On the effect of intrafraction motion in a single fraction step-shoot IMRT

Purpose: The authors studied the respiratory motion effect in a single step-shoot intensity modulated radiotherapy (IMRT) to assess the basic properties of the uncertainty in the delivered dose due to the unknown starting phase of the motion. Methods: Using computer simulations, the motion-averaged dose for open beams with various field sizes was calculated for two one-dimensional trajectories with different motion amplitudes at 20 equally spaced starting phases. The properties of the standard deviation (SD) of delivered dose were analyzed. The dependence of SD on the field size, motion amplitude, and delivery time was investigated and experimentally validated. To study effect of number of small monitor unit (MU) segments on the dose uncertainty, the authors generated 1000 pairs of multisegment beams such that each pair consists of two beams with the same total MU and different segment MU. The SD at the central axis point was compared for each pair. Results: The authors proved that the direct time-dependent dose accumulation can be calculated using a convolution formula for a single fraction step-shoot IMRT treatment. Single segment simulation showed that the maximum dose uncertainty occurred symmetrically at the beam penumbra for a sinusoidal motion. For other sinusoidal motions (sin2n n > 1), the maximum dose uncertainty occurred at asymmetrical locations and may be beyond the penumbra region. The SD of relative dose periodically varied with delivery time with decreasing envelope for both motion trajectories. The SD of absolute dose was a periodic function of the delivery time for a given field size and motion amplitude and was proved to be true for any periodic motion. The SD reduced to zero when the delivery time was an integer multiple of the motion period. Analytical function σ A = 3 β sin 2 π / T δ t − 4 / 3 sin 4 π / T δ t + 2 / 3 sin 6 π / T δ t was found to fit the delivery time dependence of the SD for motions studied in this paper and was verified with experimental data and an irregular motion. The dose uncertainty increased with motion amplitude and decreased slowly with field size. Simulations for 1000 beam pairs with multiple segments demonstrated that the probability that more small MU segments did not introduce larger dose uncertainty at central axis point for three cutoff small MUs (2.5/5/10) was 55.8%/51.9%/43.4% and 54.6%/54.4%/45%, respectively, for a sin and a sin4 motion in a conventional treatment. These probabilities became 53.6%/50.9%/47.2% and 51.0%/50.2%/47.8%, respectively, for a hypofractionated treatment. Conclusions: The periodic dependence of the dose uncertainty on the delivery time can be modeled with an analytic function, and the functional form is independent of motion trajectories in this paper. The relation of dose uncertainty between different dose schemes can be obtained using this function. The dose uncertainty at central axis point for a beam with more small MU segments may not be greater than a beam with less small MU segments. By varying the dose rate of each segment such that the delivery time is close to the integer multiples of the motion period, the interplay effect can be reduced.