Osteoblast-osteocyte transformation. A SEM densitometric analysis of endosteal apposition in rabbit femur

Transformation of osteoblasts into osteocytes is marked by changes in volume and cell shape. The reduction of volume and the entrapment process are correlated with the synthesis activity of the cell which decreases consequently. This transformation process has been extensively investigated by transmission electron microscopy (TEM) but no data have yet been published regarding osteoblast-osteocyte dynamic histomorphometry. Scanning electron microscope (SEM) densitometric analysis was carried out to determine the osteoblast and open osteocyte lacunae density in corresponding areas of a rabbit femur endosteal surface. The lining cell density was 4900.1 ± 30.03 n mm(-2), the one of open osteocyte lacunae 72.89 ± 22.55 n mm(-2). This corresponds to an index of entrapment of one cell every 67.23 osteoblasts (approximated by defect). The entrapment sequence begins with flattening of the osteoblast and spreading of equatorial processes. At first these are covered by the new apposed matrix and then also the whole cellular body of the osteocyte undergoing entrapment. The dorsal aspect of the cell membrane suggests that closure of the osteocyte lacuna may be partially carried out by the same osteoblast-osteocyte which developed a dorsal secretory territory. A significant proportion of the endosteal surface was analysed by SEM, without observing any evidence of osteoblast mitotic figures. This indicates that recruitment of the pool of osteogenic cells in cortical bone lamellar systems occurs prior to the entrapment process. No further additions occurred once osteoblasts were positioned on the bone surface and began lamellar apposition. The number of active osteoblasts on the endosteal surface exceeded that of the cells which become incorporated as osteocytes (whose number was indicated by the number of osteocyte lacunae). Therefore such a balance must be equilibrated by the osteoblasts' transformation in resting lining cells or by apoptosis. The current work characterised osteoblast shape changes throughout the entrapment process, allowing approximate calculation of an osteoblast entrapment index in the rabbit endosteal cortex.

Morphometry and patterns of lamellar bone in human Haversian systems

The lamellar architecture of secondary osteons (Haversian systems) has been studied with scanning electron microscopy (SEM) in transverse sections of human cortical bone. Na(3) PO(4) etching was used to improve the resolution of the interface between neighboring lamellae and the precision of measurements. These technical improvements permitted testing of earlier morphometry assumptions concerning lamellar thickness while revealing the existence of different lamellar patterns. The mean lamellar thickness was 9.0 ± 2.13 μm, thicker and with a wider range of variation with respect to earlier measurements. The number of lamellae showed a direct correlation with the lamellar bone area, and their thickness had a random distribution for osteonal size classes. The circular, concentrical pattern was the more frequently observed, but spiral and crescent-moon-shaped lamellae were also documented. Selected osteons were examined by either SEM or SEM combined with polarized light microscopy allowing comparisons of corresponding sectors of the osteon. The bright bands observed with polarized light corresponded to the grooves observed in etched sections by SEM. The dark bands corresponded to the lamellar surface with the cut fibrils oriented approximately longitudinally along the central canal axis. However, lamellae with large and blurred bright bands could be observed, which did not correspond to a groove observed by SEM. These findings are in contrast with the assumption that all the fibril layers within a lamella are oriented along a constant and unchangeable angle. The different lamellar patterns may be explained by the synchronous or staggered recruitment and activation of osteoblasts committed to the osteon's completion.

The fibrillar organisation of the osteon and cellular aspects of its development : a morphological study using the SEM fractured cortex technique

The collagen architecture of secondary osteons was studied with scanning electron microscopy (SEM) employing the fractured cortex technique and osmic maceration. Fibrillar orientation and the change in their direction in sequential lamellae was documented where lamellar formation was ongoing, as well as in resorption pits where osteoclasts had exposed the collagen organisation of the underlying layers. Applying an adaptive stereo matching technique, the mean thickness of matrix layers removed by osteoclasts was 1.36 ± 0.45 μm. It was also documented that osteoclasts do not attack the cellular membrane of the exposed osteocytes. The mean linear osteoblast density in fractured hemicanals was assessed with SEM and no significant differences were observed comparing larger with smaller central canal osteons. These findings suggested a balance between the differentiated osteoblasts that have aligned on the surface of the cutting cone and those that are transformed into osteocytes, because the canal surface is progressively reduced as the lamellar apposition advances.

