A novel analytical model for predicting 3D positron emitter distributions for PET-based range verification in carbon ion therapy

Du, Tianxue (2026): A novel analytical model for predicting 3D positron emitter distributions for PET-based range verification in carbon ion therapy. Dissertation, LMU München: Fakultät für Physik

Abstract

Radiotherapy plays an important role in cancer treatment, and particle therapy has emerged as an advanced modality due to its superior dose conformity compared to conventional photon radiation therapy. Among particle modalities, carbon ions offer distinct physical and biological advantages. However, carbon ion therapy is sensitive to range uncertainties, as small deviations in beam range can lead to tumor underdosage or unnecessary radiation exposure to surrounding healthy tissue. Positron emission tomography (PET) monitoring is one viable approach for in vivo range verification, in which measured PET signals are typically compared with predicted beta+-activity distributions derived from positron emitter distributions (PED). Monte Carlo (MC) simulations are commonly used to predict PED, but their computational cost limits routine clinical applicability. This motivates the development of fast and reliable alternative prediction methods. The objective of this thesis is the development and comprehensive validation of an analytical framework for predicting 3D PED and corresponding beta+-activity distributions in carbon ion therapy, enabling a computationally efficient and clinically applicable tool for PET-based range verification in carbon ion therapy. To this end, an analytical framework for PED prediction was developed by combining an improved 1D analytical approach with a 3D spreading kernel inspired by the pencil beam algorithm (PBA) commonly used in dose calculation. A previously proposed 1D analytical approach for predicting PED from depth dose profiles for carbon ions was further revised by introducing finer modelling functions and considering additional positron emitters (PEs). In addition, a mapping strategy was developed to better handle longitudinal heterogeneity effects in projectile PED. Based on the improved 1D model, a PBA-based framework was established to enable full 3D PED prediction in heterogeneous media by integrating material information and lateral spreading parameters. The analytical approach was first validated through in-silico studies against MC simulations for several slab phantoms as well as realistic computed tomography (CT) scans from patient data. For range assessment, the differences between distal fall-off positions of predicted and simulated 1D PED profiles were below 0.8 mm for all validation cases. The agreement between predicted and simulated 3D PED was evaluated using global gamma index analysis with the 2%/2 mm and 1%/1 mm criteria. For patient cases, the passing rates for 1%/1 mm criteria were above 95%. These results demonstrated the capability of this approach to predict 3D PED with good accuracy in terms of range and magnitude. Next, the analytical approach was validated using real clinical cases where offline PET/CT monitoring was employed. Four carbon ion therapy patients treated at the Heidelberg Ion Beam Therapy Center were selected, and their treatment plans and CT images were used for MC simulations and analytical prediction of beta+-activity distributions. The analytically predicted activity distributions, derived from the simulated dose distributions with the analytical approach, were then compared with both simulated results and measured offline PET data. The analytical and MC activity distributions demonstrated a good match in range with mean deviations less than 0.5 mm, and in amplitude with mean normalized root mean square error less than 2%. Range shifts between the measured PET signals and the analytical activity patterns were evaluated and found to be consistent with published results. In addition, a preliminary validation was performed using in-beam PET data acquired in a polymethylmethacrylate phantom provided by the National Institutes for Quantum Science and Technology in Chiba. Initial comparisons revealed pronounced discrepancies in the earliest acquisition window (0–60 s after irradiation), which were primarily attributed to inaccurate predictions of short-lived PEs. To mitigate this effect, isotope-dependent scaling factors were introduced. After applying these corrections, good agreement between analytical predictions and measurements was achieved for most cases in terms of both longitudinal range and lateral activity profiles, especially at later acquisition times, with range shifts below 2 mm. Nevertheless, further refinement of the model parameters based on improved MC simulations or directly on experimental measurement data will be required. Overall, this thesis developed and validated an analytical framework for fast and accurate prediction of PED and beta+-activity distributions in carbon ion therapy, achieving a computational speed-up of at least a factor of 40 compared to full MC simulations. By leveraging the PBAs commonly used in analytical carbon ion dose engines, the proposed analytical approach enables a straightforward integration into treatment planning systems, thereby facilitating its translation into routine clinical practice.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: Carbon ion therapy, Particle therapy, Range verification, Positron emission tomography
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 530 Physik
• Fakultäten: Fakultät für Physik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 5. März 2026
• 1. Bericht­erstatter:in: Parodi, Katia