Nonlinear methods of vehicle velocity determination based on inverse systems and tensor products of Legendre polynomials in compact car class.

The article presents research on the methods of crash velocity determination based on the Compact car class. The database used in the research is provided by the NHTSA (National Highway Traffic Safety Administration) and includes numerous frontal crash tests, which allowed the determination of the mathematical model parameters. Two methods are presented that enable the determination of vehicle velocity before the collision. The first researched method is the so-called inversed system method and is based on the assumption that the relationship between bk coefficient Cs is an inverse function. The second line of research focuses on the tensor product method, which is grounded in the Legendre polynomials, orthogonal on the interval [-1, 1] (Axler, 1997; Cheney and Kincaid, 2002). The article presents the calculation algorithm for both cases and the results with reference to the NHTSA database (Sharma et al., 2007; Siddall and Day, 1996). The application of the least square method provides more precise results in both cases than in previously researched solutions, with a slight advantage of the tensor product method. The obtained mean relative error of the velocity determination using the inverse system method is approximately 16,22% for the linear model and 10,58% for the nonlinear model. In the case of the tensor product method the errors for linear and nonlinear models are respectively 6,74% and 6,3%.

Positively charged dextran resin inhibits trabecular bone repair in the rabbit tibial physis.

Because exposure to positively charged dextran resin (PCDR) inhibits the growth of cultured rat and human bone cells, we tested the hypothesis that PCDR might inhibit bone repair in vivo. Central physeal defects were created by drilling 3.0-mm holes from the proximal tibial plateau into the metaphysis. The defects in left tibiae were packed with neutral resin (control); those in right tibiae were filled with PCDR. At the end of the 1st, 2nd, 3rd, and 10th postoperative weeks, the outcomes were quantitated by documenting the percent trabecular bone volume within the defect. The PCDR-filled defects showed a significant decrease in trabecular bone formation as early as the 2nd week. By the 10th postoperative week, formation of trabeculae had been reduced by nearly 40%. The inhibition conferred by PCDR suggests that the resin could be used as a suppressive interpositional material.

Antitumor effect of positively charged resin in the hamster cheek pouch model.

Following the signal observation that contact with positively charged dextran resin (PCDR) inhibited the growth of cultured mammary (Hs578T and MDA-MB-231), pancreatic (H2T), and myeloma (RR-658) tumor cell lines, studies were developed in the hamster cheek pouch model using hamster H2T pancreatic tumor cells to determine if the antiproliferative effect of PCDR could inhibit tumorigenesis. In these studies, the control population represented groups injected with H2T cells alone or in combination with either neutral or negatively charged resin. When cells (5 x 10(2) to 1 x 10(5)) and PCDR were administered simultaneously, the tumor incidence (percent engraftment) and growth of tumors that already had been established were significantly reduced. When PCDR was injected into already established 1-35-mm2 H2T tumors (engraftment for 21 days = 96%), the resin suppressed the growth of the smallest tumors (< 10 mm2). In none of these trials was the somatic growth of the host hamsters affected. PCDR contact with H2T cells in vitro for 4 days or used to treat growing solid tumors for 72 days significantly reduced cellular ornithine decarboxylase activity. While the mechanism of PCDR action has not been established, the observations have implications for in vivo tumor therapeutic models.

Efficacy of positively charged ion exchange beads in radiation-impaired models of wound healing.

We have previously demonstrated in a rat surgical incision model that charged dextran beads enhance wound repair in a charge-specific manner: positively charged beads increased wound breaking strength (WBS), whereas neutral or negatively charged beads were ineffective. The present work extends these observations into two models of radiation-impaired healing. One hundred five rats were divided into three groups: group 1, controls, no irradiation; group 2, total body irradiation; group 3, surface irradiation. Three days after irradiation, 0.1 ml of a suspension of either positively charged beads, neutral beads, or vehicle alone was applied to paired 6-cm incisions on the dorsum of the rats. Ten days later, wounds were excised and sample strips were harvested for determination of WBS and for histological analysis. Following total body irradiation, positively charged beads enhanced WBS 84% compared to beadless controls. When results with positively charged beads were compared to those with neutral beads, a 39% increase in WBS was noted. Healing, as measured by WBS, was more impaired in surface-irradiated animals, but when results with positively charged beads were compared with those obtained with neutral beads, a similar degree of healing (+38%) was noted. Neutral beads proved ineffective. Histology revealed that neutral beads evoked a modest foreign body response, yet there was a consistently greater clustering of giant cells around positively charged beads in wound sites. This paralleled in vitro experiments demonstrating increased monocyte aggregation around positively charged beads in tissue culture. The results suggest that positively charged ion exchangers, such as these positively charged beads, perhaps through their recruitment and/or activation of wound macrophages, may have a potential clinical role in the treatment of impaired wounds.

