a recording medium in accordance with this disclosure, readable by the processor 202 and on which is recorded a computer program in accordance with this disclosure, comprising instructions for the execution of process steps in accordance with this disclosure.

[0054]

[0048] The Compton camera 100 comprises a detection chamber 110, a scintillation signal detector, an ionization signal detector and a camera computer 120. The general characteristics of these elements are known in themselves (see for example Ref.1).

[0055]

[0049] However, the Compton 100 camera has the distinctive feature of a detection chamber 110, filled with liquid xenon, and in the shape of a hollow cylinder with a chamber axis denoted Z. In Fig. 2, the effective volume of the detection chamber 110 is represented by a thin dashed line, which marks the limits of the detection zone. The X, Y, and Z axes represent the principal axes of the chamber.

[0056]

[0050] To enable optimal detection of gamma rays, more generally, the detection volume of the chamber is filled with a liquid active medium, rich in electrons to provide high sensitivity for the detection of high-energy gamma rays. This active medium preferably consists of pure liquefied noble gases, such as xenon, argon, or neon.

[0057]

[0051] The instrumentation of the Compton camera can be constructed from any sensors suitable for acquiring scintillation or ionization signals; in particular, any photodetection sensor for acquiring the scintillation signal. For acquiring the ionization signal, sensors such as wire chambers, parallel-plate ionization chambers, etc., can be used.

[0058]

[0052] A cylindrical passage 112, with the same axis as the enclosure axis Z, is provided inside the detection enclosure 110. This passage is open on both external faces of the Compton camera. It therefore allows objects (or sources) whose gamma radiation is to be evaluated to pass through the camera 100. These objects then follow a straight trajectory along the z-axis of the enclosure 110.

[0059]

[0053] In this embodiment, due to its cylindrical shape, the enclosure 110 allows the detection of gamma rays over a 360° angle around the z-axis. However, it is understood that a Compton camera whose detection enclosure is close to the axis of movement of the object under study, but without surrounding it over 360°, would also allow (albeit with less efficiency) the application of the methods according to this disclosure. It is sufficient, in fact, that the Compton camera be able to acquire the scintillation and ionization signals resulting from interactions of a portion of the gamma rays emitted by the object during its movement near the measurement enclosure.

[0060]

[0054] When a gamma radiation source is in the measurement chamber, or even in the vicinity of the Compton camera, the scintillation signal detector and the ionization signal detector of the Compton camera acquire interaction data representative of the interactions taking place between gamma rays emitted by the radiation source and the active medium contained in the chamber 110.

[0061]

[0055] The camera 100 is designed in particular to allow elongated objects to pass through the passage 112 along an object axis, and of a diameter sufficiently small to pass through the passage 112.

[0062]

[0056] In the example presented here, we seek to evaluate the content of radioactive elements in nuclear fuel pellets.

[0063]

[0057] The object under study is therefore, in this case, an assembly of nuclear fuel pellets, assembled along an object axis, and collectively forming a rigid body C called a 'pencil'. In this example, the pencil C comprises 50 pellets Pi where i=1 ...M (M=50).

[0058] The radioactive element content of the pellets Pi of the pencil C is evaluated by implementing a method for determining the radioactive element content of an object measured according to this disclosure, for example, the method illustrated in Fig. 3.

[0059] This determination is made possible because the radioactive element composition of the pellets is known: for this reason, the radioactive element content of a pellet can be deduced from the intensity of the gamma rays emitted by it, using calculation methods or nomograms known per se.

[0064]

[0060] The determination of the radioactive element content of the pellets is therefore carried out first (step A) by determining the activity of each of the pellets by implementing a determination process according to this disclosure, then (step B) by determining the radioactive element content of each of the pellets from the activities calculated for the different pellets.

[0065]

[0061] An example of a method for determining the position and / or activity of gamma ray sources forming part of an object will now be presented in relation to Figs. 4 and 5.

[0066]

[0062] In this example, the object studied is the pencil C, which is therefore an assembly of nuclear fuel pellets, assembled along an object axis.

[0067]

[0063] In a first step of the process (step a), the pencil C is moved along the z-axis by means of movement not shown.

[0068]

[0064] During this movement, the successive gamma rays emitted by the different pellets are detected by the scintillation signal detector and the ionization signal detector of the camera 100, which continuously record all the signals that reach them (step b).

