Statistics for Spatial Data.

RACTITIONERS OF BONE HISTOMORPHOMETRY communicate P with each other in a variety of arcane languages, which in general are unintelligible to those outside the field. Many in the bone and mineral scientific community would like to keep abreast of the contributions of histology to their subject, but are dismayed by the semantic barriers they must overcome. The need for standardization has been recognized for many years,(') during which there has been much talk but no action. To meet the needs of ASBMR members, Dr. B.L. Riggs (President, 19851986) asked the senior author to convene a committee of the Society to develop a unified system of termnology, suitable for adoption by the Journal of Bone and Mineral Research as part of its Instructions to Authors. The committee includes members from Europe and Canada as well as the U.S., and represents most existing systems of nomenclature. A circular letter seeking suggestions and information on current usage was sent to several hundred persons, with names drawn from the Society membership roster and lists of attendees at various recent conferences, to which approximately 40 replies were obtained. These confirmed the magnitude of the semantic problem (for some measurements as many as nine different terms were in use) and suggested a range of solutions likely to be generally acceptable. In formulating the new system. the committee kept in mind certain agreed general principles. First, the primary reason for change was to help other scientists understand bone histomorphometry, not to help bone histomorphometrists undcntand each other. Second. names should be self-explanatory and dcscriptive, without implicit assumptions. Third. symbols should consist mainly of abbreviations that included the first letter of each word in the same order as in the name. without subscripts or superscripts. Fourth. each symbol component should have one and only one meaning, and so eliminate ambiguity. Fifth, primary measurements should be clearly distinguished from derived indices. Finally, the chosen system should be sufficiently flexible to apply to all surfaces and all types of bone, and to accommodate any new primary measurement or derived index. The recommended system shares common elements with. but also differs substantially from. all those in current usc. was tested in practice for several months before the final forniat was chosen, and is as complex and conceptually difficult ;I\\ the field with which it deals. For those within the field we hope that increased readership of their papers will be adequate conipensation for the inconvcnicncc of learning a new systcm. For those outside the field, mastering the new system will be hard work, but if we are able to secure its acceptance by all journals with an interest in bone and mineral metabolism, the effort will only have to be expended once rather than. as at present. rcpeated many times. To this end we give the reasons for our decisions in the areas of controversy and, as well as definitions, provide methods for calculation of derived indices and

Bone histomorphometry: Standardization of nomenclature, symbols, and units: Report of the asbmr histomorphometry nomenclature committee

The superior efficiency of systematic sampling at all levels in stereological studies is emphasized and various commonly used ways of implementing it are briefly described. Summarizing recent theoretical and experimental studies a set of very simple estimators of efficiency are presented and illustrated with a variety of biological examples. In particular, a nomogram for predicting the necessary number of points when performing point counting is provided. The very efficient and simple unbiased estimator of the volume of an arbitrary object based on Cavalieri's principle is dealt with in some detail. The efficiency of the systematic fractionating of an object is also illustrated.

The efficiency of systematic sampling in stereology and its prediction

Use of high-resolution micro-computed tomography (microCT) imaging to assess trabecular and cortical bone morphology has grown immensely. There are several commercially available microCT systems, each with different approaches to image acquisition, evaluation, and reporting of outcomes. This lack of consistency makes it difficult to interpret reported results and to compare findings across different studies. This article addresses this critical need for standardized terminology and consistent reporting of parameters related to image acquisition and analysis, and key outcome assessments, particularly with respect to ex vivo analysis of rodent specimens. Thus the guidelines herein provide recommendations regarding (1) standardized terminology and units, (2) information to be included in describing the methods for a given experiment, and (3) a minimal set of outcome variables that should be reported. Whereas the specific research objective will determine the experimental design, these guidelines are intended to ensure accurate and consistent reporting of microCT-derived bone morphometry and density measurements. In particular, the methods section for papers that present microCT-based outcomes must include details of the following scan aspects: (1) image acquisition, including the scanning medium, X-ray tube potential, and voxel size, as well as clear descriptions of the size and location of the volume of interest and the method used to delineate trabecular and cortical bone regions, and (2) image processing, including the algorithms used for image filtration and the approach used for image segmentation. Morphometric analyses should be based on 3D algorithms that do not rely on assumptions about the underlying structure whenever possible. When reporting microCT results, the minimal set of variables that should be used to describe trabecular bone morphometry includes bone volume fraction and trabecular number, thickness, and separation. The minimal set of variables that should be used to describe cortical bone morphometry includes total cross-sectional area, cortical bone area, cortical bone area fraction, and cortical thickness. Other variables also may be appropriate depending on the research question and technical quality of the scan. Standard nomenclature, outlined in this article, should be followed for reporting of results.