Potentiation of osteoclast bone-resorption activity by inhibition of nitric oxide synthase.

We have examined the effects of modulating nitric oxide (NO) levels on osteoclast-mediated bone resorption in vitro and the effects of nitric oxide synthase (NOS) inhibitors on bone mineral density in vivo. Diaphorase-based histochemical staining for NOS activity of bone sections or highly enriched osteoclast cultures suggested that osteoclasts exhibit substantial NOS activity that may account for basal NO production. Chicken osteoclasts were cultured for 36 hr on bovine bone slices in the presence or absence of the NO-generating agent sodium nitroprusside or the NOS inhibitors N-nitro-L-arginine methyl ester and aminoguanidine. Nitroprusside markedly decreased the number of bone pits and the average pit area in comparison with control cultures. On the other hand, NOS inhibition by N-nitro-L-arginine methyl ester or aminoguanidine dramatically increased the number of bone pits and the average resorption area per pit. In a model of osteoporosis, aminoguanidine potentiated the loss of bone mineral density in ovariectomized rats. Aminoguanidine also caused a loss of bone mineral density in the sham-operated rats. Inhibition of NOS activity in vitro and in vivo resulted in an apparent potentiation of osteoclast activity. These findings suggest that endogenous NO production in osteoclast cultures may regulate resorption activity. The modulation of NOS and NO levels by cells within the bone microenvironment may be a sensitive mechanism for local control of osteoclast bone resorption.

Negatively charged resins stimulate bone formation in subperiosteal sites in rats. The effect of age.

The osteogenic response to subperiosteal injection of negatively charged ion exchange resins was compared in the tibiae of one-month and 16- to 22-month-old rats. The resins were administered either in the form of beads (CM Sephadex) or as particles (CM cellulose, carboxymethylcellulose), and the animals were killed at two weeks and at one month after injection. Histologically, the resins did not produce an inflammatory response. Periosteal bone formation was observed wherever resin was in contact with bone, and in the resin bed the connective tissues that invested the charged materials ossified within the first month. Marrow spaces commonly formed where periosteal growth was most rapid. The osteogenic effect was independent of resin conformation, and it was more pronounced in the younger rats.

Enhancement of repair in experimental calvarial bone defects using calcium sulfate and dextran beads.

Granular medical-grade calcium sulfate hemihydrate (MGCSH) and negatively charged dextran beads (DB) were evaluated both separately and in combination in cranial defects. Thirty-six rats received bilateral parietal inlay reconstructions using MGCSH, MGCSH plus DB, or DB alone or the defects were left unfilled. Postoperative evaluation at 45, 90, and 135 days was done by visual inspection, caliper measurements of defect thickness, and histologic examination. The best fibro-osseous repair of the defects occurred with the use of MGCSH in combination with DB. Repair tissue, which was confluent with the adjacent cranium, was noted to have good thickness, and a high bone content. By contrast, defects repaired with either DB or MGCSH alone had poorer quality repair tissue, with concavities, voids, bead migration, decreased thickness, and minimal bony replacement/ingrowth. Unfilled control defects showed only a thin, friable, translucent connective tissue layer of repair. No method produced complete bony closure.

Enhanced healing of cutaneous wounds in rats using beads with positively charged surfaces.

The efficacy of electrical fields in soft-tissue repair is unclear. Materials with a charged surface provide a localized charged environment. We examined the effects of surface-charged particles in wound healing in rats with paired dorsal incisions with one side serving as a control. Tensiometry demonstrated that after 10 days, wounds with positively charged particles were 53 percent stronger (p less than 0.001) than controls (10 rats, 30 wound strips), whereas differences with negatively charged (6 rats, 15 strips) or uncharged beads (11 rats, 33 strips) were insignificant. Histologically, wounds with positively charged particles were characterized by large quantities of collagen-rich connective tissue and by prominent bead-associated giant cells. At 94 days, no differences in wound strength were noted. This method of creating charged local environments has potential clinical implications and may add insights into the behavior of cells in response to charged stimuli.

