# Estimating Airway Resistance from Forced Expiration in Spirometry
## 4 Discussion  
In this study, we described the dynamics of forced expiration in spirometry by using a model of a deflating balloon. With this model, we proposed a methodology to estimate a parameter \(\zeta\) representative of airway resistance in the lungs. We proved our hypothesis by demonstrating that \(\zeta\) was significantly (\(p\) < 0.0001) greater in COPD than in healthy smokers. It increased significantly with the severity of airflow limitation in COPD and it significantly correlated with Raw and sGaw, which are known indices of airway resistance. \(\zeta\) also showed significant correlations with DLCO and air-trapping (RV/TLC), and with CT densitometric indices of emphysema in COPD patients. Moreover, simulation studies showed that an increase in \(\zeta\) resulted in decreased airflows, and therefore a reduced FEV1 and FVC, which further validates our claim that \(\zeta\) quantifies airway resistance. The parameter \(\zeta\) is not dependent on expiratory effort, but rather, it stems from the narrowing of the small airways (<2 mm diameter). Narrower airways result in increased airway resistance that is reflected by an elevated \(\zeta\). In COPD, narrowing of the small airways during forced expiration is a result of a multitude of factors such as loss of elasticity in lung parenchyma leading to dynamic. Airway collapse [9]; and airway abnormalities such as cellular inflammation [28], smooth muscle contraction [29], mucosal thickening [30], and fibrotic retraction [31]. Finally, a higher value of \(\zeta\) also indicates the severity of airflow limitation, which itself is a functional consequence of a complex interaction between airway abnormalities and destruction of parenchyma elasticity. Our method is the first to estimate airway resistance from forced expiration in spirometry. The use of a second-order linear differential equation in our method further validates the existence of second-order transfer functions to describe the dynamics of forced expiration [32]. Nevertheless, the application of second-order differential equations to describe respiratory mechanics is not a new concept [33]. In fact, the estimation of airway resistance during mechanical ventilation [34], body-plethysmography, and the interrupter technique is made possible by a simplification of these equations under tidal breathing conditions [7]. However, our method has an important distinction in that it does not require a measurement of alveolar pressure. Since spirometry does not measure alveolar pressure, we make a reasonable assumption on the variation of the latter (Equation (6)) that nonetheless, provides a good estimate of airway resistance. We believe that this is an important development in the field of respiratory mechanics because until now, the consensus has been that measuring alveolar pressure is indispensable for the calculation of airway resistance [7; 35; 36]. The clinical usefulness of \(\zeta\) can be illustrated by the fact that it quantifies an important physiological phenomenon using spirometry alone, which is a simple but widely used pulmonary function test. In fact, our results show that \(\zeta\) is superior to its counterparts, Raw and sGaw, in their association with CT densitometry, which is considered as the most direct method for assessing the severity of emphysema [37]. It is also better correlated with DLCO, which is an index for alveolar destruction and loss of capillary bed in COPD [38]. Compared to the interrupter technique, which estimates airway resistance using measurements obtained at a single instant of time under tidal breathing [7], we achieve a more robust value of airway resistance as we consider the entire manoeuver of forced expiration. This motivates the application of our methodology, especially, in primary care where spirometers are more abundantly available than bulky and expensive equipment such as a body-box or FOT machine.