Electron microscopic stereological study of collagen fibrils in bovine articular cartilage: volume and surface densities are best obtained indirectly (from length densities and diameters) using isotropic uniform random sampling

Results obtained by the indirect zonal isotropic uniform random (IUR) estimation were compared with those obtained by the direct point and interception counting methods on vertical (VS) or IUR sections in a stereological study of bovine articular cartilage collagen fibrils at the ultrastructural level. Besides comparisons between the direct and indirect estimations (direct IUR vs indirect IUR estimations) and between different sampling methods (VS vs IUR sampling), simultaneous comparison of the 2 issues took place (direct VS vs indirect IUR estimation). Using the direct VS method, articular cartilage superficial zone collagen volume fraction (V_v 41%) was 67% and fibril surface density (S_v 0.030 nm²/nm³) 15% higher (P<0.05) than values obtained by the indirect IUR method (V_v 25% and S_v 0.026 nm²/nm³). The same was observed when the direct IUR method was used: collagen volume fraction (V_v 40%) was 63% and fibril surface density (S_v 0.032 nm²/nm³) 21% higher (P<0.05) than those obtained by the indirect IUR technique. Similarly, in the deep zone of articular cartilage direct VS and direct IUR methods gave 50 and 55% higher (P<0.05) collagen fibril volume fractions (V_v 43 and 44% vs 29%) and the direct IUR method 25% higher (P<0.05) fibril surface density values (S_v 0.025 vs 0.020 nm²/nm³) than the indirect IUR estimation. On theoretical grounds, scrutiny calculations, as well as earlier reports, it is concluded that the direct VS and direct IUR methods systematically overestimated the V_v and S_v of collagen fibrils. This bias was due to the overprojection which derives from the high section thickness in relation to collagen fibril diameter. On the other hand, factors that during estimation tend to underestimate V_v and S_v, such as profile overlapping and truncation (‘fuzzy’ profiles), seemed to cause less bias. As length density (L_v) and collagen fibril diameter are minimally biased by the high relative section thickness, the indirect IUR method, based on utilisation of these estimates, is here regarded as representing a ‘gold standard’. The sensitivity of these 3 methods was also tested with cartilage from an in vitro loading experiment which caused tissue compression. In the superficial zone of articular cartilage V_v and S_v of collagen fibrils increased (P<0.05). This difference in the stereological estimates was only detected by the indirect IUR estimation but not by the direct VS or direct IUR methods. This indicated that the indirect IUR estimation was more sensitive than the direct VS or direct IUR estimations. On the basis of these observations, the indirect zonal IUR estimation can be regarded as the technique of choice in the electron microscopic stereology of cartilage collagen.