Air Kerma Calculation in Diagnostic Medical Imaging Devices Using Group Method of Data Handling Network

The air kerma, which is the amount of energy given off by a radioactive substance, is essential for medical specialists who use radiation to diagnose cancer problems. The amount of energy that a photon has when it hits something can be described as the air kerma (the amount of energy that was deposited in the air when the photon passed through it). Radiation beam intensity is represented by this value. Hospital X-ray equipment has to account for the heel effect, which means that the borders of the picture obtain a lesser radiation dosage than the center, and that air kerma is not symmetrical. The voltage of the X-ray machine can also affect the uniformity of the radiation. This work presents a model-based approach to predict air kerma at various locations inside the radiation field of medical imaging instruments, making use of just a small number of measurements. Group Method of Data Handling (GMDH) neural networks are suggested for this purpose. Firstly, a medical X-ray tube was modeled using Monte Carlo N Particle (MCNP) code simulation algorithm. X-ray tubes and detectors make up medical X-ray CT imaging systems. An X-ray tube’s electron filament, thin wire, and metal target produce a picture of the electrons’ target. A small rectangular electron source modeled electron filaments. An electron source target was a thin, 19,290 kg/m3 tungsten cube in a tubular hoover chamber. The electron source–object axis of the simulation object is 20° from the vertical. For most medical X-ray imaging applications, the kerma of the air was calculated at a variety of discrete locations within the conical X-ray beam, providing an accurate data set for network training. Various locations were taken into account in the aforementioned voltages inside the radiation field as the input of the GMDH network. For diagnostic radiology applications, the trained GMDH model could determine the air kerma at any location in the X-ray field of view and for a wide range of X-ray tube voltages with a Mean Relative Error (MRE) of less than 0.25%. This study yielded the following results: (1) The heel effect is included when calculating air kerma. (2) Computing the air kerma using an artificial neural network trained with minimal data. (3) An artificial neural network quickly and reliably calculated air kerma. (4) Figuring out the air kerma for the operating voltage of medical tubes. The high accuracy of the trained neural network in determining air kerma guarantees the usability of the presented method in operational conditions.


Introduction
There are two steps in the process by which photons impart their energy to matter. The interaction of photons with matter first transfers energy to the charge carriers of matter. The charge carriers' kinetic energy is then deposited by the ionized and excited atoms. By dividing the total kinetic energy of the charged particles (such as electrons, protons, and 1.
The heel effect is taken into account while calculating air kerma.

2.
Calculating the air kerma by employing an artificial neural network and training it with a limited amount of data in varying angles, distances, and voltages of tubes. 3.
Using an artificial neural network, the calculation of air kerma was executed extremely quickly and accurately compared to earlier efforts. 4.
Calculating the air kerma for medical tubes' operating voltage.

Methodology
As shown in Figure 1, the two main components of a medical X-ray CT imaging system are the X-ray tube and the detector. An X-ray tube's electron filament (a thin wire) and metal target allow for the production of an X-ray image (the object the electrons hit). After being generated by the filament, electrons are propelled through a large potential difference in the X-ray source's hoover chamber before striking the target. The Bremsstrahlung process converts just a small proportion of the energy in electrons into photons, therefore most of the energy ends up as heat. Several projections, or 2D pictures, are taken when the X-ray tube and detector spin around the subject at the same time. The system takes 2D photos of the patient and uses powerful computer technology to recreate 3D images of their body in accordance with Lambert Beer's law. In the medical X-ray imaging sector, air kerma has only been studied using a model of an X-ray tube (as shown in Figure 2). A medical X-ray tube is simulated using code written in MCNPX. To model electron filaments, a tiny rectangular electron source was examined. If you want to simulate focal spots, you will need to use a surface source rather than a point source. A thin tungsten cube with a density of 19,290 kg/m 3 was placed in a tubular vacuum chamber as an electron source target. The electron source-object axis of the simulation object has an angle of 20 • to the vertical. It is important to note that at the maximum tilt angle of the X-ray tube target, the emitted X-rays leave the tube within the cone. To create the illusion of a hoover chamber, the electrons and the target are encased in a steel shell. The only section of the hoover chamber that has any action was the exposed circle. At the entrance to the vacuum chamber is a beryllium window with a density of 1850 kg/m 3 and a thickness of 1 mm. Two-stage point detector counting was used to determine air kerma (tally F5). At each detector, the photon flux was first measured. The floating air kerma conversion factor recommended in the ICRP-51 report of the International Committee on Radiation Protection was used to determine the air kerma in the second stride [18]. It should be noted that the overall statistical uncertainty did not exceed 4% in all Monte Carlo simulations in this study. In this article, we employ a spherical coordinate system to precisely locate point detectors (according to the inherent spherical symmetry of the X-rays produced) at various tangent angles (0
x(x 1 , x 2 , . . . , x m ) represents the input (the features vector), a(a 1 , a 2 , . . . , a m ) represents the coefficient or weight, and y(x) represents the network's output. The following procedures should have been carried out in order to use a GMDH network: In the first step, new variables should have been created and quadratic regression polynomials are calculated based on Equation (2) for each combination and two at a time for all characteristics (x 1 , x 2 . . . x m ).
Coefficient C was determined using the least squares method in this investigation. Take note of how each of the quadratic polynomials computed is quite close to the target value. A quadratic polynomial is calculated by each neuron. Secondly, dead neurons are those that could not accurately forecast the required product. The leftover neurons are employed for the layer-up procedure. This process not only creates the first neural layer, but also chooses the most effective neurons. The third phase involves using the polynomial found in the second stage to generate the next layer. This means that the old polynomial is used as a basis for creating a new polynomial, and the second step is repeated until an effective neuron is located. The GMDH neural network is not complete until this process is repeated several times. In the final stage, accuracy is guaranteed and test data are used to assess the efficiency of the designed network. Training data and test data are created throughout the neural network construction phases. The training data are used to create the neural network, and the error is minimized by tuning the network's various parameters. After the training process is complete, the network's effectiveness ought to be evaluated against data it has never seen before to ensure it has retained what it has learned. If this step is completed successfully, the network will behave as expected under operating circumstances. Around 70% of the data were used for training and the remaining 30% of the data were used for evaluation.