https://asbmr.onlinelibrary.wiley.com/doi/pdf/10.1002/jbmr.141

Guidelines for assessment of bone microstructure in rodents using micro–computed tomography

A stereological method for obtaining estimates of the total number of neurons in five major subdivisions of the rat hippocampus is described. The new method, the optical fractionator, combines two recent developments in stereology: a three-dimensional probe for counting neuronal nuclei, the optical disector, and a systematic uniform sampling scheme, the fractionator. The optical disector results in unbiased estimates of neuron number, i.e., estimates that are free of assumptions about neuron size and shape, are unaffected by lost caps and over-projection, and approach the true number of neurons in an unlimited manner as the number of samples is increased. The fractionator involves sampling a known fraction of a structural component. In the case of neuron number, a zero dimensional quantity, it provides estimates that are unaffected by shrinkage before, during, and after processing of the tissue. Because the fractionator involves systematic sampling, it also results in highly efficient estimates. Typically only 100–200 neurons must be counted in an animal to obtain a precision that is compatible with experimental studies. The methodology is compared with those used in earlier works involving estimates of neuron number in the rat hippocampus and a number of new stereological methods that have particular relevance to the quantitative study of the structure of the nervous system are briefly described in an appendix.

Unbiased stereological estimation of the total number of neurons in the subdivisions of the rat hippocampus using the optical fractionator

This paper deals with isolated, countable items, often termed particles, in three-dimensional space. Its substance is the unbiased stereological estimation of the number, height, surface and volume of such particles without any assumptions about their shape. The full range of estimators is described, some of them for the first time, some in an improved form, several in more than one version, and all of them under the single, absolute requirement that one can in fact identify what one is quantifying on sections. In terms of the minimal number of sections for the analysis, the estimators may be classified as follows: On a single section it is possible to estimate vV, the mean volume of particles in the volume-weighted or 'sieving'-distribution. On two parallel sections, separated by a known distance, estimators exist of particle number and of all mean sizes (height, surface and volume) in the ordinary number distribution, as well as of SDN(v), the standard deviation in the number distribution of particle volumes. If the containing space is relatively transparent the sections may be two optical sections within one thick physical section. On a stack of parallel sections, at least as high as the largest particle, and separated by known distances, one can get twelve mean sizes and twelve distributions of individual sizes: all combinations of three sizes: height, surface and volume in four different types of distributions: number, height, surface and volume. Fulfilling the sampling requirements of the above two estimation principles it has been shown very recently that by combining them one may even estimate mean sizes and number of arbitrary particles in a stack of sections with constant but unknown separation. Finally, a unique, unbiased estimator of the total number of items in a specimen is described for the use of which one need not measure the distance between sections, nor their thickness, nor the volume of the specimen, nor assume anything about shrinkage/swelling, sectioning compression or lost caps. It is the fractionator.

Stereology of arbitrary particles. A review of unbiased number and size estimators and the presentation of some new ones, in memory of William R. Thompson

In the present paper, we summarize and further develop recent reseach in the estimation of the variance of sterelogical estimators based on systematic sampling. In particular, it is emphasized that the relevant estimation procedure depends on the sampling density. The validity of the variance estimation is examined in a collection of data sets, obtained by systematic sampling. Practical recommendations are also provided in a separate section.

The efficiency of systematic sampling in stereology--reconsidered.

This paper is a review of the stereological problems related to the unbiased estimation of particle number and size when tissue deformation is present. The deformation may occur during the histological processing of the tissue. It is especially noted that the widely used optical disector may be biased by dimensional changes in the z-axis, i.e. the direction perpendicular to the section plane. This is often the case when frozen sections or vibratome sections are used for the stereological measurements. The present paper introduces new estimators to be used in optical fractionator and optical disector designs; the first is, as usual, the simplest and most robust. Finally, it is stated that when tissue deformation only occurs in the z-direction, unbiased estimation of particle size with several estimators is possible.

H. J. G. Gundersen

Papers

The efficiency of systematic sampling in stereology and its prediction

Stereology of arbitrary particles. A review of unbiased number and size estimators and the presentation of some new ones, in memory of William R. Thompson

The efficiency of systematic sampling in stereology--reconsidered.

Tissue shrinkage and unbiased stereological estimation of particle number and size.

The impact of recent stereological advances on quantitative studies of the nervous system.