[0069]

[0065] We consider an emission instant tj at which a gamma ray of index j, denoted Rj, is emitted by a pellet of the pencil C located in the enclosure 110.

[0070]

[0066] Fig.2 schematically shows the trajectory of a gamma ray Rj emitted by the pellet P.

[0071]

[0067] The point RjO of origin of the ray Rj, from which it was emitted, is located substantially at the center of the enclosure 110. The dashed line (also noted Rj) represents the trajectory of the ray Rj through the enclosure.

[0072]

[0068] In the example presented, two interactions Ij1 and Ij2 occurred between the ray Rj and particles located in the enclosure 110. For this reason, the trajectory Rj of the ray is not a straight line, but a polyline which has two vertices Rj 1 and Rj2 at the two points of interaction between the ray Rj and the particles of the enclosure.

[0073]

[0069] During each interaction Iji between a gamma ray and a particle in the enclosure 110, from the information collected during the interaction by the scintillation detector and the ionization signal detector, the camera computer 120 of the Compton camera 100 calculates an interaction data, or electronic recoil.

[0074]

[0070] As previously stated, an electron recoil REi (of index i) relative to a given interaction li includes the emission time tj, a three-dimensional position Rji at which the gamma radiation interaction took place in the detection chamber, and the energy Eji exchanged during this interaction.

[0075]

[0071] The electronic recoil REji is determined from the measurable signal of light, called scintillation signal and the measurable signal of electric charge, called ionization signal, which are measured by the scintillation and ionization signal detectors, in a manner known per se.

[0076]

[0072] Fig.4 shows the different steps of a method of implementing a process for determining the position and / or activity of one or more gamma radiation sources.

[0077]

[0073] Radioactive activity here refers to the quantity of gamma rays emitted per unit of time (expressed in counts per second). In practice, the method makes it possible to evaluate the quantity (the number) of gamma rays emitted by different gamma ray sources integrated into an object under study as it passes through the detection chamber of the Compton 100 camera.

[0078]

[0074] During step a of the process, the pencil C is passed through the camera 100 through the passage 112.

[0079]

[0075] Before the passage of the pencil C through the enclosure 110, during this passage and after this passage, the scintillation signal detector and the ionization signal detector of the camera 100 record all the signals which reach them.

[0080]

[0076] Thus, in step b, the camera 100 acquires these signals; from these, it then calculates the set of electronic recoils REji generated during the movement of the pencil C.

[0081]

[0077] It transmits the electronic recoil values ​​REji thus determined to the post-processing computer 200.

[0082]

[0078] Based on this information, the calculator 200 performs the following operations:

[0083]

[0079] In step c, the electron recoil is grouped into groups Gj, j=1 ....N. The idea is that for each emitted beam, all the electron recoil REji generated by that beam are grouped into the same group (provided that there are at least two electron recoil for that beam). Thus, the groups can be created by respecting the following rules:

[0084] (1) if the information received contains only one electronic recoil for a certain time of transmission, no group is formed for that electronic recoil;

[0085] (2) Conversely, if at least two electronic recoils are detected at the same emission time (taking into account the measurement uncertainty of the emission time recordings), these electronic recoils are grouped together;

[0086] (3) noting that an electron recoil REi can belong to at most only one group.

[0080] At step d (which is optional), a filtering of the groups is carried out according to the cumulative energy of the energies Eji of the different interactions Iji associated with the group Gj under consideration.

[0087]

[0081] Specifically, during step d, it is possible to retain for the remainder of the algorithm only those groups for which the cumulative energy of the energies Eji of the different interactions is greater than a certain predetermined value. This value can be chosen so as to retain only high-energy groups, corresponding therefore to high-energy gamma rays.

[0088]

[0082] This filtering thus makes it possible to execute the process only on the basis of high energy rays (for example greater than 200 keV).

[0089]

[0083] Thanks to this filtering, the process effectively takes into account substantially all of the gamma rays generated by the pellet (the gamma ray source) during its movement, which would not be the case if lower energy rays were taken into account, a part of these latter rays being in fact absorbed by the outer layers of the pellet and therefore not being measured.

[0090]

[0084] At the end of step c (or d if it takes place), we therefore have a set of groups Gj, each group Gj therefore contains a set of electronic recoils REji for i=1,...N corresponding to the different interactions Iji which took place at the emission time tj.