Osteoclast recruitment in response to human bone matrix is age related.

The effect of bone matrix age on the recruitment and differentiation of osteoclast precursors was studied using the chick chorioallantoic membrane (CAM) implant system. Devitalized mineralized bone particles (75-250 microns) were prepared from human femoral cortical bone obtained postmortem from 8 men (age range: 18-72 years). The particles were implanted onto the CAM and 8 days later implants were harvested and processed for light microscopic, morphometric or immunohistochemical analysis. Histomorphometric analysis was performed on samples representing each donor age. The analysis was grouped into three categories consisting of bone from young adults (18-20 years), adults (34-53 years) and aged individuals (67 years and older). Total osteoclast number, osteoclast number per bone particle, cell area, cell size, number of nuclei per cell profile, nucleocytoplasmic ratio, and the presence of a distinctive osteoclast antigen defined by monoclonal anti-body 121F were determined. Bone matrix from older individuals, and therefore the oldest age group (67 years and older), elicited significantly fewer multinucleated cells when compared to bone matrix from younger donors. The number of nuclei per cell profile was highest in the adult population (34-53 years), and there was a continuous increase in cell area with aging. As a consequence, the nucleocytoplasmic ratio decreased from the youngest to the oldest age group. These findings indicate that, relative to factors that affect the recruitment and differentiation of osteoclast precursor cells, bone matrix of older individuals is changed in quality and/or quantity compared to bone matrix from younger individuals. It is hypothesized that this decline in osteoclast formation in response to older bone matrix may contribute to the impaired bone remodeling associated with aging.

Osteoclast formation is related to bone matrix age.

Little is known about the relationship between the age of the skeleton and the development of multinucleated bone-resorbing cells, osteoclasts. It has been shown that mineralized bone implanted onto the chick chorioallantoic membrane (CAM) is effective in the recruitment and differentiation of osteoclast precursors. In studies reported here we used the CAM system to examine the influence of bone matrix age on osteoclast formation. Devitalized mineralized bone particles (75-250 microns) were prepared from rats of various ages (2, 4, 9, 12, and 16 months). The particles were implanted onto the chick chorioallantoic membrane and 8 days later implants were harvested and processed for morphometric or immunohistochemical analysis. Osteoclast number, cell area, nucleocytoplasmic ratio, and the presence of a distinctive osteoclast antigen, defined by the 121F monoclonal antibody, were determined. Bone particles of each age group resulted in the formation of osteoclast-like giant cells. Compared with multinucleated cells that formed in response to bone particles obtained from 2-month-old rats, matrix from the oldest age group (16 months) elicited significantly fewer and smaller cells which contained a smaller number of nuclei. These data suggest that with aging, bone undergoes qualitative and/or quantitative changes that affect the recruitment and differentiation of osteoclast precursor cells.

Stimulation of craniofacial and intramedullary bone formation by negatively charged beads.

To test for their osteogenic stimulating capacity, charged beads were implanted into cranial or mandibular defects, used as an onlay on the nasal bone surface, or injected into femoral medullary cavities of young adult rats. One month later, negatively charged beads were found to have stimulated extensive bone formation resulting in closure of craniofacial defects, a new layer of bone on the nasal bone surface, and a bead-bone lattice within marrow cavities of long bones. Positively charged beads were nonosteogenic, but elicited a pronounced fibroblastic response in the craniofacial skeleton. Positively charged beads were found associated with multinucleated giant cells at all implantation sites. Uncharged beads failed to elicit formation of new bone and were associated with connective tissue that was less cellular and less organized than was seen with positively charged beads. It was concluded that beads that have ben chemically treated to confer either a negative or positive surface charge, when placed in contact with bone, evoke osteogenesis or formation of dense connective tissue, the response depending on the surface charge of the bead. The mechanism(s) by which the charged beads foster the osteogenic or fibroblastic response is not clear. The use, however, of alloplastic materials with charged surfaces in repair and augmentation of bone, and in wound repair, warrants further investigation.

Correlation of an osteoclast antigen and ruffled border on giant cells formed in response to resorbable substrates.

