Mathematical Models of Diffusion in Physiology.

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 deltac/deltat=DDeltac where D is diffusion coefficient and Delta 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.

3D microscopic imaging and evaluation of tubular tissue architecture.

3D microscopy and image analysis provide reliable measurements of length, branching, density, tortuosity and orientation of tubular structures in biological samples. We present a survey of methods for analysis of large samples by measurement of local differences in geometrical characteristics. The methods are demonstrated on the structure of the capillary bed in a rat brain.

Correcting the axial shrinkage of skeletal muscle thick sections visualized by confocal microscopy.

Confocal microscopy is a suitable method for measurements and visualization of skeletal muscle fibres and the neighbouring capillaries. When using 3D images of thick sections the tissue deformation effects should be avoided. We studied the deformation in thick sections of the rat skeletal muscle from complete stacks of images captured with confocal microscope. We measured the apparent thickness of the stacks and compared it to the slice thickness deduced from calibrated microtome settings. The ratio of both values yielded the axial scaling factor for every image stack. Careful sample preparation and treatment of the tissue cryosections with cold Ringer solution minimize the tissue deformation. We conclude that rescaling by the inverse of the axial scaling factor of the stack of optical slices in the direction of the microscope optical axis satisfactorily corrects the axial deformation of skeletal muscle samples.

The branching pattern of villous capillaries and structural changes of placental terminal villi in type 1 diabetes mellitus.

Maternal diabetes is associated with changes of the placental structure. These changes include great variability of vascularity manifested by strikingly hypovascular as well as hypervascular terminal villi. In this paper, normal placental terminal villi and pathological villi of type 1 diabetic placentas were compared concerning the structure of villous stroma, spatial arrangement of villous capillary bed and quantitative assessment of capillary branching pattern. Formalin fixed and paraffin embedded specimens of 14 normal and 17 Type 1 diabetic term placentas were used for picrosirius staining, vimentin and desmin immunohistochemistry and confocal microscopy. 3D models of villi and villous capillaries were constructed from stacks of confocal optical sections. Hypervascular as well as hypovascular villi of diabetic placenta displayed changed structure of villous stroma, i.e. the collagen envelope around capillaries looked thinner and the network of collagen fibers seemed less dense. The desmin immunocytochemistry has shown that stromal cells of hypervascular as well as hypovascular villi appeared nearly or completely void of desmin filaments. In comparison with normal villi, capillaries of hypovascular villi had a smaller diameter and displayed a markedly wavy course whereas in hypervascular villi numerous capillaries occurred in reduced stroma and often had a large diameter. The quantitative assessment of capillary branching has shown that villous capillaries are more branched in diabetic placentas. It is concluded that type 1 maternal diabetes enhances the surface area of the capillary wall by elongation, enlargement of diameter and higher branching of villous capillaries and disrupts the stromal structure of terminal villi.

Characterization of the capillary network in skeletal muscles from 3D data.

In this review we present immunohistochemical methods for visualization of capillaries and muscle fibres in thick muscle sections. Special attention is paid to the procedures that preserve good morphology. Applying confocal microscopy and virtual 3D stereological grids, or tracing of capillaries in virtual reality, length of capillaries within a muscle volume or length of capillaries adjacent to a muscle fibre per fibre length, fibre surface area or fibre volume can be evaluated by an unbiased approach. Moreover, 3D models of capillaries and muscle fibres can be produced. Comparison of the developed methods with counting capillary profiles from 2D sections is discussed and the reader is warned that counting capillary profiles from 2D sections can underestimate the capillary length by as much as 75 percent. Application of the described 3D methodology is illustrated by the anatomical remodelling of capillarity during acute denervation and early reinnervation in the rat soleus and extensor digitorum longus muscles.

Transcription-dependent rearrangements of actin and nuclear myosin I in the nucleolus.

Nuclear actin and nuclear myosin I (NMI) are important players in transcription of ribosomal genes. Transcription of rDNA takes place in highly organized intranuclear compartment, the nucleolus. In this study, we characterized the localization of these two proteins within the nucleolus of HeLa cells with high structural resolution by means of electron microscopy and gold-immunolabeling. We demonstrate that both actin and NMI are localized in specific compartments within the nucleolus, and the distribution of NMI is transcription-dependent. Moreover, a pool of NMI is present in the foci containing nascent rRNA transcripts. Actin, in turn, is present both in transcriptionally active and inactive regions of the nucleolus and colocalizes with RNA polymerase I and UBF. Our data support the involvement of actin and NMI in rDNA transcription and point out to other functions of these proteins in the nucleolus, such as rRNA maturation and maintenance of nucleolar architecture.

