METHOD FOR IMPROVING THE POSITION RESOLUTION OF A POSITRON SOURCE DURING POSITRON EMISSION TOMOGRAPHY

Abstract

The investigated object containing a source of positrons is placed into a system of n position and energy-sensitive gamma radiation detectors (D.sub.i), each having detection elements (D.sub.ijk), where one of a pair of annihilation photons interacts in the detection element (D.sub.1jk) and the other interacts in another detection element (D.sub.2jk). The detectors store the coordinates of simultaneously affected detector elements, the time of interactions and the energies E.sub.1 and E.sub.2 of the annihilation photons. The recorded events in the detection elements (D.sub.1jk) and (D.sub.2jk) leads to recognition of individual pairs of annihilation photons. An analysis is performed of the registration of the photons by the detection elements (D.sub.1jk) and (D.sub.2jk) with energies in the interval from 507 keV to 513 keV to obtain an approximate spatial depiction of positions of positron annihilation and, registration of the photons from the positron annihilation with significantly Doppler shifted energies outside of that interval.

Claims

1. The method of improvement of the positron source position determination in an object investigated by the positron emission tomography utilizing Doppler effect comprises the following steps: the investigated object containing a source of positrons, which annihilate through the production of pairs of annihilation photons, is placed into a system of n position and energy-sensitive detectors (D.sub.i) of gamma radiation each comprised of a system of detection elements (D.sub.ijk), whose placement is described by a three-dimensional coordinate system, where one of the pairs of annihilation photons interacts in the first of the affected detection elements (D.sub.1jk) and the second one of this pair of annihilation photons interacts in the second of the affected detection elements (D.sub.2jk), which then record the data about such events consisting of the coordinates of positions of the interactions in the three-dimensional coordinate system describing the positions of the detection elements (D.sub.ijk) in relation to the investigated object, the time of interactions of the annihilation photons with the affected detection elements (D.sub.1jk) and (D.sub.2jk), and energies E.sub.1 and E.sub.2, which the individual photons from the pair left in the affected elements (D.sub.1jk) and (D.sub.2jk), and then the mutual assignment of the events recorded in the detection elements (D.sub.1jk) and (D.sub.2jk) to the individual pairs of annihilation photons is performed according to their time of interactions and the events are transmitted through the interface, used to control the detectors (D.sub.i) and detection elements (D.sub.ijk) and for reading the signal from them, to a control and evaluation computer, in which they are analyzed for the purpose of the reconstruction of a three-dimensional depiction of the spatial placement of the positron emitters in the source of the positrons in the investigated object, while the analysis concerns both, the coincidental events of registrations of the annihilation photons with energies in the interval from 507 keV to 513 keV to obtain the spatial depiction of the positions of positron annihilations, and the coincidental events of registrations of the annihilation photons with significantly Doppler shifted energies outside of that interval, which simultaneously fulfill the condition that the sum of the measured energies of these photons is, within the energy resolution of the affected detection elements (D.sub.1jk) and (D.sub.2jk), equal 1022 keV in CMS, which, according to the kinematics of positron annihilation, proves, that the positrons annihilated in flight closer to the position of the positron source, and thus allow to refine the positron source position determination in the investigated object initially obtained from the aforementioned spatial depiction of the positions of positron annihilations taking into account the annihilation photons with energies from 507 keV to 513 keV.

2. The method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 1 wherein the reconstruction of positions of the source of positrons in the object is performed using the kinematics of positron in flight annihilation with electrons on the basis of the measured energies of the individual pairs of concurrently occurring annihilation photons and of the coordinates of the positions of their registration in the affected detection elements (D.sub.ijk) and (D.sub.2jk) in the three-dimensional coordinate system according to the relativistic relations resulting from the energy and momentum conservation laws,
cos θ=mc.sup.2[(E.sub.1+E.sub.2)/E.sub.1 E.sub.2]−1, where E.sub.1E.sub.2=(¼)[(E.sub.1+E.sub.2).sup.2−(E.sub.1−E.sub.2).sup.2],
cos ϕ=(E.sub.1−E.sub.2 cos θ)/[(E.sub.1+E.sub.2)(E.sub.1+E.sub.2−2mc.sup.2)].sup.1/2,
T.sub.+=E.sub.1+E.sub.2−2mc.sup.2, where E.sub.1 and E.sub.2 are the measured energies of photons resulting from annihilation of the positron with kinetic energy T.sub.+ with an electron that was at rest or in thermal motion, that are influenced by the Doppler shift, where E.sub.1 pertains to the photon with the Doppler shift towards higher energy, E.sub.2 towards lower energy, the mc.sup.2 gives the rest energy of the positron or electron, p.sub.+ represents the momentum vector of the annihilating positron, p.sub.1 and p.sub.2 represent the momentum vectors of each annihilation photon from the pair, θ indicates the angle expressing the non-collinearity of those photons, ϕ the angle between the directions of vectors p.sub.1 and p.sub.+, while the position of positron annihilation in such an event is determined from the coordinates of the affected detection elements (D.sub.ijk) and (D.sub.2jk), which in coincidence measure E.sub.1 and E.sub.2 of the relevant annihilation photons, and the calculated values of T.sub.+ and the angles θ and ϕ.