Atherosclerotic alterations in human carotid observed by scanning electron microscopy

Atherosclerosis involves all the layers of the artery wall, but the events involving the intimal portion are fundamental to understand the evolution and gravity of lesions. This study shows that scanning microscopy is instrumental for better understanding the physiopathology of this disease.

Anatomy of the intracortical canal system: scanning electron microscopy study in rabbit femur

The current model of compact bone is that of a system of longitudinal (Haversian) canals connected by transverse (Volkmann's) canals. Models based on histology or microcomputed tomography lack the morphologic detail and sense of temporal development provided by direct observation. Using direct scanning electron microscopy observation, we studied the bone surface and structure of the intracortical canal system in paired fractured surfaces in rabbit femurs, examining density of canal openings on periosteal and endosteal surfaces, internal network nodes and canal sizes, and collagen lining of the inner canal system. The blood supply of the diaphyseal compact bone entered the cortex through the canal openings on the endosteal and periosteal surfaces, with different morphologic features in the midshaft and distal shaft; their density was higher on endosteal than on periosteal surfaces in the midshaft but with no major differences among subregions. The circumference measurements along Haversian canals documented a steady reduction behind the head of the cutting cone but rather random variations as the distance from the head increased. These observations suggested discontinuous development and variable lamellar apposition rate of osteons in different segments of their trajectory. The frequent branching and types of network nodes suggested substantial osteonal plasticity and supported the model of a network organization. The collagen fibers of the canal wall were organized in intertwined, longitudinally oriented bundles with 0.1- to 0.5-mum holes connecting the canal lumen with the osteocyte canalicular system.

Scanning electron microscopy evaluation of the link between a new dentinal desensitizer and dentine

AIM

The purpose of this study was to evaluate the interaction of a novel dentinal desensitizer Twin Pro with enamel-dentinal adhesive preparations or filling materials and dentine using scanning electron microscopy (SEM) technology.

METHODS

Black's I class cavities were drilled extracted molar teeth free of caries or fissures, and the cavities disinfected. The specimens were divided into 4 groups of 2 teeth each treated as follows: Group A: Twin Pro, fluid (Tetric-Flow Vivadent) and micro-hybrid (Tetric-Ceram Vivadent) composites placed on the etched (Liner Bond 2V Clearfil) cavities. Group B: Twin Pro, PQ1-Ultradent loaded Primer-Bonding plus fluid and micro-hybrid composites applied to the acid-etched (37% orthophosphoric acid) cavities. Group C: Twin Pro plus Silver amalgam alloy (Phasealloy- Sybram Kerr). Group D (control group): self-etching primer plus fluid and micro-hybrid composite. Specimens were investigated by SEM.

RESULTS

The results obtained in all groups show that the application of Twin Pro does not alter the adhesiveness of the restorative composite materials to the dental wall. In fact the desensitizer and the adhesive layers are indistinguishable at SEM observation, and well adherent to the dentinal surface of the cavities.

CONCLUSION

The results of SEM investigations show that Twin Pro does not decrease the adhesion of restorative materials to the tooth surface, as it establishes an efficient interconnection with the different materials used, and it forms a uniform layer covering and occluding dentine tubules, and this might constitute an efficacious sealing of dentinal tubules which possibly contribute to decrease dentinal sensitivity to environmental nociceptive stimuli.

Ultrastructural localization of tyrosine hydroxylase in human peripheral blood mononuclear cells: effect of stimulation with phytohaemagglutinin

Using immunocytochemistry coupled to fluorescence and electron microscopy, we investigated the expression and ultrastructural localization of tyrosine hydroxylase (TH, EC 1.14.16.2), the rate-limiting enzyme in the biosynthesis of catecholamines, in human peripheral blood mononuclear cells (PBMCs), with PC12 cells as positive controls. In unstimulated PBMCs, TH-specific immunoreactivity was localized to the plasma membrane. However, after stimulation with the polyclonal mitogen phytohaemagglutinin (PHA), TH immunoreactivity was almost completely localized to electron-dense cytoplasmic granules, which resembled those found in PC12. TH-positive granules, however, were larger (300-500 nm) than in PC12 cells (100-200 nm). Flow cytometry analysis of TH expression showed about 46-50% positive cells in unstimulated PBMCs and in PHA-stimulated PBMCs in the G0/G1 phase of the cell cycle, but more than 80% positive cells in PHA-stimulated PBMCs in the S+G2/M phase. In agreement with previous observations, PHA stimulation also induced de novo expression of TH mRNA as well as increased intracellular catecholamine content, suggesting the occurrence of TH upregulation at the level of both gene expression and enzyme activity. The ultrastructural localization of TH in human PBMCs seems therefore regulated by cell stimulation and related to the functional activity of the enzyme.

