Dose-volume histogram analysis for risk factors of radiation-induced rib fracture after hypofractionated proton beam therapy for hepatocellular carcinoma

Figures & data

Figure 1. Time to rib fracture after hypofractionated proton beam therapy [proportion per patient (a) and proportion per irradiated rib (b)]. a) Among 67 patients, 11 (16.4%) developed rib fracture after proton beam therapy. The 5-year cumulative incidence of rib fracture was 22%. b) Among 310 irradiated ribs in all 67 patients, 27 ribs (8.7%) developed fracture, and the 5-year cumulative incidence of rib fracture was 13%.

Figure 2. Mean irradiated rib volume and mean biologically effective dose (BED₃) to irradiated ribs. DVH parameters were all significantly higher in fractured ribs than in non-fractured ribs (p < 0.05).

Figure 3. Receiver operating characteristics and rate of rib fracture at V60. (a) Among DVH parameters, the area under the curve was largest for V60. With receiver operating characteristics analysis at V60, the optimal cut-off point was 4.48 cm³. The sensitivity of this point was 0.89 and the specificity was 0.77. (b) Curves of cumulative rates were significantly different between the irradiated volumes <4.48 cm³ and volumes ≥4.48 cm³ according to the log-rank test (p = 0.000).

Table I. The calculated areas under the curve of receiver operating characteristics curves and optimal cut-off point*.

	Calculated AUC	95% Confidence interval	Optimal cut-off point	The crude fracture rate above/below the cut-off point
V1	0.798	0.730–0.867	12.6 cm^3	21% / 2.0%
V30	0.822	0.762–0.882	9.80 cm^3	25% / 3.0%
V60	0.857	0.791–0.923	4.48 cm^3	26% / 1.4%
V90	0.837	0.763–0.911	3.10 cm^3	28% / 2.2%
V120	0.815	0.728–0.903	1.22 cm^3	26% / 2.6%
V150	0.798	0.701–0.895	0.21 cm^3	26% / 3.0%
V180	0.754	0.640–0.867	0.28 cm^3	35% / 3.8%
V210	0.519	0.401–0.636	0.09 cm^3	100% / 8.4%
Dmax	0.854	0.784–0.925	150 Gy3 (RBE)	25% / 2.7%
D1cm^3	0.854	0.788–0.920	108 Gy3 (RBE)	24% / 2.3%
D2cm^3	0.852	0.790–0.914	96 Gy3 (RBE)	25% / 2.2%
D5cm^3	0.852	0.793–0.911	56 Gy3 (RBE)	28% / 1.8%
D10cm^3	0.830	0.757–0.904	20 Gy3 (RBE)	23% / 2.7%

AUC, area under the curve; D_max, maximum dose for irradiated ribs; D_Xcm³, doses received by irradiated rib volumes of X-cm³; Vx, volume of rib receiving >x Gy₃ (RBE); *The doses Gy₃ (RBE) shown in this table denote biologically effective doses with 3 Gy (BED₃).

Figure 4. Volume-response curve at V60 (a) and dose-response curves at D_max (b) and D_1cm³ (c). Using logistic regression, each diagram (a)–(c) showed as following. The irradiated volume/dose points of each non-fractured or fractured rib were plotted on the lines y = 0 (non-fractured rib) or y = 1 (fractured rib) with circle both. The estimated volume- or dose-response curves within the range the x-values being observed are solid curve, but those exceeding the range are dotted one. The 68% confidence interval of each curve was drawn by dashed curve. The observed data was divided into three bins [according to each 10 cm³ of V60 for diagram (a), each 100 Gy₃ (RBE) of D_max for diagram (b), and each 100 Gy₃ (RBE) of D_1cm³ for diagram (c)], and showed the mean (triangle point) and its standard deviation (SD) (mean ± SD was drawn by horizontal line segment) in each bin, respectively. Vertical line segment at each mean showed the 68% confidence interval for the observed probability calculated with binomial statistics. (a) Volume-response curve of the fracture proportion (p), a function of volume of irradiated rib at V60, was estimated by the equation p = 1/{1 + exp[21 × (23.511 + 0.204 × V60)]}. The volume yielding 50% probability was 17.2 cm³, and gamma 50 (representing the steepness of the curve at the point of 50% probability) was 0.88, respectively. b), c) Dose-response curves of the fracture rate (p), functions of dose of irradiated rib at D_max and D_1cm³, were generated using the regression p = 1/{1 + exp[21 × (25.535 + 0.024 × D_max)]}, and p = 1/{1 + exp[21 × (24.791 + 0.022 × D_1cm³)]}, respectively. The doses that yields 50% probability / gamma 50 based on D_max and D_1cm³ were 231 Gy₃ (RBE) / 1.38 and 218 Gy₃ (RBE) / 1.20, respectively.