A model for the relative biological effectiveness of protons: The tissue specific parameter α/β of photons is a predictor for the sensitivity to LET changes

Figures & data

Table I. The cell lines used in this study with the published α and β values given in the order of increasing α/β of the reference radiation.

cell line	LET [keV/μm]	α [Gy^−1]	β [Gy^−2]	Reference
V79-379A	240 kV x-rays	0.13 ± 0.022	0.048 ± 0.003	[12]
	10.1	0.32 ± 0.058	0.039 ± 0.011
	17.8	0.45 ± 0.035	0.028 ± 0.006
	27.6	0.74 ± 0.025	0.011 ± 0.004
V79-753B	200 kV x-rays	0.129 ± 0.012	0.046 ± 0.003	[10]
	7.7	0.289 ± 0.023	0.024 ± 0.006
	11.0	0.372 ± 0.032	0.036 ± 0.009
	20.0	0.469 ± 0.029	0.043 ± 0.009
DLD1	^60Co γ-rays	0.37 ± 0.09	0.12 ± 0.02	[17]
	7.7	0.47 ± 0.05	-
SQ20B	^60Co γ-rays	0.13 ± 0.02	0.017 ± 0.002	[13]
	7.7	0.15 ± 0.05	0.011 ± 0.012
	19.8	0.23 ± 0.04	0.004 ± 0.007
	30.0	0.57 ± 0.05	-
C1-1	^60Co γ-rays	0.23 ± 0.042	0.030 ± 0.008	[16]
	7.7	0.194 ± 0.072	0.023 ± 0.021
	27.6	0.539 ± 0.027	-
C3H10T1/2	^60Co γ-rays	0.24 ± 0.06	0.016 ± 0.013	[11]
	11.0	0.47 ± 0.06	0.019 ± 0.014
	19.7	0.43 ± 0.06	0.038 ± 0.013
	28.8	0.55 ± 0.12	0.053 ± 0.031
SCC25	^60Co γ-rays	0.57 ± 0.05	0.031 ± 0.012	[13]
	7.7	0.41 ± 0.11	0.092 ± 0.036
	19.7	0.87 ± 0.05	-
	29.5	0.81 ± 0.03	-
HCT116	^60Co γ-rays	1.39 ± 0.06	0.02 ± 0.01	[17]
	7.7	0.32 ± 0.08	0.06 ± 0.03
H184B5 F5-1M/10	^60Co γ-rays	0.52 ± 0.02	-	[13]
	9.1	0.50 ± 0.03	-
	21.4	0.49 ± 0.02	-
HF19	^137Cs γ-rays	0.64 ± 0.02	-	[13]
	7.7	0.55 ± 0.01	-
	19.5	0.54 ± 0.02	-
	29.0	0.52 ± 0.01	-

Figure 1. Experimentally obtained α/α_phot values as a function of LET. Panel A with (α/β)_phot 2.7−3.1: V79-379A cells [12], V79-753B cells [10], and DLD1 cells [17]. Panel B with (α/β)_phot 7.7−7.7: SQ20B [13], and C1-1 cells [16]. Panel C with (α/β)_phot 15Ȣ18: C3H10T1/2 [11], and SCC25 [13]. Panel D with (α/β)_phot ≥ 70: HCT116 [17], M/10 cells and HF19 cells [13]. The error bars show the 95% CI. The dashed lines are obtained with Equation 2 where the highest and lowest (α/β)_phot in each panel is used.

Figure 2. k is the slope from the linear relation between α/α_phot and LET (see Equation 1) and is here plotted as a function of the α/β ratio of the reference radiation using Equation A6 in Appendix with the parameter q = 0.434. The shaded areas under the curve show the (α/β)_phot ranges used in the different panels of Figure 1.

Table II. The resulting slope k of Equation A6 used in Figure 1.

(α/β)phot [Gy]	k [keV/μm]^−1
2.7–3.1	0.14–0.16
7.7–7.7	0.057–0.057
15–18	0.024–0.029
70–∞	0–0.0060

Figure 3. RBE as a function of LET at 2 Gy photon dose for cell lines with (α/β)_phot ratio < 4 (circles) and (α/β)_phot ratio ≥ 70 (squares). The experimental data is shown with filled symbols and the calculated data from Equation 3 has open symbols.

Figure 4. Analytically obtained RBE values (see Equation 3) vs. experimental RBE values for all cell lines used in this study. Pearson's correlation coefficient is 0.89. The RBE is obtained at 2 Gy photon dose.

Figure 5. RBE as a function of α/β of the reference radiation using Equation 3. Three doses, 0.5, 2 and 5 Gy, and two LETs, 1 and 10 keV/µm, are compared.

Folkard M, Prise KM, Vojnovic B, Newman HC, Roper MJ, Michael BD. Inactivation of V79 cells by low-energy protons, deuterons and helium-3 ions. Int J Radiat Biol 1996;69: 729–38.

 PubMed Web of Science ®Google Scholar

Belli M, Cera F, Cherubini R, Dalla Vecchia M, Haque AM, Ianzini F, . RBE-LET relationships for cell inactivation and mutation induced by low energy protons in V79 cells: Further results at the LNL facility. Int J Radiat Biol 1998;74:501–9.

 PubMed Web of Science ®Google Scholar

Baggio L, Cavinato M, Cherubini R, Conzato M, Cucinotta F, Favaretto S, . Relative biological effectiveness of light ions in human tumoural cell lines: Role of protein p53. Radiat Prot Dosimetry 2002;99:211–4.

 PubMed Web of Science ®Google Scholar

Belli M, Bettega D, Calzolari P, Cera F, Cherubini R, Dalla Vecchia M, . Inactivation of human normal and tumour cells irradiated with low energy protons. Int J Radiat Biol 2000;76:831–9.

 PubMed Web of Science ®Google Scholar

Sgura A, Antoccia A, Cherubini R, Dalla Vecchia M, Tiveron P, Degrassi F, . Micronuclei, CREST-positive micronuclei and cell inactivation induced in Chinese hamster cells by radiation with different quality. Int J Radiat Biol 2000;76:367–74.

 PubMed Web of Science ®Google Scholar

Bettega D, Calzolari P, Marchesini R, Noris Chiorda GL, Piazzolla A, Tallone L, . Inactivation of C3H10T1/2 cells by low energy protons and deuterons. Int J Radiat Biol 1998;73:303–9.

 PubMed Web of Science ®Google Scholar