[Comparative study of minimally invasive titanium elastic nail and steel plate on the treatment of fracture of tibiofibular fracture in adults].

OBJECTIVE: To compare the clinical outcomes of using elastic intramedullary nail and plate to fix fibular fracture. METHODS: The 60 patients with tibiofibular fractures admitted from January 2015 to December 2022 were divided into two groups:intramedullary nail group and plate group, 30 cases each, intramedullary nail group was treated with elastic intramedullary nail fixation group, plate group was treated with steel plate and screw fixation group. Intramedullary nail group, there were 18 males and 12 females, aged from 22 to 75 years old with an average of (39.4±9.8) years old, including 24 cases of traffic accidents injury, 6 cases of falling injury, 23 cases of closed fractures, 7 cases of open fractures. Steel plate group, there were 15 males and 15 females, aged from 24 to 78 years old with an average of (38.6±10.2) years old. The 22 cases were injured by traffic accident, 8 cases were injured by falling. The 24 cases were closed fractures and 6 cases were open fractures. The operation time, intraoperative bleeding, American Orthopedic Foot and Ankle Society (AOFAS) ankle and hind foot scores, clinical healing time of fibula and the incidence of wound complications were compared between the two groups. RESULTS: The patients in both groups were followed up for 6 to 21 months, with an average of (14.0±2.8) months. Compared with plate group, intramedullary nail group had shorter operative time, less bleeding, shorter clinical healing time of fibula, and lower infection rate of incision, and the difference was statistically significant (P<0.05). There were 2 cases of delayed healing in intramedullary nail group, 1 case of nonunion in plate group, and 2 cases of delayed healing in plate group, and there was no statistically significant difference between the two groups (P>0.05). In the last follow-up, according to the AOFAS scoring standard, the ankle function in intramedullary nail group was excellent in 17 cases, good in 12 cases, fair in 1 case, with an average of (88.33±4.57) points, while in plate group, excellent in 16 cases, good in 10 cases, fair in 4 cases, with an average of (87.00±4.14) points;There was no statistical difference between the two groups (P>0.05). CONCLUSION: Elastic intramedullary nail has the advantages of short operation time, less intraoperative bleeding, short fracture healing time and less incision complications in the treatment of fibular fracture, which is worthy of clinical application.

[A comparative study of vancomycin loaded bone cement in the treatment of Wagner â ¡-â £ diabetic foot].

OBJECTIVE: To investigate the clinical effect of vancomycin bone cement in the treatment of diabetic foot ulcer (DFU) ruptured Wagner gradeⅡ-Ⅳ. METHODS: From March 2019 to April 2021, 32 patients with Wagner gradeⅡ-Ⅳ diabetic foot were divided into vacuum sealing drainage (VSD) group and bone cement group according to different treatment methods. There were 16 cases in VSD group, 8 males and 8 females;the age ranged from 66 to 81 (70.50±7.20) years, and the course of disease ranged from 8 to 40 (27.56±8.55) months;Wagner gradeⅡin 2 cases, grade Ⅲin 7 cases and grade Ⅳin 7 cases;debridement and VSD were used. There were 16 cases in the bone cement group, 9 males and 7 females;the age ranged from 63 to 79 (69.56±7.29) years, and the course of disease ranged from 11 to 39(22.75±11.43) months;Wagner gradeⅡ in 2 cases, grade Ⅲin 5 cases and grade Ⅳ in 9 cases;vancomycin loaded bone cement was used for treatment. The types of bacteria, negative time of bacterial culture, skin healing time, hospital stay, operation times and complications were observed and compared between two groups. RESULTS: All patients were followed up for 3 to 6 (4.00±1.07) months. The bacterial negative time, skin healing time and hospital stay in bone cement group were significantly lower than those in VSD group (P<0.05). The median number of operations in both groups was 2, and there was no significant difference (P>0.05). According to the analysis of pathogens in two groups, there were 13 cases of G+ patients, 14 cases of G- patients and 5 cases of mixed bacteria. The number of G+, G- and mixed bacteria in bone cement group was 6, 7 and 3 cases respectively, and the number of G+, G- and mixed bacteria in VSD group was 7, 7 and 2 cases respectively. The wounds of 32 patientsin two groups healed completely without complications. CONCLUSION: Vancomycin loaded bone cement is effective in the treatment of Wagner grade Ⅱ-Ⅳ diabetic foot ulceration wounds. It can reduce the length of hospital stay, shorten the healing time of skin and kill pathogens as soon as possible. It is one of the effective methods to treat Wagner gradeⅡ-Ⅳdiabetic foot ulceration.

