Time-constant histograms from the forced expired volume signal

The forced expired volume signal was analyzed using a parallel compartment model in which each compartment emptied exponentially. With this model the forced expired volume signal was represented by a histogram showing the fraction of the vital capacity as a functional of compartmental time constants. We developed an algorithm to compute this histogram from the volume signal. The algorithm used the least-squares criterion function with both smoothness and nonnegativity constraints. In a stimulation study reasonable histograms were obtained even in the presence of realistic random error. Three dependent forced expired volume signals from 16 subjects were analyzed, and the histograms were reproducible. Most histograms were bimodal with fast time constants of 0.12-0.55 s and slow time constants of 1.3-2.7 s. In all normal subjects and patients with restrictive disease more than 75% of the vital capacity was in the fast time-constant mode. Subjects with obstructive disease had more than 40% of the vital capacity in the slow time-constant mode.