The paracoronal (marginal) cells of fungiform papilla of Rana esculenta

Paracoronal secretory cells can be observed outside the sensorial area of the fungiform papilla of Rana esculenta. The morphology of these cells, the type of secretion and their function have, to date, only been incidentally described. By scanning electron microscopy (SEM), the paracoronal cells appear as swallow's-nest-shaped formations with openings 10-15 microns in diameter. The walls of paracoronal cells are characterized by laminar processes subdividing the interior hollow. The cavity of these formations is occupied by amorphous material as demonstrated by light microscopy (LM) pictures. The secretory material fills 7/8 of the upper part of the cytoplasm and appears rather transparent. The secretory material is PAS-negative, unlike the secretory granules contained in laminar processes. By transmission electron microscopy (TEM), they appear as clear ovoid structures, the nucleus of which is situated in the deeper part of the cell, enveloped by a thin cytoplasmic layer and characterized by secretory apparatus and the presence of secretory granules of middle electron-opacity. The apical part of these cells presents large mucous droplets. These cells adhere both to ciliated and parietal cells. Following cytochalasin-B treatment, cells do not show any considerable ultrastructural modification, while after terbutaline treatment the profiles of secreted paracoronal cells increase greatly. Histochemical properties of their secretory products are similar to those of parietal cells and their particular anatomical localization may exclude the direct implication of these cells in taste transduction.

The role of proteoglycans in maintaining collagen fibril morphology

The aortic wall contains various heterogenous proteoglycan populations which interact in different ways with other components of extracellular matrix. Proteoglycans (PGs) are known to provide structural support to the vessel wall as well as to influence specific physiological functions of the tissues. The aim of the present study was to investigate the effects of Chondroitinase AC (Chase), Streptococcal Hyaluronidase (Hyase) and Heparanase on human aortic wall collagen which had been treated previously with 4M GuHCl, in order to verify the effects of selective glycanolytic treatment on type I collagen fibril ultrastructure. Following 4M GuHCl treatment, collagen fibrils are seen to have a clearly visible period. Subsequent to GuHCl and Streptococcal Hyase treatment all collagen fibrils appear to be completely swollen in thin aperiodic filaments; the typical 64 nm collagen period is completely undetectable. After GuHCl and Chase treatment a small number of collagen fibrils are seen to be swollen in thin fibrils which are mainly localized at some distance from elastic fibres. Following GuHCl and Heparanase/Heparitinase III treatment a considerable number of collagen fibrils appear to be swollen in thin fibrils; the majority of which are situated in the vicinity of elastic fibrils. The swelling of collagen fibrils underlines the fundamental role of proteoglycans in maintaining collagen fibril integrity and periodicity. It is as yet impossible to precisely map interactions between these proteoglycans and collagen fibres. The role of Hyaluronic acid requires further investigation, although the nature of this interaction is undoubtedly a matter of considerable interest.

Morphological features of different regions in frog crista ampullaris (Rana esculenta)

The cellular organization of different regions of the crista epithelium from the frog posterior semicircular canal was studied by light, transmission and scanning microscopy. The sensory epithelium consists of hair cells surrounded by supporting cells and basal cells located close to the basement membrane. Three types of hair cells, namely club-like, cylindrical and pear-like cells differentially distributed along the crista could be recognized on the basis of their shape. Club-like cells are located only in the peripheral regions, cylindrical cells both in the central and in the peripheral regions, and pear-like cells appear segregated into the intermediate regions. Sensory cells of the central region are characterized by a ciliary apparatus consisting of stereocilia usually shorter--and in some cases less numerous--than those of cells of the other regions. The presence of large evaginations of the apical membrane of hair cells and of several vesicles of microexocytosis demonstrates that receptor cells have a considerable secretory activity. This secretory activity is also proven by the presence in the supranuclear region of hair cells of numerous Golgi complexes. Moreover, the presence of two kinds of Golgi complexes, one constituted by dilated cisternae containing a moderately electron-dense material and the other made up of flattened electron-transparent cisternae, suggests a diversified secretion of material by the hair cells. This heterogeneous material may provide substances important for cupula formation and the composition of the endolymph.