[0091]

[0085] We then consider all possible interaction sequences in the group Gj. Suppose, for example, that the group Gj includes the electron recoils for three interactions Ij1, Ij2 and Ij3. The possible interaction sequences are the following sequences Sjk, k=1...6: Ij1-lj2-lj3, Ij1-lj3-lj2, Ij2-lj1-lj3, Ij2-lj3-lj1, Ij3-lj1-lj2 and Ij3-lj2-lj1.

[0092]

[0086] In step e, for each possible sequence Sjk of electron recoils from group Gj, a Compton cone of sequence CCjk associated with the sequence Sjk is calculated. This cone is based on all the electron recoils of the sequence and constitutes a Compton cone delimiting a surface from which the gamma ray that gave rise to the interactions was in principle emitted.

[0093]

[0087] This CCjk cone can be calculated in different ways. In a simplified version, it can be the Compton cone calculated simply from the first two interactions of the interaction sequence.

[0094]

[0088] Next, for each interaction sequence Sjk, after calculating the Compton cone of sequence CCjk, we determine (if it exists) the possible intersection(s) between the Compton cone constructed for the sequence Sjk and the object axis (the z-axis).

[0095]

[0089] Following this calculation, since the emission time tj is known, for each intersection, its axial position (point RjO) is determined on the object axis, that is, in the object's own frame of reference. This position therefore represents an axial position of the object from which the gamma ray Rj is estimated to have been emitted.

[0090] Thus, for each possible interaction sequence Sjk for each group Gj, zero, one, or two possible intersections are determined. These intersections are collectively denoted Pjkl; they can therefore be more specifically Pjkl and possibly Pjk2.

[0096]

[0091] The intersections Pjkl thus determined are advantageously obtained in the proper frame of reference of the measured object. They therefore do not depend on the instant (the emission instant) at which the electronic recoils that made it possible to determine these intersections were acquired.

[0097]

[0092] At step f, for each intersection Pjkl determined at step e, a weighted fraction Rjkl of gamma ray emitted at the intersection Pjkl considered is estimated.

[0098]

[0093] This is a probabilistic approach.

[0099]

[0094] Since each group Gj of electronic recoils is the grouping of electronic recoils detected for an emission instant, we know that (except in exceptional cases) each group Gj corresponds to a gamma ray, emitted at the emission instant tj.

[0100]

[0095] The calculations carried out in step e made it possible to calculate the possible origins of this gamma ray on the pencil C: these are the different intersections Pjkl.

[0101]

[0096] In step f, for each intersection Pjkl, the probability is calculated that the intersection is indeed the origin point of the gamma ray detected for group Gj and, furthermore, that this gamma ray generated the interactions following the interaction sequence Sjk. This probability is represented by the quantity Rjkl.

[0102]

[0097] This quantity Rjkl, called the weighted fraction of gamma ray emitted at the intersection Pjkl considered, therefore represents an estimated number (a fraction, following a probabilistic approach) of gamma ray emitted at time tj at the intersection Pjkl considered and having generated the sequence of interactions Sjk.

[0103]

[0098] Advantageously, in step f, the weighted gamma ray fractions Rjkl are calculated only for the intersections Pjkl identified in step e. Thus, a portion of the measured electron recoil is not taken into account. This advantageous arrangement therefore significantly limits the amount of computation performed, as the number of intersections Pjkl considered, defining possible emission positions of the gamma radiation emitted at a given time tj, is relatively limited. This arrangement also increases accuracy.

[0104]

[0099] The calculation of the weighted Rjkl gamma ray fractions in step f takes into account the fact that the sum of the probabilities for a gamma ray (and therefore for the corresponding group of electron recoils) of having been emitted at one or the other of the identified intersections must equal 1. This allows the weighted gamma ray fractions to be distributed over the identified intersection(s), corresponding to the different CCjk Compton cones identified for the different Sjk sequences.

[0100] Any suitable method can be used to calculate the weighted Rjkl fractions.

[0105]

[0101] During this calculation, the probability for a gamma ray to have been emitted from an intersection Pjkl (and therefore the weighted fraction Rjkl) can be calculated by taking into account all or part of the following considerations. The weighted fraction Rjkl can thus be a function of: the solid angle of the Compton cone of sequence CCjk, in particular a ratio between this solid angle and the maximum solid angle equal to 4TI; the probability of scattering the gamma ray at a given angle, for each electron recoil associated with an interaction; the distance or cumulative distances traveled by the gamma ray, from the emission point RjO of the gamma ray to the first interaction point Rj1, or between any pair of consecutive interaction points Rjk and rjk+1, taking into account in particular the attenuation coefficients of gamma rays in matter (either in air when the ray is in passage 112, or in the active medium contained in the detection chamber 110).

