This paper presents the Monte Carlo simulation of the attenuation correction for Positron Emission Tomography (PET) data using MCNP6 code. Two attenuation correction maps have been generated, one for correcting the attenuation effect in a homogeneous phantom, which is a cylindrical volume of water and the other for correcting the attenuation effect in a heterogeneous phantom, which is a cylindrical volume of water within which, there are two small cylinders of bone-equivalent materials. These maps are derived from the data acquired as a result of transmission scans using a positron-emitting rod source. The attenuation map generated using this method does not need to be scaled because it is directly built for an energy of 511 keV. For each phantom, three types of simulations are done, one to estimate the radiotracer distribution in the phantom (emission scan) and two to estimate the distribution of attenuation coefficients in this phantom (transmission scans), the first with a blank field of view (FOV) and the second when the phantom exists in the FOV. From the transmission scans data, the attenuation map for each phantom is derived and after that it has been applied to the corresponding emission scan data during PET image reconstruction process to obtain the attenuation-corrected image. The images of the radiotracer distribution in each phantom reached in this study illustrate the quantitative and qualitative improvements in the image quality after attenuation correction than that before the attenuation correction.

Positron Emission Tomography (PET) has become an important instrument in nuclear medicine diagnostics. It allows to study the metabolic and biochemical processes and organic structures in living organisms following the detection of positrons produced by a radioactive substance administered to the patient through intravenous. Each positron emits from the radiotracer used in PET can traverse a few millimeters through the patient's body until losing its kinetic energy. It annihilates with ambient electrons in the body producing a pair of gamma photons which travel in two opposite directions with an energy of 511 keV each. In order to determine the annihilation position, this pair of gamma photons must be detected simultaneously or in coincidence by two different detectors which are parts of detectors series constituting a ring around the patient. But not all annihilation photons are measured as coincidence events due to their attention in the body or their scattering out of the detector's field of view. Each two detectors lie by a line along which the events occurred. This line is called line of response (LOR). The count rates of the coincidences events detected for all lines of response (LORs) passing through the body provides the data required for reconstructing an image of positron-emitting source concentration. The resulting image can be affected by many factors such as, attenuation, scattered coincidences, random coincidences, dead time, variations in detector efficiencies between detector pairs, and radial elongation. Each of these factors contributes to the image quality degradation; therefore, these factors need to be corrected during the image reconstruction process. Several of these factors have been investigated in details by many studies in order to improve PET image quality ( Brasse et al., 2005 , D'Ambrosio et al., 2013 , Daube-Witherspoon and Carson, 1991 , Ollinger, 1995 and Wollenweber, 2002 ). The attenuation is the most important factor increases image noise, image artifacts, and image distortion. So, accurate attenuation correction is necessary to obtain high quality PET images. Attenuation correction is typically performed in two steps: Firstly the attenuation correction map is determined, and then it is applied to the PET emission data during the image reconstruction process. The attenuation maps can be generated by transmission-less and/or transmission-based methods ( Zaidi & Hasegawa, 2003 ). Transmission-less correction method depends on the calculation of the object boundaries and the attenuation coefficient distribution inside this object using mathematical methods, statistical modeling for simultaneous estimation of attenuation and emission distribution and criteria of consistency condition ( Ay and Sarkar, 2007 and Zaidi and Hasegawa, 2003 ). This method is useful for homogeneous and simple geometry object such as the brain imaging. Transmission-based method relies on estimated the attenuation correction map by transmission scan using external radionuclide sources. This method is used for heterogeneous and complex objects, for instance the chest imaging ( Beyer et al., 1994 and Wagenknecht et al., 2013 ).

In our work, we focus to correct the attenuation effect in both homogeneous and heterogeneous middles based on the Transmission-based method. So, the MCNP6 simulation code is employed to scan the FOV with and without phantoms using a positron-emitting source. From the simulation results, the attenuation correction maps for each phantom is generated and used to correct the corresponding emission data.

MCNP6 code is one of the general codes that based on the Monte Carlo technique, which is one of numerical methods that allow to solve complex problems by using pseudo-random numbers generated by computers. The MCNP6 code is used to simulate the particle transport in matter. It is developed by Los Alamos National Laboratory (LANL) (“ Los Alamos National Laboratory: MCNP Home Page ,” n.d.). Recently, it is commonly used in more peaceful applications, such as medical physics, neutronic, radio-protection and detectors physic. Our simulation via MCNP6 starts by introducing some modifications on the MCNP6 code source in order to be able to write directly the important data representing the coincidence events and exclude the unnecessary data which related to the escaped out of the FOV and the attenuated photons. The objective of these modifications is to reduce the needed memory that is required for storing the simulation output data. After that, this modified code used to run three types of simulations for each phantom, two to generate the attenuation correction map (transmission data acquire using a positron-emitting source which transmits in the FOV with and without phantom) and the third to estimate the radiotracer distribution in the phantom (emission data acquire using a positron-emitting source uniformly distributed in water-filled environment). Finally, the emission data are being corrected using the generated attenuation correction maps during the image reconstruction process.

In this study, MCNP6 code version (6.1) has been employed to simulate the generation of PET data which are used to reconstruct attenuation-corrected PET images. Our simulation model is based on specific parameters of GEMINI TF scanner (number of detectors in the ring, ring diameter, dimensions and material of each detector). The detection system consists of 644 individual Lutetium-yttrium oxyorthosilicate (LYSO) crystals arranged in one ring (28 detectors block, each block contains 23 LYSO crystals). The size of each crystal is 4 × 4 × 22 mm³ in the axial, trans-axial, and radial dimensions, respectively. The PET detector ring diameter is 90 cm with axial and trans-axial fields of view (FOVs) of 0.4 and 62 cm, respectively. The first studied phantom is a homogeneous cylindrical volume of water with 20 cm in diameter. The second studied phantom is a heterogeneous phantom, which is a cylindrical volume of water with 20 cm in diameter; inside it, there are two cylindrical containers filled with bone-equivalent materials each. These containers placed at the positions (4, 0, 0) and (−4, 0, 0) respecting the phantom coordinates. Each container has a diameter of 2 cm. The phantoms are placed in a supine position on the central axis of the detection system. These phantoms were simulated to be uniformly filled with positron-emitting source in a water-filled environment. This source emits positrons with an energy equal to the energy emitted by ¹⁸F source, which is arranged between 0 and 635 keV. The radiotracer has been assumed uniformly distributed at all points into each phantom except in the region of the bone-equivalent materials in the heterogeneous phantom; where, the radiotracer concentration assumed equal zero ( Fig. 1 ).