title: Application of the continuity equation to a breathing motion model.
abstract: OBJECTIVE
  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 alpha and beta vector fields, respectively. The continuity equation resulted in a prediction that the volume integral of the divergence of the alpha vector field was 1.11 for all patients. The integral of the divergence of the beta vector field was expected to be zero.
  
  
  RESULTS
  For 35 patients, the alpha vector field prediction was 1.06 +/- 0.14, encompassing the expected value. For the beta 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.
authors.affiliation: Washington University School of Medicine, St. Louis, Missouri 63110, USA. low@wustl.edu
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Low
authors.forename: Tianyu
authors.initials: T
authors.lastname: Zhao
authors.forename: Benjamin
authors.initials: B
authors.lastname: White
authors.forename: Deshan
authors.initials: D
authors.lastname: Yang
authors.forename: Sasa
authors.initials: S
authors.lastname: Mutic
authors.forename: Camille E
authors.initials: CE
authors.lastname: Noel
authors.forename: Jeffrey D
authors.initials: JD
authors.lastname: Bradley
authors.forename: Parag J
authors.initials: PJ
authors.lastname: Parikh
authors.forename: Wei
authors.initials: W
authors.lastname: Lu
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008168:Lung / Q000503:physiopathology*; D008175:Lung Neoplasms / Q000503:physiopathology*; D008954:Models, Biological; D015656:Respiratory Mechanics
references.citation: Int J Radiat Oncol Biol Phys. 2005 Nov 1;63(3):921-9
references.pmid: 16140468
references.citation: Med Phys. 2006 Aug;33(8):2964-74
references.pmid: 16964875