[0106]

[0102] The calculation method may be iterative. In particular, calculation methods using an MLEM (Maximum Likelihood Expectation Maximization) algorithm may be used.

[0107]

[0103] Next, in step g, the radiation curve of the object studied is established, so in this example, for pencil C.

[0108]

[0104] An example of a measured radiation curve for a pencil, CR, is given by Fig.6A.

[0109]

[0105] The x-axis corresponds to the object axis of the measured object.

[0110]

[0106] On the ordinate, the curve represents the axial density of radiation emitted by the object, along the z-axis of the pencil C.

[0111]

[0107] This axial density is preferably obtained by considering consecutive intervals of the same length along the object axis (the z-axis) and, within each interval, by summing the weighted fractions Rjkl of all the intersections detected in that interval. This yields a value for the radiation density for each of the intervals considered.

[0112]

[0108] The CR curve has three parts: two end parts P1 and P3, and a central part P2. The central part P2 extends over an axial extent along the z-axis which corresponds approximately to the extent of the pencil C along this axis. The pencil C is symbolically represented under the CR curve in Fig. 6A to show that the part P2 of the CR curve corresponds to the axial extent of the pencil C along the object axis z.

[0109] In the present case, in the pencil C, the different pellets P exhibit relatively similar levels of radioactivity. For this reason, the radiation density obtained from the weighted fractions Rjkl is relatively constant over the central part P2, that is, over the axial extent of the pencil C.

[0113]

[0110] Conversely, no gamma ray can be emitted from a position along the z-axis outside the axial extent of the pencil. However, due to the probabilistic approach used, non-zero probabilities are logically assigned in step f to intersections Pjkl located at positions outside the pencil, which explains why the points of the CR curve can have non-zero ordinates even in parts P1 and P3.

[0114]

[0111] The exploitation at step h of the obtained CR radiation curve will now be explained.

[0115]

[0112] To carry out this step and thus calculate the position and / or activity of the pellets of pencil C, different procedures can be followed.

[0116]

[0113] Step h can be carried out in a single step h1.

[0117]

[0114] For example, if the object comprises a single source, the CR radiation curve can be used to determine the position of this source within the object. For instance, the position of the source can be considered to be the axial position of the centroid of the surface located under the CR curve.

[0118]

[0115] Or, if the object includes several sources, at least one of which has a known activity, the CR radiation curve can be used to determine the activity of the other sources within the object relative to the known source of radioactivity.

[0119]

[0116] In this case, it is necessary to distinguish in the CR curve the respective contributions of the different sources.

[0120]

[0117] An example is illustrated by Fig.7. This figure represents the first five pellets P1 to P5 of the pencil C, along the z-axis. Adjacent pellets are separated by a distance d.

[0121]

[0118] Each pad Pk therefore corresponds to an interval E or Ek extending a distance d / 2 forward of the pad and a distance d / 2 backward of the pad on the z-axis.

[0122]

[0119] An approximate solution for distinguishing in the CR curve the respective contributions of the different Pi pellets, i=1...M, consists of considering that the part of the radiation curve located axially on the interval Ei associated with a Pi pellet represents the radiation of that pellet.

[0123]

[0120] Thus, if we assume that the activity (or activity density) of the pellet P1 is known, the activity (or activity density) of each of the other pellets Pi can be calculated for example by taking the ratio between the surface Si located under the radiation curve on the interval El associated with the pellet Pi, and the corresponding surface S1 located under the radiation curve on the interval E1 associated with the pellet P1.

[0124] Use of pre-calculated radiation curves

[0125]

[0121] During a step h1, one or more pre-calculated radiation curves may be used to determine the position and / or activity of the object's gamma ray sources.

[0126]

[0122] A radiation curve can be calculated as follows: first, the interaction data produced during a displacement of a considered gamma ray source along the trajectory axis, respecting the trajectory kinematics, are estimated by simulation or determined by performing steps a and b; then, from these interaction data, steps c to g are performed so as to obtain at step g the radiation curve of the considered source: this then constitutes a pre-calculated radiation curve for the considered source, which can be used for subsequent calculation steps.

[0127]

[0123] It is therefore understood that steps c to g can be carried out on the basis of data acquired from either simulation or the actual execution of steps a and b.

