A simple model for calculating relative biological effectiveness of X-rays and gamma radiation in cell survival

Objectives: The relative biological effectiveness (RBE) of X-rays and γ radiation increases substantially with decreasing beam energy. This trend affects the efficacy of medical applications of this type of radiation. This study was designed to develop a model based on a survey of experimental data that can reliably predict this trend. Methods: In our model, parameters α and β of a cell survival curve are simple functions of the frequency-average linear energy transfer (LF) of delta electrons. The choice of these functions was guided by a microdosimetry-based model. We calculated LF by using an innovative algorithm in which LF is associated with only those electrons that reach a sensitive-to-radiation volume (SV) within the cell. We determined model parameters by fitting the model to 139 measured (α,β) pairs. Results: We tested nine versions of the model. The best agreement was achieved with [Formula: see text] and β being linear functions of [Formula: see text] .The estimated SV diameter was 0.1–1 µm. We also found that α, β, and the α/β ratio increased with increasing [Formula: see text] . Conclusions: By combining an innovative method for calculating [Formula: see text] with a microdosimetric model, we developed a model that is consistent with extensive experimental data involving photon energies from 0.27 keV to 1.25 MeV. Advances in knowledge: We have developed a photon RBE model applicable to an energy range from ultra-soft X-rays to megaelectron volt γ radiation, including high-dose levels where the RBE cannot be calculated as the ratio of α values. In this model, the ionization density represented by [Formula: see text] determines the RBE for a given photon spectrum.

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An empirical model to predict survival curve and relative biological effectiveness after helium and carbon ion irradiation based solely on the cell survival after photon irradiation

10.1101/2020.06.19.161836 ◽

2020 ◽

Author(s):

David B. Flint ◽

Scott J. Bright ◽

Conor H. McFadden ◽

Teruaki Konishi ◽

Daisuke Ohsawa ◽

...

Keyword(s):

Cell Survival ◽

Cell Lines ◽

Empirical Model ◽

Linear Correlation ◽

Relative Biological Effectiveness ◽

Ion Irradiation ◽

Survival Curve ◽

Carbon Ion ◽

Wide Range ◽

Biological Effectiveness

ABSTRACTPurposeTo develop an empirical model to predict radiosensitivity and relative biological effectiveness (RBE) after helium (He) and carbon (C) ion irradiation with or without DNA repair inhibitors.MethodsWe characterized survival in eight human cancer cell lines exposed to 6 MV photons and to He- and C-ions with linear energy transfer (LET) values of 2.2-60.5 keV/μm to verify that the radiosensitivity parameters (D5%, D10%, D20%, D37%, D50% and SF2Gy) correlate linearly between photon and ion radiation with or without DNA-PKcs or ATR inhibitors. Then, we parameterized the LET response of the parameters governing these linear correlations up to LET values of 225 keV/μm using the data in the Particle Irradiation Data Ensemble (PIDE) v3.2 database, creating a model that predicts a cell’s ion radiosensitivity, RBE and ion survival curve for a given LET on the basis of the cell’s photon radiosensitivity. We then trained this model using the PIDE database as a training dataset, and validated it by predicting the radiosensitivity of the cell lines we exposed to He- and C- ions with LET ranging from 2.2-60.5 keV/μm.ResultsRadiosensitivity to ions depended linearly with radiosensitivity of photons in the range of investigated LET values and the slopes and intercepts of these linear relationships within the PIDE database vary exponentially and linearly, respectively. Our model predicted ion radiosensitivity (e.g., D10%) within 5.1–21.3%, RBED10% within 5.0-17.1%, and ion mean inactivation dose within 6.7-25.1% for He- and C-ion LET ranging from 2.2-60.5 keV/μm.ConclusionsRadiosensitivity to He- and C-ions depend linearly with radiosensitivity to photons and can be used to predict ion radiosensitivity, RBE and cell survival curves for clinically relevant LET values from 2.2–60.5 keV/μm, with or without drug treatment.SUMMARYWe present a new empirical model capable of predicting clonogenic cell survival of cell lines exposed to helium and carbon ion beams. Our model is based on an observed linear correlation between radiosensitivity to ions and photons across a wide range of LET values. This linear correlation can be used to predict ion RBE, radiosensitivity, and the cell survival curve for a given LET all based on a cell’s photon survival curve.

