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.

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.

[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.

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.

Formation of the BMP activity gradient in the Drosophila embryo.

The dorsoventral axis of the Drosophila embryo is patterned by a gradient of bone morphogenetic protein (BMP) ligands. In a process requiring at least three additional extracellular proteins, a broad domain of weak signaling forms and then abruptly sharpens into a narrow dorsal midline peak. Using experimental and computational approaches, we investigate how the interactions of a multiprotein network create the unusual shape and dynamics of formation of this gradient. Starting from observations suggesting that receptor-mediated BMP degradation is an important driving force in gradient dynamics, we develop a general model that is capable of capturing both subtle aspects of gradient behavior and a level of robustness that agrees with in vivo results.

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 series of Muskone on heart hemodynamics and myocardial consumption of oxygen in experimental dogs].

OBJECTIVE: To observe the effects of series of Muskone (the muskone includes Slender Dutchmanspipe Root, Inula Root and neither kind of Common Aucklandia Root) on the heart hemodynamics and myocardial consumption of oxygen in experimental dogs, and to explain its pharmacological action on cardiovascular system. METHOD: Arterial blood pressure, coronary blood flow, resistance in coronary artery, total peripheral resistance, work of left artrium and oxygen consumption index of the cardiac muscles were observed in anaesthetic dogs. RESULT: The series of Muskone decreased arterial blood pressure significantly, dilated coronary artery and peripheral arteries significantly, increased coronary blood flow, decreased resistance in coronary artery, improved the work of left artrium, the oxygen availability of cardiac muscles and the complaisance of arteries in cardiac muscles.

[Study on therapeutic effects of series of muskone on myocardial infarction canines].

OBJECTIVE: To observe the effects of the series of Muskone (the Muskone includes Slender Dutchmanspipe Root, Tumuxiang, and not Slender Dutchmanspipe Root) on myocardial ischemia, myocardial infarction and hematological index in experimental canines, and to explain the pharmacological action and characteristic of its therapeutic effect on ischemic heart disease. METHOD: The range and degree of myocardial ischemia was evaluated by epicardial electrogram mapping, and the range extent of myocardial infarction was determined by quantitate histology (N-BT staining method). Meanwhile, the changes of ET, TXB2, 6-Keto-PGF1alpha were determined to study the effects of the series of Muskone on myocardial ischemia, myocardial infarction and hematological index in experimental canines. RESULT: The series of Muskone can improve myocardial ischemia and infarction in experimental canines, and relieve significantly the degree of myocardial ischemia (Sigma-ST) determined by epicardial electrogram mapping, decrease the range of myocardial ischemia (N-ST) determined by epicardial electrogram mapping and decrease infarction zone determined by N-BT staining method. And it has a significant inhibition on activity of ET induced by myocardial ischemia and infarction, and increases 6-Keto-PGF1alpha and 6-Keto-PGF1alpha/TXB2 induced by myocardial ischemia. CONCLUSION: The series of Muskone has significant therapeutic effect on myocardial infarction.

[Study on comparative pharmacology of series of Muskone].

OBJECTIVE: To study the therapeutic effects of the series of Muskone (the Muskone includes Slender Dutchmanspipe Root, Tumuxiang, and not Slender Dutchmanspipe Root) on experimental myocardial infarct and pain in rats. METHOD: Coronary artery ligation was applied for the model of myocardial infarct. Therapeutic effects were evaluated by measuring parameters of histomorphometry, blood plasm of ET, 6- keto-PGF1alpha and TXB2. Intraperitoneal injection acetic was applied for the model of ache, the frequency and eclipse period of writhing were evaluated its effect of resisting pain. RESULT: The Muskone including Radix Aristolociae, the Muskone including Radix Inulae and the Muskone without Radix Aucklandiae all can decrease the area of myocardial infarction in rats, the level of TXB2, ET, and the frequency of writhing significantly. Also it can increase the level 6-keto-PGF1alpha, the ratio of 6-keto-PGF1alpha and TXB2. Single Radix Aristolociae or Radix Inulae only relieved pain. CONCLUSION: The Muskone including Radix Aristolociae, the Muskone including Radix Inulae and the Muskone without Radix Aucklandiae all have significant therapeutic effect on both myocardial infarction and pain, while single Radix Aristolociae or Radix Inulae only can relieve pain.

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.

Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers.

A quantitative study is carried out in this paper to investigate the size of numerical viscosities and the resolution power of high-order weighted essentially nonoscillatory (WENO) schemes for solving one- and two-dimensional Navier-Stokes equations for compressible gas dynamics with high Reynolds numbers. A one-dimensional shock tube problem, a one-dimensional example with parameters motivated by supernova and laser experiments, and a two-dimensional Rayleigh-Taylor instability problem are used as numerical test problems. For the two-dimensional Rayleigh-Taylor instability problem, or similar problems with small-scale structures, the details of the small structures are determined by the physical viscosity (therefore, the Reynolds number) in the Navier-Stokes equations. Thus, to obtain faithful resolution to these small-scale structures, the numerical viscosity inherent in the scheme must be small enough so that the physical viscosity dominates. A careful mesh refinement study is performed to capture the threshold mesh for full resolution, for specific Reynolds numbers, when WENO schemes of different orders of accuracy are used. It is demonstrated that high-order WENO schemes are more CPU time efficient to reach the same resolution, both for the one-dimensional and two-dimensional test problems.

[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.