The osteoclast is the specialized multinucleated cell primarily responsible for the degradation of the organic and inorganic components of bone matrix. The functional and developmental relationship between osteoclasts and foreign body giant cells is unclear. The osteoclast plasma membrane ruffled border juxtaposed to the bone surface is a unique morphologic characteristic of active osteoclasts. In the studies reported here giant cell formation was induced in response to a variety of materials implanted onto the richly vascularized chick chorioallantoic membrane. Light and electron microscopic techniques were used to examine the morphologic characteristics of the giant cells. In addition, immunohistochemical methods were used to demonstrate the appearance of a 150 kD cell surface antigen on chicken osteoclasts recognized by monoclonal antibody 121F. Giant cells that formed in response to mineralized bone particles exhibited ruffled borders and stained positively with the 121F antibody. Many giant cells that formed in response to hydroxyapatite possessed ruffled borders similar to but not as extensive as those observed on giant cells formed on bone. Immunohistochemical localization of the 121F antigen on these cells suggested that the antigen was present, but staining intensity was reduced compared to that of bone-associated giant cells. The formation of mineral matrix complexes by the adsorption to hydroxyapatite of bone extract or osteocalcin enhanced ruffled borders and the presence of the 121F antigen on elicited giant cells. In contrast, giant cells that formed on non-resorbable materials, such as Sepharose beads, mica, and methacrylate, lacked ruffled borders and were negative for the 121F antigen. It appears that expression of the 121F osteoclast antigen correlates with the appearance and extent of ruffled membranes on giant cells. Furthermore, it appears that giant cell ruffled membrane development and the presence of the 121F osteoclast antigen are related to giant cell formation in response to resorbable materials that are subject to extracellular dissolution. Expression of this antigen may be indicative of the developmental and/or functional state of giant cells (osteoclasts) that form on resorbable substrates. In addition, components of the bone matrix, including osteocalcin, in association with bone mineral, lead to elevated levels of this osteoclast antigen.

Charged beads: generation of bone and giant cells.

Based on reports of electrically induced bone formation and findings that some materials used to promote bone ingrowth are stimulatory in bead form, the osteogenic potential of beads with different surface charges was examined. In this preliminary study, three types of Sephadex beads were injected into chick femora: type I, DEAE beads, positively charged; type II, CM beads, negatively charged; type III, G-25, uncharged. Beads were injected into the femoral midshaft, and after 3 days, 4 days, and 1 week, birds were sacrificed and femora were processed for histology. Type I beads: at 3 days, were surrounded by multinucleated giant cells; by 4 days, patches of bead-associated new bone were present along with giant cells; after 1 week, occasional bead-associated multinucleated cells were seen, but now most beads were surrounded by new intramedullary bone, forming an extensive bead-bone lattice. With bead types II and III, bead-associated new bone was seen at 3 days and 4 days only when beads lodged near the endosteum or in the metaphysis. At 7 days, no bone was seen with either of these two bead types. The response to the type I beads may be likened to a remodeling phenomenon with large numbers of giant cells at 3 days, new bone and giant cells at 4 days, and evidence only of bone formation at 7 days.

Osteoclast development: the cell surface and the bone environment.

Bone development and remodelling processes depend on complex interactions between bone cell precursors, mature bone cells, extracellular matrix molecules, growth factors, the immune system and humoral factors. The exact molecular nature of many of the cell-cell and cell-matrix interactions occurring during bone remodelling remains to be resolved. Cell surface molecules are likely to have important roles in both bone cell differentiation and regulatory processes. However, little is known about changes in the osteoclast cell surface during development and there is only limited information on the cell surface composition of the mature cell phenotype. We describe how one osteoclast-specific monoclonal antibody has been used to identify, characterize and purify a 96 kDa/140 kDa osteoclast membrane protein. The antibody has also been used as a phenotypic marker in studies designed to identify soluble and matrix-related bone factors involved in the terminal stages of osteoclast differentiation. In parallel studies using marrow-derived giant cells and the chick chorioallantoic membrane (CAM), immunohistochemical and enzyme-linked immunoassays (ELISA) have been used to investigate the influence of calvaria, calvaria-conditioned medium, bone matrix, and bone matrix components on osteoclast development. Marrow-derived giant cells express osteoclast-specific cell surface antigens when co-cultured with live calvariae or when exposed to calvaria-conditioned medium. In the richly vascularized and mesenchymal cell-containing CAM, intact bone matrix induces the formation of giant cells that express the osteoclast-specific antigens. In contrast, isolated bone matrix components implanted on the CAM recruit only mononuclear cells which are not recognized by the osteoclast-specific antibody.

