Stereological estimation using vertical sections in a complex tissue

A method designed for stereological estimation in a very complex tissue using vertical sections is presented. In some tissues, the random rotation of the tissue for vertical sections may obscure recognition of the anatomical structures of interest. The present method overcomes this problem by generating sections with both a particular orientation, 'mapping sections', and ordinary random vertical sections usable for the required observations. A map describing the positions of the vertical sections is produced to make the complex reference space recognizable. The method is illustrated by estimating the number and size of neurones in the dorsal raphe nucleus of the human brainstem with its dense packing of roughly 100 nuclei within a volume less than 50 cm³.     

Design-based estimation of surface area in thick tissue sections of arbitrary orientation using virtual cycloids

Surface area is a first‐order stereological parameter with important biological applications, particularly at the intersection of biological phases. To deal with the inherent anisotropy of biological surfaces, state‐of‐the‐art design‐based methods require tissue rotation around at least one axis prior to sectioning. This paper describes the use of virtual cycloids for surface area estimation of objects and regions in thick, transparent tissue sections cut at any arbitrary (convenient) orientation. Based on the vertical section approach of Baddeley et al., the present approach specifies the vertical axis as the direction of sectioning (i.e. the direction perpendicular to the tissue section), and applies computer‐generated cycloids (virtual cycloids) with their minor axis parallel to the vertical axis. The number of surface‐cycloid intersections counted on focal planes scanned through the z‐axis is proportional to the surface area of interest in the tissue, with no further assumptions about size, shape or orientation. Optimal efficiency at each x–y location can be achieved by three virtual cycloids orientated with their major axes (which are parallel to the observation planes) mutually at an angle of 120°. The major practical advantage of the present approach is that estimates of total surface area (S) and surface density (S_V) can be obtained in tissue sections cut at any convenient orientation through the reference space.     

Estimation of surface area from vertical sections

‘Vertical’ sections are plane sections longitudinal to a fixed (but arbitrary) axial direction. Examples are sections of a cylinder parallel to the central axis; and sections of a flat slab normal to the plane of the slab. Vertical sections of any object can be generated by placing the object on a table and taking sections perpendicular to the plane of the table. The standard methods of stereology assume isotropic random sections, and are not applicable to this kind of biased sampling. However, by using specially designed test systems, one can obtain an unbiased estimate of surface area. General principles of stereology for vertical sections are outlined. No assumptions are necessary about the shape or orientation distribution of the structure. Vertical section stereology is valid on the same terms as standard stereological methods for isotropic random sections. The range of structural quantities that can be estimated from vertical sections includes V_v, N_v, S_v and the volume-weighted mean particle volume v?_v, but not L_v. There is complete freedom to choose the vertical axis direction, which makes the sampling procedure simple and ‘natural’. Practical sampling procedures for implementation of the ideas are described, and illustrated by examples.     

Stereological estimation of mean linear intercept length using the vertical sections and trisector methods

A method for estimating the mean linear intercept length of anisotropic microstructures using vertical sections is presented. A test system of cycloids and points is overlaid on the vertical sections, and the mean linear intercept length is estimated from a simple counting procedure — no length measurements are required. The vertical direction is either arbitrarily chosen or chosen perpendicular to most of the surface boundaries of the objects of interest. A design with the latter choice of the vertical direction and three vertical sections — a trisector — will optimize the precision of the estimate from only three vertical sections. The method was applied to two metallic structures, but it may also be used in a biomedical context.     

Estimating the surface area of nonconvex particles from central planar sections

In this paper, we present a new surface area estimator in local stereology. This new estimator is called the ‘Morse‐type surface area estimator’ and is obtained using a two‐stage sampling procedure. First a plane section through a fixed reference point of a three‐dimensional structure is taken. In this section plane, a modification of the area tangent count method is used. The Morse‐type estimator generalizes Cruz‐Orive's pivotal estimator for convex objects to nonconvex objects. The advantages of the Morse‐type estimator over existing local surface area estimators are illustrated in a simulation study. The Morse‐type estimator is well suited for computer‐assisted confocal microscopy and we demonstrate its practicability in a biological application: the surface area estimation of the nuclei of giant‐cell glioblastoma from microscopy images. We also present an interactive software that allows the user to efficiently obtain the estimator.     