[0128]

[0124] A pre-calculated radiation curve may be, in particular, a curve obtained for a source that is part of the object studied, or for a reference source, a reference source here designating a source whose position and / or activity is or are known.

[0129]

[0125] The pre-calculated radiation curves can be used in different ways to carry out a step h1.

[0130]

[0126] In particular, the values ​​obtained during a step h1 can be used in a subsequent step h1 to calculate the desired values ​​more precisely. In these implementations, step h is then carried out in several steps h1, iteratively.

[0131]

[0127] This is particularly the case when the object has several sources. Step h can then be carried out by successively performing several series of steps h1, each series allowing a more precise value (a position and / or an activity) to be determined for each of the sources.

[0132]

[0128] Such a procedure will be explained in relation to Fig. 5.

[0133]

[0129] Step h, in particular the repetition of steps h1, can be conducted in different ways depending on the axial distribution and / or the number of gamma radiation sources in the object being measured, and depending on the information one seeks to obtain.

[0134] Curves

[0130] One way of carrying out step h1 is to use one or more parametric radiation curves.

[0135]

[0131] A radiation curve of a source in this case is modeled as a parametric curve, that is to say a curve whose values ​​are only a function of the position along the object axis and of a finite number of parameters.

[0136]

[0132] The parametric curve can be explicit, that is to say, there is a function lk(z) giving the activity density of the source as a function of the axial position (z). For example, the radiation curve emitted from the pellet P1 illustrated in Fig. 6B can be modeled as a continuous curve as a function of three parameters: the height (I ref 1 ) of the peak of the curve, the width (m1 ) at half-height of this peak and the axial position (z1 ) of the maximum.

[0137]

[0133] In other embodiments, the parametric curve is represented only by the set of its values ​​at different axial positions: it is only known in the form of a histogram. However, this histogram can be parametric: the histogram values ​​can be recalculated as a function of a finite set of parameters. For example, the histogram can be recalculated as a function of parameters for maximum height, axial extent, and an axial position (relative to the object axis) of the histogram.

[0138]

[0134] It is understood that when a radiation curve associated with a source (or a set of sources) is defined as a parametric curve, once the values ​​of the curve's parameters are known, it can be recalculated taking into account the actual values ​​of its parameters; the activity of the source(s) can then be easily calculated from the curve thus recalculated. This property is exploited in the following way.

[0139]

[0135] Consider an object whose radiation curve was determined in step g. The activity density of the radiation it emits can be modeled as a function of the object by the equation: this equation being graphically represented by the CR radiation curve.

[0140]

[0136] It is also known that the object consists of a certain number of sources: in this case, it consists of a stack of 50 Pk pellets, k=1...M (M=50).

[0141]

[0137] It is further assumed that the radioactive activity of each pellet can be represented by a parametric curve, associated with an equation: for a pellet Pk, the activity density lk(z) of the radiation emitted by the pellet (represented by the radiation curve of the pellet) can be modeled by the equation (E1): lk(z) = Izk, mk, Irefk (z) (E 1 )

[0138] For each pellet Pk, the radiation curve of the pellet Pk is thus a parametric curve with three parameters zk, mk, Irefk representing respectively the axial position zk of the peak of the curve, the axial extent mk of the curve, and the maximum height of the curve Irefk.

[0142]

[0139] The radiation curve of the set of pellets Pk, k=1....M distributed at axial positions zk, is the superposition (the sum) of the individual curves of the different pellets.

[0143]

[0140] The activity density of the radiation from all the pellets is therefore expressed by the equation:

[0144]

[0141] Thus, identifying the position and / or activity of the different pellets will be done by determining the optimal values ​​of the parameters of the radiation curves of the different pellets, (zk*, mk*, Irefk*) for k=1...M, which minimize the difference between the radiation curve of the object (equation E1) and the combined curve of the 50 pellets (equation E2). Once these parameters have been calculated, the position and / or activity of each of the different pellets is calculated.

[0145]

[0142] Step h1 of determining the position and / or activity of the sources of the object studied therefore consists in this case mainly of searching for these optimal values ​​of parameters (zk*,mk*, Irefk*), therefore of searching for:

[0146]

[0143] Any minimization algorithm, including iterative, that allows minimizing the integral indicated in the above formula may be used.

[0147]

[0144] One can use, for example, an algorithm based on iterative Markov models.