Collagenase-extractable proteoglycans from lesion-free areas of human aorta

Different proteoglycan (PG) populations were isolated from normal human aorta by extraction of minced tissue with 4M GuHCl and by further digestion of the residue with collagenase. Dissociative extraction induced a complete disappearance of Alcian Blue positive material, which was demonstrable by transmission electron microscopy before the treatment around collagen fibrils and in pericellular areas. However, 4M GuHCl extraction solubilized only an average of 60% of aorta total hexuronate content. Collagenase treatment of the residue resulted in a complete loss of collagen fibril organization, which was coupled with a further hexuronate recovery, accounting for about one third of total tissue content. The bulk of PGs obtained in collagenase digest was retained by Sepharose CL-4B column. Their sulphated glycosaminoglycan (GAG) composition differed from PGs extracted with 4M GuHCl, containing only chondroitin sulphate (CS) and heparan sulphate (HS), without detectable traces of dermatan sulphate (DS). Moreover, they contained hyaluronic acid. The results obtained by agarose polyacrylamide gel electrophoresis (APGE) and Octyl-Sepharose chromatography, followed by further APGE and Sepharose CL-4B gel-filtration, carried out before and after treatment with Chondroitinase ABC and AC and Heparinase I and III, suggested that collagenase digest contained different PG populations, carrying mainly either CS or HS chains. Moreover, HS containing PGs showed higher hydrodynamic size and stronger properties of hydrophobic interactions than CS containing PGs.

Primary osteoma cutis. Clinical, morphological, and ultrastructural study

Primary osteoma cutis arises in the deeper dermis for no apparent reason and presents as mature, lamellar, and osteonic bone; secondary cutaneous osteomas are correlated with inflammatory processes, scars, or dysembryoplasia and are always composed of osteoid. Ultrastructural findings of primary cutaneous osteomas have not been reported to date. Light and electron microscopic findings of a case of primary osteoma cutis are described: mineralized areas may be divided into macrocalcification and microcalcification. Macrocalcification consists of lamellar bone. Osteocytes populate the lamellae, whereas collagen fibril distribution is bone-like. Hydroxyapatite deposition presents as globular or needle-like electron-dense material progressively masking the connective tissue matrix. Microcalcifications, which are found in macroscopically normal dermis around the calcified plaque, consist of osteoid tissue inhabited by osteoblast-like cells. Microcalcifications may be interpreted as metastatic calcifications related to the primary osteoma calcified plaque. Primary osteoma cutis may be considered as true bone amartothic formation rather than dermal mineralization.

Collagen fibril ultrastructure alters after glycanolytic digestion

Fixed fragments of bovine nasal septum cartilage were digested for six hours either with testicular hyaluronidase or streptomyces hyaluronidase or flavobacter chondroitinase ABC, and observed with a transmission electron microscope. Collagen fibril diameters (D) were measured to evaluate the effect of enzymatic digestion on the fibril size. This resulted in an increased frequency (17% to 47%) of "thin" fibrils (80 to 32 nm), followed by a decrease (65% to 31%) of the frequency of "mid" fibrils (32 to 64 nm). The frequency of "thick" fibrils (over 64 nm) showed a moderate increase (18% to 22%). Considering the relationship between fibril diameter, fibril volume and collagen content, the apparently relevant increase in number of the "thin" fibrils corresponds to an alteration of only 4% of the total collagen. On the other hand the increase of the "thick" fibrils implies a conspicuous alteration of 20% of the total collagen. The observed fibril rearrangement after digestion may be explained in terms of the wrap of matrix proteoglycans around each fibril. The enzymatic removal of the proteoglycans could make "mid" collagen fibrils free to regress into "thin" as well as to merge together into "thick" fibrils.

