Design and simulation of a semiconductor detector-based Compton imaging system with efficiency analysis

doi:10.21203/rs.3.rs-1964046/v3

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Design and simulation of a semiconductor detector-based Compton imaging system with efficiency analysis

https://doi.org/10.21203/rs.3.rs-1964046/v3

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In recent years, Compton cameras that use electronic collimators have become common. One or more scatterer detectors and an absorber detector make up the Compton camera, which is sensitive to the energy and location of scattered gamma rays. It predicts the distribution of gamma-ray sources by reflecting all valid events in the image space using conical surfaces. Compton cameras are designed for specific applications and image reconstruction using various methods.

Based on studies on the efficiency of the Compton camera, the current work provides a novel detector design that includes scatterer and absorber detectors. This design includes eight scatterer detectors spaced 1 mm apart and an absorber detector 30 mm from the last scatterer detector. The distance between the source and the first scatterer detector was 5 mm. The scatterer and absorber detector plates were 70x70x2.125mm³ and 70x70x10mm³, respectively. The Compton imaging system is simulated using the GEANT4 toolkit.

In addition, this study uses an analytical method to reconstruct Compton camera images. The method used for analytical reconstruction in the Compton imaging system differs slightly from simple restoration methods used in other imaging systems. In the analytical method, the equation related to the data reflected by the image must be solved to reconstruct the image directly. This method, the C + + code was developed to reconstruct Compton camera images.

According to the results, using the analytical method to identify the best circumstances and the parameters impacting efficiency, the value of FWHM achieved was 3.7 mm with an angular uncertainty of about 2.7 at an energy of 0.662 MeV. Furthermore, the FWHM value decreased by 0.7 mm, compared to another (experimental) design that employed the analytical image reconstruction approach.

Compton camera

Semiconductor detectors

Efficiency

Analytical reconstruction method

GEANT4

Nuclear imaging systems are widely used for detection, diagnosis, therapy, and other applications. The two main procedures in nuclear imaging can be distinguished based on the type of radioactive source used. Single-photon emission computed tomography (SPECT) and Compton imaging systems are two well-known examples of single-photon imaging of radioactive nuclei that decay by emitting gamma rays [1, 2]. Positron emission tomography (PET) uses positron-emitting radioisotopes as radioactive materials [3].

In recent years, in imaging systems, the use of electronic collimators instead of mechanical collimators has received less attention owing to limitations. In SPECT, the direction of gamma rays is determined using a mechanical collimator. Using positron-emitting nuclides, PET can detect the coincidence of two 511 keV gamma rays that are emitted in opposite directions when a positron annihilates with an electron [4]. A Compton camera is an imaging system based on an electronic collimator [5]. A mechanical collimator is unnecessary for the Compton imaging system to perform multinuclear imaging. Several studies have described in vivo multi-tracer imaging [6–8].

Compton cameras were the first used by Everett et al.. for nuclear medicine imaging [9]. Also, the Compton and PET cameras were used for imaging [10, 11]. Comparing the Compton camera with PET and SPECT in terms of economic effectiveness and appropriate performance in medical applications proved that the Compton camera has high capability in these situations in most studies [12–14]. Several research groups have also investigated the application of Compton cameras in ion-beam therapy using scintillation and semiconductor detectors [15–17].

Compton cameras are used in astrophysical applications. The Compton imaging method was first used to detect gamma rays with scintillation detectors in the mid-twentieth century [18]. It was developed in 1961 and 1964 as the Compton telescope and Compton spectrometer [19, 20]. COMPTEL became the first Compton telescope to orbit Earth [21–25]. Due to their detection application, Compton cameras are being developed in astrophysics [26].

The different structures of the Compton camera have been extensively studied to improve its performance. In 1983, Singh and colleagues at the University of Southern California used the first Compton camera with pixelated arrays of Ge for the scatterer detector and NaI(TL) for the absorber detector [27]. Dogan and his colleagues developed a new design for Compton cameras. A series of thin, independent, two-dimensional, position-sensitive layers were applied to the Compton camera. The thin layers minimized multiple interactions [28]. In recent years, many Compton camera designs have been introduced according to their type of application, and various methods have been used to reconstruct images [29–31].