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.

Three-dimensional arrangement of the capillary bed and its relationship to microrheology in the terminal villi of normal term placenta.

Spatial arrangement of the capillary bed, manifestations of its growth and symmetry of capillary branching were studied in peripheral villi of normal human placenta at term using confocal microscopy and image analysis. Unlike the model that has been accepted so far, it was shown that the arrangement of the capillary bed in terminal villi varied from simple, U-like loops to a richly branched network. Three different categories of terminal villi (TV) were recognised: Signs of capillary elongation and sprouting were observed in the villous capillary bed. Based on the assessment of the mean cross-sectional areas of capillaries constituting simple, Y-like capillary bifurcation in terminal villi, the capillary branching was found to be asymmetric. Therefore, we conclude that the conditions for the "plasma skimming" effect are met in human placenta.

Interactive measurement and characterization of DNA molecules by analysis of AFM images.

BACKGROUND: In the past few years, computer-based analysis of atomic-force microscopic images has acquired increasing importance for studying biomolecules such as DNA. On the one hand, fully automated methods do not allow analysis of complex shapes; on the other hand, manual methods are usually time consuming and inaccurate. The semiautomated approach presented in this report overcomes the drawbacks of both methods. METHODS: Two kinds of images were analyzed: computer-generated filaments that modeled circular DNA molecules on a surface and real atomic-force microscopic images of DNA molecules adsorbed on an appropriate substrate surface. RESULTS: The algorithm was tested on a group of 140 simulated and 189 real plasmids with a nominal length of 913 nm. The accuracy of the length measurement was statistically evaluated on the ensemble of molecules, with particular attention to the influence of the noise. Mean contour lengths of 912 +/- 5 nm and 910 +/- 47 nm were found for simulated and real plasmids, respectively. The measured end-to-end distance of lambda-DNA molecules as a function of their contour length is reported, from which it is possible to estimate the stiffness of the DNA molecules adsorbed onto a surface; the value obtained for the DNA persistence length (42 +/- 5 nm) is consistent with values measured by other imaging techniques. CONCLUSIONS: An interactive algorithm for DNA molecule measurements based on the detection of the filament ridge line in a digitized image is presented. The simulation of artificial filaments combined with the experimental data demonstrates that the proposed method can be a valuable tool for the DNA contour length evaluation, especially in the case of complex shapes where the use of automatic methods is not possible.

Quantitative analysis of embryonic kidney impairment by confocal microscopy and stereology: effect of 1,2-dibromoethane in the chick mesonephros.

1. Chick embryos in ovo were treated with a teratogenic dose of 1,2-dibromoethane (DBE) on embryonic day (ED) 3. On ED 6 and 10, histological sections of whole embryos were prepared for confocal microscopy. In parallel, mesonephroi of 10-d-old embryos were dissected for in situ staining with acridine orange (AO), a fluorescence probe for lysosomes. 2. DBE impaired differentiation of renal vessels which manifested as a delay in rearrangement of primitive renal vascular architecture on ED 6 and a significant reduction of the mesonephric vascularisation on ED 10. This was accompanied by delayed functional maturation of embryonic kidney, as suggested by staining with AO. 3. Renal vessels appeared to be more susceptible to DBE than tubules. Unequal growth of these renal components might be a cause of DBE-induced spatial disorganisation of tubular apparatus. 4. Nephrotoxic effects of DBE during the embryonic period are associated primarily with damage to the renal blood supply. 5. Confocal microscopy, stereological methods and three-dimensional reconstruction of developing tissues are useful tools to investigate pathogenic processes during embryonic development.

Improvement in volume estimation from confocal sections after image deconvolution.

The confocal microscope can image a specimen in its natural environment forming a 3D image of the whole structure by scanning it and collecting light through a small aperture (pinhole), allowing in vivo and in vitro observations. So far, the confocal fluorescence microscope (CFM) is considered a true volume imager because of the role of the pinhole that rejects information coming from out-of-focus planes. Unfortunately, intrinsic imaging properties of the optical scheme presently employed yield a corrupted image that can hamper quantitative analysis of successive image planes. By a post-image collection restoration, it is possible to obtain an estimate, with respect to a given optimization criterium, of the true object, utilizing the impulse response of system or Point Spread Function (PSF). The PSF can be measured or predicted so as to have a mathematical and physical model of the image-formation process. Further modelling and recording noise as an additive Gaussian process has used the regularized Iterative Constrained Tykhonov Miller (ICTM) restoration algorithm for solving the inverse problem. This algorithm finds the best estimate iteratively searching among the possible positive solutions; in the Fourier domain, such an approach is relatively fast and elegant. In order to compare the effective improvement in the quantitative image information analysis, we measured the volume of reference objects before and after image restoration, using the isotropic Fakir method.

