A new stereological principle for test lines in three-dimensional space

A new principle is presented to generate isotropic uniform random (IUR) test lines hitting a geometric structure in three-dimensional space (3D). The principle therefore concerns the estimation of surface area, volume, membrane thickness, etc., of arbitrary structures with piecewise smooth boundary. The principle states that a point-sampled test line on an isotropic plane through a fixed point in 3D is effectively an invariant test line in 3D. Particular attention is devoted to the stereology of particles, where an alternative to the surfactor method is obtained to estimate surface area. An interesting case arises when the particle is convex. The methods are illustrated with synthetic examples.     

Edge detection,three-dimensional cell boundary reconstruction and volume and surface area estimation from differential interference contrast images

Three-dimensional (3-D) cell morphology is important for the understanding of cell function and can by quantified in terms of volume and surface area. Differential interference contrast (DIC, or Nomarski) imaging can enable cell edges to be clearly visualized in unstained tissue due to the slight difference in refractive index between aqueous media and cytoplasm. DIC is affected in only one direction - the direction of the optical shear. A 1-D edge detector was used in that direction with a scale length equal to that of an in-focus edge to highlight cell boundaries. By comparison with the signal from the edge detector on an out-of-focus slice, the in-focus slices could be segmented and, after noise suppression, cell outlines obtained. A voxel paradigm was used to calculate cell volume and differential geometry was used for surface area estimation. We applied this approach to obtain 3-D dimensional information by optical sectioning of motile Amoeba proteus.     

Comments on the shortcomings of predicting the precision of Cavalieri volume estimates based upon assumed measurement functions

It is well known that the estimation of an object's volume by means of serial cross-sections, the so-called Cavalieri method, yields an unbiased estimate. But by itself it provides no means by which to estimate how precise this estimate is unless the shape of the volume is fully known beforehand. This knowledge can only be partially determined from the serial section information that is collected. Methods have been developed that claim to surmount this difficulty by using the serial section data to create a mathematical model of the volume's shape properties. The model then is used to estimate (predict) the precision of the volume estimate (its CE) from the single set of data available. Unfortunately, the theory underlying the model is flawed and so the model itself amounts to no more than an unsubstantiated guess about the shape of the volume. Therefore, the precision of the volume estimates that one obtains from the method is only as good as the model and this cannot be ascertained from the single set of acquired data. In this letter I explain the inadequacies of the modelling method. I suggest that it be used only with caution, if at all. Instead I suggest two alternative ways to predict the CE, one that is based upon a rule-of-thumb approach to the object's shape, and another that is based upon spectral analysis of the measurement function and that is easy to implement with available computer software.     

Stereological estimation of the total volume of MR visible brain lesions in patients with multiple sclerosis

Point counting represents a convenient and efficient technique for estimating the area of transects through multiple sclerosis (MS) lesions on magnetic resonance (MR) images obtained for sections through the brain. When sectioning has been performed according to the Cavalieri method, unbiased estimates of the total volume of MR-visible MS plaques can be obtained with a precision of 3–5% in 5–10 min.     

The smooth fractionator

A modification of the general fractionator sampling technique called the smooth fractionator is presented. It may be used in almost every situation in which sampling is performed from distinct items that are uniquely defined, often they are physically separated items or clusters like pieces, blocks, slabs, sections, etc. To each item is associated a ‘guesstimate’ or an associated variable with a more‐or‐less close – and possibly biased ? relationship to the content of the item. The smooth fractionator is systematic sampling among the items arranged according to the guesstimates in a unique, symmetric sequence with one peak and minimal jumps. The smooth fractionator is both very simple to implement and so efficient that it should probably always be used unless the natural sequence of the sampling items is equally smooth. So far, there is no theory for the prediction of the efficiency of smooth fractionator designs in general, and their properties are therefore illustrated with a range of real and simulated examples. At the cost of a slightly more elaborate sampling scheme, it is, however, always possible to obtain an unbiased estimate of the real precision and of some of the variance components. The only real practical problem for always obtaining a high precision with the smooth fractionator is specimen inhomogeneity, but that is detectable at almost no extra cost. With careful designs and for sample sizes of about 10, the sampling variation for the primary, smooth fractionator sampling step may in practice often be small enough to be ignored.     

