# Estimating Airway Resistance from Forced Expiration in Spirometry
## 1 Introduction  
Airflow limitation or obstruction is the characteristic feature of obstructive lung diseases such as chronic obstructive pulmonary disease (COPD) and asthma. In COPD, it arises out of the dual effects of permanent parenchymal destruction (emphysema) and small airway dysfunction due to prolonged exposure of the lungs to cigarette smoke [1]. While in asthma, it arises due to narrowing of airways from excessive inflammation and mucus production as a result of bronchial hyper- responsiveness to allergens [2]. In clinical practice, spirometry is the gold standard to measure airflow limitation [3]. During a spirometry test, a subject performs a forced expiration using a spirometer that measures the flow and volume of exhaled air. Several indices of diagnostic importance, such as forced expiratoryvolume in 1 second (FEV1), forced vital capacity (FVC), and Tiffeneau's index (FEV1/FVC) are obtained from spirometry [4]. Two widely accepted criteria for the presence of airflow limitation are a FEV1/FVC ratio below a fixed cutoff of 0.7 [3] or below the lower limits of normal (LLN, defined as the 5 th percentile of a normally distributed set of values of FEV1/FVC for a population of non-smoking, normal individuals) [5]. The plot of expiratory flow against volume measurements is termed as maximal expiratory flow-volume curve (MEFVC), and it is also known to be associated with different pathological states [6]. Although spirometry is used to indicate airflow limitation, the latter itself is an end-result of many factors. One of these factors is an increased airway resistance, and therefore, measuring it may directly provide additional insight into the occurrence of airflow limitation. Traditionally, body-plethysmography has been used to determine airway resistance (Raw) as a ratio of driving alveolar pressure to airflow. Other methods of measuring airway resistance include forced oscillation technique (FOT), which estimates respiratory system resistance (RRS) and reactance (XRS), and the interrupter technique which measures interrupter resistance (Rint) at a single moment of tidal breathing [7]. All of the above-mentioned techniques measure airway resistance during tidal breathing. Nevertheless, factors affecting airway resistance during a forced expiration such as loss of lung elasticity [8] and dynamic airway collapse cannot be underestimated [9], and often compose the main reason for airflow limitation and clinical symptoms [10]. Measures of airway resistance obtained during forced expiration will provide better insight into these mechanisms, which are potentially amendable for intervention. Currently, there exists no method in the literature to calculate dynamic airway resistance from the forced expiratory manoeuvre. The consensus is that spirometry cannot be used to estimate airway resistance since it does not measure alveolar pressure [7; 11; 12]. In the past, researchers have proposed parameters reflective of airway resistance [13] that only describes the shape of MEFVC, without any physiological basis. In this study, we describe the dynamics of forced expiration using a model of a deflating balloon, and thereby propose a method to estimate a parameter representative of airway resistance from spirometry. We hypothesized that this resistance parameter would be significantly higher in COPD compared to healthy smokers, increase with the severity of airflow limitation in COPD patients [14] and show a significant correlation with Raw and its flow standardized inverse, specific airway conductance (sGaw). We investigated the relationship of this parameter with other pulmonary function tests (PFT) parameters such as diffusion capacity for carbon monoxide (DLCO) [15] and the ratio of residual volume (RV) to total lung capacity (TLC), an index that quantifies air-trapping in COPD subjects [16]. We also associated this parameter with computed tomography (CT)-based densitometric quantification of emphysema, a condition of severe airflow limitation in COPD when lung parenchyma is permanently destroyed [17].