Estimation of the three-dimensional wall thickness of completed remodeling sites in iliac trabecular bone

The wall thickness of completed remodeling sites in trabecular bone was estimated in 25 normal individuals and 5 patients with arthrosis of the knee, using 7 micron sections of undecalcified iliac crest bone. A systematic sampling procedure which gives a surface referent estimate of the thickness was applied. The efficiency of the sampling design was optimized by means of a cost-variance analysis. The proposed method of sampling which eliminates a common bias in bone histomorphometry is recommended for determinations of wall thickness, osteoid thickness, lamellar thickness, and distance between fluorochrome markers in trabecular bone. The intraindividual distributions of three-dimensional wall thickness were reconstructed from the measurements of apparent width by an unfolding procedure based on the geometric probability density function pertaining to randomly sectioned plates. Distributions of true wall thickness for the young normal individuals were unimodal and resembled normal distributions. The three-dimensional mean wall thickness was 61.4 +/- 4.4 micron (+/- SD). It was demonstrated that the conventionally applied stereological transformation, which calculates the three-dimensional mean wall thickness from the mean apparent width by multiplying the latter by pi/4, underestimates the three-dimensional mean wall thickness. An improved transformation is illustrated and is recommended for estimating three-dimensional mean thickness of plates from two-dimensional measurements in trabecular bone.