Intrauterine exposure to 2,3',4,4',5-pentachlorobiphenyl alters spermatogenesis and testicular DNA methylation levels in F1 male mice.

Polychlorinated biphenyls (PCBs) are synthetic biphenyl compounds with high toxicity. There are a total of 209 homologs, among which 2,3',4,4',5-pentachlorobiphenyl (PCB118) is one of the dioxin-like PCBs. PCB118 can accumulate in pregnant mice, leading to fetus directly exposure during development. The stage of migration of mouse primordial germ cells ranges from 8.5 to 13.5 days of pregnancy, which is the stage undergoing a genome-wide DNA demethylation process. In this study, the mice were exposed to 20 µg/kg/day and 100 µg/kg/day PCB118 from 8.5 to 13.5 days of pregnancy. During the embryo stage at 18.5 days (E18.5 days), the expression level of DNA methyltransferase 1 (Dnmt1) was reduced in the testes, and the DNA methylation level in mouse testes were also decreased. We found that the seminiferous tubules showed vacuolization and that the sperm deformity rate increased in the treated groups compared with the control group in 7-week-old mice. Because exposure to PCB118 during pregnancy causes damage to the reproductive system of male offspring mice, attention should be devoted to the toxicity transmission of persistent environmental pollutants such as PCBs.

Biopromoters for Gas Hydrate Formation: A Mini Review of Current Status.

Gas hydrates have promising application prospects in the fields of future energy sources, natural gas storage and transportation, CO2 capture and sequestration, gas separation, and cold energy. However, the application of hydrate technologies is being restricted due to the slow formation rate of gas hydrates. Kinetic promoters have been receiving increased attention, given that they can improve the hydrate formation rate with very small doses and do not affect gas storage capacity. However, most kinetic promoters are non-renewable, petrochemical-derived, non-degradable materials, inevitably leading to resource waste and environmental pollution. Biopromoters, derived from biomass, are renewable, biodegradable, environmentally friendly, non-toxic (or low toxic), and economically feasible. This mini review summarizes the current status of already discovered biopromoters, including lignosulfonate, amino acid, biosurfactant, and biological porous structures, which have the potential to replace petrochemical-derived promoters in hydrate technologies. Finally, future research directions are given for the development of biopromoters.

Effects of 2,3',4,4',5-pentachlorobiphenyl exposure during pregnancy on DNA methylation in the testis of offspring in the mouse.

Polychlorinated biphenyls (PCBs) are persistent organic pollutants, and the widespread use of PCBs has had adverse effects on human and animal health. This study experiment explored the effects of 2,3',4,4',5-pentachlorobiphenyl (PCB118) on the mammalian reproductive system. PCB118 was administered to pregnant mice from 7.5 to 12.5 days of gestation; F1 mice were obtained and the reproductive system of F1 male mice was examined. PCB118 damaged the reproductive system in male F1 mice, as evidenced by negative effects on the testicular organ coefficient (testes weight/bodyweight), a decrease in the diameter of seminiferous tubules and a significant reduction in the anogenital distance in 35-day-old F1 mice. In addition, methylation levels of genomic DNA were reduced, with reductions in the expression of the DNA methyltransferases DNMT1, DNMT3A and DNMT3B, as well as that of the epigenetic regulatory factor ubiquitin like with PHD and ring finger domains 1 (Uhrf1). Together, the results of this study provide compelling evidence that exposure of pregnant mice to PCB118 during primordial germ cell migration in the fetus affects the reproductive system of the offspring and decreases global methylation levels in the testis.

Effects of intrauterine exposure to 2,3',4,4',5-pentachlorobiphenyl on the reproductive system and sperm epigenetic imprinting of male offspring.