Confocal stereology and image analysis: methods for estimating geometrical characteristics of cells and tissues from three-dimensional confocal images.

A short review of confocal stereology and three-dimensional image analysis is presented, pointing out the achievements accomplished in this field by the Department of Biomathematics (Institute of Physiology, Prague). One of the methods of confocal stereology, the fakir method for surface area estimation, developed by this laboratory, is described. Methods for automatic measurement of geometrical characteristics of microscopical structures, based on 3-D image processing or surface triangulation, are discussed and compared with interactive stereological methods. Three-dimensional reconstruction programs and software implementation of stereological and digital methods as well as their practical applications are presented. The future trends are discussed.

Mental health patients in criminal justice populations: needs, treatment and criminal behaviour.

BACKGROUND: Government policy requires that health and social care agencies work more closely together and in partnership with the criminal justice system. There is a well-established relationship between crime and mental disorder. METHOD: The Tracking Project provides for the first time in England the means of collating and analysing data on mental disorder (defined as receiving secondary care as patients of a Mental Health Trust) and crime (defined as all those charged with an offence). Data were collected over a three-year period for all individuals who had contact with the criminal justice system and mental health services in an English county. RESULTS: In a county population of 800,400, some 30,329 were offenders. More than a third had used a health or social care service during the three-year period; 8.0% were mentally disordered. Those offenders aged 25-64 and who contacted the police more than once were significantly more likely to be mentally disordered. Type of offence was also a relevant variable. The probation service showed broadly similar results. DISCUSSION: The research has provided for the first time substantive quantitative evidence of the relationship between crime and mental disorder. The results can be used as the basis for further work to target assessment and risk reduction measures at those most at risk.

LR White is preferable to Unicryl for immunogold detection of fixation-sensitive nuclear antigens.

The purpose of this study was to compare two electron microscopy embedding media - LR White and Unicryl - with regard to cell morphologyical and immunohistochemical preservation properties for the study of fixation-sensitive nuclear antigens. Human cervical carcinoma (HeLa) cells were fixed with 2% paraformaldehyde and 0.1% glutaraldehyde, and embedded in parallel in the two resins: LR White and Unicryl using; two different polymerization protocols were used for each resin. Preservation of fine nuclear structure was good after LR White and poor after Unicryl embedding. Immunogold labeling of Sm antigen was significantly stronger on LR White sections. Polymerization by UV light resulted in stronger and more specific labeling than heat polymerization. These results show that LR White is advantageous over Unicryl for the study of nuclear antigens requiring delicate aldehyde fixation.

Confocal microscopy and stereology: estimating volume, number, surface area and length by virtual test probes applied to three-dimensional images.

The opportunities of confocal microscopy applied to morphometry of microscopical structures are presented and demonstrated on stereological methods based on evaluation of optical sections within a thick slice and using computer-generated virtual test probes. Such methods, allowing arbitrary orientation of the thick slice, can be used for estimating volume, number, surface area, and length. The methods using spatial grid of points, disector, fakir, and slicer probes are described and illustrated by different examples using our freeware 3DTOOLS software and their variance and applicability are discussed. It is shown that shifted triple or quadruple spatial grids of lines are very efficient for the surface area and volume estimation by the fakir method.

Three-dimensional study of the capillary supply of skeletal muscle fibres using confocal microscopy.

Three-dimensional (3D) study of capillary network of individual muscle fibres in rat extensor digitorum longus (EDL) and soleus (SOL) muscles is presented. Stereology and 3D reconstruction techniques were applied to stacks of serial optical sections recorded by a confocal microscope from thick muscle slices. The results suggest that SOL muscle fibres have a larger surface area and volume as well as a larger length of capillaries per fibre length than EDL. On the other hand, these two muscles have a similar ratio of capillary length to fibre surface area. The 3D approach to evaluation of muscle fibre capillarization brings many advantages over traditional measurements made on single muscle sections and could also be applied to the study of angiogenesis in other tissues.

Statistical evaluation of colocalization patterns in immunogold labeling experiments.

