SIMULATION-BASED ANALYSIS AND FEEDBACK CONTROL OF PARAMETER ERRORS IN RADIATION BEAM DELIVERY SYSTEMS

ABSTRACT

A linear accelerator (LINAC) is a key system in radiation therapy, used to deliver high-energy radiation beams to tumour. However, beam alignment errors and positioning uncertainties remain serious problems, as existing approaches rely primarily on offline quality control and provide limited real-time error correction. Proper setup of the system parameters is critical for accurate beam delivery using LINACs. Any slight deviations can lead to serious alignment issues. This article examines the propagation of parameter errors during beam delivery using a simulation experiment. A simplified model is developed to evaluate the impact of systematic and random errors on the alignment process. An improved feedback controller is developed to compensate for these errors. The simulation study demonstrates significant improvement in error mitigation.

АННОТАЦИЯ

Правильная настройка параметров оборудования является критически важной для точной доставки радиационного пучка с использованием линейных ускорителей. Любые незначительные отклонения могут привести к серьёзным проблемам с выравниванием. В данной работе исследуется распространение ошибок параметров в процессе доставки пучка с помощью моделирования. Рассматривается упрощённая модель для оценки влияния систематических и случайных ошибок на процесс выравнивания. Для компенсации этих ошибок разработан усовершенствованный регулятор с обратной связью. Результаты моделирования показывают существенное улучшение в снижении ошибок.

Keywords: radiation therapy, beam delivery, error propagation, feedback control, automation, linear accelerator, quality assurance, simulation, positioning accuracy, radiotherapy systems.

Ключевые слова: радиотерапия, доставка пучка, распространение ошибок, обратная связь, автоматизация, линейный ускоритель, контроль качества, моделирование, точность позиционирования.

I. INTRODUCTION

Radiation therapy is a common treatment method for cancer patients; however, this method requires extremely precise delivery of radiation beams. The slightest error in equipment calibration or even patient positioning can lead to significant errors and expose healthy tissue around the tumor.

Previous studies have shown that errors during radiation therapy are quite common and can negatively impact treatment quality [1], [3]. Quality control and failure mode and effects analysis (FMEA) processes are often used to identify any errors during radiation therapy [4], [10]. However, in all these methods, correction is performed only in an autonomous mode.

With the increasing automation and use of intelligent technologies in radiation therapy, there is a need to adapt and implement a feedback control approach [9]. In this paper, we propose using a modeling method to study error propagation and determine the effectiveness of feedback control. The overall structure of the proposed system is illustrated in Fig. 1.

II. MATERIALS AND METHODS

A. Simulation Model

The proposed model treats radiation beam delivery as a two-dimensional positioning problem, with the target located at the origin. The effective position of the radiation beam is influenced by several factors, including beam misalignment, incorrect couch position, and random noise.

The effective beam position is defined as:

Where:

,  – beam axis deviations;

,  – couch positioning errors;

,  – random noise 

B. Error Modeling

Errors are modeled as a combination of:

• systematic deviations (beam axis and couch errors)
• stochastic disturbances (Gaussian noise)

Such modeling reflects real-world uncertainties observed in radiotherapy systems [2], [5].

C. Feedback Control Mechanism

A proportional feedback controller is implemented to reduce positioning errors:

Where:

 – control gain;

 – positioning error.

The controller adjusts the beam position iteratively when the error exceeds a predefined tolerance threshold (2 mm), which is commonly used in image-guided radiotherapy (IGRT).

The overall system architecture, including error modeling and feedback control, is shown in Fig. 1.

Figure 1. Overall system block diagram

D. Simulation Interface

The simulation environment allows interactive adjustment of system parameters and enables controlled experimentation with error propagation and correction mechanisms.

The simulation interface used for parameter configuration and experimentation is presented in Fig. 2.

Figure 2. Graphical user interface of the simulation framework showing adjustable beam alignment, couch parameters, and feedback control settings

III. RESULTS AND ANALYSIS

The simulation results are illustrated in Figs. 3–6 and summarized in Table I.

A. Residual Error Convergence

The residual error behavior was analyzed over several tests. Without feedback, the residual error remains above the acceptable tolerance, with an average value of 2.285 mm. It can be concluded that the system cannot achieve an acceptable level of accuracy.

In the presence of a feedback controller, the error gets considerably decreased to less than 1 mm, as given in Fig. 2.

As shown in Fig. 3, the residual error without control remains above the acceptable threshold, while the controlled system exhibits stable convergence below 1 mm.

Figure 3. Residual error convergence with and without feedback control. The dashed line indicates the tolerance threshold of 2 mm

B. Beam Position Trajectory

As shown in Fig. 3, the uncontrolled path is out of the tolerance bounds, which implies bad alignment. However, in the controlled mode, the path approaches the target value. The spatial behavior of the beam position relative to the target is illustrated in Fig. 4.