A scatterer and an absorber detector, sensitive to the energy and location of the scattered gamma rays, comprise the Compton camera. The fundamentals of the Compton imaging system are described as follows. As shown in Fig. 1, after being scattered by the scatterer detector (Compton scattering), the photons from the source are absorbed in the absorber detector.

Because the scatterer and absorber detectors operate in the same coincident timing mode, photons are electrically and limitlessly detected along their entry path in a Compton camera. A scatterer detector was used to detect the Compton scattering. The prompt gamma energy range was designed to increase Compton scattering probability while reducing the so-called Doppler broadening effect caused by electron binding and motion [32]. Finally, the Compton-scattered photons are collected in the absorber detector via the photoelectric effect. The opening angle of the cone is the Compton scattering angle, the line connecting the two scattering locations is the cone axis, and the interaction position in the first scatterer is the cone apex. The junction of numerous cones indicates the source. The radiation source distribution was obtained using the correct events through the conical surfaces [27]. Eq. (1) can be used to describe the Compton scattering angle $\theta$ [33]:

$$\theta ={\cos ^{ - 1}}\left[ {1 - {m_e}{c^2}(\frac{1}{{{E_1}}} - \frac{1}{{{E_0}}})} \right]$$

where, ${E_0}$ is the incoming gamma-ray energy, ${E_1}$ is the dispersed gamma-ray energy immediately after contact, and ${m_e}{c^2}$ is the electron's rest mass energy.

Image reconstruction in a Compton camera is a challenging task. The Compton camera has not proven a viable alternative to the SPECT device in modern clinics due to the difficulty of image reconstruction and the computing needs for executing image reconstruction procedures. Although both Compton and gamma cameras are utilized in SPECT technology, the data produced by each method differ significantly. As a result, the analytical image reconstruction methods established for gamma-based SPECT systems cannot be directly used. Analytical image reconstruction is one of the Compton camera image reconstruction techniques. The analytical method's goal is to discover an analytical solution or to utilize operators that enable an analytical solution to be found.

One of the most influential parameters of the output image of a Compton camera is its efficiency [34]. The Compton camera efficiency is defined as the ratio of photons absorbed by Compton scattering in the scatter detector without any interaction in the absorber detector [35].

A new design was developed in this study based on research on Compton camera efficiency using semiconductor detectors [36]. The simulations used the GEANT4(Monte Carlo code) toolkit [37].

The purpose of simulating the Compton imaging system and using the efficiency sensitivity results in this study is to obtain the optimal mode to improve the output image and reduce the image noise obtained from the Compton camera.

The remainder of this paper is summarized as follows: The theory of analytical image reconstruction in the Compton camera is presented in Section 2, and the simulation of the Compton camera using the GEANT4 code as a technique is presented. The design of a new Compton camera based on semiconductor detectors is presented in Section 3. The new design was also simulated based on the efficiency study in this section and compared with the experimental data. Finally, Section 4 discusses the results and conclusions of this study.

2.1. Analytical image reconstruction in Compton camera

In the method used for analytical reconstruction in the Compton imaging system to directly reconstruct the image, the equation related to the data reflected by the image must be solved. The data provided by the Compton camera contain a list of simultaneous events, each involving a pair of interactions, one in the scatterer detector and the other in the absorber detector.

This method uses pixelated screens for two-dimensional imaging to determine the location of the source. The count is added to each pixel by passing the cone sections consisting of the correct events and cutting the page and cone sections. Finally, the number of cone passes per pixel is recorded. In Fig. 2, the analytical method is pixelated on a two-dimensional screen for four events, showing how to perform this method.

