Homothety ratio of airway diameters and site of airway resistance in healthy and COPD subjects

- The homothety ratio, constant over generations, is the diameter of child/parent bronchus.
- A decrease in the homothety ratio explains the shift in airway resistance in COPD.
- A formula of resistance using tracheal dimensions and homothety ratio is provided.

Our objective was to evaluate whether a decrease in the homothety ratio (h: diameter of child/parent bronchus, constant over generations) explains the shift in airway resistance toward periphery in chronic obstructive pulmonary disease (COPD). Using a validated computational model of fluid motion, we determined that reduced values of h (<0.76) were associated with a shift in resistance toward periphery. The calculated luminal diameters of terminal bronchioles using normal h (0.80-0.85) or reduced h (0.70-0.75) fitted well with measured micro-CT values obtained by McDonough et al. (N. Engl. J. Med., 2011; 365:1567-75) in control and COPD patients, respectively. A semi-analytic formula of resistance using tracheal dimensions and h was developed, and using experimental data (tracheal area and h from patients [Bokov et al., Respir. Physiol. Neurobiol., 2010; 173:1-10]), we verified the agreement between measured and calculated resistance (r = 0.42). In conclusion, the remodeling process of COPD may reduce h and explain the shift in resistance toward lung periphery.