On semiautomatic estimation of surface area

In this paper, we propose a semiautomatic procedure for estimation of particle surface area. It uses automatic segmentation of the boundaries of the particle sections and applies different estimators depending on whether the segmentation was judged by a supervising expert to be satisfactory. If the segmentation is correct the estimate is computed automatically, otherwise the expert performs the necessary measurements manually. In case of convex particles we suggest to base the semiautomatic estimation on the so‐called flower estimator, a new local stereological estimator of particle surface area. For convex particles, the estimator is equal to four times the area of the support set (flower set) of the particle transect. We study the statistical properties of the flower estimator and compare its performance to that of two discretizations of the flower estimator, namely the pivotal estimator and the surfactor. For ellipsoidal particles, it is shown that the flower estimator is equal to the pivotal estimator based on support function measurements along four perpendicular rays. This result makes the pivotal estimator a powerful approximation to the flower estimator. In a simulation study of prolate and oblate ellipsoidal particles, the surfactor also performs well for particles which are not extremely elongated. In particular, the surfactor is not very much affected by the singularity in the surfactor formula or by possible inaccuracies in the necessary angle measurements. We also assess the performance of the semiautomatic procedure in a study of somatostatin positive inhibitory interneurons from mice hippocampi. Only 35% of the cells needed to be analysed manually and an important decrease in workload was obtained by using the semiautomatic approach.     

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.     

Gross morphological and surface ultrastructural investigation on the gills of the European barracuda Sphyraena sphyraena

The present work examined 10 gill systems of European barracuda grossly and by scanning electron microscopy (SEM). Grossly, there were four pairs of the gill arches. The convex border of the gill arch carried the gills filaments, but there were abundance of spines near to its concave border and the gill rakers were absent. Laterally near to the convex border of the gill arch, SEM observations revealed that the first gill arch carried small elliptical, oval, cuboidal, and triangular groups of two shapes of spines; spearhead-like spines and canine-like spines, but the other three gill arches carried larger groups of the same shaped spines with the appearance of waterfalls. Medially near to the convex border of the first gill arch, the canine-like spines were observed only in the form of vertical rectangular groups that adhered in some areas. Laterally near to the concave border, the two shapes of spines were present in the form of longitudinal groups separated by spaces at the first gill arch, but these spaces were absent in the other three gill arches. Medially near to the concave border of the first gill arch, the two shapes of spines were presented in oval groups, while the other three gill arches were covered entirely by cuboidal groups of the two shapes of spines. The absence of the gill rakers in conjunction with an abundance of spines helps the European barracuda to control the food particles from escaping to the gill filaments to prevent its suffocation.     

Some remarks on the accuracy of surface area estimation using the spatial grid

A set of three line grids in three orthogonal directions is called a spatial grid. This spatial grid can be used for surface area estimation by counting the number of intersection points of a surface with the grid lines. If direction and localization of the spatial grid are suitably randomized, the expectation of this number is proportional to the surface area of interest. The method was especially developed for cases where the surface to be measured is embedded in a medium, which is the usual case in microscopical applications, and where a stack of serial optical sections of the surface is available. The paper presents an improvement of an earlier version of the counting rule for intersection points. Furthermore, if the direction of sectioning is not uniform random, a bias results. This bias is calculated for a disc as a perfectly anisotropic object. A generalization of the estimator is considered by introducing a weighted mean instead of the usual arithmetic mean. The variance due to the randomized direction is investigated depending on the weights, and the minimum of this variance is derived. The relationship between the covariogram and the variance of the surface area estimated with the spatial grid is considered.     