The cones reconstructed in Eq. (2), where ${r_a}$ and ${r_s}$ are the interaction coordinates in the absorber and scatterer detectors, $\theta$ is the scattering angle, and is the position of the photon emission coordinates:

$$\cos \theta =\frac{{({{\vec {r}}_s} - \vec {r}).({{\vec {r}}_a} - {{\vec {r}}_s})}}{{\left| {{{\vec {r}}_s} - \vec {r}} \right|.\left| {{{\vec {r}}_a} - {{\vec {r}}_s}} \right|}}$$

Eq. (2) identifies points from where the photon is emitted for each event and produces a cone of possible locations. If ${\vec {r}_s} - \vec {r}$ and ${\vec {r}_a} - {\vec {r}_s}$ decompose into components, it becomes Eq. (3):

$$\left\{ \begin{gathered} ({{\vec {r}}_a} - {{\vec {r}}_s})=({x_a} - {x_s})\hat {i}+({y_a} - {y_s})\hat {j}+({z_a} - {z_s})\hat {k} \hfill \\ ({{\vec {r}}_s} - \vec {r})=({x_s} - x)\hat {i}+({y_s} - y)\hat {j}+({z_s} - z)\hat {k} \hfill \\ \end{gathered} \right\}$$

Eq. (4) derived by inserting Eq. (3) into Eq. (2):

$${[{n_x}(x - {x_s})+{n_y}(y - {y_s})+{n_z}(z - {z_s})]^2}={\cos ^2}\theta .[{(x - {x_s})^2}+{(y - {y_s})^2}+{(z - {z_s})^2}]$$

The values of ${n_x}$, ${n_y}$, and ${n_z}$ are as Eq. (5):

$$\left\{ \begin{gathered} {n_x}=\frac{{{x_a} - {x_s}}}{{\sqrt {[{{({x_a} - {x_s})}^2}+{{({y_a} - {y_s})}^2}+{{(z{}_{a} - {z_s})}^2}]} }} \hfill \\ {n_y}=\frac{{{y_a} - {y_s}}}{{\sqrt {[{{({x_a} - {x_s})}^2}+{{({y_a} - {y_s})}^2}+{{(z{}_{a} - {z_s})}^2}]} }} \hfill \\ {n_z}=\frac{{{z_a} - {z_s}}}{{\sqrt {[{{({x_a} - {x_s})}^2}+{{({y_a} - {y_s})}^2}+{{(z{}_{a} - {z_s})}^2}]} }} \hfill \\ \end{gathered} \right\}$$

By placing the position of the image plane, which is considered perpendicular to the z-axis, Eq. (4) of the conic section resulting from the intersection of the image plane in Eq. (6) can be derived as follows:

$${[{n_x}(x - {x_s})+{n_y}(y - {y_s})+{n_z}({z_p} - {z_s})]^2}={\cos ^2}\theta .[{(x - {x_s})^2}+{(y - {y_s})^2}+{({z_p} - {z_s})^2}]$$

Calculating the return of cones on the still image screen reduces the three-dimensional problem to a two-dimensional state. Finally, conic sections can be drawn on an image screen (${z_p}$).

2.2. Compton camera simulation using GEANT4 toolkit and analytical image reconstruction

The Compton camera simulation program had seven output values for each desired event. The simulation was performed using GEANT4(Monte Carlo code). The values include the interaction location in the scatterer and absorber detectors and the energy lost in the scatterer detector. Unlike the gamma camera, each event alone does not provide complete and comprehensive information about the place it is emitted. Consequently, many events must be examined (decoding the outputs) to construct an image of the source location.

