Estimating the Chord Length of Alveoli

Two methods to  estimate the ‘mean linear intercept length’ (chord length, Lm) of alveoli in lung are examined (Knudsen, et al., 2010); an indirect (Knudsen, et al., 2010, Methods, 1-a) and a direct method (Knudsen, et al., 2010, Methods, 1-b). In the direct method, the chord length is measured (a probe like Point Sampled Intercepts could be used for this), but in the indirect method, based on earlier work (Chalkley, et al., 1949) points (P) are marked on the alveoli air-space to estimate volume and intersections (I) are marked on the alveolar walls to estimate surface. If it can’t be shown that the alveoli themselves are arranged isotropically in space, then the sections must be isotropic. The sections are thin, and since larger cells have a better chance of being selected, the sampling is volume weighted. The chord length is estimated based on the number of points and intersections:


Lm = 2 * k * d * P/I                     (Knudsen, et al., 2010, equation 2)


Lm is the mean linear intercept length of the alveoli

k = length of line used to probe

d = number of lines per point

P = number of points marked in the alveoli air-spaces

I = number of intersections marked between the probe-lines and the surface of the alveoli

In the paper a dashed-line test system is used, but there is no reason why a semi-circle test system with points can’t be used, as in the Merz probe.


Chalkley, H.W., J. Cornfield and H. Park (1949) A Method for Estimating Volume-Surface Ratios. Science, 110, 295-297.

Knudsen, L., Weibel, E.R., Gundersen, H.J.G., Weinstein, F.V., and M. Ochs (2010) Assessment of Air Space Size Characteristics by Intercept (Chord) Measurement: an Accurate and Efficient Stereological Approach. J. of Applied Physiology, 108, 412 – 421.