Results
For this research, the air kerma was calculated using a GMDH neural network. After extracting the function, it was fed into the network. For accurate air kerma estimation, the functions φ, θ, r, and V were found to be most useful. Figure 3 depicts the intended structure of the GMDH neural network.
those that could not accurately forecast the required product. The leftover neurons are employed for the layer-up procedure. This process not only creates the first neural layer, but also chooses the most effective neurons. The third phase involves using the polynomial found in the second stage to generate the next layer. This means that the old polynomial is used as a basis for creating a new polynomial, and the second step is repeated until an effective neuron is located. The GMDH neural network is not complete until this process is repeated several times. In the final stage, accuracy is guaranteed and test data are used to assess the efficiency of the designed network. Training data and test data are created throughout the neural network construction phases. The training data are used to create the neural network, and the error is minimized by tuning the network's various parameters. After the training process is complete, the network's effectiveness ought to be evaluated against data it has never seen before to ensure it has retained what it has learned. If this step is completed successfully, the network will behave as expected under operating circumstances. Around 70% of the data were used for training and the remaining 30% of the data were used for evaluation.

Results
For this research, the air kerma was calculated using a GMDH neural network. After extracting the function, it was fed into the network. For accurate air kerma estimation, the functions ф, θ, r, and V were found to be most useful.  The GMDH network took into consideration the voltage of the X-ray tube and the position inside the radiation field as inputs. Output was measured in kerma of air. A neural network was trained by randomly picking 5775 samples from the provided data. When training was complete, the remaining data was utilized to evaluate the neural network. Two hidden layers, each with 4 neurons, were able to give accurate correlations between inputs and outputs. Two error measures, mean relative error (MRE) and root mean square error (RMSE), were used to determine the discrepancy between the MCNP code's air kerma volume and the neural network's air kerma prediction. These requirements are represented by the following equations: X(Exp) and X(Pred) are the experimental and predicted values, whereas N is the total number of samples.

Discussion
The air kerma, calculated using the Monte Carlo model, is shown in Figure 4 for two different tube voltages (60 kV and 120 kV) based on the X-ray field of view at a distance of 75 mm from the source. Figure 4a,b demonstrate how the heel effect of the X-ray tube causes the anticipated air kerma to be smaller on the right side of the field of view (towards the target) than on the left, despite being almost uniform from top to bottom. The kerma of the air increases as the voltage in the tube increases. To demonstrate the effect of distance, the air kerma is computed with the voltage held constant at 80 kV and the detector placed at distances of 500 mm and 1000 mm, respectively, in Figure 5a,b. Air kerma drops down dramatically with distance from the source, as predicted. This implies if the radiation source travels away from the treated region, the quantity of radiation that reaches that area goes lower. X(Exp) and X(Pred) are the experimental and predicted values, whereas N is the total number of samples.

Discussion
The air kerma, calculated using the Monte Carlo model, is shown in Figure 4 for two different tube voltages (60 kV and 120 kV) based on the X-ray field of view at a distance of 75 mm from the source. Figure 4a,b demonstrate how the heel effect of the X-ray tube causes the anticipated air kerma to be smaller on the right side of the field of view (towards the target) than on the left, despite being almost uniform from top to bottom. The kerma of the air increases as the voltage in the tube increases. To demonstrate the effect of distance, the air kerma is computed with the voltage held constant at 80 kV and the detector placed at distances of 500 mm and 1000 mm, respectively, in Figure 5a,b. Air kerma drops down dramatically with distance from the source, as predicted. This implies if the radiation source travels away from the treated region, the quantity of radiation that reaches that area goes lower.    Figure 6 exhibits two error histograms and regression plots on the training and testing data to visually emphasize the neural network's performance. In the regression graph, the green circle represents the neural network's prediction and the yellow line represents the optimal answer (the value of air kerma generated using the MCNP algorithm). These coincide, proving the network's high precision. Some input and output data of the GMDH neural network are displayed in Table 1. In this table, some of the tube voltage values and the location that is considered inputs of the network can be seen, along with the amount of air kerma calculated by the MCNP code. In this table, you can see the performance of the neural network in finding the input-output relationship. It should be noted that for the best possible performance of the neural network, first the inputs and outputs are nor-  Figure 6 exhibits two error histograms and regression plots on the training and testing data to visually emphasize the neural network's performance. In the regression graph, the green circle represents the neural network's prediction and the yellow line represents the optimal answer (the value of air kerma generated using the MCNP algorithm). These coincide, proving the network's high precision. Some input and output data of the GMDH neural network are displayed in Table 1. In this table, some of the tube voltage values and the location that is considered inputs of the network can be seen, along with the amount of air kerma calculated by the MCNP code. In this table, you can see the performance of the neural network in finding the input-output relationship. It should be noted that for the best possible performance of the neural network, first the inputs and outputs are normalized, and then after predicting the output, the data are returned to their initial state. The amount of air kerma predicted by the neural network is also provided. As it is clear, the value predicted by the neural network has a slight difference from the calculated value, which indicates the acceptable performance of the neural network.