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Diffusion is a mass transport phenomenon caused by chaotic thermal movements of molecules. Studying the transport in specific domain is simplified by using evolutionary differential equations for local concentration of the molecules instead of complete information on molecular paths [1]. Compounds in a fluid mixture tend to smooth out its spatial concentration inhomogeneities by diffusion. Rate of the transport is proportional to the concentration gradient and coefficient of diffusion of the compound in ordinary diffusion. The evolving concentration profile c(x,t) is then solution of evolutionary partial differential equation ∂c/∂t = DΔC where D is diffusion coefficient and Δ is Laplacian operator. Domain of the equation may be a region in space, plane or line, a manifold, such as surface embedded in space, or a graph. The Laplacian operates on smooth functions defined on given domain. We can use models of diffusion for such diverse tasks as: a) design of method for precise measurement of receptors mobility in plasmatic membrane by confocal microscopy [2], b) evaluation of complex geometry of trabeculae in developing heart [3] to show that the conduction pathway within the embryonic ventricle is determined by geometry of the trabeculae. [ABSTRACT FROM AUTHOR]

Certain morphological parameters of the skeletal muscle tissue can be better understood via 3D considerations. Fluorescent confocal microscopy of thick tissue sections is a well‐established method for visualising and measuring skeletal muscle fibres and surrounding capillaries in 3D. However, thick tissue sections are prone to deformations which may significantly influence some stereological and morphometric results like muscle fibre diameter and capillary length, but not dimensionless parameters like object number and Euler‐Poincaré characteristics. To better understand this phenomenon, we studied the horizontal deformation of thick (100 µm) transverse skeletal muscle sections, by comparing the muscle fibre diameters measured on thick sections to muscle fibre diameters measured on thin (10 µm) sections of the same sample. Diameter changes were further correlated with shrinkage in the Z direction (axial shrinkage) and deviation of the muscle fibre preferential axis from the Z‐axis. We showed that the thick sections dilated in horizontal and shrunk in Z direction, and that the magnitude of horizontal dilation was associated with the magnitude of shrinkage in the Z direction. The latter was more pronounced in transversely than obliquely cut tissue sections. The results emphasise that even when shrinkage in the Z direction can be corrected using calibration, it is important to optimise histological protocols to minimise the Z‐axis collapse that could cause horizontal dilation. Lay description: In skeletal muscle research, 3D analysis is especially important for studying the microvasculature. Laser scanning confocal microscopy of skeletal muscle thick tissue sections is a well‐established method for visualising and measuring skeletal muscle fibres and surrounding capillaries in 3D. However, such sections are prone to deformations which may significantly influence the study results. To better understand this phenomenon, we studied the horizontal deformation of thick transverse skeletal muscle sections. We compared the average muscle fibre diameters measured on thick skeletal muscle sections, thin fixed skeletal muscle sections and immunohistochemically stained thin skeletal muscle sections with the muscle fibre diameters measured on thin native skeletal muscle sections of the same sample, with the latter condition serving as the standard diameters (ie the control condition). We further studied the association among muscle fibre diameter changes, shrinkage of the thick skeletal muscle sections in the Z direction and their sectioning angle. We showed that the thick skeletal muscle sections dilated in the horizontal direction and shrunk in the Z direction, and that the magnitude of horizontal dilation was associated with the magnitude of shrinkage in Z direction. The shrinkage in the Z direction was more pronounced in transversely than obliquely cut tissue sections. These results emphasise that even when shrinkage in the Z direction can be corrected using Z‐axis calibration, it is very important to optimise histological protocols to minimise the Z‐axis collapse that could cause horizontal dilation in order to enhance the integrity of study results. [ABSTRACT FROM AUTHOR]

The volume tensor provides a robust estimate of the shape and orientation of an object in space. In this paper, we introduce Fakir method for estimating the tensor of an object in 3D data set based on the intersections of objects boundary with virtual lines. We calculate the precision of shape estimates by predicting the variance of estimators of integrals based on systematic sampling. To demonstrate the ability of the Fakir method, we measure changes in shape and orientation of compartments in the pheasant brain during development. [ABSTRACT FROM AUTHOR]

Key message: Needle cross-section parameters differ according to needle orientation on a shoot corresponding to irradiance microgradient. Irradiance is a stronger morphogenic factor determining needle size and shape than CO2 concentration.Abstract: We investigated the effects of irradiance on macroscale and microscale, elevated CO2 concentration [CO2], and their interaction on Norway spruce (Picea abies L. Karst.) needles. The irradiance macroscale was represented by sun and shade shoots from two vertical positions in a crown and the irradiance microscale corresponded to spatial orientation of individual needles on a shoot (upper, side, and lower needles relative to the shoot axis). Determination of needle cross section shape using generalized Procrustes analysis and principal component analysis provided a novel approach for evaluating needle morphometry. As expected, shade needles on the irradiance macrogradient were flatter and had less cross-sectional area and smaller volume than did sun needles. The irradiance microgradient was detected within both sun and shade shoots, being steeper in sun shoots than shade shoots. On the microscale, the irradiance gradient induced changes in needle size and cross section shape according to needles’ orientation on a shoot. Due to a more favourable light environment the traits of the upper needles within both sun and shade shoots resembled more the sun needle traits. The sun needle volume was significantly larger in the case of elevated [CO2] as compared to ambient [CO2]. Irradiance was a stronger morphogenic factor determining needle size and cross section shape compared to CO2 concentration. We demonstrated that generalized Procrustes analysis can be a very powerful tool in ecophysiological studies for evaluating small-scale, subtle leaf shape changes on an intraspecific level caused by environmental factors. [ABSTRACT FROM AUTHOR]

Capillary network characteristics are invaluable for diagnostics of muscle diseases. Biopsy material is limited in size and mostly not accessible for intensive research. Therefore, especially in human tissue, studies are performed on autopsy material. To approach the problem whether it is reliable to deduce hypotheses from autopsy material to explain physiological and pathological processes, we studied capillarity in pig soleus muscle 1 and 24 hr after death. Capillaries and muscle fibers were immunofluorescently marked, and images were acquired with a confocal microscope. Characteristics of the capillary network were estimated by image analysis methods using several plugins of the Ellipse program. Twenty-four hours after death, the measured characteristics of the capillary network differ by up to 50% when compared with samples excised 1 hr after death. Muscle fiber diameter, the measured capillary length, and tortuosity were reduced, and capillary network became more anisotropic. The main postmortem change that affects capillaries is evidently geometric deformation of muscle tissue. In conclusion, when comparing results from biopsy samples with those from autopsy samples, the effect of postmortem changes on the measured parameters must be carefully considered. [ABSTRACT FROM AUTHOR]

Image analysis methods are widely used tools for an objective pilling evaluation. However, due to their intrinsic limitations, simple image analysis of digital photographs is not a suitable procedure for the pilling evaluation of fabrics with complex structures and distinct patterns. Generally, a fabric pattern or a complex fabric structure have presented significant problem to the pills detection. This paper describes a system of the objective pilling evaluation of unicolor fabrics and even fabrics with complex patterns. The main points of the pilling evaluation system include a 3D fabric surface reconstruction from shading based on gradient field method, using image analysis tools for the pills detection and an estimation of an objective pilling grade. In order to enable the estimation of the objective pilling grade, a relationship between the pilling grades obtained by a subjective method and selected pill characteristics was specified using a linear regression model. The method was tested on a set of different fabrics and estimated pilling grades were compared with subjective pilling grades of the samples. Results showed that the proposed method is suitable and reliable tool for the objective pilling evaluation of various types of fabrics. [ABSTRACT FROM PUBLISHER]