Calcium deficiency during lactation and in the first two weeks after weaning: decreased ash and increased magnesium in bone of rat pups.

The mineral and skeletal status of offspring of calcium-deficient lactating dams was examined. At weaning pups of calcium deficient dams weigh less than controls and are hypocalcemic and hypermagnesemic, but have normal phosphorus levels. Bone ash expressed as percent dry weight is decreased, as is ash content of calcium and phosphorus, while magnesium is high. Histologically, except for thinner layers of lamellar bone, long bones and calvariae are unremarkable. Calcium-deficient pups subsequently fed a normal diet for two weeks gain weight rapidly, recover bone ash (increase of 62%) and normalize magnesium content of both blood and bone. At this point, bones from experimental and control animals are histologically indistinguishable. Weanlings of calcium-deficient mothers, themselves put onto the calcium-deficient diet for two weeks, show a further decline of blood calcium and a further decrease in bone ash. Blood and bone magnesium remain elevated. Long bone trabecular architecture and marrow cavity formation appear normal, but less compact bone is evident. These doubly deprived animals recover rapidly when placed on a normal diet. Within two weeks, mineral content of blood is in the control range, bone ash increases by 93%, and the slope of the weight gain curve parallels that of controls. However, in spite of the profound bone ash increase and linear weight gain, these animals remain deficient in both parameters when examined at 9 weeks of age. Similarly, bone mineral content, which also tended to normalize, fails to completely correct by this time point.

Inductive specificity of mineralized bone matrix in ectopic osteoclast differentiation.

The present report describes the first in a series of studies designed to identify the factor or factors responsible for eliciting osteoclast differentiation. Particles of mineralized and demineralized bone, hydroxyapatite (HA), and eggshell were grafted onto the chorioallantoic membranes (CAMs) of chick embryos. After 3 of 6 days, portions of CAMs with associated grafts were harvested, processed for light and electron microscopy, and examined for the presence of multinucleated giant cells with the morphological characteristics of osteoclasts. Light microscopic examination revealed that, within only 3 days, many particles of mineralized materials had become surrounded or engulfed by multinucleated giant cells. Ultrastructurally, all such cells possessed a vacuolated and mitochondria-enriched cytoplasm, but they differed in the nature of the contacts formed at the cell-particle interface. With eggshell, the cells developed filopodia but lacked clear zones and ruffled membranes. With HA, clear zones were evident but cytoplasmic extensions and membrane ruffling were absent. Implants of mineralized bone, however, elicited the formation of giant cells with prominent clear zones and ruffling of the plasma membrane like that observed in bonafide osteoclasts. In contrast, grafts of demineralized bone did not evoke giant cell formation but rather recruited two cell types morphologically akin to either fibroblasts or macrophages. We conclude that the factor(s) responsible for osteoclast differentiation resides specifically within bone matrix and is intimately associated with the mineral phase. Further, in response to such a factor(s), osteoclast differentiation can occur ectopically, outside of the developing vertebrate body.

The relationship of monocytic cells to the differentiation and resorption of bone.

Osteogenesis in the developing limb is, as elsewhere, the result of two functionally integrated processes, bone matrix synthesis and matrix degradation. The latter process is a manifestation of the resorptive activity of osteoclasts (OCs), multinucleated giant cells which arise by fusion of mononuclear, blood-borne precursors. For the past several years, we have focused our efforts on several different aspects of OC development and differentiation. These efforts have included observations on patients with osteopetrosis, an analysis of monocyte (OC precursor) chemotaxis in response to bone matrix proteins, and the use of histochemical and bone grafting techniques to establish the lineage and expression of the osteoclast phenotype in the avian embryonic limb. Here, we (1) briefly review the evidence establishing the hematopoietic and probable monocytic origin of OCs, (2) present new data on the role of L-gamma-carboxyglutamic acid in osteocalcin-evoked chemotaxis and (3) describe the time course and likely developmental relationships between the appearance of circulating OC precursor cells, osteoclast differentiation, and the formation of mineralized bone matrix in the chick embryo. The results of the latter study indicate that OC differentiation is initiated by contact between precursor cells and mineralized bone, and suggest that the expression of the OC phenotype is dependent upon proteins or glycoproteins closely associated with bone mineral. We note that osteocalcin is one such protein.