Using biased image analysis for improving unbiased stereological number estimation – a pilot simulation study of the smooth fractionator

The smooth fractionator was introduced in 2002. The combination of a smoothing protocol with a computer‐aided stereology tool provides better precision and a lighter workload. This study uses simulation to compare fractionator sampling based on the smooth design, the commonly used systematic uniformly random sampling design and the ordinary simple random sampling design. The smooth protocol is performed using biased information from crude (but fully automatic) image analysis of the fields of view. The different design paradigms are compared using simulation in three different cell distributions with reference to sample size, noise and counting frame position. Regardless of clustering, sample size or noise, the fractionator based on a smooth design is more efficient than the fractionator based on a systematic uniform random design, which is more efficient than a fractionator based on simple random design. The fractionator based on a smooth design is up to four times more efficient than a simple random design.     

A simple and efficient alternative to implementing systematic random sampling in stereological designs without a motorized microscope stage

When properly applied, stereology is a very robust and efficient method to quantify a variety of parameters from biological material. A common sampling strategy in stereology is systematic random sampling, which involves choosing a random sampling relevant objects start point outside the structure of interest, and sampling at sites that are placed at pre‐determined, equidistant intervals. This has proven to be a very efficient sampling strategy, and is used widely in stereological designs. At the microscopic level, this is most often achieved through the use of a motorized stage that facilitates the systematic random stepping across the structure of interest. Here, we report a simple, precise and cost‐effective software‐based alternative to accomplishing systematic random sampling under the microscope. We believe that this approach will facilitate the use of stereological designs that employ systematic random sampling in laboratories that lack the resources to acquire costly, fully automated systems.     

A simple technique to measure the movements of the microscope stage along the x and y axes for stereological methods

Measurements of microscope stage movements in the x and y directions are of importance for some stereological methods such as the optical disector and optical fractionator. The length of stage movements can be measured with great precision and accuracy using a suitable motorized stage, which is generally a computer-assisted instrument. This type of equipment is generally too expensive for and not readily available in many laboratories. This paper describes a simple method to measure the movements of the microscope stage along the x and y directions, which can be used for purposes such as systematic uniform random sampling. It needs a microscope attachment consisting of two dial indicators; one of them is used to measure the amount of stage movement along the x -axis and the other measures the amount of movement along the y -axis. Movements of the stage on the micrometre-scale can be measured easily using this device.     

Centred contact density functions for the statistical analysis of random sets A stereological study on benign and malignant glandular tissue using image analysis

Real structures investigated in the material and biological sciences, such as minerals or tissues, can often be reduced to two phases. In a stochastic approach, the components of such binary structures may be considered as the union of grains — random sets implanted with their centres at random points — and their complementary space, which is called the pore space. The simplest stochastic germ-grain model is the Boolean model of random sets, which we use here instrumentally as a null model (reference model) for comparison with our biological material. After a brief review of basic properties of the Boolean model and related statistical methods, we introduce centred contact density functions as a new approach. Empirical contact density functions are estimated from the empirical contact distribution functions with an image analyser by dilation of the grain phase. Theoretical contact density functions are then predicted from a set of image parameters, under the assumption that the Boolean model holds. A centred contact density function is the difference between the estimated and the predicted contact density function. Apart from a random error term, centred contact density functions amount to zero irrespective of the area fraction of the grain phase, when the germ-grain model is Boolean. As a section of a spatial Boolean model is a planar Boolean model, the method is also applicable in stereological studies where digitized images are obtained from sections of a three-dimensional structure. Centred contact density functions were determined for mastopathic tissue as compared to mammary cancer, and for tumour-free prostatic tissue as compared to prostatic cancer. For each category of specimens, twenty cases with 10 images each were analysed. Benign and malignant glandular tissue of the aforementioned types deviates significantly from the Boolean model. Centred contact density functions show that malignant transformation is connected with profound geometric remodelling of the pore space.