Application of the continuity equation to a breathing motion model

Daniel A. Low, Tianyu Zhao, Benjamin White, Deshan Yang, Sasa Mutic, Camille E. Noel, Jeffrey D. Bradley, Parag J. Parikh, Wei Lu

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Purpose: To quantitatively test a breathing motion model using the continuity equation and clinical data. Methods: The continuity equation was applied to a lung tissue and lung tumor free breathing motion model to quantitatively test the model performance. The model used tidal volume and airflow as the independent variables and the ratio of motion to tidal volume and motion to airflow were defined as α→ and β→ vector fields, respectively. The continuity equation resulted in a prediction that the volume integral of the divergence of the α→ vector field was 1.11 for all patients. The integral of the divergence of the β→ vector field was expected to be zero. Results: For 35 patients, the α→ vector field prediction was 1.06±0.14, encompassing the expected value. For the β→ vector field prediction, the average value was 0.02±0.03. Conclusions: These results provide quantitative evidence that the breathing motion model yields accurate predictions of breathing dynamics.

Original languageEnglish
Pages (from-to)1360-1364
Number of pages5
JournalMedical physics
Issue number3
StatePublished - 2010


  • Breathing motion model
  • Free breathing
  • Radiation therapy


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