Sampling theory and automated simulations for vertical sections,applied to human brain

In recent years, there have been substantial developments in both magnetic resonance imaging techniques and automatic image analysis software. The purpose of this paper is to develop stereological image sampling theory (i.e. unbiased sampling rules) that can be used by image analysts for estimating geometric quantities such as surface area and volume, and to illustrate its implementation. The methods will ideally be applied automatically on segmented, properly sampled 2D images – although convenient manual application is always an option – and they are of wide applicability in many disciplines. In particular, the vertical sections design to estimate surface area is described in detail and applied to estimate the area of the pial surface and of the boundary between cortex and underlying white matter (i.e. subcortical surface area). For completeness, cortical volume and mean cortical thickness are also estimated. The aforementioned surfaces were triangulated in 3D with the aid of FreeSurfer software, which provided accurate surface area measures that served as gold standards. Furthermore, a software was developed to produce digitized trace curves of the triangulated target surfaces automatically from virtual sections. From such traces, a new method (called the ‘lambda method’) is presented to estimate surface area automatically. In addition, with the new software, intersections could be counted automatically between the relevant surface traces and a cycloid test grid for the classical design. This capability, together with the aforementioned gold standard, enabled us to thoroughly check the performance and the variability of the different estimators by Monte Carlo simulations for studying the human brain. In particular, new methods are offered to split the total error variance into the orientations, sectioning and cycloid components. The latter prediction was hitherto unavailable – one is proposed here and checked by way of simulations on a given set of digitized vertical sections with automatically superimposed cycloid grids of three different sizes. Concrete and detailed recommendations are given to implement the methods.     

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.     

搜索区域和目标尺度自适应的无人艇海面目标跟踪

海面目标跟踪任务是实现水面无人艇自主化航行、智能化作业的重要基础。相比于普通场景的目标跟踪,海面目标跟踪需要面对目标抖动剧烈及目标尺度变化大等问题。针对海面目标在图像画面中抖动剧烈的问题,本文提出了搜索区域自适应算法,该方法通过对海面场景的分割完成了海天线位置的提取,然后通过海天线运动模型自适应地确定了每帧图像中目标搜索的区域;针对跟踪过程中海面目标尺度变化较大的问题,本文通过分割搜索区域的方法实现了目标尺度变化的自适应跟踪。基于相关滤波跟踪框架并结合上述两种改进策略,在真实的海面目标图像测试序列中,本文算法相比传统的相关滤波算法在跟踪精度上至少提升了26%,有效地解决了目标抖动剧烈和尺度自适应问题,提高了海面目标跟踪任务的精度。     

Improved capacity to evaluate changes in intestinal mucosal surface area using mathematical modeling

Quantification of intestinal mucosal growth typically relies on morphometric parameters, commonly villus height, as a surrogate for presumed changes in mucosal surface area (MSA). We hypothesized that using mathematical modeling based on multiple unique measurements would improve discrimination of the effects of interventions on MSA compared to standard measures. To determine the ability of mathematical modeling to resolve differences in MSA, a mouse model with enhanced serotonin (5HT) signaling known to stimulate mucosal growth was used. 5‐HT signaling is potentiated by targeting the serotonin reuptake transporter (SERT) molecule. Selective serotonin reuptake inhibitor‐treated wild‐type (WT‐SSRI), SERT‐knockout (SERTKO), and wild‐type C57Bl/6 (WT) mice were used. Distal ileal sections were H&E‐stained. Villus height (VH), width (VW), crypt width (CW), and bowel diameter were used to calculate surface area enlargement factor (SEF) and MSA. VH alone for SERTKO and SSRI was significantly increased compared to WT, without a difference between SERTKO and WT‐SSRI. VW and CW were significantly decreased for both SERTKO and WT‐SSRI compared to WT, and VW for WT‐SSRI was also decreased compared to SERTKO. These changes increased SEF and MSA for SERTKO and WT‐SSRI compared to WT. Additionally, SEF and MSA were significantly increased for WT‐SSRI compared to SERTKO. Mathematical modeling provides a valuable tool for differentiating changes in intestinal MSA. This more comprehensive assessment of surface area does not appear to correlate linearly with standard morphometric measures and represents a more comprehensive method for discriminating between therapies aimed at increasing functional intestinal mucosa.     

