A review of emerging trends in experimental, simulation, and theoretical methods for dose calculation in radiation processing

One of the challenges associated with experimental approaches, often determined by user experience, is selecting the appropriate dosimeter for irradiation processing [7]. Key considerations include the dose range, thickness, and post-irradiation stability time. For applications such as food irradiation and medical device sterilization, the dosimeter thickness does not always accurately represent the surfaces being measured [30, 31]. Additionally, positioning the dosimeter within the object can be challenging, often leading to low-precision dose measurements.

Another significant issue is the post-irradiation stabilization time required to obtain reliable readings. Given the demand for rapid dose measurements in the field, alanine dosimeters are not commonly used as routine options owing to their lengthy stabilization time and high operational costs. This highlights the need for dosimeters with shorter post-irradiation stabilization times as well as improved methods for precise positioning during measurements. These highlights represent promising research and innovation.

For many years, polystyrene calorimeters have been a standard tool in the radiation processing field [21]. However, recent advancements indicate a growing interest in developing active dosimeters for use in ultra-high-dose applications in medical physics [48, 49]. This technology can be adapted for the radiation processing field, as it shares similarities with high-dose rate requirements. Such adaptation would require modifications to account for positioning challenges and dose variations. These developments present a valuable opportunity for future calorimetry research.

Recent studies on the use of MC simulations in radiation processing have primarily focused on two areas: facility modeling and food irradiation. Table 3 lists the articles that specifically addressed MC simulations for facility modeling and food irradiation.

Facility modeling plays an important role in supporting dose mapping, a key component of operational qualification activities. As shown in Table 3, these facilities are categorized as first and second gamma irradiators, which have relatively smaller geometries than the larger fourth category [14, 25, 61, 62]. Despite their smaller size, these configurations can present challenges due to the high number of radiation sources, which can include up to 48 individual sources [61]. In contrast, fourth category irradiators involve much larger geometries, such as large totes that require detailed modeling. For example, Tran Van Hung’s dose mapping study modeled 68 tote boxes, each with dimensions of 50 cm × 50 cm × 90 cm [50]. Futher classification and comparison of these facility categories can be found in the sub-section discussing the combination and simulation methods..

Particular attention must be given to the activity and measurement dates of each Co-60 radionuclide because variations in these parameters can significantly affect the dose distribution. Furthermore, not all manufacturers ensure a uniform distribution of pencil sources across all pencil slots, leading to non-uniform radiation source distribution [63]. This variability increases the complexity of achieving consistent dose distribution within the facility. To address these challenges effectively, it is crucial to thoroughly examine the facility design drawings to obtain accurate geometric details. Proper geometry is essential for creating precise models that reflect the actual configuration of the facility, ensuring reliable dose mapping and operational accuracy.

In addition to gamma irradiators, there are studies modeling machine-based sources, such as electron beam and X-ray irradiation facilities [46, 64]. However, only a few studies have focused on the detailed modeling of machine-based sources, presenting comprehensive modeling concepts in their publications [64, 65]. While other studies involving electron beams exist, they do not specifically address e-beam modeling in detail [11, 58, 66].

Accurate e-beam modeling requires careful configuration of the nominal electrical current to realistically represent the operational conditions of the facility. The e-beam and X-ray facility modeling share similar complexities with the gamma plant modeling. For instance, Eychenne obtained MC spectrum results from an X-ray facility in Aerial, France [46]. The radiation spectrum, whether from electron beams or X-rays, is a critical factor because beam quality can vary across facilities. Ideally, the spectrum produced by MC modeling should closely approximate a realistic electron or X-ray spectrum to ensure that dose calculations align with experimental results.

Another unique challenge addressed by MC approaches is estimating the dose of fruit phytosanitary irradiation. By employing MC simulations, accurate dose estimations can be achieved without generating fruit waste. This method is particularly valuable for food materials with complex shapes, such as broccoli, chicken, and fruits, where traditional methods may be less efficient or wasteful [11]. From both technical and economic perspectives, direct measuring of doses in fresh products is often not ideal for quality control in mass-production processes, although it remains a common practice for dose mapping [67].

