A novel analytical approach to the prediction of respiratory diaphragm motion based on external torso volume change.

An analytical approach to predict respiratory diaphragm motion should have advantages over a correlation-based method, which cannot adapt to breathing pattern changes without re-calibration for a changing correlation and/or linear coefficient. To quantitatively calculate the diaphragm motion, a new expandable 'piston' respiratory (EPR) model was proposed and tested using 4DCT torso images of 14 patients. The EPR model allows two orthogonal lung motions (with a few volumetric constraints): (1) the lungs expand (ΔVEXP) with the same anterior height variation as the thoracic surface, and (2) the lungs extend (ΔVEXT) with the same inferior distance as the volumetrically equivalent 'piston' diaphragm. A volume conservation rule (VCR) established previously (Li et al 2009 Phys. Med. Biol. 54 1963–78) was applied to link the external torso volume change (TVC) to internal lung volume change (LVC) via lung air volume change (AVC). As the diaphragm moves inferiorly, the vacant space above the diaphragm inside the rib cage should be filled by lung tissue with a volume equal to ΔVEXT (=LVC–ΔVEXP), while the volume of non-lung tissues in the thoracic cavity should conserve. It was found that ΔVEXP accounted for 3–24% of the LVC in these patients. The volumetric shape of the rib cage, characterized by the variation of cavity volume per slice over the piston motion range, deviated from a hollow cylinder by −1.1% to 6.0%, and correction was made iteratively if the variation is >3%. The predictions based on the LVC and TVC (with a conversion factor) were compared with measured diaphragm displacements (averaged from six pivot points), showing excellent agreements (0.2 ± 0.7 mm and 0.2 ± 1.2 mm, respectively), which are within clinically acceptable tolerance. Assuming motion synchronization between the piston and points of interest along the diaphragm, point motion was estimated but at higher uncertainty (~10% ± 4%). This analytical approach provides a patient-independent technique to calculate the patient-specific diaphragm motion, using the anatomical and respiratory volumetric constraints.