A sample of DVHs with (gray dotted curves) calculated according to the Lyman NTCP model (a) and the CV population NTCP model (b) for the end-point heart pericarditis. Also shown in each of these subplots are the average of all DVHs with along with the constraint points interpolated from this curve (solid black curve with diamond points). The Emami constraints for the heart are shown for comparison as circles, along with the 5% iso-NTCP envelope that passes near to the Emami points. The DVH point probabilities (curves in the plane) calculated for heart are shown for the Lyman model (c) and the CV population model (d). The average of DVHs with is shown (dark curve in plane) for comparison, along with the 67% confidence limits (dashed curves in plane) that were calculated by means of the DVH point probabilities. Panels (e) and (f) show the most probable DVH curves for the heart, calculated from the DVH point probabilities in (c) and (d). The Lyman model was used for (e), and the Lyman NTCP of the most probable DVH is shown in the upper right corner. For (f), the CV population model results are shown, along with the CV population NTCP for this curve.
Plot of the average DVH for each of six NTCP intervals for the end-point heart pericarditis. Averages were calculated based on the Lyman NTCP model (a) and the CV population model (b). From the lowest volume to the highest volume curves, the intervals are (first solid line), [10%, 20%] (first dotted line), [20%, 30%] (dash-dotted line), [50%, 60%] (dashed line), [70%, 80%] (second solid line), and [90%, 100%] (second dotted line).
A subset of DVHs that have a CV population NTCP of for the end-point lung pneumonitis (gray dashed curves), the average of these DVHs, and the interpolated constraint points (solid curve with black diamonds). Each subplot shows these curves for a different DVH dose scaling: (a) , (b) , (c) , and (d) . In each subplot, the 5% iso-NTCP envelope is shown along with the Emami points for lung pneumonitis. The NTCPs are those of the average DVHs.
Lyman (left) and CV population (right) NTCP probability distributions for the end-point brain necrosis for the given sets of calculated dose-volume constraint points. A total of DVHs were simulated in order to build these distributions, and of those, the ones that passed within a vicinity of were deemed to satisfy the constraints. Shown in each subplot are two additional quantities: the probability that a DVH that satisfies the given constraint(s) will have a NTCP that is greater than 5.5% and the 95% confidence intervals (CIs) for the distributions. In Figs. 4(a) and 4(b), the NTCP distributions for the Emami , constraint point is shown for comparison (black line).
Averaged DVH (dotted line) and dose-volume constraint estimates (diamonds) for the rectum, calculated by means of the reverse mapping method. The Lyman NTCP model with the Burman parameters was used to obtain these constraint points. Shown for comparison are the averaged DVH for nonbleeders from Jackson et al. (Ref. 60) (upper solid curve) and the lower limit of its 67% confidence range (lower solid curve). The Lyman NTCP of the nonbleeder DVH is given in the upper right corner of this plot.
Estimates for the clinical maximum dose range to 16 critical structures (, ) that typically occur during the listed treatments (values based on treatments given at the Cross Cancer Institute). Also shown are values for the maximum dose range ( and ) calculated according to both the Lyman and CV population models. The parameters and are used to scale randomly generated DVHs appropriately to calculate constraint points using the reverse mapping method. The following abbreviations are used: CNS—central nervous system; PTV—planning target volume; H&N—head and neck.
Constraint points interpolated from the average of DVHs with a Lyman NTCP of for 16 organs. For each of the relative volumes shown across the top of the chart, the interpolated dose in grays is given for each organ if this value is nonzero. The far right column in the table shows the fraction of randomly generated DVHs, out of a total of , that have a NTCP of , .
Same as Table II, but calculated using the CV population NTCP model.
This table illustrates the effect of range on calculated constraint points. Dose-volume constraint points were calculated for the lungs with the random DVHs scaled according to ranges of , , , and , using both the Lyman and CV population models.
This table shows three quantities calculated for the end-point brain necrosis for the given sets of constraints. Calculations were done with both the Lyman and CV population NTCP models, and for each constraint volume given, a dose value from either Table II (for the Lyman model analysis) or Table III (for the CV population model analysis) was selected (except for the Emami constraint point, for which the dose was ). The first quantity in this table is , which represents the probability that a DVH with passes within the -vicinity of the chosen constraint(s). The value is the probability that a DVH that satisfies the chosen constraint(s) has a NTCP that is greater than 5.5%. Finally, this table shows the NTCP range in which 95% of the DVHs satisfying the constraint(s) result.
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