Both facility modeling and food irradiation modeling share a common focus on physical quantities, specifically the calculation of absorbed doses, whether as dose distribution or specific doses in targeted regions. However, their areas of emphasis differ. In food irradiation, the dose distribution is primarily observed on the fruit surface, particularly when using electron beams [58, 68]. This focus aligns with the goal of phytosanitary irradiation, which targets the fruit surface where pest eggs are typically laid [69]. In contrast, for industrial facilities, the focus of dose distribution is on identifying regions with the best dose uniformity to optimize processing efficiency and product quality, thereby completing the performance qualification steps [8, 50, 70].

In MC modeling studies that do not involve experimental validation, the emphasis is often placed on understanding the physical interactions within the simulated processes. While some studies present results in absolute terms, this is usually because the MC model has already been validated in previous research. For instance, Jongsoon Kim’s series of publications over the past decade (2005, 2007, 2010, 2011, 2013, 2015, 2019) includes early works with validation, allowing later studies to focus solely on simulation without revalidating the model [67, 71,72,73,74,75,76]. Conversely, some studies presented results in relative terms rather than absolute values, especially when no experimental validation was conducted.

In addition, MC studies without experimental validation often enable the rapid exploration of various parameters and configurations, which may be difficult or costly to replicate through experimental means. This flexibility makes MC modeling an invaluable tool for preliminary assessments and hypothesis testing. By adjusting variables such as geometry, source strength, and material composition, researchers can investigate potential outcomes without the need for extensive laboratory setups. A representative example is the study conducted by Moradi et al., which employed MC simulations to design a mini collimator for use in a Category I Gamma Cell with the goal of improving the dose uniformity ratio [61]. This work exemplifies the strength of MC methods in allowing for the modeling of various components and evaluating their effects as part of an important design analysis before fabrication. The study systematically compared multiple collimator configurations, including different shapes and materials, to identify the most effective design. As a result, the manufacturing process could be directed toward a single optimized model, improving both cost-efficiency and the accuracy of subsequent experimental measurements.

In addition to its powerful capability to simulate radiation interactions, simulation studies must validate their findings to ensure accuracy. MC simulations offer flexibility in modeling objects and allow for the use of assumptions when specific details or specifications are unavailable. Therefore, validation through experimental data or benchmarking against established models is essential to confirm the reliability of the simulations. This process not only enhances the credibility of the findings but also ensures that the results can be effectively applied in real experiments, such as optimizing radiation processes or improving facility designs.

The challenges in the MC approach include (i) accurately modeling objects, particularly in assigning their mass density, (ii) the limited ability of MC simulations to account for dynamic rather than static objects, and (iii) the complexity of the program preparation. These challenges represent key limitations of the MC approach, despite its notable advantages in understanding physical processes and estimating the absorbed dose. Nonetheless, MC estimation results are generally acceptable compared with experimental data if they fall within the expanded uncertainty range of the dosimeter.

Fruit modeling was conducted using two methods: model based on DICOM images obtained from computer tomography (CT) scans and CAD model [58, 67]. Using DICOM images and converting them into MC code provided a more accurate way to mimic the fruit’s geometry. However, this approach does not account for the true mass density distribution within the fruit. Real fruits often have varying mass densities, even within a single layer of flesh. The conventional approach involves simplifying the fruit into two distinct regions with different mass densities: the flesh and seeds. These two regions were assigned separate mass densities, a method commonly used in MC-based fruit studies. Although this method is effective, the accuracy of fruit modeling can be further enhanced by assigning the true density distribution for each region of the fruit.

The latest development of the PHITS MC code introduced a feature to convert DICOM images into MC code, automatically defining mass density based on the gray values of CT numbers (Hounsfield units [HU]) [80]. However, this feature was primarily designed for human tissue and not for fruits. Therefore, the conversion of a fruit’s CT numbers to its mass density still requires validation to ensure accuracy. Nevertheless, accurately measuring fruit density remains a significant challenge.

Another significant challenge associated with the MC approach is its limitation in simulating dynamic objects, whether in the context of fruit studies or irradiation facilities. In the case of MC simulations for fruit, this issue was addressed by Jongsoon Kim [68] and Kataoka [79], who introduced object rotation to mimic dynamic movement. Their method involved manually rotating the object to various angles and averaging the absorbed dose across the rotations. This approach demonstrated good agreement with expectations and provided valuable insights into uniform irradiation across the object’s surface.

