Asymptotical tracking control for the complex network based on the dynamic topology.

A tracking control scheme is proposed for complex dynamic network (CDN), where the CDN is regarded wholly as a dynamic composite system which consists of two mutually coupled subsystems. One subsystem consists of all nodes and the other consists of all links, and consider the weights of the links to be state variables in the latter subsystem. There are two parts in the structure of the proposed tracking control scheme: the designed controller of nodes and the synthesis of the coupling term in links. These two parts can guarantee two subsystems to asymptotically track the given reference targets, respectively. This approach originates from the communication transmission network (CTN). In CTN, for the network optimization management, the reference network topology (NT), such as the star topology, is required as a target for tracking in communication transmission (links) when each node in network needs to track its own target. The control scheme provided of this paper coincides with above requirement. And finally, a comparative simulation example is given for illustrating the effectiveness of the provided control scheme.

Position Tracking of Multiple Robotic Manipulator Systems Associated with Communication Strength Dynamics.

In general, a multiple robotic manipulator system (MRMS) with uncertainties can be considered a composition system with a robotic manipulator subsystem (RMS) and a communication strength subsystem (CSS), and both subsystems are coupled to each other. In this paper, a new position tracking control scheme is proposed for the MRMS while considering the communication strength dynamics between robotic manipulators. The control scheme designed in this paper consists of two parts: the first part is to design the control protocol in the RMS, and the second part is to design the coupling relationship in the CSS. Through these two parts, we can achieve the position tracking of an MRMS. Firstly, the dynamical mathematical model of the RMS and CSS in the MRMS is constructed, and the corresponding assumptions are given. Then, the corresponding stability analysis is proposed, which provides the basis for a theoretical understanding of the underlying problem. Finally, an illustrative example is presented to verify the effectiveness of the proposed control scheme.

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics.

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network's topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.

Double Model Following Adaptive Control for a Complex Dynamical Network.

This paper formulates and solves a new problem of the double model following adaptive control (MFAC) of nodes and links in a complex dynamical network (CDN). This is different from most existing studies on CDN and MFAC. Inspired by the concept of composite systems, the CDN with dynamic links is regarded as an interconnected system composed of an interconnected node group (NG) and link group (LG). Guided by the above-mentioned new idea of viewing a CDN from the perspective of composite systems, by means of Lyapunov theory and proposed related mathematical preliminaries, a new adaptive control scheme is proposed for NG. In addition, to remove the restriction that the states of links in a CDN are unavailable due to physical constraints, technical restraints, and expensive measurement costs, we synthesize the coupling term in LG with the proposed adaptive control scheme for NG, such that the problem of double MFAC of nodes and links in CDN is solved. Finally, a simulation example is presented to verify the theoretical results.

The stationarity control of the average links for the Hebb complex dynamical network via external stimulus signals.

The model of complex dynamical network (CDN) can be represented as the mathematic graph, in which some characteristics may emerge from the dynamic nodes group (NG) and links group (LG). This paper primarily focuses on the feature appearing from the dynamic links. The average link weight (ALW), as a novel quantitative index to describe the characteristic of dynamic links is introduced. Inspired by the Hebb's neuroscience theory, the Hebb complex dynamical network (HCDN) is constructed. The ALW of the HCDN can track a given target via external stimulus signals with adaptive amplifiers' proportional coefficients. In other words, the stationary network implies the ALW is a constant in time. Finally, two simulation examples are performed to validate the proposed adaptive update law's effectiveness.

Cluster-Delay Mean Square Consensus of Stochastic Multi-Agent Systems with Impulse Time Windows.

This paper investigates the cluster-delay mean square consensus problem of a class of first-order nonlinear stochastic multi-agent systems with impulse time windows. Specifically, on the one hand, we have applied a discrete control mechanism (i.e., impulsive control) into the system instead of a continuous one, which has the advantages of low control cost, high convergence speed; on the other hand, we considered the existence of impulse time windows when modeling the system, that is, a single impulse appears randomly within a time window rather than an ideal fixed position. In addition, this paper also considers the influence of stochastic disturbances caused by fluctuations in the external environment. Then, based on algebraic graph theory and Lyapunov stability theory, some sufficiency conditions that the system must meet to reach the consensus state are given. Finally, we designed a simulation example to verify the feasibility of the obtained results.

A modified intrafocal pinning technique with three-dimensional planning to facilitate volar plating in dorsally comminuted AO/OTA C2 and C3 distal radius fractures.

