Lumen areas and homothety factor influence airway resistance in COPD

Abstract

The remodelling process of COPD may affect both airway calibre and the homothety factor, which is a constant parameter describing the reduction of airway lumen (h_d: diameter of child/parent bronchus) that might be critical because its reduction would induce a frank increase in airway resistance. Airway dimensions were obtained from CT scan images of smokers with (n = 22) and without COPD (n = 9), and airway resistance from plethysmography. Inspiratory airway resistance correlated to lumen area of the sixth bronchial generation of right lung, while peak expiratory flow correlated to the area of the third right generation (p = 0.0009, R = 0.57). A significant relationship was observed between h_d and resistance (p = 0.036; R² = 0.14). A modelling approach of central airways (5 generations) further described the latter relationship. In conclusion, a constant homothety factor can be described by CT scan analysis, which partially explains inspiratory resistance, as predicted by theoretical arguments. Airway resistance is related to lumen areas of less proximal airways than commonly admitted.

Introduction

The ability to measure airway dimensions is important for clinicians, interventional bronchoscopists and researchers in order to accurately quantify structural abnormalities and track their changes over time or in response to treatment, and emerging techniques have been developed for those goals (Williamson et al., 2009). The structure/function relationships between emerging techniques and conventional tests deserve to be determined (de Jong et al., 2005, Williamson et al., 2009). Accordingly, several studies already have assessed the relationships between forced expiratory flows (especially FEV₁) and airway dimensions obtained from multidetector computed tomography (MDCT) in chronic obstructive pulmonary disease (COPD) patients (de Jong et al., 2005, Nakano et al., 2005, Orlandi et al., 2005, Hasegawa et al., 2006, Achenbach et al., 2008, Matsuoka et al., 2008, Fain et al., 2009, Williamson et al., 2009). From a physiological point of view, forced expiratory flows would not be the best lung function tests to correlate with airway dimensions because flow limiting sections move down along bronchial tree during the forced expiration and the decrease in FEV₁ in COPD patients has further been related to loss of lung recoil and dynamic airway compression due to forced expiration. By contrast, airway resistance (Raw) and calibre are physically related, but the recent ATS/ERS task force on standardisation of lung function testing stated that airflow resistance is more sensitive for detecting narrowing of extrathoracic or large central intrathoracic airways than of more peripheral intrathoracic airways (Pellegrino et al., 2005), based on theoretical arguments. However, we recently found that Raw better correlated to FEF_50% than to FEV₁, suggesting that Raw explores less proximal airways than previously believed (Mahut et al., 2009).

The progression of COPD has been associated with an increase in the volume of tissue in the wall of the small airways (Hogg et al., 2004), the remodelling process, which reduces lumen areas of these airways, increasing the wall area ratio. Nevertheless, the finite airway calibre depends on both magnitude of remodelling and initial size of bronchi. Physiologically, in healthy lung, the progressive reduction of airway lumen after each division can be described by a quantitative parameter called the homothety factor that is the ratio of the diameter of one child bronchus related to the diameter of the parent bronchus (h_d). Based on a purely mathematical argument, it has been demonstrated that the successive airway segments of an ideal tree are homothetic with a constant size ratio equal to ∼0.79 (Mauroy et al., 2004). If h_d decreases then Raw increases. Mauroy et al. (2004) have shown that this physical optimisation is critical in the sense that small variations in the geometry can induce very large variations in Raw. One may hypothesize that the remodelling process could increase the wall area ratio and result in a mild modification of the homothety factor leading to a significant functional consequence. If the homothety concept is relevant, one may expect a low intra-individual variation of h_d among the airway tree, a relationship between h_d and Raw and perhaps, a link between wall area ratio and h_d. To the best of our knowledge the correlation of homothety and Raw has not been tested.

Consequently, the first aim of our study was to assess the relationships between airway geometry and pulmonary function indices (resistance and forced expiratory flows), and the second aim was to determine h_d, and to establish its relationships with Raw and wall area ratio (proof-of-concept study). For these two objectives, we used MDCT scan images acquired in smokers with and without COPD together with a physical model to further reinforce our main results.