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.

Coordinated Rhythms Of Digestion Absorption And Excretion In Mytilus-Edulis (Bivalvia Mollusca)

Sequential alternation of extracellular digestion in the stomach and intracellular digestion in the diverticula appears widespread among bivalves. The present study documents some physiological consequences of such processes in Mytilus edulis L. collected during 1981 from Whitsand Bay, Cornwall, England. Pronounced temporal fluctuations in faecal deposition are described that relate, in terms of amplitude and period, to both sinusoidal rhythmicity established for ammonia excretion and changes in the morphology of digestive tubules. Although at least partially synchronised among replicate groups of mussels, these cycles bore no consistent relationship with exogenous influences. Hourly fluctuation in the net absorption efficiency for nitrogen, as evidenced by the mean percentage ±2 SE, measured over 24 h sampling periods, was considerable (16.0±53.7, 49.3±10.9 and 52.8±6.6 for mussels acclimated in March, June and October, respectively). This variation in absorption derived from an inverse relationship between the percentage nitrogen within faeces and the rate of faecal egestion. Accordingly, peaks of faecal deposition presumably represented the pulsed remnants of intracellular digestion. Co-ordinated rhythms of digestion, absorption and excretion were thus evident in M. edulis. These processes displayed seasonally dependent periodicities of approximately 8, 3 and 4 h in March, June and October, respectively. It was concluded that, at least for M. edulis, this previously unquantified rhythmicity of physiological processes warrants careful consideration during assays commonly undertaken in the complication of nutrient and energy budgets.

Use Of Micro-Stereology And Quantitative Cyto-Chemistry To Determine The Effects Of Crude Oil-Derived Aromatic-Hydrocarbons On Lysosomal Structure And Function In A Marine Bivalve Mollusk Mytilus-Edulis

The marine bivalve mollusc,Mytilus edulis (blue mussel), is a noted accumulator of many environmental pollutants and is increasingly used for the chemical and biological assessment of environmental impact. The toxic effects of crude oil-derived aromatic hydrocarbons (30 μg/l total hydrocarbons) on the lysosomal-vacuolar system of the digestive cells have been investigated in cryostat sections of hexane-frozen digestive glands. Exposure to aromatic hydrocarbons reduced the cytochemically determined latency of lysosomal β-N-acetylhexosaminidase; lysosomal volume density and surface density increased while the numerical density decreased. Experimental exposure resulted in the formation of very large lysosomes which are believed to be largely autophagic in function and these results indicate a significant structural and functional disturbance of digestive cell lysosomes in response to hydrocarbons.

Some Practical Considerations In The Measurement Of Pollution Effects On Bivalve Mollusks And Some Possible Ecological Consequences

A consideration of some physiological (rates of oxygen consumption, the scope for growth) and cellular (the cytochemical latency of a lysosomal enzyme) processes in bivalve molluscs suggests that animal size and seasonal changes related to the gametogenic cycle are important sources of natural variability. Correcting for size using regression techniques, and limiting measurements to one part of the gametogenic cycle, reduces observed natural variability considerably. Differences between populations are then still apparent, but the results of laboratory experiments with hydrocarbons from crude oil suggest that it should be possible to detect sub-lethal effects due to pollution (the ‘signal’) in the presence of the remaining natural variability (the ‘noise’). Statistical considerations, taken together with results from current studies on Mytilus edulis and Scobicularia plana, indicate that sample sizes of 10–15 individuals should suffice for the detection of possible pollution effects. The physiological effects to be expected in the presence of sub-lethal levels of polluting hydrocarbons are on a scaie that can cause significant ecological damage to a population through a reduction in fecundity and the residual reproductive value of the individuals.

Effects Of Oil On Digestive Cells In Mussels - Quantitative Alterations In Cellular And Lysosomal Structure

Structural changes were observed in the digestive tubule epithelial cells of Mytilus edulis following long-term exposure to the water accommodated fraction (WAF) of North Sea crude oil (30 μg · l−1 total oil derived aromatic hydrocarbons). The changes observed involved a reduction in the height of the digestive cells beyond that demonstrated in a normal feeding cycle. In addition there was a loss of the normal synchrony of the digestive cells to a point where nearly all the tubules exhibited an appearance similar to that which is usually termed ‘reconstituting’. These alterations were quantified using an image analysis technique and the mean height of the digestive cells used as an index of digestive function or state. Long-term exposure also induced a radical alteration of the structure of secondary lysosomes within the digestive cells, resulting in the formation of large lysosomes, believed to be autolysosomes. Stereological analyses showed that these lysosomes are reduced in numbers and greatly increased in volume in comparison with controls. There is a concomitant increase in surface area of lysosomes per unit volume of digestive cell compared with control conditions. These alterations are indicative of fundamental changes in secondary lysosomal function involving an autophagic response to oil derived hydrocarbons. which would contribute to the reduction of digestive cell cytoplasm. These cellular alterations are discussed in terms of their use as indices of cell injury, in response to oil.

Statistical Techniques In Stereology

Stereology typically concerns estimation of properties of a geometric structure from plane section information. This paperprovides a brief review of some statistical aspects of this rapidly developing field, with some reference to applications in the earth sciences. After an introductory discussion of the scope of stereology, section 2 briefly mentions results applicable when no assumptions can be made about the stochastic nature of the sampled matrix, statistical considerations then arising solelyfrom the ‘randomness’ of the plane section. The next two sections postulate embedded particles of specific shapes, the particular case of spheres being discussed in some detail. References are made to results for ‘thin slices’ and other prob-ing mechanisms. Randomly located convex particles, of otherwise arbitrary shape, are discussed in section 5 and the review concludes with a specific application of stereological ideas to some data on neolithic mining.