Estimation of internal organ motion-induced variance in radiation dose in non-gated radiotherapy

Sumin Zhou, Xiaofeng Zhu, Mutian Zhang, Dandan Zheng, Yu Lei, Sicong Li, Nathan Bennion, Vivek Verma, Weining Zhen, Charles Arthur Enke

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


In the delivery of non-gated radiotherapy (RT), owing to intra-fraction organ motion, a certain degree of RT dose uncertainty is present. Herein, we propose a novel mathematical algorithm to estimate the mean and variance of RT dose that is delivered without gating. These parameters are specific to individual internal organ motion, dependent on individual treatment plans, and relevant to the RT delivery process. This algorithm uses images from a patient's 4D simulation study to model the actual patient internal organ motion during RT delivery. All necessary dose rate calculations are performed in fixed patient internal organ motion states. The analytical and deterministic formulae of mean and variance in dose from non-gated RT were derived directly via statistical averaging of the calculated dose rate over possible random internal organ motion initial phases, and did not require constructing relevant histograms. All results are expressed in dose rate Fourier transform coefficients for computational efficiency. Exact solutions are provided to simplified, yet still clinically relevant, cases. Results from a volumetric-modulated arc therapy (VMAT) patient case are also presented. The results obtained from our mathematical algorithm can aid clinical decisions by providing information regarding both mean and variance of radiation dose to non-gated patients prior to RT delivery.

Original languageEnglish (US)
Pages (from-to)8157-8179
Number of pages23
JournalPhysics in medicine and biology
Issue number23
StatePublished - Nov 2 2016


  • 4D CT
  • Fourier transformation
  • dose variance
  • interplay effect
  • intra-fraction organ motion
  • non-gated radiotherapy

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging


Dive into the research topics of 'Estimation of internal organ motion-induced variance in radiation dose in non-gated radiotherapy'. Together they form a unique fingerprint.

Cite this