Polychlorinated biphenyls (PCBs) are a class of persistent organic environmental pollutants with a total of 209 homologs. The homolog 2,3',4,4',5-pentachlorobiphenyl (PCB118) is one of the most important dioxin-like PCBs and is highly toxic. PCB118 can accumulate in human tissues, serum and breast milk, which leads to direct exposure of the fetus during development. In the present study, pregnant mice were exposed to 0, 20 and 100 µg/kg/day of PCB118 during the stage of fetal primordial germ cell migration. Compared with the control group, we found morphological alterations of the seminiferous tubules and a higher sperm deformity rate in the male offspring in the treatment groups. Furthermore, the methylation patterns in the treatment groups of the imprinted genes H19 and Gtl2 in the sperm were altered in the male offspring. We also characterized the disturbance of the expression levels of DNA methyltransferase 1 (Dnmt1), Dnmt3a, Dnmt3b, Dnmt3l, and Uhrf1. The results indicated that intrauterine exposure to low doses of PCB118 could significantly damage the reproductive health of the male offspring. Therefore, attention should be paid to the adverse effects of PCB118 exposure during pregnancy on the reproductive system of male offspring.

Repair of Osteochondral Defects in a Rabbit Model Using Bilayer Poly(Lactide-co-Glycolide) Scaffolds Loaded with Autologous Platelet-Rich Plasma.

BACKGROUND To examine the effects of the addition of autologous platelet-rich plasma (PRP) into bilayer poly(lactide-co-glycolide) (PLGA) scaffolds on the reconstruction of osteochondral defects in a rabbit model. MATERIAL AND METHODS Porous PLGA scaffolds were prepared in a bilayered manner to reflect the structure of chondral and subchondral bone. Bone defects, measuring 4 mm in diameter and 4 mm in thickness, were created in both knee joints in 18 healthy New Zealand white rabbits, aged between 120-180 days old. Rabbits were randomly divided into three groups: rabbits with bone defects implanted with bilayer PLGA scaffolds (PLGA group) (N=6); or with bilayer PLGA and autologous PRP (PLGA/PRP group) (N=6); and the untreated group (control group) (N=6). The gross morphology, histology, and immunohistochemistry for the expression of collagen type II and aggrecan were observed at 12 weeks after surgery and compared using a scoring system. Micro-computed tomography (CT) imaging and relative expression of specific genes were also assessed. RESULTS The platelet concentrations in the PRP samples were found to be 4.9 times greater than that of whole blood samples. The total score on gross appearance and histology was greatest in the PLGA/PRP group, as was the expression of collagen II and aggrecan of the neo-tissue. Micro-CT imaging showed that more subchondral bone was formed in the PLGA/PRP group. CONCLUSIONS Bilayer PLGA scaffolds loaded with autologous PRP improve the reconstruction of osteochondral defects in the rabbit model.

Managing Complications of Percutaneous Surgery of the First Metatarsal.

The percutaneous osteotomy based on a Hohmanntype first metatarsal subcapital linear osteotomy was introduced into Mainland China in the late 1980s. No internal fixation is used for stabilization of the osteotomy, leading unfortunately to unpredictable results. Despite its high acceptance by patients and enthusiasm by surgeons at present, the clinical outcomes of percutaneous surgery have not been promising. The authors have no experience of performing this osteotomy and report only on their management of the complications of this technique and their recommended treatment algorithm.

[Investigation on the role on perindopril for prevention and treatment of glucocorticoid-induced osteoporosis in rabbits].

OBJECTIVE: To investigate the role of perindopril for prevention and treatment of glucocorticoid-induced osteoporosis (GIOP) in rabbits. METHODS: A total of 45 male New Zealand white rabbits (10 months old, weight 3.0 to 3.5 kg) were randomly divided into 3 groups involving normal control group (muscle injection of saline solution, n = 15, group NC), model group (muscle injection of dexamethasone, n = 15, group GIOP), and treatment group (muscle injection of dexamethasone combined with oral perindopril, n = 15, group GIOP+ACEI). All rabbits put to death after 12 weeks' treatment. The changes of bone mass and strength were observed and analyzed by bone histomorphology, biomechanics, metabolic bone related serological indexes and mRNA expression. RESULTS: At 12 weeks, the analysis of bone histomorphology and biomechanics results showed that the bone mass and bone strength of group GIOP were significantly lower than that of group NC (P < 0.05); after perindopril treatment, the bone mass and bone strength of group GIOP+ACEI were higher obviously than that of group GIOP (P < 0.05). Mineralizing surface,mineral apposition rate and serum osteocalcin in group GIOP decreased than group NC; however, osteoclast number, osteoclast surface, eroded surface, and urinary deoxypyridinoline in group GIOP increased than group NC (P < 0.05); these changes were inhibited after perindopril treatment (P < 0.05). Quantitative RT-PCR revealed that after dexamethasone treatment, the ratio of SOST mRNS expression and RANKL/OPG mRNA expression obviously increased than that of group NC (P < 0.05); and Runx2 expression decreased significantly (P < 0.05); while the changes of mRNA expression were improved by perindopril treatment. CONCLUSION: Perindopril can promote bone formation and inhibit bone resorption to deduce glucocorticoid-induced osteoporosis. This study provides a new method for prevention and treatment of GIOP.

