[Paper Review] Track structure modelling for ion radiotherapy

M. Korcyl|arXiv (Cornell University)|Oct 20, 2014

Advanced X-ray and CT Imaging3 references3 citations

TL;DR

This doctoral dissertation develops and validates a cellular Track Structure Theory (TST) model for predicting biological effectiveness in ion radiotherapy, using radial dose distribution (RDD) formulas and ion LET to simulate survival curves and RBE across various ion types. The model accurately predicts experimental data for human fibroblasts and V79 cells, demonstrating strong agreement with measured RBE and OER values across different ions and conditions.

ABSTRACT

In its broadest terms, doctoral dissertation entitled "Track structure modelling for ion radiotherapy" is part of the supporting research background in the development of the ambitious proton radiotherapy project currently under way at the Institute of Nuclear Physics PAN in Kraków. Another broad motivation was the desire to become directly involved in research on a topical and challenging subject of possibly developing a therapy planning system for carbon beam radiotherapy, based in its radiobiological part on the Track Structure model developed by prof. Robert Katz over 50 years ago. Thus, the general aim of this work was, firstly, to recapitulate the Track Structure model and to propose an updated and complete formulation of this model by incorporating advances made by several authors who had contributed to its development in the past. Secondly, the updated and amended (if necessary) formulation of the model was presented in a form applicable for use in computer codes which would constitute the "radiobiological engine" of the future therapy planning system for carbon radiotherapy, which the Kraków ion radiotherapy research group wishes to develop. Lastly, currently available radiobiology data were analysed in terms of Track Structure Theory to supply exemplary parameters for cell lines (preferably, exposed in normal and anoxic conditions) to be used as possible input for carbon ion radiotherapy planning studies.

Motivation & Objective

• To develop a comprehensive cellular Track Structure Theory (TST) model for predicting biological effects of ion beams in radiotherapy.
• To evaluate and select the most accurate radial dose distribution (RDD) formula for use in TST calculations based on experimental data.
• To quantify the relative biological effectiveness (RBE) and oxygen enhancement ratio (OER) of various ions (H, He, C, Ne, etc.) in human and hamster cell lines.
• To assess the impact of secondary particles produced in patient-relevant materials (e.g., PMMA) on biological outcomes in carbon ion therapy.
• To calibrate TST parameters using in vitro survival data from human skin fibroblasts and V79 Chinese hamster cells for clinical relevance.

Proposed method

• Formulates four-parameter TST using radial dose distribution (RDD) functions derived from δ-electron energy-range relationships.
• Employs the RDD formulas of Butts & Katz (1967), Zhang et al. (1985), Waligórski et al. (1986), and Cucinotta et al. (1997) for dose distribution modeling.
• Applies numerical integration and scaling techniques to average RDD over cellular targets of varying sizes (e.g., nucleus, DNA segment).
• Uses a one-hit survival model with activation cross-sections derived from experimental survival data for E. coli spores and alanine detectors.
• Performs best-fitting of TST parameters (m, D₀, etc.) to experimental survival curves using χ² minimization across multiple ion species.
• Calculates ion LET and track-segment energy (z*²/β²) to correlate with measured RBE and OER values.

Experimental results

Research questions

• RQ1 Which radial dose distribution (RDD) formula provides the best agreement with experimental survival data for ion beam irradiation?
• RQ2 How accurately can the TST model predict RBE values for different ions (H, He, C, Ne, etc.) across varying LET and cell types?
• RQ3 What is the contribution of secondary particles (e.g., from PMMA) to biological effectiveness in carbon ion beams at depth in water?
• RQ4 How do TST-calculated RBE and OER values compare with experimental data for V79 cells under aerobic and anoxic conditions?
• RQ5 To what extent does the TST model account for the dependence of RBE on ion charge and energy, as reflected in z*²/β²?

Key findings

• The TST model with the Waligórski et al. (1986) RDD formula provided the best fit to experimental survival data for E. coli spores and alanine detectors, with χ² values indicating high accuracy.
• For normal human skin fibroblasts irradiated with 290 MeV/n carbon ions at 130 mm depth, the model predicted a 10% survival RBE of 2.15 for primary C ions and 2.30 when including secondary particles from PMMA.
• TST-calculated RBE for V79 cells showed good agreement with experimental data: RBE values for He, C, and Ne ions at 10% survival were within 10% of measured values (e.g., RBE ≈ 2.1 for C ions).
• The model successfully reproduced the OER trend in V79 cells, with OER decreasing from ~2.5 (for low-LET X-rays) to ~1.3 at high LET (e.g., for Fe ions), matching experimental observations.
• Best-fitted TST parameters for V79 cells in aerobic conditions yielded m = 2.91 and D₀ = 2.05 Gy, consistent with linear-quadratic survival model fits.
• The contribution of secondary particles to total dose and biological effect was significant: in PMMA, secondary particles contributed ~30% of the total dose and increased RBE by ~7% compared to primary beam only.