Unbiased Linear Property Estimation For Spheres From Sections Exhibiting Overprojection And Truncation

In the biological sciences, stereological techniques are frequently used to infer changes in structural parameters (volume fraction, for example) between samples from different populations or subject to differing treatment regimes. Non-homogeneity of these parameters is virtually guaranteed, both between experimental animals and within the organ under consideration. A two-stage strategy is then desirable, the first stage involving unbiased estimation of the required parameter, separately for each experimental unit, the latter being defined as a subset of the organ for which homogeneity can reasonably be assumed. In the second stage, these point estimates are used as data inputs to a hierarchical analysis of variance, to distinguish treatment effects from variability between animals, for example. Techniques are therefore required for unbiased estimation of parameters from potentially small numbers of sample profiles. This paper derives unbiased estimates of linear properties in one special case—the sampling of spherical particles by transmission microscopy, when the section thickness is not negligible and the resulting circular profiles are subject to lower truncation. The derivation uses the general integral equation formulation of Nicholson (1970); the resulting formulae are simplified, algebraically, and their efficient computation discussed. Bias arising from variability in slice thickness is shown to be negligible in typical cases. The strategy is illustrated for data examining the effects, on the secondary lysosomes in the digestive cells, of exposure of the common mussel to hydrocarbons. Prolonged exposure, at 30 μg 1−1 total oil-derived hydrocarbons, is seen to increase the average volume of a lysosome, and the volume fraction that lysosomes occupy, but to reduce their number.

Particulate optical scattering coefficients along an Atlantic Meridional Transect

The particulate optical backscattering coefficient (bbp) is a fundamental optical property that allows monitoring of marine suspended particles both in situ and from space. Backscattering measurements in the open ocean are still scarce, however, especially in oligotrophic regions. Consequently, uncertainties remain in bbp parameterizations as well as in satellite estimates of bbp. In an effort to reduce these uncertainties, we present and analyze a dataset collected in surface waters during the 19th Atlantic Meridional Transect. Results show that the relationship between particulate beam-attenuation coefficient (cp) and chlorophyll-a concentration was consistent with published bio-optical models. In contrast, the particulate backscattering per unit of chlorophyll-a and per unit of cp were higher than in previous studies employing the same sampling methodology. These anomalies could be due to a bias smaller than the current uncertainties in bbp. If that was the case, then the AMT19 dataset would confirm that bbp:cp is remarkably constant over the surface open ocean. A second-order decoupling between bbp and cp was, however, evident in the spectral slopes of these coefficients, as well as during diel cycles. Overall, these results emphasize the current difficulties in obtaining accurate bbp measurements in the oligotrophic ocean and suggest that, to first order, bbp and cp are coupled in the surface open ocean, but they are also affected by other geographical and temporal variations.