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A Novel Approach to Computing Expected Value and Variance of Point Dose From Non-Gated Radiotherapy Delivery

S Zhou

S Zhou*, X Zhu , M Zhang , D Zheng , Q Zhang , Y Lei , S Li , J Driewer , S Wang , C Enke , University of Nebraska Medical Center, Omaha, NE


SU-E-T-56 (Sunday, July 12, 2015) 3:00 PM - 6:00 PM Room: Exhibit Hall


Randomness in patient internal organ motion phase at the beginning of non-gated radiotherapy delivery may introduce uncertainty to dose received by the patient. Concerns of this dose deviation from the planned one has motivated many researchers to study this phenomenon although unified theoretical framework for computing it is still missing. This study was conducted to develop such framework for analyzing the effect.


Two reasonable assumptions were made: a) patient internal organ motion is stationary and periodic; b) no special arrangement is made to start a non-gated radiotherapy delivery at any specific phase of patient internal organ motion. A statistical ensemble was formed consisting of patient’s non-gated radiotherapy deliveries at all equally possible initial organ motion phases. To characterize the patient received dose, statistical ensemble average method is employed to derive formulae for two variables: expected value and variance of dose received by a patient internal point from a non-gated radiotherapy delivery. Fourier Series was utilized to facilitate our analysis.


According to our formulae, the two variables can be computed from non-gated radiotherapy generated dose rate time sequences at the point’s corresponding locations on fixed phase 3D CT images sampled evenly in time over one patient internal organ motion period. The expected value of point dose is simply the average of the doses to the point’s corresponding locations on the fixed phase CT images. The variance can be determined by time integration in terms of Fourier Series coefficients of the dose rate time sequences on the same fixed phase 3D CT images.


Given a non-gated radiotherapy delivery plan and patient’s 4D CT study, our novel approach can predict the expected value and variance of patient radiation dose. We expect it to play a significant role in determining both quality and robustness of patient non-gated radiotherapy plan.

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