GEANT4 was used to simulate a simple Compton camera pattern, as illustrated in Fig. 3. This model has also been applied to the analysis of the Compton camera efficiency [36]. The absorber and scatterer detectors were first pixelated for the simulation. In the geometry section in GEANT4, the absorber and scatterer detectors are pixelated using “G4PVReplica”. Each event in any area of the pixel shifts to the center. There is a pixel position in the “comptonresult.txt” output file where the correct event occurred. The "Comptonresult.txt" file is read using the C + + code developed for analytical reconstruction. For the image screen size, “xmin”, “xmax”, “ymin”, and “ymax” are determined, using which and the number of pixels intended for the image screen, the interval of each pixel, “xstep” and “ystep” are obtained. The values in Eq. (6), according to the read input file (constant z). There are two unknowns, x, and y, in Eq. (6). To solve, “x = xmin” and the value of “y” are calculated given that the equation is quadratic. Finally, the overlap of the produced curve and the required plane was checked for each pixel. This process is repeated for all events, and the pixel findings are stored in the "array1.txt" file as two-dimensional arrays for image reconstruction.

The Gnuplot data analysis software uses image reconstruction for 10, 100, and 1000 events, as shown in Fig. (4) to (6). Therefore, the position of the source can be obtained by overlapping the conical sections and planes with more events. As shown in Fig. (4) to (6), the more events that are used to reconstruct the images, the better the position and intensity of the source are determined.

A model (Fig. 3) based on the efficiency sensitivity results of the Compton imaging system is designed to improve the output image [36]. This model was developed without considering the results of the analyses while changing the detector material and the radioactive source. Other factors were also considered based on the results of the analyses.

According to the efficiency sensitivity analysis of the Compton camera, a newly proposed design of the Compton camera was also obtained by considering the results from Table 1. Scatterer detector arrays with dimensions of $1 \times 1 \times 2.125m{m^3}$ and absorber detector arrays with dimensions of $1 \times 1 \times 2.5m{m^3}$, and image screen arrays with dimensions of $1 \times 1m{m^2}$ are required to define the image. As shown in Fig. 7, the distance between the first scatterer detector and the radioactive source selected is 5 mm. 8 scatterer layers with a thickness of 2.125 mm, and a distance from one to another of 1 mm. The simulation was performed using GEANT4(Monte Carlo code).

Figure 8 shows the 2D image reconstruction of the location of the source at the intersection of the image screen and cones from the correct events in the Compton imaging system in a gray background. Figure 8 is drawn using the Gnuplot tool. The image screen was then placed where the source was not to check the source's location. For distances of 10, 15, 20, 25, and 50 mm from the screen of the first scatterer detector, the image was reconstructed using the Gnuplot tool, as shown in Fig. 9. According to the results, the further the image is from the source, the less intense the events used for reconstruction, and the more unclear the source location. There is uncertainty in the z-axis at a distance of 10 mm from the first scatterer detector.

Next, the FWHM, the spatial resolution of the Compton camera, was obtained to reconstruct the image along the y-axis (Fig. 10). The angular uncertainty is 2.7, and the spatial uncertainty is 3.7 mm for energy of 0.662 MeV. The calculations were performed without accounting for electronic noise.

The new experimental research design was examined as part of the study’s continuance. The image of the gamma-ray source was acquired using the Compton imaging system design in an experimental study [38] (Fig. 11).

The new design of the proposed Compton imaging system is shown in Fig. 12 for this experimental research. In this experimental study, the source was positioned in a hollow sphere with a thickness of less than 1 mm. The radioisotope in the experiment emits two gamma rays with energies of 0.024 and 0.392 MeV. Gamma with an energy of 0.392 MeV was almost certainly emitted. Considering the high energy level, false electrical signals were eliminated when the signal was received. This threshold level allows for the interaction of gamma rays with conical half-angles greater than 20 degrees. The image was reconstructed using gamma-ray interactions with an energy of 0.392 MeV. These two sources are located at different distances and positions from the detector. Although these two sources did not accurately identify their positions according to the detector, the longitudinal distance between the sources, which is the x-axis, was measured at 10 mm. It was used to construct the universe, and detectors using “G4BOX” has four arguments that the coordinate origin is at the cube center. The “G4Sphere” uses to construct the chamber. This class specifies an inner radius of 1.8 mm, an outer radius of 2 mm, and a diameter of 4 mm for the source. The volume of the universe was cubic and contained air. Polyethylene was used as the polymer in the chamber. The elements and materials used in the geometries use the “G4ELement” and “G4Material” classes, which specify the type of atoms, atomic number, mass number, molar weight, and percentage of the constituent elements. The “G4GeneralParticleSource” was used to create a radioactive source. The radioactive source used was of the volumetric type, with a radius of 1.8 mm, and was located inside the chamber.