BACKGROUNDS: Theaim of this study was to assess the efficacy of a modified intrafocal pinningtechnique with three-dimensional (3D) planning to facilitate volar plating in dorsally comminuted intra-articular distal radius fractures. METHODS: Intotal 35 AO/OTA type C2 and C3 fractures were finally included.The 3D digital model of the fracture was reconstructed based on preoperative computedtomographic (CT) images, with the displacement of the comminuted dorsalfragment and the intra-articular fragment analyzed for preoperative planning. During operation, amodified intrafocal pinning technique was applied percutaneously from thedorsal aspect of the radius to reduce the collapsed intra-articular fragmentfollowing volar plating. Adequate reduction was confirmed in all of patientsconsidering radial height, radial inclination and volar tilt in postoperativeradiographs. RESULTS: No significant fracture re-displacement wasobserved in most of the cases during a mean follow-up period of 17.4 months, exceptfor two patients withthe C3 fracture. All of the patients achieved adequate clinicalROMs at 12 months postoperatively, with a mean DASH score of 12.0. Most of the patients achievedan excellent (n = 21) or good (n = 12) Gartland and Werley wrist score. CONCLUSIONS: Ourmodified intrafocal pinning technique with 3D planning contributes to a satisfactoryclinical and radiological outcome in dorsally comminuted intra-articular distalradius fractures fixed with a volar locking plate. TRIALREGISTRATION: Notapplicable because the design of the study is retrospective.

Selenium status in the body and cardiovascular disease: a systematic review and meta-analysis.

Background: Both experimental and observational studies have provided conflicting evidence on the associations of selenium with incidence and mortality of cardiovascular disease (CVD). The aim of this study was to evaluate the association between selenium status in the body and incidence and mortality of CVD by performing a systematic review and meta-analysis of observational studies and randomized controlled trials. Methods: A systematic search for articles in MEDLINE (Ovid), Embase, Web of Science (Thomson Reuters) and Cochrane library (Wiley) was conducted. Thirteen of the 1811 articles obtained from the databases met our inclusion criteria and were considered in the final analysis. The effect sizes were presented as weighted relative risk (RR) and 95% confidence intervals (CIs) using random-effects model. To detect dose-response relationships, we used meta-regression. Results: Overall, there was a reduced risk of CVD incidence (RR = 0.66; 95% CI: 0.40-1.09) and mortality (RR = 0.69; 95% CI: 0.57-0.84) in physiologically high selenium status compared to low selenium status in the body. There was a 15% (RR = 0.85, 95% CI: 0.76-0.94) decreased risk of CVD incidence per 10 µg increment in blood selenium concentration. In addition, a statistically significantly nonlinear dose-response relationship was found between CVD mortality and increased blood selenium concentration with the lowest risk at the 30-35 µg increment in blood selenium. Conclusions: Physiologically high selenium levels in the body are associated with decreased risk for CVD incidence and mortality, however, people should be cautious about the potential harmful effects from excessive intake of selenium.

A Silent Infection Pandemic of COVID-19: Epidemiological Investigation and Hypothetical Models.

To explore the epidemic mode of COVID-19, we made an epidemiological investigation, set up hypothetical models, and compared them with hepatitis A virus (HAV) age-specific epidemic characteristic. In the epidemiological investigation, we reported the first familial COVID-19 silent infection in the world. A 19-year-old healthy female COVID-19 virus carrier without any symptoms caused two mild and one severe pneumonia. In hypothetical models, the silent infection rate ranges from 60% to 80% based on 3 sources: China mainland, evacuation of 4 nationals, and the ship "Diamond Princess," respectively. In comparison with HAV, COVID-19 shows the same infection mode in children (aged 0-9 years), but significant difference in young adults (aged 10-44 years) and the elderly (aged 45 years or older). Therefore, we prejudged that COVID-19 is a silent infection pandemic mainly in young adults but threatens the elderly.

A Questionnaire Study on the Attitude towards Death of the Nursing Interns in Eight Teaching Hospitals in Jiangsu, China.