The ultrastructural localization of various antigens in a cell using antibodies conjugated to gold particles is a powerful instrument in biological research. However, statistical or stereological tools for testing the observed patterns for significant clustering or colocalization are missing. The paper presents a method for the quantitative analysis of single or multiple immunogold labeling patterns using interpoint distances and tests the method using experimental data. The clustering or colocalization of gold particles was detected using various characteristics of the distribution of distances between them. Pair correlation and cross-correlation functions were used for exploratory analysis; second order reduced K (or cross-K) functions were used for testing the statistical significance of observed events. Confidence intervals of function values were estimated by Monte Carlo simulations of the Poisson process for independent particles, and results were visualized in histograms. Furthermore, a suitability of K functions modified by censoring or weighting was tested. The reliability of the method was assessed by evaluating the labeling patterns of nascent DNA and several nuclear proteins with known functions in replication foci of HeLa cells. The results demonstrate that the method is a powerful tool in biological investigations for testing the statistical significance of observed clustering or colocalization patterns in immunogold labeling experiments.

Comparison of several digital and stereological methods for estimating surface area and volume of cells studied by confocal microscopy.

BACKGROUND: The implementation of different methods for estimating the surface area and volume of cells studied by confocal microscopy was developed. The methods were compared from the point of view of their precision, applicability and efficiency. METHODS: Interactive stereological methods (spatial grid method, fakir method, Cavalieri principle) as well as automatic digital methods (digital Crofton method, voxel counting, triangulation method, iso-intensity contouring method) were considered. The methods were tested on model geometrical solids and on real volume images consisting of a stack of serial sections encompassing entire tobacco BY-2 cells or cell chains. RESULTS: It is shown that many of the studied methods are very precise when applied to cells of simple or moderately complex shapes. The automatic digital methods are fast and precise but their applicability is limited by the necessity to segment automatically the object surface and to find an optimal resolution. This limitation is not present in stereological methods which are applied interactively and thus are more time-consuming. CONCLUSIONS: The presented implementations of the fakir method and the Cavalieri principle enable interactive, unbiased and efficient estimation of the cell surface area and volume. The recommended steps for measuring the surface area and/or volume of objects studied by confocal microscopy are described.

Estimating surface area by the isotropic fakir method from thick slices cut in an arbitrary direction.

The proposed fakir method for estimating surface area is based on counting the intersections between the surface lying within a thick slice, and an isotropic spatial grid consisting of a combination of linear probes called fakir probes. An unbiased procedure using a directly randomized spatial grid rather than sections with randomized directions is presented. The method is applicable if perfectly registered serial sections of the surface are available in a thick slice while the direction of the slice can be arbitrary. The efficiency of the fakir method using different arrangements of orthogonal triplets of fakir probes is evaluated and it is shown that mutually shifted probes are superior to non-shifted ones. The application software for interactive counting of intersections between computer-generated fakir probes and the surface within the stack of digitized images is described and demonstrated by two examples: estimation of the surface area of individual tobacco cell chains using a confocal microscope, and estimation of the total area of exposed surface of mesophyll cells in a barley leaf using a wide-field transmission microscope.

[Cyclic 3',5'-adenosine monophosphate in macrophages, intestinal mucosa, and blood plasma of germ-free and ordinary animals]. / Tsiklicheskii 3',5'-adenozinmonofosfat v makrofagakh, slizistoi obolochke kishechnika i plazme krovi bezmikrobnykh i obychnykh zhivotnykh.

The level of cAMP in macrophages, intestinal mucosa and blood plasma as well as its formation in intestinal mucosa of germfree animals under the effect of lipopolysaccharide E. coli 055 (LPS) were studied in experiments on germfree and ordinary mice and guinea-pigs. The concentration of cAMP in intestinal mucosa of ordinary guinea-pigs was 5-fold higher than in germfree animals. LPS induced an increase in cAMP level in intestinal mucosa, but this level did not reach that in ordinary animals. The levels of cAMP in blood plasma of germfree guinea-pigs in macrophages of germfree mice increased 2-fold and 4-fold, respectively, 30 minutes following the treatment with LPS. The increased level of cAMP was accompanied by its intensive secretion into the exocellular medium. Macrophages of ordinary animals had a moderate output of cAMP. A conclusion is made about the relationship between cAMP formation and microbial contamination of the microorganism as well as about an important role of the cyclic nucleotide in the mechanism of nonspecific resistance and homeostatic reactions of the body to microbial exposure.