Stereological Estimation of Tubular Length from Thin Vertical Sections

In this study tubular structures are represented by stem villous arteries of the human placenta. The architecture of the vascular tree in the human placenta makes it appropriate to use vertical histological sections. Describing tubules, estimates of total length and diameter are informative. The aim of the study was to derive a new stereological estimator of the total length of circular tubules observed in thin vertical sections. Design: Dual perfusion fixed human placentas. Systematic, uniformly random sampling of vertical sections. Five-μm-sections were stained by haematoxylin and eosin (H&E) and the vertical axis was identified in all sections. A test system with cycloid test lines was used. Since tubular surface area is proportional to length and diameter, S ∝ πdL, surface-weightening is equivalent to diameter×lengthweightening. As each diameter (extra weight) is known, one may eliminate the diameter-weightening by computing the harmonic mean diameter, which is thus the correct, length-weighted mean tubular diameter, h L S d d . = Surface area is estimated in the ordinary way from vertical sections, and with unbiased and robust estimates of S anddL, respectively, total length may be estimated h S S L . d π = Conclusion: A new stereological estimator of total length of a circular tubular structure observed in thin vertical sections is presented.