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Incorporating Patient Random Irregular Respiratory Motion Effect Into Radiotherapy Dose Calculation

S Zhou

S Zhou*, D Zheng , S Wang , Q Fan , X Wang , C Enke , University of Nebraska Medical Center, Omaha, NE


SU-I-GPD-T-379 (Sunday, July 30, 2017) 3:00 PM - 6:00 PM Room: Exhibit Hall

Purpose: To create a mathematical model that enables non-gated 4D radiotherapy dose calculation in the presence of random irregular respiratory motion.

Methods: In this study, we have considered those patients whose irregularity breathings are primarily caused by randomness in their respiratory phases. Two approximations are made to facilitate the study: 1) For dose calculation purpose the patient's actual state during radiotherapy delivery can be indexed back to the patient's 4D CT image set through its Instantaneous Respiratory Phase (IRP); 2) The unwrapped IRP consists of an initial phase at the start of radiotherapy delivery (φ₀), a periodic breathing term (ωt with ω and t being the patient 4DCT breathing frequency and treatment delivery elapse time respectively), and a stochastic Brownian motion portion with volatility σ. Then the instantaneous dose rate to a given anatomical point inside the patient is determined by the IRP and the external radiotherapy delivery process. Both expected value and variance of the point radiation dose from a non-gated delivery are derived via statistical ensemble average over an evenly distributed φ₀ and all feasible subsequent IRP configurations. Fourier series is used in our analysis to simplify the mathematical derivations.

Results: We have obtained mathematical formulas for both the expected value and the variance of radiation dose to a non-gated radiotherapy patient with irregular breathing. The variance of radiation dose is influenced by patient's irregular respiratory motion, while the expected value remains the same nevertheless. The volatility σ of a patient’s irregular respiratory motion can elevate or reduce the variance in the delivered dose due to the randomness in the initial respiratory phase.

Conclusion: We have developed a novel model for estimating the effect of patient's random-phase induced irregular breathing on radiation dose from a non-gated radiotherapy. This effect, in general, is very complex and warrants further investigations.

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