The dependency of collagen fibrillogenesis in vitro on fibroblast culture conditions. Fibroblasts in mono- and multi-layers

The extracellular matrix produced by monolayer and tridimensional cultures of fibroblasts was investigated using histochemical and ultrastructural methods. In monolayer cultures, collagen and proteoglycans produced by fibroblasts could not be organized into morphologically recognizable structures. Tridimensional fibroblast cultures produced a well organized matrix with periodic, parallel ordered collagen fibrils of 50 nm diameter, criss-crossed by alcianophylic segments 6-10 nm thick in diameter and 100-300 nm in length, parallel to each other, perpendicular to the collagen fibrils and spaced 67 nm from each other. Some alcianophylic segments lay perpendicular to the above described ones, with maximum lengths of 65-70 nm. Alcianophylic segments are the ultrastructural evidence of structural proteoglycans. These observations suggest that the culture conditions influence the collagen and proteoglycans secretion, so that the final organization of the matrix results quite different.

Morphology of epiphyseal apparatus of a ranid frog (Rana Esculenta)

Morphological, histochemical and ultrastructural investigations on epiphyseal apparatus of Rana Esculenta were made. The most important findings were the following: 1) metaphyseal cartilage is localized inside proximal diaphyseal compact bone as a plug; 2) metaphyseal cartilage do not reduce in thickness during ageing; 3) metaphyseal cartilage do not show vascular invasion and do not mineralize in degenerative zone; 4) trabecular bone was not at all evident in this animal; 5) external periosteum is well vascularized and proliferates in correspondence to marginal epiphyseal end of the diaphyseal. From these results the hypothesis that the ranid frog bone growth is not due to metaphyseal metabolism (as in avian and mammals) but to bone periosteal marginal mineralization is reached.

Ultrastructural findings of congenital dyserythropoietic sickle cell beta thal-associated anemia

The ultrastructural findings of erythroblasts and reticulocytes in one case of congenital dyserythropoiethic anemia (CDA) associated with a haemoglobinopathy, sickle cell beta thalassemia minor (Type V CDA), is described. The observations can be summarized as follows: 1) A lot of large breaks are present in the erythroblast nuclear envelope. 2) Nuclear membrane evaginations are filled with dense loose chromatin. 3) Electron-transparent areas (moth eaten chromatin) are evident in dense chromatin. 4) Electron-dense granular material, related to altered haemoglobin chain storage, is evident in the nucleus and in the cytoplasm. 5) Iron deposits are present in mitochondrial matrix. 6) Myelinic figures are present in reticulocyte cytoplasm. For the first time the ultrastructural findings in this type of associated CDA are described and related to the double origin of clinical symptoms.

Ultrastructure of periprosthetic Dacron knee ligament tissue. Two cases of ruptured anterior cruciate ligament reconstruction

Light- and electron-microscopic investigations were performed on two failed Dacron ligaments that had been removed from 2 patients shortly after failure of the implant 2-3 years after reconstruction of the anterior cruciate ligament. Two different cell populations and matrices were correlated with closeness to the Dacron threads. Fibroblasts surrounded by connective tissue with collagen fibrils were located far from the Dacron threads. Roundish cells, appearing to be myofibroblasts surrounded by a more lax connective tissue and elastic fibers, were found close to the Dacron threads. The presence of myofibroblasts and the matrix differentiation could be attributed to the different mechanical forces acting on the Dacron and on the connective tissue because of their different coefficients of elasticity. The sparse occurrence of inflammatory cells in the synovial membrane and in the connective tissue surrounding the Dacron supports the biologic inertness of this artificial material. However, the repair tissue was not structured to resist tension stresses.

Ultrastructural aspects of human nonunion

A histological study on the tissue of nonunion of tibias of two young patients was performed to evaluate the ability of cells to start the mineralization of the matrix. The observations can be summarized as follows: 1) Tissue vessels often appear occluded by thrombotic material; 2) Fibroblasts and chondrocytes found in the nonunion tissue seemed normal, with a good secretion apparatus; 3) The cell membranes were able to produce matrix vesicles; 4) Matrix vesicles and cell membrane looked positive to ALPase reaction, 5) Hydroxyapatite crystals could be observed in the cell matrix or inside matrix vesicles. It may be concluded that cells populating nonunion tissue are well equipped to induct the mineralization of the matrix, but the absence of a blood supply, enough to bring them a normal calcium amount, is the real reason for the nonunion.

Morphological aspects of rat metaphyseal cartilage pericellular matrix

In order to verify whether it is possible to observe morphological evidence of a Ca-P amorphous phase (the first step of Ca-P crystalline deposition), the pericellular area of metaphyseal cartilage was investigated. In the pericellular zone of proliferative, maturation, hypertrophic, degeneration and calcification cartilage, many electron-opaque granules, having a very regular diameter of about 12 nm, disposed in closely-packed chains (chain granules) and increasing in number from the proliferation to the calcification zone, are evident. These chain granules, which are closely connected with proteoglycans, disappear after decalcification and are spatially related to ALPase and ATPase activities. They may be the morphological reflection of the Ca-P amorphous phase.

Infantile cortical hyperostosis (Caffey disease): ultrastructural and immunohistochemical characterization of the peritrabecular cells

The ultrastructure and the immunohistochemical pattern of the cells which are responsible for the bone resorption in the cortical infantile hyperostosis were investigated. The osteoclasts present a great positivity to MB1 antigen and a low positivity to OKM5. Mononuclear cells with primary lysosomes, looking like osteoclast ones are present in high concentration in peritrabecular spaces. These cells show a high positivity to OKM5 antigen and a low positivity to MB1 antigen. The mononuclear granulated cells are positive to tartrate-resistent acid phosphatase. The possible common origin and their co-operation in bone resorption is discussed.

Type I procollagen in the severe non-lethal form of osteogenesis imperfecta. Defective pro-alpha 1(I) chains in a patient with abnormal proteoglycan metabolism and mineral deposits in the dermis

We have screened type I procollagen synthesized in vitro by skin fibroblasts from several patients with the severe non-lethal form of osteogenesis imperfecta. Cells from one patient synthesized and secreted both normal and a larger amount of abnormal type I procollagen. The abnormal alpha chains are larger in size due to post-translational overmodifications involving the whole triple helical domain. Abnormal collagen heterotrimers had a melting temperature 2.5 degrees-3 degrees C lower than normal ones or from controls. Chemical analysis of collagen in the medium showed a greater degree of both lysyl hydroxylation and hydroxylysyl glycosylation, the major increase in molecular mass of overmodified alpha chains being due to the higher hydroxylysine-bound hexose content. The proband's cells modify proteoglycan metabolism and mineral crystals form in the dermis, possibly a response to abnormal collagen-proteoglycan interactions. These findings can be explained by a small defect in the product of one allele for pro-alpha 1(I) chains: three-quarters of the synthesized type I procollagen molecules are composed of trimers containing one or two chains defective near the C-terminus of the triple helix or in the C-propeptide. The data obtained for this patient confirmed that the severity of clinical manifestations in osteogenesis imperfecta strongly depends on the location and nature of the mutations, and that the phenotype could be a consequence of a collagen defect(s) and its influence on collagen-collagen interactions and collagen interactions with other connective tissue components.

In vitro fibroblast and dermis fibroblast activation by laser irradiation at low energy. An electron microscopic study

The effects of laser irradiations have been estimated both from the clinical point of view (rate of reduction of the ulcerated area) and in ultrastructural terms. The modification produced by laser in human fibroblasts in culture have also been investigated. Under our clinical and experimental conditions, laser stimulates the secretion of fibroblasts, both in vivo and in vitro, for reasons that are still the object of research. After irradiation the formation of periodic collagen fibrils is not observed, so that complete ' restitutio ad integrum' of the dermal matrix does not occur.

Electron microscopic visualization of proteoglycans with Alcian Blue

The intercellular matrices of bovine nasal cartilage, chick embryo perichordal cartilage, and chick embryo mesenchymal cells cultured in vitro have been examined by electron microscopy after staining them with Alcian Blue in salt solutions according to Scott & Dorling (1965). Matrix granules, which are typical components of cartilage at the ultrastructural level, are not visible after Alcian Blue staining and are replaced by alcianophilic rod-like particles, varying in length and width. With tissue cultures, Alcian Blue stains 40-120 A thick filaments which display an orthogonal and longitudinal relationship to collagen fibrils. We assume that cartilage matrix granules represent linear proteoglycans that are coiled as a consequence of the usual glutaraldehyde-osmium fixation. It is thought that Alcian Blue, on the other hand, contributes to the stabilization of the proteoglycans in their original structural arrangement. This stabilizing property presumably also results in the sharp visualization of fine filaments in the tissue culture matrix.