[0148]

[0145] Next, from the parameter values ​​thus determined, and thus from the emitted radiation curves determined, the position and / or activity of the sources considered is calculated. The radioactive activity, as implicitly indicated in the explanation given for Fig. 7, can be calculated as being proportional to the area under the radiation curve of the source considered, this curve in fact representing an axial activity density.

[0149]

[0146] That being said, when the object has several sources, it can be difficult to simultaneously evaluate the position and / or activity of all the sources (or, in the case where parametric curves are used, it can be difficult to estimate the parameters for all the sources). Restricting the calculation to only certain sources

[0150]

[0147] One solution to overcome this difficulty is to restrict the calculation of position and / or activity to only a limited number of sources (preferably a single source), called 'remaining sources'. This can be done by performing a preliminary step h11 during which the information (or contributions) considered to come from the other sources, called the 'to be occulted' sources, is removed from the object's radiation curve.

[0151]

[0148] In this case, a pre-calculated radiation curve must be available for each of the sources to be occulted.

[0152]

[0149] A so-called 'cleaned' radiation curve is then calculated by subtracting the pre-calculated radiation curves of each of the sources to be occulted from the object's radiation curve. After step h11 of calculating the cleaned curve, step h1 continues with the following step h12: h12) the position and / or activity of the remaining source(s) is determined from the cleaned radiation curve.

[0153]

[0150] This procedure will be illustrated in the detailed example presented here, namely the determination of the radioactivity of the pellets in pencil C shown in Fig. 2, and also schematically represented in Fig. 6A. This pencil consists of 50 pellets denoted Pi with i=1....M (M=50). It is assumed that the position of these pellets is known, but that their individual radioactivity is not.

[0154]

[0151] A reference pellet P is also available ref, whose activity is known. The emitted radiation curve for this reference pellet is curve C re f_i is represented in Fig. 6B. The maximum of the curve corresponds to a radiation intensity l re f.

[0155]

[0152] The aim is to determine the radioactive element content of each of the Pi to PM pellets. To do this, we will calculate the activity of each pellet; then, from the activity of each pellet, we will calculate its radioactive element content in a manner known per se.

[0156]

[0153] The calculation of the activity of the different pellets is done iteratively, by iteratively carrying out series of steps h1. An index J is incremented at each iteration (Fig.5).

[0157]

[0154] During each series of steps h1, M steps h1 are performed, each of these steps allowing the activity of one of the M pellets to be evaluated.

[0158]

[0155] In one of these steps h1 (of index k), the activity of a pellet Pk is evaluated as follows:

[0159]

[0156] All the pellets other than the pellet Pk (called the remaining pellet) are pellets to be occulted: these are the pellets Pi with i different from k.

[0157] The pre-calculated radiation curves of all the pellets Pi to be occulted are subtracted from the object radiation curve CR.

[0160]

[0158] During the first series of steps h1 (J=1), the pre-calculated radiation curve CR is used. re f_i, for each pellet Pi, a curve identical to the reference curve CR re f of the reference Pref disc, except that the CR curve re f_i is axially centered on the Pi disc.

[0161]

[0159] During step h1 relating to the pellet Pk, during substep h11, the CR curves are subtracted from the CR radiation curve of the pencil ref_i of all the occulting pellets Pi, i different from k: this leads to removing from the CR radiation curve the estimated contribution (what could be called 'the estimated quantities of radiation') of all the occulting pellets Pi.

[0162]

[0160] This gives us the purified radiation curve CR ep Figure 5 shows the CR curve. ep obtained for step h1 relating to the P1 pad: all contributions from the P2 to P50 pads were removed. The CR curve ep therefore mainly presents a peak located axially at the level of the P1 disc.

[0163]

[0161] Once the contributions of the occulting pellets have been removed from the CR radiation curve, the calculation can be performed for the remaining pellet Pk (P1 in this case). This calculation will be presented for pellet P1 but could be presented for any other pellet as a source on which the calculation is performed.

[0164] Using a pre-calculated radiation curve to determine the position and / or activity

[0165]

[0162] For the first iteration, the pre-calculated radiation curve CR is used for the pellet P1 re f_i of the Pref pad positioned in position z1.

[0166]

[0163] The position and / or activity of the pellet P1 is determined by comparison with the purified radiation curve CR ep and the pre-calculated radiation curve CR re f_i.

