A simple model illustrating the respiratory system's time constant concept.

This notion is true for a perfect elastic body. Because the lungs do not present perfect elastic behavior, the relationship among V, compliance, and P is not linear along all the vital capacity range, as showed by Eq. 1. When the respiratory system is subjected to P, time is needed until V occurs, and the time necessary to inflate 63% of its volume is called the time constant ( ) (3). It describes the monoexponencial behavior of the time profile of the simplest model of respiratory system: the single-compartment linear model, which incorporates, in series, two lumped elements– one single compartment of elastance served by a pathway of resistance (2). The one-compartment linear model cannot describe the variations of resistance and elastance associated with the frequency of ventilation, tidal volume, and mean lung volume. These complex mechanical behaviors of the lung reflect many physical properties of the system, including viscoelastic properties, “series” and “parallel” inhomogeneities in the distribution of ventilation, nonlinearities, and plastic behavior. Therefore, to better describe and quantify the respiratory system mechanical profile, more complex models are needed, and, when the respiratory system exhibits parallel inequalities of resistance and compliance, the overall mechanical behavior of the lung cannot be described by a single value. One way to calculate is to multiply the resistance (R) by the compliance of the respiratory system, according to following equation: