Stereological length estimation using spherical probes

Lineal structures in biological tissue support a wide variety of physiological functions, including membrane stabilization, vascular perfusion, and cell‐to‐cell communication. In 1953, Smith and Guttman demonstrated a stereological method to estimate the total length density (L_v) of linear objects based on random intersections with a two‐dimensional sampling probe. Several methods have been developed to ensure the required isotropy of object–probe intersections, including isotropic‐uniform‐random (IUR) sections, vertical‐uniform‐random (VUR) slices, and isotropic virtual planes. The disadvantages of these methods are the requirements for inconvenient section orientations (IUR, VUR) or complex counting rules at multiple focal planes (isotropic virtual planes). To overcome these limitations we report a convenient and straightforward approach to estimate L_v and total length, L, for linear objects on tissue sections cut at any arbitrary orientation. The approach presented here uses spherical probes that are inherently isotropic, combined with unbiased fractionator sampling, to demonstrate total L estimation for thin nerve fibres in dorsal hippocampus of the mouse brain.     

Estimating aggregate and overall characteristics from thick sections by transmission microscopy

The random spatial structure considered is the union X of an aggregate of random opaque convex particles in transparent space, the particle centroids being sited at the points of a homogeneous Poisson process. The model is thus the union of an aggregate of non-necessarily-convex disjoint regions. Expressions are derived for the fundamental stereological quantities V_V, S_V, K_V (integrated mean curvature density) and G_V (integrated gaussian curvature density) for X; and for A_A, L_A and C_A (integrated curvature density) for the projection of a slice of thickness t of this model onto a plane parallel to the slice, where t may take any non-negative value. The estimates relevant to transmission microscopy suggested by this theory are presented.     

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.     

On the estimation of particle number

Two methods are proposed for estimating the number of separated particles within a solid structure per unit volume of structure, N_v. Apart from being arranged with independence of any size parameter, no special assumptions upon the size, shape and orientation of the particles are made. The first method is based on the identity N_V = (N_A)_u ? μ_u^?1, where (N_A)_u is the mean number of particle sections per unit area of a plane probe T_u which is uniform random within the structure and perpendicular to a given direction u, whereas μ_u is the mean particle caliper length along u. The second method uses N_V = A_A?V^?1, where A_A is the mean areal fraction of the particles per unit area of section, whereas v is the mean particle volume. The estimation of (N_A)_u, μ_u, and v requires the examination of parallel serial sections above and below T_u. Particle model reconstructions are not needed, however. Previous approaches to the problem are discussed.     

Estimating length density and quantifying anisotropy in skeletal muscle capillaries

The accurate estimation of stereological parameters defined on anisotropic structures is a long-standing problem. In this paper we seek to estimate the capillary length density J_v in skeletal muscle tissue. A well-known model for directional anisotropy in space, namely the ‘spherical normal’ or ‘Fisher axial distribution’ model, is found to fit the relevant data satisfactorily. Based on this model, a short-cut estimation method is proposed and illustrated with a numerical example. This method essentially consists in taking the ratio of mean capillary profile counts, as obtained from transversal and longitudinal sections of the muscle tissue, and making use of a table or a graph given in the paper to estimate J_v. The conditions under which the methods are applicable and practicable are discussed in detail. Apart from an accurate estimation of J_v, an important feature of our method is the possibility of quantifying the degree of anisotropy by a coefficient K (called the concentration parameter of the Fisher axial distribution), which enjoys both a biological significance and a sound statistical basis.     

Measuring error and sampling variation in stereology: comparison of the efficiency of various methods for planar image analysis

An evaluation is made of the relative efficiency (precision of the final estimate per unit time of measurement on a given set of sections) of different methods for planar analysis aimed at estimating aggregate, overall stereological parameters (such as V_v, S_v). The methods tested are point-counting with different densities of test points (4 ≤ P_T ≤ 900 per picture), semiautomatic computer image analysis with MOP and automatic image analysis with Quantimet, for obtaining V_v and S_v estimates. One biological sample as well as three synthetic model structures with known coefficients of variation between sections are used. The standard error of an estimate is mainly determined by the coefficient of variation between sampling units (= sections in the present paper) so that measuring each sample unit with a very high precision is not necessary. Automatic image analysis and point-counting with a 100-point grid were the most efficient methods for reducing the relative standard errors of the V_v and S_v estimates to equivalent levels in the synthetic models. Using a 64-point grid was as precise, and about 11 times faster than using a tracing device for obtaining the estimate of V_v in the biological sample.     

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.     

Simultaneous measurement of quantum yield ratio and absorption ratio between acceptor and donor by linearly unmixing excitation–emission spectra

Quantum yield ratio (Q_A/Q_D) and absorption ratio (K_A/K_D) in all excitation wavelengths used between acceptor and donor are indispensable to quantitative fluorescence resonance energy transfer (FRET) measurement based on linearly unmixing excitation–emission spectra (ExEm‐spFRET). We here describe an approach to simultaneously measure Q_A/Q_D and K_A/K_D values by linearly unmixing the excitation–emission spectra of at least two different donor–acceptor tandem constructs with unknown FRET efficiency. To measure the Q_A/Q_D and K_A/K_D values of Venus (V) to Cerulean (C), we used a wide‐field fluorescence microscope to image living HepG2 cells separately expressing each of four different C–V tandem constructs at different emission wavelengths with 435 nm and 470 nm excitation respectively to obtain the corresponding excitation–emission spectrum (S_DA). Every S_DA was linearly unmixed into the contributions (weights) of three excitation–emission spectra of donor (W_D) and acceptor (W_A) as well as donor–acceptor sensitisation (W_S). Plot of W_S/W_D versus W_A/W_D for the four C–V plasmids from at least 40 cells indicated a linear relationship with 1.865 of absolute intercept (Q_A/Q_D) and 0.273 of the reciprocal of slope (K_A/K_D), which was validated by quantitative FRET measurements adopting 1.865 of Q_A/Q_D and 0.273 of K_A/K_D for C32V, C5V, CVC and VCV constructs respectively in living HepG2 cells.     

Effect of two medium chain triglycerides‐supplemented diets on synaptic morphology in the cerebellar cortex of late‐adult rats

Ketogenic diets (KDs) have shown beneficial effects in experimental models of neurodegeneration, designating aged individuals as possible recipients. However, few studies have investigated their consequences on aging brain. Here, late‐adult rats (19 months of age) were fed for 8 weeks with two medium chain triglycerides‐supplemented diets (MCT‐SDs) and the average area (S), numeric density (Nv_s), and surface density (S_v) of synapses, as well as the average volume (V), numeric density (Nv_m), and volume density (V_v) of synaptic mitochondria were evaluated in granule cell layer of the cerebellar cortex (GCL‐CCx) by computer‐assisted morphometric methods. MCT content was 10 or 20%. About 10%MCT‐SD induced the early appearance of senescent patterns (decreased Nv_s and Nv_m; increased V), whereas 20%MCT‐SD caused no changes. Recently, we have shown that both MCT‐SDs accelerate aging in the stratum moleculare of CA1 (SM CA1), but are “antiaging” in the outer molecular layer of dentate gyrus (OML DG). Since GCL‐CCx is more vulnerable to age than OML DG but less than SM CA1, present and previous results suggest that the effects of MCT‐SDs in the aging brain critically depend on neuronal vulnerability to age, besides MCT percentage. Microsc. Res. Tech. 2009. © 2009 Wiley‐Liss, Inc.     

Measurement of geometrical parameters in cocontinuous polymer blends: 3D versus 2D image analysis

Formulae of stereology are used to estimate 3D geometrical parameters of cocontinuous structures measured from 2D micrographs of polymer blends. 3D images of symmetric and nonsymmetric polymer blends made of fluorescently labelled polystyrene and styrene‐ran‐acrylonitrile copolymer were obtained with laser scanning confocal microscopy. Geometrical parameters of the blend interface, specifically volume fraction, surface area per unit volume (S _V ) and average of local mean curvature were measured directly from the 3D images and compared to the values estimated from analysis of a number of 2D slices combined with stereological relations. When the total length of phase boundary considered in the analysis of the 2D slices (L_Tot ) was at least 6000 times bigger than the characteristic length of the microstructure (S^?1_V ), the standard deviation for all the parameters measured became negligible. However, considerable discrepancies between the average values computed from 3D and 2D images were observed for any value of L_Tot . The mean curvature distribution was also measured from both the 3D images and the 2D slices. The distribution was estimated from the 2D slices but with a width about 2.4 times that of the true value obtained from the 3D images.     

Analysis of tensile properties for composites with wrinkled fabric

During the fiber preform loading process of resin transfer moldings (RTMs), fabric layers can be wrinkled in the preform, which affects the quality of the composite. This study considers several wrinkled models with different wrinkled lengths (L _W ) and different numbers of wrinkled layers in the preform. To study the effects of wrinkling on tensile properties, two matrix materials with different moduli are used to enhance understanding. It is found that the tensile moduli of wrinkled models are lower than those of the normal model, for the same fiber volume fraction (V _f ). The effects of wrinkling on the tensile modulus increase with the number of layers as well as V _f . In addition, the effect of wrinkling with a low-modulus matrix on the tensile modulus is larger than that with a high-modulus matrix in the composite. Based on the failure modes and the stiffness of materials, the failure mechanisms of wrinkled models can be separated into two regimes as a function of wrinkled length, L _W , depending on the critical wrinkled length (L _WC ).     

材质气孔率和气孔大小与表面粗糙度的数学模拟与特征

为提高光学系统的成像质量,研究了光学系统中镜片表面粗糙度与镜片材质中的颗粒大小、缺陷、气孔率、气孔大小的关系.通过几何方法,建立了气孔率与气孔大小和数量的关系模型,分别给出了单位体积和单位面积中气孔率与气孔大小和数量的关系表达式.最后用数学方法建立了材质中气孔率、气孔大小与表面粗糙度的定量模型,给出了表面粗糙度与材质气孔率和气孔大小的关系表达式,表明表面粗糙度近似与材质中的气孔率成正比,与气孔大小成正比.     

The influence of tissue processing on quantitative histopathology in breast cancer

Objective grading of breast cancer by morphometry has been suggested for improving the precision of the prognostic prediction. However, the tissue components evaluated might be influenced by variations in the processing, reducing the clinical value. In the present study, the impact of the period of fixation, of the acidity of the fixative and of the embedding medium was investigated by allocating tissue samples from 27 surgical breast cancer specimens systematically randomly to different modes of processing. The volume-weighted mean volume of cancer cell nuclei, v?_V(nuc), was estimated using the method of point-sampled intercepts on vertical sections. In addition, estimates of the mean nuclear profile area, ā_H(nuc), the nuclear volume fraction, V_V(nuc), the nuclear profile density, ND, and the mitotic profile frequency, MF, were obtained. The quantitative histopathological estimates were stable with respect to the investigated variables of the tissue processing. No significant differences were found when comparing the estimates obtained in samples from five tumours fixed in formalin at pH 5·0, 6·0, 7·0, 7·4 and 8·0, respectively. Similarly, no significant correlations between the estimates and the period of formalin fixation (24 h, 3 days and 3 months) were found in samples from five other tumours. However, the v?_V(nuc) was 13% larger (2p = 0·004) and the mean ND 17% smaller (2p = 0·04) in hydroxyethyl-methacrylate-embedded samples from 17 tumours as compared to paraffin-embedded samples. Thus, the shrinkage observed in paraffin seems to affect nuclei less than tissue.     

Ants colony algorithm approach for multi-objective optimisation of surface grinding operations

An ant colony based optimisation procedure has been developed to optimise grinding conditions, viz. wheel speed, workpiece speed, depth of dressing and lead of dressing, using a multi-objective function model with a weighted approach for the surface grinding process. The procedure evaluates the production cost and production rate for the optimum grinding condition, subjected to constraints such as thermal damage, wheel wear parameters, machine tool stiffness and surface finish. The results are compared with Genetic Algorithm (GA) and Quadratic Programming (QP) techniques.Nomenclature a _p down feed of grinding (mm/pass) - a _w total thickness of cut (mm) - A _o initial wear flat-area percentage (%) - b _e empty width of grinding (mm) - b _s width of wheel (mm) - b _w width of workpiece (mm) - B _k positive definite approximation of the Hessian - doc depth of dressing (mm) - c _d cost of dressing ($) - c _s cost of wheel per mm³ ($/mm³) - CT total production cost ($/pc) - CT ^* expected production cost limit ($/pc) - d _g grind size (mm) - D _e diameter of wheel (mm) - f _b cross feed rate (mm/pass) - G grinding ratio - k _a constant dependent on coolant and wheel grind type - k _u wear constant (mm^-1) - k _c cutting stiffness (N/mm) - k _m static machine stiffness (N/mm) - k _s wheel wear stiffness (N/mm) - L lead of dressing (mm/rev) - L _e empty length of grinding (mm) - L _w length of workpiece (mm) - M _c cost per hour labour and administration ($/h) - N _d total number of pieces to be grouped during the life of dressing (pc) - N _t batch size of workpieces (pc) - N _td total number of workpieces to be grouped during the life of dressing (pc) - P number of workpieces loaded on the table (pc) - R _a surface roughness (µm) - R _a* surface finish limit during rough grinding (µm) - R _c workpiece hardness (Rockwell hardness number) - R _em dynamic machine characteristics - S _d distance of wheel idling (mm) - S _p number of spark out grinding (pass) - t _sh time of adjusting machine tool (min) - t _i time of loading and unloading workpiece (min) - T _ave average chip thickness during grinding (µm) - U specific grinding energy (J/mm) - U ^* critical specific grinding energy (J/mm³) - V _r speed of wheel idling (mm/min) - V _s wheel speed (m/min) - V _w workpiece speed (m/min) - VOL wheel bond percentage (%) - WRP workpiece removal parameter (mm³/min-N) - WRP ^* workpiece removal parameter limit (mm³/min-N) - WWP wheel wear parameter (mm³/min-N) - W _i weighting factor, 0W _i1 (W ₁+W ₂+W ₃=1)     

The use of quadrats and test systems in stereology,including magnification corrections

At present a model-free, design-based theory of unbiased estimation, and a model-based one of linear unbiased estimation of minimum variance, are available for stereology. The main developments rest upon the nested scheme {section (quadrat)}, whence the raw data are expressible in terms of area, length and number. The main aim of this paper is to complete the available model-based theory by introducing the step in which sections are analysed by point-counting via coherent test systems (CTSs). Using this development, the stereologist should be able to handle raw point and intersection counts optimally, in order to find the best estimator of a ratio R in a given specimen in a wide range of circumstances. The latter include, for instance, the use of different CTSs on different sections and of double CTSs on each section, as well as the case—(not uncommon in electron microscopy)—in which different sections from the same sample are observed at slightly different magnifications but analysed by quadrats (via automatic or semi-automatic image analysers, for instance), or CTSs of fixed sizes. The main conclusion pertaining to the latter case is that the estimators obtained via section-wise magnification corrections are in general superior to those corrected via a global, average magnification. In order to illustrate the methodology, a synthetic numerical example, and a real one, are given.     

Determining Generation–Recombination Characteristics of a Semiconductor–Dielectric Interface from the Current Kinetics of Surface Minority Carrier Generation

Conditions for the one-to-one characterization of the generation (G _s) and surface recombination (R _s) rates of minority charge carriers (MCCs) in a metal–oxide–semiconductor (MOS) structure (in the case of strong nonequilibrium depletion) by the MCC surface generation current (I(t)) flowing in an external circuit of this structure are revealed. These conditions are the following: (1) the generation current I is independent of the time t (until the structure enters an equilibrium state) and the voltage V _{g 0} corresponding to the initial nonequilibrium depletion and (2) the duration of current steps I(V _{g 0}) = const and, consequently, the equilibrium surface charge increase with increasing V _{g 0}. The observed kinetics of the MCC generation current for the MCCs induced in an n-Si MOS structure at 293 K experimentally confirms the realization of these conditions. The values of the generation and recombination rates G _s = 2.84 × 10¹⁰ cm^–2s^–1 and R _s = 6.82 cm s^–1 obtained from current levels I(V _{g 0}) = const are typical of high-quality Si MOS structure. Additionally measured capacitance–voltage characteristics were used to determine the interface state density at the Si/SiO₂ contact near the middle of the Si gap (N _ss(E) 6.4 × 10¹⁰ cm^–2eV^–1), which allowed the estimation of the effective capture cross section of these states _eff 1.4 × 10^–16 cm².     

Unbiased estimation of capillary length from vertical slices*

Previous stereological approaches to estimate feature length include isotropic sections, which tend to be inefficient for highly anisotropic structures such as skeletal muscle capillaries, and semiparametric model-based methods, which require transverse and longitudinal sections only, but are biased to a variable, unknown degree. The recent method of vertical slices combines the advantages of both approaches, namely it is unbiased, efficient and convenient. This study illustrates for the first time how to apply the vertical slices method in biology by direct light microscopy and intersection counting with a properly orientated cycloid test system. Neither image processing nor confocal microscopy are used. The purpose of the study was to estimate capillary length in the left ventricle of rat heart. Beyond this, a novel histochemical method enables the staining of the venular capillary region in red and the arteriolar capillary region in blue, and hence estimates their separate lengths. The vertical slices method to estimate feature length seems to be a promising approach for biology.     

Production planning of FMS under tool magazine constraints: A dynamic programming approach

Production planning is one of the most important activities for efficient operation of a flexible manufacturing system. This complex acivity is concerned with the decisions related to system set-up, involving solving the problems of selection of a set of part types for simultaneous processing, determining the production ratios, assigning the pallets and fixtures, and assigning operations and tools to machines. In this paper, a dynamic programming algorithm is developed to solve the above problems simultaneously by considering the flexibilities and constraints of the system in order to minimise the unbalanced workload of machines. In this context, various factors such as the tools required for operations, alternative routes available for operations, tool magazine capacity and the limited number of pallets and fixtures are considered. The method is validated with a case study.Notation B a large number - i part type,i=1,...,N - o operation,o=1,...,O _i - k machine,k=1,...,K - j stage,j=1,...,N (N is maximum number of stages required, i.e. equal to the number of part types) - n indicates the number of parts to be introduced into the system (represents the state in DP),n=j,...,nmax. In stagej at least one number of each part type should be introduced into the system. The maximum number of parts can be a user defined maximum,nmax. - P _iok processing time of part typei, operationo on machinek - OA _io set of operation alternatives available for part typei, operation - o an alternative consists of machine number, tool number along with its processing time - pw _ik average workload required by a part typei on machinek - a _i number of parts (ratio) of typei - f _i number of fixtures available to part typei - S(j) {S ₁(j),S ₂(j),...,S _p (j),...}, whereS _p (j) ispth set of selected part types with cardinalityj - |S(j)| ^N C _j - W _k a constant, indicating the average unbalanced workload on a machinek and is a user defined value - L _j,k (S _p (j),n,a _i ) load of machinek at stagej when selection isS _p (j), number of part types isn, and number of parts of type isa _i - L* _j,k (S _p (j),n) load of machinek in stagej at minimum unbalanced workload when selection isS _p (j) and number of parts in system isn - F _j (S _p )(j),n,a _i ) unbalanced workload of all machines at stagej, when selection isS _p (j), number of part types isn, and number of parts of type isa _i - F _j (S _p (j),n) minimum unbalanced workload of all machines, whenS _p (j) is the set of selected part types andn is the number of parts in the system     

Experimental investigation and optimization of EDM process parameters for machining of aluminum boron carbide (Al–B4C) composite

This study investigates the effect of electric discharge machining (EDM) process parameters [current, pulse-on time (T_on), pulse-off time (T_off) and electrode material] on material removal rate (MRR), electrode wear rate (EWR) and surface roughness (SR) during machining of aluminum boron carbide (Al–B₄C) composite. This article also summarizes a brief literature review related to aluminum metal matrix composites (Al-MMCs) based on different process and response parameters, work and tool material along with their sizes, dielectric fluid and different optimization techniques used. The MMC used in the present work is stir casted using 5% (wt) B₄C particles of 50 micron size in Al 6061 metal matrix. Taguchi technique is used for the design of experiments (L₉-orthogonal array), while the experimental results are analyzed using analysis of variance (ANOVA). Response table for average value of MRR, EWR and SR shows that current is the most significant factor for MRR and SR, while electrode material is most important for EWR. ANOVA also confirms similar results. It is also observed that the optimum level of process parameters for maximum MRR is A₃B₁C₃D₃, for minimum EWR is A₁B₂C₃D₁, and for SR is A₁B₃C₃D₃.