INTRODUCTION: Nurses play an important role in caring for dying patients. However, little is known about the attitude towards death of the registered nurses in China. MATERIALS AND METHODS: A knowledge, attitude, and the practice (KAP) survey using standardized questionnaires was conducted at eight teaching hospitals in Jiangsu Province, China. In total, 366 nursing interns were recruited and 357 turned in valid response. Data about the interns' demographic characteristics and their attitudes to death in five domains, including fear of death, death avoidance, natural acceptance, approach acceptance, and escape acceptance, were collected. RESULTS: Compared to the norms, the nursing interns had statistically significantly higher scores in the domains death avoidance, approach acceptance, and fear of death (14.9 vs. 11.1, 26.2 vs. 24.2, and 20.3 vs. 19.0, respectively); however, statistically significantly lower scores were in the domains natural acceptance and escape acceptance (18.4 vs. 22.0, and 13.6 vs. 15.1, respectively). Religious belief, experience of a deceased relative in family, death education, and family atmosphere of discussing death are positively associated with one or more domains of attitude towards death. CONCLUSION: The positive attitude towards death and death education before clinical practice are helpful for nursing interns when they care for dying patients. In general, the scores of attitude towards death are at a moderate level in the surveyed Chinese nursing interns. The death education for nursing students needs to be reinforced in China.

C7 peptide inhibits hepatocellular carcinoma metastasis by targeting the HGF/c-Met signaling pathway.

Hepatocellular carcinoma (HCC), characterized by a high rate of metastasis and recurrence after surgery, is caused by malignant proliferation of hepatocytes with epigenetic and/or genetic mutations. In particular, abnormal activation of the hepatocyte growth factor (HGF)-/c-mesenchymal-epithelial transition receptor (c-Met) axis is closely associated with HCC metastasis. Unfortunately, effective treatments or drugs that target the HGF/c-Met signaling pathway are still in the research pipeline. Here, a c-Met inhibitor named the C7 peptide, which can inhibit both HGF and c-Met, can significantly inhibit HGF-induced (but not EGF-induced) cell migration and suppress the phosphorylation of c-Met, Akt and Erk1/2. Moreover, the C7 peptide can also significantly suppress tumor metastasis in nude mice and the phosphorylation of c-Met. Together, our current findings, demonstrated that the C7 peptide can inhibit HGF-induced cancer cell migration and invasion through the inhibition of Akt and Erk1/2. Identification of a peptide that can block HGF/c-Met signaling provides new insight into the mechanism of HCC and future clinical treatments.

The structural balance analysis of complex dynamical networks based on nodes' dynamical couplings.

The nodes and their connection relationships are the two main bodies for dynamic complex networks. In existing theoretical researches, the phenomena of stabilization and synchronization for complex dynamical networks are generally regarded as the dynamic characteristic behaviors of the nodes, which are mainly caused by coupling effect of connection relationships between nodes. However, the connection relationships between nodes are also one main body of a time-varying dynamic complex network, and thus they may evolve with time and maybe show certain characteristic phenomena. For example, the structural balance in the social networks and the synaptic facilitation in the biological neural networks. Therefore, it is important to investigate theoretically the reasons in dynamics for the occurrence. Especially, from the angle of large-scale systems, how the dynamic behaviors of nodes (such as the individuals, neurons) contribute to the connection relationships is one of worthy research directions. In this paper, according to the structural balance theory of triad proposed by F. Heider, we mainly focus on the connection relationships body, which is regarded as one of the two subsystems (another is the nodes body), and try to find the dynamic mechanism of the structural balance with the internal state behaviors of the nodes. By using the Riccati linear matrix differential equation as the dynamic model of connection relationships subsystem, it is proved under some mathematic conditions that the connection relationships subsystem is asymptotical structural balance via the effects of the coupling roles with the internal state of nodes. Finally, the simulation example is given to show the validity of the method in this paper.

A Randomized Controlled Trial Evaluating the Effects of Diosmin in the Treatment of Radicular Pain.

Diosmin has been widely used to treat patients with vascular pain for its potent anti-inflammatory and analgesic effects. To evaluate the therapeutic effects of Diosmin in the treatment of radicular pain, we conducted an investigator-initiated, randomized, active-controlled noninferiority trial between January 1, 2009, and December 1, 2010. Diosmin (50 mg/kg/day) was orally administered to treat the radicular pain in 150 patients for one month. Another 150 patients with the same symptom were given 20% 250 ml mannitol (1 g/kg/day) for 7 days and dexamethasone (10 mg/day) for 3 days intravenously guttae. Short-term relief and long-term relief were measured. Secondary outcomes include improvement in functional and psychological status, return to work, and reduction in anti-inflammatory analgesic drugs intake. Patients treated with oral Diosmin achieved reduction in radicular pain. The total satisfaction rate of Diosmin group was 84.7% [95% confidence interval (CI): 77.9%, 90.0%], and the complete satisfaction rate was 50.7% (95% CI: 42.4%, 58.9%). No statistically significant difference was found between the Diosmin group and the active-control group regarding patient satisfaction. No adverse effects were found during the study period. Our study suggests that clinical application of Diosmin with a dose of 50 mg/kg/day might reduce the radicular pain. This trial is registered with ISRCTN97157037.