High-Pressure Water Swelling Sealant Injection Injury to the Hand: a Case Report and Review of the Literature.

High-pressure injection injuries (HPII) caused by water swelling sealant are rare at present. The patient generally has small-sized skin lesions, and the misleadingly benign presentation may cause delayed treatment at the early stage of management. In addition, radiographic examination may be underestimated. Subsequently, the inadequate surgical intervention may cause tissue necrosis and poor prognosis. Furthermore, the early recognition of water swelling sealant injected into tissue and emergent surgical intervention are the key to successful management for the patient with HPII caused by injecting water swelling sealant to tissue.

[Growth responses of six leguminous plants adaptable in Northern Shaanxi to petroleum contaminated soil].

To select appropriate native species in Northern Shaanxi for phytoremediation, the growth index of six kinds of leguminous plants planted in petroleum contaminated soils were investigated through pot culture. Petroleum concentrations were set at 0, 5 000, 10 000, 20 000, 40 000 mg x kg(-1) respectively with three replicates. Using different levels of seed germination rate, germination time, individual height, wilting rate, dry weight and chlorophyll content in leaves of tested plants as the ecological indicator. The results showed that tested plants have significantly different responses to petroleum pollution. Compared with those planted in clean soils, seed germination rate and individual height were promoted when petroleum concentration was lower than 5000 mg x kg(-1), but inhibition occurred when petroleum concentrations were higher than 10000 mg x kg(-1). Strong endurance of Medicago sativa was observed to petroleum polluted soil, especially at lower petroleum concentration. Leaf wilting of Robinia pseudoacacia was unobserved even when petroleum concentration was 40 000 mg x kg(-1), thus displaying the potential of remediating petroleum contaminated soils. The petroleum concentration was significantly and negatively correlated with seed germination rate, individual height and dry weight, but positively correlated with chlorophyll content in leaves.

[Case-control study on effects of external fixation combined with limited internal fixation for the treatment of Pilon fractures of Rüedi-Allgower type III].

OBJECTIVE: To analyze the effects of three surgical operations in the treatment of Pilon fracture of Rüedi-Allgower type III, and put forward the best therapeutic method. METHODS: The clinical data of 33 patients with Pilon fracture who received surgical operations (plaster immobilization group, 10 cases; distal tibia anatomical plate group, 11 cases; external fixation with limited internal fixation group, 12 cases) from October 2009 to January 2012 were analyzed. There were 5 males and 5 females, ranging in age from 24 to 61 years in the plaster immobilization group. There were 7 males and 4 females, ranging in age from 21 to 64 years in the distal tibia anatomical plate group. There were 7 males and 5 females, ranging in age from 23 to 67 years in the external fixation with limited internal fixation group. The Ankle X-ray of Pilon fracture after operation, ankle score, early and late complications were collected. Bourne system was used to evaluate ankle joint function. RESULTS: After 8 months to 3 years follow-up, it was found that three kinds of treatment had significant differences in the outcomes and complications (P < 0.05): the external fixation with limited internal fixation group got the best results. The number of anatomic reduction cases in the external fixation with limited internal fixation group (7 cases) and the distal tibia anatomical plate group (8 cases) was more than the plaster immobilization group (2 cases). According to the ankle score, 8 patients got an excellent result, 3 good and 1 poor in the limited internal fixation group ,which was better than those of distal tibia anatomical plate group (5 excellent, 4 good and 2 poor) and the plaster immobilization group (3 excellent, 4 good and 3 poor). The number of early and late complications in the external fixation with limited internal fixation group was more than those in the plaster immobilization group and the distal tibia anatomical plate group (P< 0.05). CONCLUSION: Treatment of external fixation with limited internal fixation in the treatment of Pilon fracture of Rüedi-Allgower type III is effective and safe.

Downregulation of microRNA-26a is associated with metastatic potential and the poor prognosis of osteosarcoma patients.