Figure 4. Beam position trajectory relative to the target center. The dashed circle represents the tolerance region

C. Error Metrics

A quantitative comparison of error metrics is presented in Fig. 5.

The quantitative results show:

• Mean error reduced from 2.285 mm to 0.973 mm
• Maximum error reduced from 2.474 mm to 1.156 mm
• Final error reduced from 2.312 mm to 0.991 mm

Figure 5. Comparison of mean, maximum, and final residual errors for controlled and uncontrolled scenarios

D. Success Rate Analysis

The success rate improves from 2.5% to 100%, demonstrating that the system consistently meets clinical accuracy requirements when feedback control is applied. The improvement in system success rate is demonstrated in Fig. 6.

Figure 6. Success rate comparison based on the percentage of iterations within the tolerance limit

E. Summary

Analysis of Table I shows that feedback significantly improves system performance. Without control, error values ​​exceed the acceptable threshold, resulting in a low success rate of 2.5%. With control, all error values ​​are reduced to less than 1 mm, and the success rate reaches 100%, indicating stable and accurate beam positioning.

Table I.

 Performance Comparison

IV. DISCUSSION

The results obtained clearly demonstrate that errors in radiation beam delivery can cause numerous problems for the patient if not properly controlled. Without control, the error always exceeded the acceptable level, indicating that even minor deviations in the alignment and position of the treatment couch during treatment can lead to an unacceptable situation for the patient. Similar observations have been made previously [1], [3].

The feedback control scheme significantly improves the overall system efficiency. The reduction in mean and maximum errors, along with 100% success within the tolerance region, demonstrates the ability of the proposed method to compensate for deterministic and probabilistic disturbances. The results are consistent with existing studies highlighting the need for adaptive and automated methods in radiation therapy [5], [9].

One of the key features of this research is the incorporation of automation principles into radiation therapy processes. Traditional quality assurance approaches were developed primarily for offline testing and, therefore, may not be able to support real-time adjustments. The methodology presented in this study demonstrates how a feedback-based control process can facilitate real-time adjustments without any human intervention [4], [10].

However, despite the successful results of this study, several limitations must be considered. First, the proposed model relies on assumptions regarding two-dimensional dynamics and cannot adequately account for anatomical complexities or multi-axial beams. Furthermore, the assumption of noise dynamics based on a Gaussian distribution may also be inaccurate in some cases. Therefore, further research is needed to incorporate more accurate dynamic models and account for three-dimensional dynamics.

Overall, the obtained results indicate great potential for the application of control and automation theory in medical equipment. The trends observed in Figs. 3–6 confirm that feedback control significantly improves system performance.

V. CONCLUSION

In this study, a simulation model was developed to study the impact of parameter error propagation on beam emission systems and analyze the performance of the feedback method.

The results of the simulation study clearly demonstrate that without a feedback mechanism, parameter deviations can lead to significant positioning errors beyond clinical norms. However, using the feedback method ensures faster error correction and rapid convergence to the desired position.

The proposed methodology highlights the importance of automation in modern radiation therapy. A feedback mechanism can significantly improve the accuracy of radiation therapy and minimize the risk of accidental exposure to ionizing radiation by correcting errors in the device's parameters in real time.

Despite the simplicity of the existing model, it still represents a very good starting point for further research. Further development will likely include the use of more complex control algorithms, multivariate models, and even machine learning to predict corrections.

In conclusion, simulation-based analysis combined with automated feedback control represents a very promising direction in radiation therapy. The effectiveness of the proposed approach highlights the importance of automated error correction.

References:

1. Huang, G., Medlam, G., Lee, J., et al., “Error in the delivery of radiation therapy: Results of a quality assurance review,” International Journal of Radiation Oncology, Biology, Physics, 2005.
2. Lis, M., et al., “Pre-clinical testing for quality and safety of beam delivery in radiotherapy,” Radiation Oncology, 2021.
3. Siebert, F. A., et al., “Errors detected during physics plan review for external beam radiotherapy,” Physics and Imaging in Radiation Oncology, 2022.
4. Huang, S. F., et al., “Failure mode and effects analysis for errors detected during radiotherapy plan review,” Translational Cancer Research, 2022.
5. Iijima, K., et al., “Analysis of human errors in treatment planning for radiation therapy,” Journal of Radiation Research, 2024.
6. Margalit, D. N., et al., “Technological advancements and error rates in radiation therapy delivery,” International Journal of Radiation Oncology, 2011.
7. Palta, J. R., et al., “Current external beam radiation therapy quality assurance guidance and limitations,” International Journal of Radiation Oncology, 2008.
8. Cheong, K. H., et al., “Statistical quality control for VMAT delivery using machine log data,” Medical Physics / arXiv preprint, 2015.
9. Yu, L., et al., “First implementation of full-workflow automation in radiotherapy,” arXiv preprint, 2022.
10. Rahman, M., et al., “Failure mode and effects analysis (FMEA) for clinical accelerator systems,” arXiv / Medical Physics context, 2021.