Table 1. The parameter under investigation is efficiency sensitivity analysis in the Compton camera[36]

The single-energy source, 0.392MeV, which is the angular distribution of the produced isotropic rays, is emitted uniformly at all angles. The standard model, which includes electromagnetic processes, generates a physical list for the simulation. Events with a scattering angle of more than 20 ° were extracted by writing the code in C++. The screen to reconstruct the image is pixelated in the center of the source and is two-dimensional. The algorithm used to reconstruct an image was an analytical method.

The center of the source used was correctly determined, as shown in Fig. 13. In the experimental results, two sources, each with a diameter of 4 mm, appeared to have a diameter of 7 mm. In comparison, two sources with a diameter of 4 mm were separated by 10 mm and were identifiable in the simulation results (Fig. 14).

The amplitude of the image obtained from the experimental research and the simulation, owing to more significant errors in the cone reconstruction, is one of the parameters observable in the experimental research. The differences between the experimental image and the simulation test results are the errors in the energy recorded in the detector, the resolution for the event synchronization used, the systems used to record the data, and the effects of the underlying signal on the output image.

The goal of simulating the Compton imaging system and analyzing the efficiency sensitivity results in this study was to find the best model for improving the output image and reducing the image noise from the Compton camera. Based on the analysis and efficiency analysis results, it can be said that the new design of the Compton camera reduced its FWHM.

According to the results, applying the optimal conditions and the parameters affecting the efficiency using the analytical method, the value of FWHM obtained was 3.7 mm with an angular uncertainty of approximately 2.7 at an energy of 0.662 MeV.

The FWHM value decreased by 0.7 mm. The amplitude of the image obtained from the experimental research and the simulation, owing to more significant errors in the cone reconstruction, is one of the parameters observable in the experimental research. The interactions in the simulation are highly accurate for a detection system with no uncertainty in energy, position, interactions, or time.

The differences between the experimental image and the simulation test results are the errors in the energy recorded in the detector, the resolution for the event synchronization used, the systems used to record the data, and the effects of the underlying signal on the output image.

As a result, the efficiency can help obtain a better image of the radioactive source in the Compton camera. The effect of angular uncertainty, spatial uncertainty, energy uncertainty, image reconstruction, and electronics approaches should all be considered when designing a Compton camera, in addition to efficiency.

Acknowledgments

The authors thank Sharif University of Technology's research office for supporting the present work.

Ethical Approval

Not applicable

Competing interests

The author has NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

Funding

No funding in this manuscript.

Author Statement

The contributions of Mr. Mostafa Niknami:

• Study conception and design (50%)

• Acquisition of data (60%)

• Analysis and interpretation of data (60%)

• Drafting of manuscript (60%)

The contributions of Dr. Seyed Abolfazl Hosseini:

• Study conception and design (40%)

• Acquisition of data (10%)

• Analysis and interpretation of data (10%)

• Drafting of manuscript (30%)

The contributions of Dr. Mahdy Ebrahimi Loushab:

• Study conception and design (10%)

• Acquisition of data (30%)

• Analysis and interpretation of data (30%)

• Drafting of manuscript (10%)

Availability of data and materials

Not applicable

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No competing interests reported.

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Design and simulation of a semiconductor detector-based Compton imaging system with efficiency analysis

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Abstract

Figures

1. Introduction

2. Methodology

2.1. Analytical image reconstruction in Compton camera

2.2. Compton camera simulation using GEANT4 toolkit and analytical image reconstruction

3. Results And Discussion

4. Conclusion

Declarations

References

Additional Declarations

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