Accumulating evidence indicates that microRNAs are involved in multiple processes in cancer development and progression. microRNA-26a (miR-26a) has been identified as a tumor suppressor and its downregulation is associated with poor prognosis in several types of human cancer. However, the specific function of miR-26a in osteosarcoma remains unclear. In the present study, we found that the expression of miR-26a in osteosarcoma tissues and cell lines was much lower than that in the normal controls, respectively. In addition, downregulation of miR-26a more frequently occurred in osteosarcoma specimens with adverse clinical stage and with the presence of distant metastasis. Moreover, multivariate survival analyses demonstrated that loss of miR-26a is an independent prognostic factor for both disease-free and overall survival in osteosarcoma. In addition, restoration of miR-26a expression inhibited the invasion and migration in osteosarcoma cells, and miR-26a directly inhibited enhancer of zeste homolog 2 (EZH2) expression by targeting its 3'-UTR. Moreover, EZH2 was upregulated and inversely correlated with miR-26a expression in the osteosarcoma tissues. Thus, for the first time, we provide convincing evidence that downregulation of miR-26a is associated with tumor aggressiveness and tumor metastasis, and miR-26a inhibits cell migration and invasion by targeting the EZH2 gene in osteosarcoma. Thus, miR-26a is an independent prognostic marker for osteosarcoma patients.

Mathematical modeling of vertebrate limb development.

In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.

Operator Splitting Implicit Integration Factor Methods for Stiff Reaction-Diffusion-Advection Systems.

For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction-diffusion systems with both stiff reaction and diffusion terms, implicit integration factor (IIF) method and its higher dimensional analog compact IIF (cIIF) serve as an efficient class of time-stepping methods, and their second order version is linearly unconditionally stable. For nonlinear hyperbolic equations, weighted essentially non-oscillatory (WENO) methods are a class of schemes with a uniformly high-order of accuracy in smooth regions of the solution, which can also resolve the sharp gradient in an accurate and essentially non-oscillatory fashion. In this paper, we couple IIF/cIIF with WENO methods using the operator splitting approach to solve reaction-diffusion-advection equations. In particular, we apply the IIF/cIIF method to the stiff reaction and diffusion terms and the WENO method to the advection term in two different splitting sequences. Calculation of local truncation error and direct numerical simulations for both splitting approaches show the second order accuracy of the splitting method, and linear stability analysis and direct comparison with other approaches reveals excellent efficiency and stability properties. Applications of the splitting approach to two biological systems demonstrate that the overall method is accurate and efficient, and the splitting sequence consisting of two reaction-diffusion steps is more desirable than the one consisting of two advection steps, because CWC exhibits better accuracy and stability.

Spatial dynamics of multistage cell lineages in tissue stratification.

In developing and self-renewing tissues, terminally differentiated (TD) cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit-amplifying) cell stages, which ultimately give rise to TD cells. As the tissue reaches a tightly controlled steady-state size, cells at different lineage stages assume distinct spatial locations within the tissue. Although tissue stratification appears to be genetically specified, the underlying mechanisms that direct tissue lamination are not yet completely understood. Herein, we use modeling and simulations to explore several potential mechanisms that can be utilized to create stratification during developmental or regenerative growth in general systems and in the model system, the olfactory epithelium of mouse. Our results show that tissue stratification can be generated and maintained through controlling spatial distribution of diffusive signaling molecules that regulate the proliferation of each cell type within the lineage. The ability of feedback molecules to stratify a tissue is dependent on a low TD death rate: high death rates decrease tissue lamination. Regulation of the cell cycle lengths of stem cells by feedback signals can lead to transient accumulation of stem cells near the base and apex of tissue.

Bare bones pattern formation: a core regulatory network in varying geometries reproduces major features of vertebrate limb development and evolution.

