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Machine Learning-Based Modeling of the Anode Heel Effect in X-ray Beam Monte Carlo Simulations

Hussein Harb, Didier Benoit, Axel Rannou, Chi-Hieu Pham, Valentin Tissot, Bahaa Nasr, Julien Bert

TL;DR

This work tackles the challenge of accurately modeling the anode heel effect in X-ray beam Monte Carlo simulations with limited calibration data. It combines a standard virtual source MC model with a machine learning framework, notably Gradient Boosting Regression, to predict angular-weight factors that encode the heel effect as a function of energy and position, and integrates these weights into OpenGATE 10 and GGEMS. The study demonstrates that GBR provides high-fidelity predictions ($MSE\approx0.0014$, $R^2\approx0.963$) and that a six-point-per-energy fine-tuning protocol enables rapid cross-machine adaptation with as few as 48 measurements, achieving errors below about $1.4\%$. By validating with dose maps and phantom imaging, the approach yields more realistic fluence and image quality, offering a scalable, generalizable solution for dosimetry and radiology simulation workflows.

Abstract

To develop a machine learning-based framework for accurately modeling the anode heel effect in Monte Carlo simulations of X-ray imaging systems, enabling realistic beam intensity profiles with minimal experimental calibration. Multiple regression models were trained to predict spatial intensity variations along the anode-cathode axis using experimentally acquired weights derived from beam measurements across different tube potentials. These weights captured the asymmetry introduced by the anode heel effect. A systematic fine-tuning protocol was established to minimize the number of required measurements while preserving model accuracy. The models were implemented in the OpenGATE 10 and GGEMS Monte Carlo toolkits to evaluate their integration feasibility and predictive performance. Among the tested models, gradient boosting regression (GBR) delivered the highest accuracy, with prediction errors remaining below 5% across all energy levels. The optimized fine-tuning strategy required only six detector positions per energy level, reducing measurement effort by 65%. The maximum error introduced through this fine-tuning process remained below 2%. Dose actor comparisons within Monte Carlo simulations demonstrated that the GBR-based model closely replicated clinical beam profiles and significantly outperformed conventional symmetric beam models. This study presents a robust and generalizable method for incorporating the anode heel effect into Monte Carlo simulations using machine learning. By enabling accurate, energy-dependent beam modeling with limited calibration data, the approach enhances simulation realism for applications in clinical dosimetry, image quality assessment, and radiation protection.

Machine Learning-Based Modeling of the Anode Heel Effect in X-ray Beam Monte Carlo Simulations

TL;DR

This work tackles the challenge of accurately modeling the anode heel effect in X-ray beam Monte Carlo simulations with limited calibration data. It combines a standard virtual source MC model with a machine learning framework, notably Gradient Boosting Regression, to predict angular-weight factors that encode the heel effect as a function of energy and position, and integrates these weights into OpenGATE 10 and GGEMS. The study demonstrates that GBR provides high-fidelity predictions (, ) and that a six-point-per-energy fine-tuning protocol enables rapid cross-machine adaptation with as few as 48 measurements, achieving errors below about . By validating with dose maps and phantom imaging, the approach yields more realistic fluence and image quality, offering a scalable, generalizable solution for dosimetry and radiology simulation workflows.

Abstract

To develop a machine learning-based framework for accurately modeling the anode heel effect in Monte Carlo simulations of X-ray imaging systems, enabling realistic beam intensity profiles with minimal experimental calibration. Multiple regression models were trained to predict spatial intensity variations along the anode-cathode axis using experimentally acquired weights derived from beam measurements across different tube potentials. These weights captured the asymmetry introduced by the anode heel effect. A systematic fine-tuning protocol was established to minimize the number of required measurements while preserving model accuracy. The models were implemented in the OpenGATE 10 and GGEMS Monte Carlo toolkits to evaluate their integration feasibility and predictive performance. Among the tested models, gradient boosting regression (GBR) delivered the highest accuracy, with prediction errors remaining below 5% across all energy levels. The optimized fine-tuning strategy required only six detector positions per energy level, reducing measurement effort by 65%. The maximum error introduced through this fine-tuning process remained below 2%. Dose actor comparisons within Monte Carlo simulations demonstrated that the GBR-based model closely replicated clinical beam profiles and significantly outperformed conventional symmetric beam models. This study presents a robust and generalizable method for incorporating the anode heel effect into Monte Carlo simulations using machine learning. By enabling accurate, energy-dependent beam modeling with limited calibration data, the approach enhances simulation realism for applications in clinical dosimetry, image quality assessment, and radiation protection.
Paper Structure (25 sections, 10 equations, 7 figures, 2 tables)

This paper contains 25 sections, 10 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Standard X-ray tube virtual source model
  4. Incorporating the anode heel effect
  5. Machine Learning-based weight modeling
  6. Model parametrization
  7. Learning the weights with Machine Learning
  8. Cross-machine fine-tuning strategies
  9. Evaluation
  10. Experimental data collection
  11. Machine Learning model evaluation
  12. Experimental data for cross-machine validation
  13. Effectiveness of fine-tuning versus training without prior knowledge
  14. Implementation into Monte Carlo softwares
  15. Evaluation on the fluence calculation
  16. ...and 10 more sections

Figures (7)

  • Figure 1: (a) Simplified schematic of the X-ray tube showing the anode–cathode orientation and the direction along which dose measurements were performed. (b) Schematic representation of the virtual X-ray source model, illustrating the emission angles $(\alpha: altitude, \beta: azimuthal)$ defining photon projection in the simulation.
  • Figure 2: Overview of the experimental configuration. (a) Experimental setup for measuring X-ray dose values along the anode–cathode axis using a PTW NOMEX Multimeter dosimeter. (b) Posterior–anterior chest X-ray positioning of the anthropomorphic phantom.
  • Figure 3: Comparison of experimental measurements and their corresponding weights affected by the anode heel effect along the anode–cathode axis. (a) Dose value profiles as a function of distance from the X-ray beam center for various tube potentials. (b) Beam weight distributions illustrating the energy-dependent asymmetry caused by the anode heel effect.
  • Figure 4: Comparison between experimentally measured and AI-predicted weights from Model M1 (P1) across different tube potentials. The negative side corresponds to the anode, and the positive side to the cathode.
  • Figure 5: Comparison of predicted weights from fine-tuned Model M2' (P2') and Model M2 (P2) against experimental weights, including percentage relative errors less than 1.5%.
  • ...and 2 more figures