For irradiation facilities, a key challenge lies in modeling the transit dose in Type I irradiators, such as Gamma-Cell or Gamma-chamber systems. The transit dose refers to the radiation dose absorbed by the sample during its movement from the initial position to the irradiation position [8]. While the transit dose is generally measured in the order of Gray (Gy), it becomes critical when the target dose is also in the Gy range. However, it is less problematic when the target dose is kilogray (kGy). Accurate modeling of transit doses in these systems remains a complex task. Mannai et al. [81] addressed this challenge by calculating the transit dose at three distinct time points along the sample chamber’s transfer path, summing the dose from all sampling points. More recently, El-Ouardi [82] employed a semi-analytical approach combined with MC simulations to calculate the transit dose. Their method, inspired by Mannai’s work, focused on shorter time intervals (4–35 s) to improve the accuracy of the simulations [82].

The challenge of addressing dynamic motion in MC simulations has been overcome using updated MC codes, specifically 4D Monte Carlo (4D MC) codes. These codes incorporate time as a fourth dimension in addition to conventional 3D geometry (X, Y, Z) axes [83, 84]. The primary application of 4D MC has been in medical physics, particularly for dose reconstruction and verification in scenarios involving dynamic organ motion [85]. By integrating time into dose calculations, 4D MC significantly improved accuracy compared with conventional static models. However, these advanced features increase computational demands, requiring high-performance computing systems to achieve reliable results with low uncertainties.

Looking ahead, 4D MC simulations offer a promising solution to address the challenges posed by dynamic motion in radiation processing facilities. One example of an MC code used for this purpose is EGSnrc/4DdefDOSXYZnrc, an extension of the EGSnrc system that incorporates time-dependent geometry and deformation capabilities [83, 85]. The application of 4D MC methods may extend beyond first-category gamma irradiators to include fourth-category systems and electron beam facilities, where objects are continuously transported via conveyors during irradiation. This dynamic modeling approach enhances both the accuracy and efficiency of dose calculations in time-dependent irradiation scenarios.

The third challenge associated with the MC approach is the complexity involved in program preparation. Developing an accurate MC model and obtaining the desired output, such as dose distribution, can take hours or even days. This process is impractical for radiation processing facilities because of the limited time and computational resources. However, a recent advancement in MC code development, released in 2024, introduced a tool called PUFFin (Penelope User-Friendly Fast Interface), which represents a breakthrough in simplifying the MC process [57]. This innovative tool allows users to input a 2D image and run simulations with ease. Its intuitive graphical user interface (GUI) offers a “plug-and-play” experience, making the process more accessible and efficient. With these advantages, it is hoped that the MC code will become a reliable daily tool for accurately estimating absorbed doses in mass-radiation processing.

Theoretical methods, such as those based on the multipole moment method, offer powerful tools for dose and flux calculations in radiation processing [87, 88]. However, their practical implementation faces significant challenges. One of the key issues is the validation of theoretical results against experimental data, as accurately reproducing the actual irradiation conditions in a theoretical framework can be complex. Additionally, these methods often require extensive computational resources, particularly when dealing with high-resolution models or large irradiation systems. Integrating diverse optimization approaches, such as the AHP and TOPSIS, with physical modeling frameworks add another layer of complexity.

Another significant challenge in theoretical methods is the variability in the source activity, geometry, and material properties, which can lead to discrepancies between the theoretical predictions and experimental outcomes. Theoretical methods typically rely on the assumption of ideal conditions to model objects; however, in practice, these ideal conditions are often unattainable. For example, the material properties of an object, such as its density, may vary because of its manufacturing processes, introducing uncertainties into the model. Such variations underscore the need for robust validation to ensure that theoretical models accurately reflect the complexities of actual conditions.

Despite these challenges, theoretical radiation processing methods are promising. Advances in computational algorithms, such as adaptive mesh refinement and machine learning, are expected to streamline the modeling process, making it faster and more accessible. Enhanced validation protocols, including benchmarking against MC simulations and experimental data, will further strengthen the confidence in these models. Resource optimization, as demonstrated by Singh’s Voronoi diagram approach, highlights the potential to reduce dosimeter usage and enhance dose mapping efficiency.