Total number and mean size of alveoli in mammalian lung estimated using fractionator sampling and unbiased estimates of the Euler characteristic of alveolar openings

Estimation of alveolar number in the lung has traditionally been done by assuming a geometric shape and counting alveolar profiles in single, independent sections. In this study, we used the unbiased disector principle to estimate the Euler characteristic (and thereby the number) of alveolar openings in rat lungs and rhesus monkey lung lobes and to obtain robust estimates of average alveolar volume. The estimator of total alveolar number was based on systematic, uniformly random sampling using the fractionator sampling design. The number of alveoli in the rat lung ranged from 17.3 (.) 10(6) to 24.6 (.) 10(6), with a mean of 20.1 (.) 10(6). The average number of alveoli in the two left lung lobes in the monkey ranged from 48.8 (.) 10(6) to 67.1 (.) 10(6) with a mean of 57.7 (.) 10(6). The coefficient of error due to stereological sampling was of the order of 0.06 in both rats and monkeys and the biological variation (coefficient of variance between individuals) was 0.15 in rat and 0.13 in monkey (left lobe, only). Between subdivisions (left/right in rat and cranial/caudal in monkey) there was an increase in variation, most markedly in the rat. With age (2-13 years) the alveolar volume increased 3-fold (as did parenchymal volume) in monkeys, but the alveolar number was unchanged. This study illustrates that use of the Euler characteristic and fractionator sampling is a robust and efficient, unbiased principle for the estimation of total alveolar number in the lung or in well-defined parts of it.