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Responses of synchronous L5178Y S/S cells to heavy ions and their significance for radiobiological theory

Proceedings of the Royal Society of London Series B Biological Sciences ◽

10.1098/rspb.1989.0034 ◽

1989 ◽

Vol 237 (1286) ◽

pp. 27-42 ◽

Cited By ~ 7

Keyword(s):

Cell Cycle ◽

Energy Transfer ◽

Linear Energy Transfer ◽

Relative Biological Effectiveness ◽

Survival Curve ◽

Heavy Ion ◽

Ion Beams ◽

X Rays ◽

Biological Effectiveness ◽

Ionizing Radiations

Synchronous suspensions of the radiosensitive S/S variant of the L5178Y murine leukaemic lymphoblast at different positions in the cell cycle were exposed aerobically to segments of heavy-ion beams ( 20 Ne, 28 Si, 40 Ar, 56 Fe and 93 Nb) in the Bragg plateau regions of energy deposition. The incident energies of the ion beams were in the range of 460 ± 95 MeV u -1 , and the calculated values of linear energy transfer (LET ∞ ) for the primary nuclei in the irradiated samples were 33 ± 3, 60 ± 3, 95 ± 5, 213 ± 21 and 478 ± 36 keV μm -1 , respectively; 280 kVp X-rays were used as the baseline radiation. Generally, the maxima or inflections in relations between relative biological effectiveness (RBE) and LET ∞ were dependent upon the cycle position at which the cells were irradiated. Certain of those relations were influenced by post-irradiation hypothermia. Irradiation in the cell cycle at mid -G 1 to mid-G 1 +3 h, henceforth called G 1 to G 1 + 3 h, resulted in survival curves that were close approximations to simple exponential functions. As the LET ∞ was increased, the RBE did not exceed 1.0, and by 478 keV μm -1 it had fallen to 0.39. Although similar behaviour has been reported for inactivation of proteins and certain viruses by ionizing radiations, so far the response of the S/S variant is unique for mammalian cells. The slope of the survival curve for X-photons ( D 0 :0.27 Gy) is reduced in G 1 to G 1 + 3 h by post-irradiation incubation at hypothermic temperatures and reaches a minimum ( D 0 : 0.51 Gy) at 25 °C. As the LET ∞ was increased, however, the extent of hypothermic recovery was reduced progressively and essentially was eliminated at 478 keV μm -1 . At the cycle position where the peak of radioresistance to X-photons occurs for S/S cells, G 1 + Sh, increases in LET ∞ elicited only small increases in RBE (at 10% survival), until a maximum was reached around 200 keV μm -1 . At 478 keV μm -1 , what little remained of the variation in response through the cell cycle could be attributed to secondary radiations (δ rays) and smaller nuclei produced by fragmentation of the primary ions. Definitions 1. Linear energy transfer (LET ∞ ) is the energy deposited per unit length of track by an ionizing particle and usually is measured in kiloelectron volts per micrometer (in water). 2. Penumbra . Atomic interactions along the track of a heavy ion result in the ejection of electrons with energies sufficient to move beyond the region of dense ionization which constitutes the track core, and so may be considered to form a penumbra of sparsely ionizing radiations around the track core. 3. RBE . The effectiveness of a densely ionizing radiation (heavy ion) compared to a sparsely ionizing radiation, e. g. X- or γ -photons, is measured by the inverse ratio of the doses of each radiation needed to produce a given radiobiological effect, and is known as the relative biological effectiveness (RBE): the usual reference radiation is 250 kVp X-rays. 4. D 0 is a measure of the radiosensitivity of a cell as determined from the (limiting) linear slope of the survival curve, and is the dose in Gray (1 Gy ≡ 1 Joule kg -1 ) required to reduce the survival at a point anywhere in that region of the survival curve to 37% of its value at that point.

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