[0167]

[0164] Regarding position determination, it is possible to estimate the position of the pellet P1 by maximizing a common area between the cleaned radiation curve CR ep and the emitted radiation curve CR re f_i.

[0168]

[0165] On the other hand, it is possible to calculate an estimated value of the quantity of radiation emitted by the pellet P1 in the following manner:

[0169]

[0166] The ratio between the area under the curve CR is calculated ep and the area under the curve CR re f_i: The estimated value of the amount of radiation for the P1 pellet is then equal to the product of this ratio by the activity of the reference pellet.

[0170]

[0167] Preferably, the estimated value of the activity of P1 is calculated by comparing the CR radiation curve ep and the CR curve ref_i, but taking into account only a limited axial interval E on the z-axis, including the axial extent of the pad P1.

[0171]

[0168] This interval E can be determined in different ways, including: It can be determined as a function of the axial extent (or position) of the source (the pellet) whose radiation we seek to estimate, the pellet P1.

[0172] It can be a function of the position of adjacent pellets (gamma radiation sources).

[0173]

[0169] For example, as illustrated by Fig.7, a distance d separates any pair of adjacent pellets.

[0174]

[0170] In this case, the interval E can preferably be used as the interval which extends not only over the axial extent of the pellet considered itself, but also extends forwards and backwards, with respect to the direction of movement, by half the distance d between a pellet and the neighboring pellet.

[0175]

[0171] Using a limited interval to calculate the radiation actually emitted by the pellet increases the accuracy of determining this radiation.

[0176]

[0172] As indicated, during a series of steps h1, a value (of position and / or activity) is determined for each of the pellets.

[0177]

[0173] We can decide to do only one series of steps h1, or several.

[0178]

[0174] If several series of steps h1 are carried out, in this case preferably at each series of steps h1, for each step h1 relating to a pellet Pk (during substep h11), precalculated radiation curves are used for the pellets Pi with i different from k, based on the position and / or activity values ​​determined during the previous series of steps h1 for the pellets Pi.

[0179]

[0175] At the end of each series of steps h1, a test can be performed to determine whether or not to carry out a new series of steps h1. For example, iterations can be stopped as soon as stationary values ​​of position and / or activity are obtained for the different pellets.

[0180]

[0176] Furthermore, in certain embodiments, during a series of steps h1, during substep h11 of a step h1, for at least part of the sources to be occulted, pre-calculated radiation curves that were calculated during previous steps h1 of the same series of steps can be subtracted (rather than using pre-calculated radiation curves that were calculated for reference sources, or that were calculated during a previous series of steps h1).

Claims

Demands 1. A method for determining a position (zk) and / or a radioactive activity of at least one gamma-ray emitting source (Pk), said at least one source being part of an object under study (C) having an object axis (z), the method comprising the following steps: b) interaction data are acquired; this interaction data being acquired or having been acquired using a Compton camera during a movement of the object; the object, during this movement, moving along a rectilinear trajectory defining a trajectory axis crossing or running alongside a detection chamber of the Compton camera, respecting a trajectory path kinematics, such that during the movement the object axis follows the trajectory axis; each interaction data, called electron recoil, being a data relating to an interaction in the detection chamber between a gamma ray emitted by the object and an active medium contained in this chamber;each electron recoil (REi) comprising an instant (ti) and a three-dimensional position (Pi) of the interaction, and an energy (Ei) exchanged during the interaction; c) the electron recoil (REi) are grouped into groups (Gj), each group (Gj) being considered as representing a set of interactions generated by the same gamma ray at an emission instant (tj); e) for each group, for each possible sequence (Sjk) of electron recoil of the group:; - we construct a Compton cone (CCjk); and - zero, one, or two possible intersections (Pjkl) are determined between the Compton cone (CCjk) constructed for the sequence and the object axis (z), each intersection being defined for an axial position (z) on the object axis; f) for each group, for each possible sequence (Sjk) of electron recoils, and for each intersection determined for this sequence, a weighted fraction (Rjkl) of gamma ray emitted at the intersection is estimated, this weighted fraction being representative of a probability that the gamma ray associated with the group was generated at the intersection considered and generated the considered electron recoil sequence (Sjk); g) a radiation curve (RC) of the object is established, comprising, on the abscissa, the axial positions (z) along the object axis of the object; and on the ordinate, an activity density, calculated from the weighted fractions of gamma ray estimated for the object;h) the following step h1 is carried out at least once: h1) the position and / or activity of said at least one source is determined from the radiation curve of the object.