A numerical-analytical approach to determining the real contact area of rough surface contact

ABSTRACT

The objective of this study is to improve the accuracy of the real contact area calculated by the semi-analytical method (SAM). Two types of surface pairs are investigated: an analytically generated sinusoidal wavy surface against a rigid flat, and a pair of real rough surfaces. The results suggest that the real contact area calculated by the SAM is extremely sensitive to the resolution of input, i.e. the grid size. The SAM results of the real contact areas show poor convergence, especially in the case of the real rough surfaces. The main reason for this difference is the ‘over-covering’ effect when SAM calculates the real contact area. An exponential extrapolation technique is proposed to predict the real contact area values when further refinement of the grid resolution is unfeasible.     

Visualizing surface area and volume of lumens in three dimensions using images from histological sections

Visualizing the interior (lumen) of a tubular structure within tissue can provide a unique perspective on anatomical organization of the tissue. Portal tracts of the liver contain several vessels and ducts in various patterns of intertwining branches and are an example of such spaces. An inexpensive method, using light microscopy and a sample of conventionally stained canine livers, was used to colorize and allow visualization of the lumens of vessels within the portal tract in three dimensions. When the colour of the background was digitally cleared and the lumen filled with a solid colour, it was possible to measure areas and volumes of the portal vein, arteries, bile ducts and lymphatics. Significant differences between vessels and ducts across lobes and gender in control samples are discussed. Differences were also found between control and mixed breed dogs and between controls and a dog that died of accidental traumatic haemorrhage. These differences are discussed in relation to visualizing lumens using images generated from a light microscope. Vessels in plants such as xylem and continuously formed spaces resulting from ice formation are other examples where this technique could be applied.     

Research of oil film thickness model and surface quality in cold rolling copper foil

Rolled copper foil is widely used in high frequency and speed transmission of fine line printed circuit board, because of its high strength, good toughness and high density. In this paper, a theoretical model for copper foil rolling in mixed lubrication regime was developed on the basis of the average volume flow model and asperity flattening model. A more accurate relation for the variation of the lubricant viscosity with pressure and temperature was considered. The cold rolled copper foil experiment was carried on with different viscosity of rolling oil and pass reduction. The effects of rolling oil viscosity and pass reduction on lubricant pressure, contact area ratio and film thickness ratio were studied. The calculation results agree well with the measured data from copper foil rolling experiment. For obtaining higher surface quality, the rolling oil viscosity is about 10 mm²/s, and the pass reduction is about 30%. Copyright © 2013 John Wiley & Sons, Ltd.     

Advantages and pitfalls of using free‐hand sections of frozen needles for three‐dimensional analysis of mesophyll by stereology and confocal microscopy

The anatomical structure of mesophyll tissue in the leaf is tightly connected with many physiological processes in plants. One of the most important mesophyll parameters related to photosynthesis is the internal leaf surface area, i.e. the surface area of mesophyll cell walls exposed to intercellular spaces. An efficient design‐based stereological method can be applied for estimation of this parameter, using software‐randomized virtual fakir test probes in stacks of optical sections acquired by a confocal microscope within thick physical free‐hand sections (i.e. acquired using a hand microtome), as we have shown in the case of fresh Norway spruce needles recently. However, for wider practical use in plant ecophysiology, a suitable form of sample storage and other possible technical constraints of this methodology need to be checked. We tested the effect of freezing conifer needles on their anatomical structure as well as the effect of possible deformations due to the cutting of unembedded material by a hand microtome, which can result in distortions of cutting surfaces. In the present study we found a higher proportion of intercellular spaces in mesophyll in regions near to the surface of a physical section, which means that the measurements should be restricted only to the middle region of the optical section series. On the other hand, the proportion of intercellular spaces in mesophyll as well as the internal needle surface density in mesophyll did not show significant difference between fresh and frozen needles; therefore, we conclude that freezing represents a suitable form of storage of sampled material for proposed stereological evaluation.