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.