3. The method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 1 wherein the positrons originating in the investigated object have energies greater than 10 keV.

4. The method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 1 wherein the source of positrons contains preferably beta plus radionuclides with high energies of beta plus decay selected from the group of .sup.22Na, .sup.18F, .sup.94Tc, .sup.11C, .sup.13N, .sup.44Sc, .sup.15O, .sup.14O, .sup.68Ga, .sup.124I, .sup.10C, .sup.152Tb, .sup.86Y, .sup.76Br, .sup.82Sr/.sup.82Rb.

5. The method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 1 wherein the coincidental events of the registration of pairs of annihilation photons with significantly Doppler shifted energies have, for refining the depiction of the spatial distribution of positron sources in the investigated object, an increasingly greater weight once the Doppler shifts of the photon energies are increasingly greater.

6. The equipment for performing the method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 1 wherein it is consisting of a system of n position and energy-sensitive detectors (D.sub.i) of gamma rays comprised of a system of detection elements (D.sub.ijk), whose placement is described by a three-dimensional coordinate system, whereby the detection elements (D.sub.ijk) are connected through an interface to computer used for controlling the detectors (D.sub.i) and detection elements (D.sub.ijk) and reading, analysis and evaluation of the signals from them with the purpose to reconstruct a three-dimensional depiction of the spatial distribution of the positron source in the investigated object.

7. The equipment for performing the method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 6 is wherein the energy-sensitive detectors (D.sub.i) of gamma rays are hybrid pixel detectors with a pixel semiconductor sensor, while the system of pixels on them corresponds to the system of detection elements (D.sub.ijk).

8. The equipment for performing the method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 6 is wherein the pixel semiconductor sensors of the hybrid pixel detectors are made from semiconductor materials with a high effective atomic number Z.sub.eff.

9. The equipment for performing the method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 8 is wherein the semiconductor materials with a high effective atomic number of Z.sub.eff are chosen from the group comprised of CdTe and CdZnTe.

10. The equipment for performing the method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 7 is wherein the system of pixels on the hybrid pixel detectors, which corresponds to the system of detection elements (D.sub.ijk), consists of pixels with 55 micrometers of size or smaller.

11. The equipment for performing the method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 6 is wherein the interface for controlling the detectors (D.sub.i) and detection elements (D.sub.ijk) and for reading of the signal from them is chosen from the group of USB, Ethernet and PCI interfaces.

Description

DESCRIPTION OF THE FIGURES ON THE DIAGRAMS

[0007] FIG. 1 depicts the schematic arrangement of the system of position and energy-sensitive detectors of gamma rays.

[0008] FIG. 2 depicts a detailed view of a detection element, which is part of the position and energy-sensitive detectors of gamma rays, which is connected through an interface to the control and evaluation computer.

[0009] FIG. 3 represents the vector scheme depicting the kinematics of the annihilation of positrons in flight within the coordinate system corresponding to the convention according to the invention with affected detection elements indicated.

EXAMPLES OF IMPLEMENTING THE INVENTION

Example 1

[0010] First the studied object 1 containing a source 2 of positrons, which annihilate primarily through the production of a pair of annihilation photons, was placed into a system 3 of n position and energy-sensitive detectors D.sub.i of gamma radiation comprised of a system of detection elements D.sub.ijk, whose mutual placement is described by a three-dimensional coordinate system. Subsequently, one of the pairs of annihilation photons interacted in the first of the affected detection elements D.sub.1jk and the second one of this pair of annihilation photons interacted in the second of the affected detection elements D.sub.2jk, which then recorded the data about such events, which are the coordinates of the positions of the interactions in the three-dimensional coordinate system of the description of the positions of the detection elements D.sub.ijk in relation to the studied object 1, the time of the annihilation photons' interaction with the detection elements D.sub.ijk and energies E.sub.1 and E.sub.2, which the individual photons from the pair left in the affected elements D.sub.ijk and D.sub.2jk. Then, the mutual allocation of the recorded events in the detection elements D.sub.1jk and D.sub.2jk to the individual pairs of annihilation photons was performed using the coincidence method. All the aforementioned events were subsequently, through an interface 4 used to control the detectors D.sub.i and detection elements D.sub.ijk and for reading the signal from them, transmitted to a control and evaluation computer 5, in which they were analysed for the purpose of the reconstruction of a three-dimensional depiction of the spatial placement of the positron emitters in the source 2 of the positrons in the studied object 1. The analysis concerned both, the coincidental events of the registrations of the annihilation photons with energies in the interval from 507 keV to 513 keV to obtain spatial depiction of the positions of positron annihilations and the coincidental events of the registrations of the annihilation photons with significantly Doppler shifted energies outside of that interval, which simultaneously fulfill the condition that the sum of the measured energies of these photons is, within the energy resolution of the affected detection elements D.sub.ijk, equal 1022 keV in CMS. This corresponds to the positron annihilation in flight in the closer vicinity of the position of its creation, which permits to refine determination of positron sources in the studied object initially obtained from the aforementioned approximated spatial depiction of the sources based only on photons with energies from 507 keV to 513 keV.

