NTCP modelling of lung toxicity after SBRT comparing the universal survival curve and the linear quadratic model for fractionation correction

Figures & data

Figure 1. Parameter space of D₀ and

for α and d_T restricted to values given in the figure. The star (*) represent parameters (D₀ = 1 Gy and

= 10) chosen for further modelling. The four points a-d represents different parameter sets of D₀ and

used for a sensitivity test of α and d_T.

Figure 2. Calculated survival curves for the LQ model with α/β = 3, and α equal to 0.206 (black line), and for the SHMT model (grey line). The grey dashed line (EXP) shows the extrapolation of the linear portion of the SHMT target curve. The smooth transition from the LQ- to the linear portion of the SHMT model is at the dose d_T = 5.8 Gy (indicated by the circle). The dose of 2 Gy, to which all DVH data were converted, is marked in the figure.

Figure 3. Dose-volume-histograms (DVHs) of the total lung volume minus GTV in cm³ for the 57 SBRT patients. Six patients with RP2+ are marked with black lines. An enlargement for better visualization is inserted.

Table I. Values of the parameter n from the NTCP modelling.

Fractionation correction type	N	m	D50 (Gy)
USC	0.71*	0.4	30
LQ	0.87	0.4	30
USC	0.63	0.3	30
LQ	0.76	0.3	30
USC	0.91	0.4	20
LQ	1.02	0.4	20
USC	0.82	0.3	20
LQ	0.93	0.3	20

Modelled NTCP = 10.5%. Doses corrected for fractionation with the universal survival curve USC and with the LQ-model (α/β = 3). The values of the parameters m and D₅₀ were fixed to 0.4 and 30 Gy or 20 Gy or 0.3 and 30 Gy or 20 Gy. *To test the sensitivity of the USC parameters D₀ and , NTCP modelling were performed on four sets of parameters from points a-d in Figure 1, resulting in n ranging between 0.55–0.74.

Table II. Summary of published SBRT data. Incidences of RP2+ and estimated EUD.

Reference	No of pts	NTCP values/MLD (Gy)	Incidense of RP2 + (%)	MLD (Gy) (LQ, n = 1.0)	EUD (Gy) (USC, n = 0.71)
Song et al. [23]	17	NTCP = 5%	5.8	10.7	14.6^M
Schefter et al. [24]	25	V15 = 10.6%	0	16.3	19.6
Hoyer et al. [25]	40	13.3 Gy^a	0	8.4	12.0^M
Nyman et al. [27]	45^b	personal communication	0	10.6	15.5^M
Wulf et al. [28]	21	4.5 Gy	3.0	4.5	5.9^M
		6.8 Gy	3.0	6.8	10.5^M
Nagata et al. [29]	40	3.1 Gy^c V20 = 4.5	4.0	3.8	6.2^R
Borst et al. [32]	128		10.9	6.4	9.1^M
Guckenberger et al. [4]	70^b	4.5 Gy	7.0	4.5	5.9^M
		6.8 Gy	7.0	6.8	10.5^M
Baumann et al. [16]	57	17.4 Gy^a	10.5	10.0	15
Yamashita et al. [30]	25	4.3 Gy^c	29.0	8.9	13.8^R
Onishi et al. [31]	35	6.9 Gy^c	9.0	13.3	18.6^R

^aMLD_uncorr physical mean lung dose for ipsilateral lung.

^bRetrospective patient data.

^cMLD_uncorr physical mean lung dose for total lung.

^MMatched clinical data.

^RReconstructed dose plan.

Figure 4. Incidence of RP2+ as a function of equivalent uniform dose (EUD) calculated with n = 0.71. The line shows NTCP calculated with parameters m = 0.30, D₅₀ = 30 Gy. The value of the parameter n was determined from the data point EUD = 15 Gy and incidence of RP2+ = 10.5% (Baumann et al. 2008). As a sensitivity test of n, the incidences 5% (0.05) and 15% (0.15) at 15 Gy, were modelled (dotted line). References in Table II.

Figure 5. Fractional NTCP_fract calculated with DVH-data corrected with USC and LQ (α/β = 3) as a function of cut-off dose for a representative patient. The plot illustrates the cumulative contribution to the NTCP. With the USC correction the low doses have less impact on NTCP compared to what is seen with the LQ correction.

Figure 6. The total uncorrected dose given in three fractions as a function of the dose given in 2 Gy per fraction (EQD2) using different fractionation correction models (LQ, uncorrected and USC). The dose level of 15 Gy × 3, used in the clinical data set is marked in the figure. Note, this refers to lung and not to tumour tissue.

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