2. A method for determining the quantity of liquid according to claim 1, wherein at least one source has a density greater than 5 g / cm³ 3 , or even greater than 8 g / cm² 3 , or even greater than 10 g / cm² 3 .

3. Method of determination according to claim 1 or 2, further comprising a step d preceding step e, during which the groups (Gj) are filtered so as to retain only those whose total energy is greater than a predetermined value.

4. Method of determination according to any one of claims 1 to 3, wherein at a step h1, the position and / or activity of a source is determined using information contained only in an axial range (Ek) of the curve of the radiation studied defined with respect to an axial extent of the source, and optionally with respect to the axial extent (Ek-1, Ek+1) of the source or sources adjacent to the source considered.

5. A method for determining according to any one of claims 1 to 4, wherein for at least one source studied, an axial activity density of a first gamma ray source during a displacement of the latter along the trajectory axis respecting the kinematics of the trajectory path is modeled in the form of a pre-calculated radiation curve of the first source, associated with the source studied; said first source being either the source studied, or a reference gamma ray source placed at the same axial position as the source studied; the pre-calculated radiation curve comprising, on the abscissa, axial positions along the object axis of the source considered, and on the ordinate, the activity density of said at least one first source;and at a considered step h1, the position and / or activity of said at least one source studied within the object is determined as a function of the pre-calculated radiation curve(s) associated with said at least one source studied.

6. Method of determination according to claim 5, wherein: in the considered step h1, the position and / or activity of said at least one source under study is determined by minimizing a difference between a radiation curve (CR) representative of an activity density of said at least one source under study and the pre-calculated radiation curve(s) associated with said at least one source under study.

7. A method for determining the value according to claim 5 or 6, wherein: The object comprises a plurality of sources rigidly fixed to one another; at least one of said sources is a gamma ray source referred to as the occulting source; and the considered step h1 comprises the following steps: h11) a cleaned radiation curve is calculated by subtracting from the object's radiation curve one or more pre-calculated radiation curves associated with said at least one radiation source to be occulted; h12) the position and / or activity of at least one source other than the source(s) to be occulted is determined from said cleaned radiation curve (CR ep ).

8. A method of determination according to claim 7, wherein step h comprises carrying out at least one preliminary step h1 followed by a subsequent step h1; and during step h11 of the subsequent step h1, the pre-calculated radiation curve(s) associated with said at least one radiation source to be occulted used to calculate the purified radiation curve (CRep) is or are calculated taking into account the position and / or activity of said at least one source to be occulted as calculated in step h12 of the preliminary step h1.

9. Method of determination according to any one of claims 5 to 8, wherein in the considered step h1, the position and / or activity of a source under study within the object (C) is determined as a function of at least a precalculated reference radiation curve attributed to a reference source disposed at a predetermined axial position on the object under study, in particular a known or estimated axial position of the source under study.

10. Method of determination according to claim 9, wherein in the considered step h1, where appropriate in step h12, the position and / or activity of the source under study is determined as a function of a ratio between a value, for example an area under a predetermined curve interval, calculated from a radiation curve representative of an activity density of the source under study, and a corresponding value calculated from said pre-calculated reference radiation curve.

11. A method for determining according to any one of claims 5 to 10, wherein at the considered step h1, - the pre-calculated radiation curve(s) associated with said at least one source studied is or are one or more parametric curve(s); - a value is determined for the parameter(s) of the pre-calculated parametric radiation curve(s) that minimizes a difference between a curve of radiation from the object or a simplified curve relating to at least one studied source and the parametric radiation curve associated with the studied source, or the sum of the parametric radiation curves associated with the studied sources; and - we determine the position and / or activity of said at least one source studied from the value(s) of parameter(s) thus determined.

12. A method for determining the radioactive element content of an object under study whose radioactive element composition is known, the method comprising: A. the determination of the activity of a gamma-ray emitting source forming part of an object, by implementing the determination method according to any one of claims 1 to 11; and B. the determination of the radioactive element content of said at least one gamma ray source from the activity of said source determined during step A.

13. Computer program comprising instructions which cause at least steps g and h of the method according to any one of claims 1 to 11 to be executed when said program is executed by a computer (200).

14. Non-volatile recording medium (204) readable by at least one processor and on which a computer program according to claim 13 is recorded.

15. Determination device (200) comprising at least one processor (202) and at least one recording medium (204) according to claim 14.

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