Example 2

[0011] The studied object 1 containing a source 2 of positrons was examined similarly as in Example 1, only differing in the method for reconstructing the position of the sources 2 of positrons in the studied object 1 using the kinematics of positron annihilation with electrons in flight on the basis of the measured energies of the individual pairs of concurrently occurring annihilation photons and the coordinates of the positions of their registration in the affected detection elements D.sub.1jk and D.sub.2jk in the three-dimensional coordinate system according to the relativistic relations ensuing from the laws of the conservation of energy and momentum,

cos θ=mc.sup.2[(E.sub.1+E.sub.2)/E.sub.1E.sub.2]−1, where E.sub.1E.sub.2=(¼)[(E.sub.1+E.sub.2).sup.2−(E.sub.1−E.sub.2).sup.2],

cos ϕ=(E.sub.1−E.sub.2 cos θ)/[(E.sub.1+E.sub.2)(E.sub.1+E.sub.2−2mc.sup.2)].sup.1/2,

T.sub.+=E.sub.1+E.sub.2−2mc.sup.2,

where E.sub.1 and E.sub.2 are the measured energies of the pair of annihilation photons that are influenced by the Doppler shift as a result of the annihilation of the positron with the kinetic energy T.sub.+ with an electron that was at rest or in thermal motion. E.sub.1 pertains to the photon with the Doppler shift towards higher energy, E.sub.2 towards lower energy. The symbol m gives the rest mass of the positron or electron, c is the speed of light, p.sub.+ represents the momentum vector of the positron at the moment of annihilation, p.sub.1 and p.sub.2 represent the momentum vectors of each annihilation photon from the pair, θ indicates the angle expressing the non-collinearity of these photons, ϕ is the angle between the directions of the vectors p.sub.1 and p.sub.+, while the positions of positron annihilations in such events are determined from the coordinates of the affected detection elements D.sub.1jk and D.sub.2jk, which in coincidence measure E.sub.1 and E.sub.2 of the relevant annihilation photons, and from the calculated values of T.sub.+ and the angles θ and ϕ. For the reconstruction it is most advantageous if the coincidental events of the registration of the pairs of annihilation photons with significantly Doppler shifted energies obtain for refining the depiction of the distribution of positron sources in the investigated object greater weight once the Doppler shifts of the energies are greater. It was experimentally verified that the proposed approach is suitable if the positrons originating in the studied object have energies greater than 10 keV. It is especially significant in the event that the sources of the positrons are beta plus radionuclides with high energies of beta plus decay selected from the following group .sup.22Na, .sup.18F, .sup.94Tc, .sup.11C, .sup.13N, .sup.44Sc, .sup.15O, .sup.14O, .sup.68Ga, .sup.124I, .sup.10C, .sup.152Tb, .sup.86Y, .sup.76Br, .sup.82Sr/.sup.82Rb, which leads to such a significant blurring of PET because of the large range of the positrons in the studied object 1 that the method of improving of the positron source depiction according to the invention is desirable and effective.

Example 3

[0012] The exemplary equipment for determination of the position of the positron sources in an investigated object by means of advanced positron emission tomography according to the invention is comprised of a system 3 of n position and energy-sensitive detectors D.sub.i of gamma radiation consisting of a system of detection elements D.sub.ijk. Their mutual placement is described by a three-dimensional coordinate system. The detectors D.sub.i and detection elements D.sub.ijk are connected through an interface 4 for their control and for reading the signal from them with a control and evaluation computer 5, which is also used for the analysis of the signal from the detectors for the purpose of reconstruction of a three-dimensional depiction of the spatial placement of positron emitters in the source 2 of the positrons in the studied object 1. In practice, for the implementation of the invention, the hybrid pixel detectors with a CdTe or CdZnTe pixel semiconductor sensors have proven most effective as the detectors D.sub.i, where the system of pixels with dimensions of 55 micrometers created on them corresponds to the system of detection elements D.sub.ijk pursuant to the invention. It has been verified that a suitable interface 4 for the control of these pixel detectors a and detection elements D.sub.ijk and for reading the signal from them is USB, Ethernet or PCI.

INDUSTRIAL APPLICABILITY

[0013] The method according to the invention is usable in several biomedical PET applications, currently especially in particular for the imaging of vitally important organs in human medicine and during the research of small animals. Other perspective applications are in non-destructive material research.