Comparison of the direct and indirect reduction techniques during the surgical management of posterior malleolar fractures.

BACKGROUND: The optimal method for the reduction and fixation of posterior malleolar fracture (PMF) remains inconclusive. Currently, both of the indirect and direct reduction techniques are widely used. We aimed to compare the reduction quality and clinical outcome of posterior malleolar fracture managed with the direct reduction technique through posterolateral approach or the indirect reduction technique using ligamentotaxis. METHODS: Patients with a PMF involving over 25% of the articular surface were recruited and assigned to the direct reduction (DR) group or the indirect reduction (IR) group. Following reduction and fixation of the fracture, the quality of fracture reduction was evaluated in post-operative CT images. Clinical and radiological follow-ups were performed at 6 weeks, 3 months, 6 months, 12 months, and then at 6 month-intervals postoperatively. Functional outcome (AOFAS score), ankle range of motion, and Visual Analog Scale (VAS) were evaluated at the last follow-up. Statistical differences were compared between the DR and IR groups considering the patient demographics, quality of fracture reduction, AOFAS score, and VAS. RESULTS: Totally 116 patients were included, wherein 64 cases were assigned to the DR group and 52 cases were assigned to the IR group. The quality of fracture reduction was significant higher in the DR group (P = 0.038). In the patients who completed a minimum of 12 months' follow-up, a median AOFAS score of 87 was recorded in the DR group, which was significantly higher than that recorded in the IR group (a median score of 80). The ankle range of motion was slightly better in the DR group, with the mean dorsiflexion restriction recorded to be 5.2° and 6.1° in the DR and IR group respectively (P = 0.331). Similar VAS score was observed in the two groups (P = 0.419). CONCLUSIONS: The direct reduction technique through a posterolateral approach provide better quality of fracture reduction and functional outcome in the management of PMF over 25% of articular surface, as compared with the indirect reduction technique using ligamentotaxis. TRIAL REGISTRATION: NCT02801474 (retrospectively registered, June 2016, ClinicalTrails.gov).

Exogenous PTHrP Repairs the Damaged Fracture Healing of PTHrP+/- Mice and Accelerates Fracture Healing of Wild Mice.

Bone fracture healing is a complicated physiological regenerative process initiated in response to injury and is similar to bone development. To demonstrate whether an exogenous supply of parathyroid hormone-related protein (PTHrP) helps in bone fracture healing, closed mid-diaphyseal femur fractures were created and stabilized with intramedullary pins in eight-week-old wild-type (WT) PTHrP+/+ and PTHrP+/- mice. After administering PTHrP for two weeks, callus tissue properties were analyzed at one, two, and four weeks post-fracture (PF) by various methods. Bone formation-related genes and protein expression levels were evaluated by real-time reverse transcriptase-polymerase chain reaction and Western blots. At two weeks PF, mineral density of callus, bony callus areas, mRNA levels of alkaline phosphatase (ALP), type I collagen, Runt-related transcription factor 2 (Runx-2), and protein levels of Runx-2 and insulin-like growth factor-1 decreased in PTHrP+/- mice compared with WT mice. At four weeks PF, total collagen-positive bony callus areas, osteoblast number, ALP-positive areas, and type I collagen-positive areas all decreased in PTHrP+/- mice. At both two and four weeks PF, tartrate-resistant acid phosphatase-positive osteoclast number and surface decreased a little in PTHrP+/- mice. The study indicates that exogenous PTHrP provided by subcutaneous injection could redress impaired bone fracture healing, leading to mutation of activated PTHrP by influencing callus areas, endochondral bone formation, osteoblastic bone formation, and bone turnover.

Label-based routing for a family of small-world Farey graphs.

We introduce an informative labelling method for vertices in a family of Farey graphs, and deduce a routing algorithm on all the shortest paths between any two vertices in Farey graphs. The label of a vertex is composed of the precise locating position in graphs and the exact time linking to graphs. All the shortest paths routing between any pair of vertices, which number is exactly the product of two Fibonacci numbers, are determined only by their labels, and the time complexity of the algorithm is O(n). It is the first algorithm to figure out all the shortest paths between any pair of vertices in a kind of deterministic graphs. For Farey networks, the existence of an efficient routing protocol is of interest to design practical communication algorithms in relation to dynamical processes (including synchronization and structural controllability) and also to understand the underlying mechanisms that have shaped their particular structure.