BACKGROUND: Major unresolved questions regarding vertebrate limb development concern how the numbers of skeletal elements along the proximodistal (P-D) and anteroposterior (A-P) axes are determined and how the shape of a growing limb affects skeletal element formation. There is currently no generally accepted model for these patterning processes, but recent work on cartilage development (chondrogenesis) indicates that precartilage tissue self-organizes into nodular patterns by cell-molecular circuitry with local auto-activating and lateral inhibitory (LALI) properties. This process is played out in the developing limb in the context of a gradient of fibroblast growth factor (FGF) emanating from the apical ectodermal ridge (AER). RESULTS: We have simulated the behavior of the core chondrogenic mechanism of the developing limb in the presence of an FGF gradient using a novel computational environment that permits simulation of LALI systems in domains of varying shape and size. The model predicts the normal proximodistal pattern of skeletogenesis as well as distal truncations resulting from AER removal. Modifications of the model's parameters corresponding to plausible effects of Hox proteins and formins, and of the reshaping of the model limb, bud yielded simulated phenotypes resembling mutational and experimental variants of the limb. Hypothetical developmental scenarios reproduce skeletal morphologies with features of fossil limbs. CONCLUSIONS: The limb chondrogenic regulatory system operating in the presence of a gradient has an inherent, robust propensity to form limb-like skeletal structures. The bare bones framework can accommodate ancillary gene regulatory networks controlling limb bud shaping and establishment of Hox expression domains. This mechanism accounts for major features of the normal limb pattern and, under variant geometries and different parameter values, those of experimentally manipulated, genetically aberrant and evolutionary early forms, with no requirement for an independent system of positional information.

[Effects of vimentin on invasion and metastasis of prostate cancer cell lines PC-3M-1E8 and PC-3M-2B4].

BACKGROUND & OBJECTIVE: Vimentin, a cytoskeleton protein, is involved in regulating the migration and proliferation of cells. This study was to detect the expression of vimentin in prostate cancer cell lines PC-3M-1E8 and PC-3M-2B4, and evaluate the effects of vimentin on invasion and metastasis of prostate cancer cells. METHODS: Two-dimensional gel electrophoresis (2-DE) followed by matrix-assisted laser desorption/time of flight mass spectrometry (MALDI TOF-MS) were used to detect the expression of vimentin in prostate cancer cell lines PC-3M-1E8 and PC-3M-2B4. Genetic intervention of vimentin gene and in vitro invasion assay were used to investigate the effects of vimentin on the invasion and metastasis of prostate cancer cells. RESULTS: The protein level of vimentin was higher in PC-3M-1E8 cells with high metastatic potential than in PC-3M-2B4 cells with low metastatic potential. Eukaryotic vectors expressing antisense-and sense-vimentin were constructed successfully and transfected into PC-3M-1E8 and PC-3M-2B4 cells separately. The number of invasive cells was significantly lower in PC-3M-1E8/vas cells with antisense-vimentin than in control PC-3M-1E8/3.1(-) cells (99.3+/-4.8 vs. 319.4+/-6.5, P<0.01), and significantly higher in PC-3M-2B4/vs cells with sense-vimentin than in control PC-3M-2B4/3.1(+) cells (330.5+/-5.8 vs. 98.6+/-7.5, P<0.01). CONCLUSION: Vimentin is a promising marker for predicting the invasion and metastasis of prostate cancer cells.

Compact integration factor methods in high spatial dimensions.

The dominant cost for integration factor (IF) or exponential time differencing (ETD) methods is the repeated vector-matrix multiplications involving exponentials of discretization matrices of differential operators. Although the discretization matrices usually are sparse, their exponentials are not, unless the discretization matrices are diagonal. For example, a two-dimensional system of N × N spatial points, the exponential matrix is of a size of N(2) × N(2) based on direct representations. The vector-matrix multiplication is of O(N(4)), and the storage of such matrix is usually prohibitive even for a moderate size N. In this paper, we introduce a compact representation of the discretized differential operators for the IF and ETD methods in both two- and three-dimensions. In this approach, the storage and CPU cost are significantly reduced for both IF and ETD methods such that the use of this type of methods becomes possible and attractive for two- or three-dimensional systems. For the case of two-dimensional systems, the required storage and CPU cost are reduced to O(N(2)) and O(N(3)), respectively. The improvement on three-dimensional systems is even more significant. We analyze and apply this technique to a class of semi-implicit integration factor method recently developed for stiff reaction-diffusion equations. Direct simulations on test equations along with applications to a morphogen system in two-dimensions and an intra-cellular signaling system in three-dimensions demonstrate an excellent efficiency of the new approach.

The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb.

A recently proposed mathematical model of a "core" set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713-1722, 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as "reactors," both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et al., Development 130, 2027-2037, 2003), the limb model of Hentschel et al. is "morphodynamic," since differentiation of new cell types occurs simultaneously with cell rearrangement. This contrasts with "morphostatic" mechanisms, in which cell identity becomes established independently of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density (i.e., the morphostatic limit of the full system). This simple reaction-diffusion system is unique in having been derived analytically from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its "Turing space." Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.