A general variance predictor for Cavalieri slices

A general variance predictor is presented for a Cavalieri design with slices of an arbitrary thickness t ≥ 0. So far, prediction formulae have been available either for measurement functions with smoothness constant q = 0, 1, … , and t ≥ 0, or for fractional q ∈ [0, 1] with t = 0. Because the possibility of using a fractional q adds flexibility to the variance prediction, we have extended the latter for any q ∈ [0, 1] and t ≥ 0. Empirical checks with previously published human brain data suggest an improved performance of the new prediction formula with respect to the hitherto available ones.     

PREFERENTIAL SITE SATURATION FOR NUCLEATION AND GROWTH OF α-PHASE AT EARLY STAGE OF AUSTENITE DECOMPOSITION IN LOW CARBON STEEL BEARING BORON

借助经典体视学方法和“扩展组织”概念,定量研究了低碳硼钢620℃过冷奥氏体等温分解早期显微组织的演变路径。结果表明,母相晶界网络仍是低碳硼钢中α相形核长大的择优位置集合,择优顺序为晶粒棱(含隅)、晶界界面.棱集和隅集的位置饱和总是早于面集。钢中有效硼量对趋于饱和的路径和晶界面集的饱和迟早有显著影响。     

Exploring thermal spray gray alumina coating pore network architecture by combining stereological protocols and impedance electrochemical spectroscopy

Complex multiscale pore network architecture characterized by multimodal pore size distribution and connectivity develops during the manufacture of ceramic thermal spray coatings from intra- and interlamellar cracks generated when each lamella spreads and solidifies to globular pores resulting from lamella stacking defects. This network significantly affects the coating properties and their in-service behaviors. De Hoff stereological analysis permits quantification of the three-dimensional (3D) distribution of spheroids (i.e., pores) from the determination of their two-dimensional (2D) distribution estimated by image analysis when analyzing the coating structure from a polished plane. Electrochemical impedance spectroscopy electrochemically examines a material surface by frequency variable current and potential and analyzes the complex impedance. When a coating covers the material surface, the electrolyte percolates through the more or less connected pore network to locally passivate the substrate. The resistive and capacitive characteristics of the equivalent electrical circuit will depend upon the connected pore network architecture. Both protocols were implemented to quantify thermal spray coating structures. Al₂O₃-13TiO₂ coatings were atmospherically plasma sprayed using several sets of power parameters, are current intensity, plasma gas total flow rate, and plasma gas composition in order to determine their effects on pore network architecture. Particle characteristics upon impact, especially their related dimensionless numbers, such as Reynolds, Weber, and Sommerfeld criteria, were also determined. Analyses permitted identification of (a) the major effects of power parameters upon pore architecture and (b) the related formation mechanisms. This article was originally published inBuilding on 100 Years of Success, Proceedings of the 2006 International Thermal Spray Conference (Seattle, WA), May 15–18, 2006, B.R. Marple, M.M. Hyland, Y.-Ch. Lau, R.S. Lima, and J. Voyer, Ed., ASM International, Materials Park, OH, 2006.     

斜投影显微图像分析法测量片状颗粒厚度的研究

与传统正投影显微图像分析方法不同,本文应用斜投影法,通过变换观测颗粒群的角度,依据获得的光学显微镜下颗粒群的信息,推导出了颗粒群厚度的计算公式,并讨论了厚度分辨能力与倾斜角、放大倍数之间的关系,同时应用实例证明了该方法的可行性。     

Estimation of individual feature surface area with the vertical spatial grid

The area of an individual bounded surface (e.g. the boundary of a properly sampled cell) can be estimated from an isotropic uniform random stack of parallel sections, or of non-invasive planar scans, using the well-known spatial grid. A standing problem was to estimate the area of an individual bounded surface with an arbitrary degree of accuracy from a vertical (i.e. not isotropic) stack of sections or scans. A new tool to do this, called the ‘vertical spatial grid’, is presented.