Exogenous Parathyroid Hormone-Related Peptide Promotes Fracture Healing in Lepr(-/-) Mice.

Diabetic osteoporosis continues to surge worldwide, increasing the risk of fracture. We have previously demonstrated that haploinsufficiency of endogenous parathyroid hormone-related peptide (PTHrP) impairs fracture healing. However, whether an exogenous supply of PTHrP can repair bone damage and accelerate fracture healing remains unclear. This study aimed to assess the efficacy and safety of PTHrP in healing fractures. Standardized mid-diaphyseal femur fractures were generated in 12-week-old wild-type and leptin receptor null Lepr(-/-) mice. After administration of PTHrP for 2 weeks, callus tissue properties were analyzed by radiography, micro-computed tomography, histology, histochemistry, immunohistochemistry, and molecular biology techniques. At 2 weeks post-fracture, cartilaginous callus areas were reduced, while total callus and bony callus areas were increased in PTHrP-treated Lepr(-/-) animals and control wild-type mice, compared with vehicle-treated Lepr(-/-) mice. The following parameters were enhanced both in Lepr(-/-) mice after treatment with PTHrP and vehicle-treated wild-type animals, compared with vehicle-treated Lepr(-/-) mice: osteoblast numbers; tissue alkaline phosphatase (ALP) and Type I collagen immunopositive areas; mRNA levels of ALP, Type I collagen, osteoprotegerin, and receptor activator for nuclear factor-κ B ligand; protein levels of Runt-related transcription factor 2 and insulin-like growth factor-1; and the number and surface of osteoclasts. In conclusion, exogenous PTHrP by subcutaneous injection promotes fracture repair in Lepr(-/-) mice by increasing callus formation and accelerating cell transformation: upregulated osteoblastic gene and protein expression, increased endochondral bone formation, osteoblastic bone formation, and osteoclastic bone resorption. However, complete repair was not obtained in PTHrP-treated Lepr(-/-) mice as in control wild-type animals.

Radiographic analysis of the restoration of hip joint center following open reduction and internal fixation of acetabular fractures: a retrospective cohort study.

BACKGROUND: Unfavorable reduction is considered one of the key factors leading to joint degeneration and compromised clinical outcome in acetabular fracture patients. Besides the columns, walls, and superior dome, the postoperative position of hip joint center (HJC), which is reported to affect hip biomechanics, should be considered during the assessment of quality of reduction. We aimed to evaluate the radiographic restoration of HJC in acetabular fractures treated with open reduction and internal fixation. METHODS: Patients with a displaced acetabular fracture that received open reduction and internal fixation in the authors' institution during the past five years were identified from the trauma database. The horizontal and vertical shifts of HJC were measured in the standard anteroposterior view radiographs taken postoperatively. The radiographic quality of fracture reduction was graded according to Matta's criteria. The relationships between the shift of HJC and the other variables were evaluated. RESULTS: Totally 127 patients with 56 elementary and 71 associated-type acetabular fractures were included, wherein the majority showed a medial (89.0%) and proximal (93.7%) shift of HJC postoperatively. An average of 2.8 mm horizontal and 2.2 mm vertical shift of HJC were observed, which correlated significantly with the quality of fracture reduction (P < 0.001 for both). The horizontal shift of HJC correlated with the fracture type (P = 0.022). CONCLUSIONS: The restoration of HJC correlates with the quality of reduction in acetabular fractures following open reduction and internal fixation. Further studies are required to address the effects of HJC shift on the biomechanical changes and clinical outcomes of hip joint, especially in poorly reduced acetabular fractures.

Haploinsufficiency of endogenous parathyroid hormone-related peptide impairs bone fracture healing.

Previous studies have demonstrated that endogenous parathyroid hormone-related peptide (PTHrP) plays a central role in the physiological regulation of bone formation. However, it is unclear whether endogenous PTHrP plays an important function in enhancing bone fracture healing. To determine whether endogenous PTHrP haploinsufficiency impaired bone fracture healing, closed mid-diaphyseal femur fractures were created in 8-week-old wild-type and Pthrp(+/-) mice. Callus tissue properties were analysed 1, 2 and 4 weeks after fracture by radiography, histology, histochemistry, immunohistochemistry and molecular biology. The size of the calluses was reduced 2 weeks after fracture, and the fracture repairs were poor 4 weeks after fractures, in Pthrp(+/-) compared with wild-type mice. Cartilaginous callus areas were reduced 1 week after fracture, but were increased 2 weeks after fracture in Pthrp(+/-) mice. There was a reduction in the number of ostoblasts, alkaline phosphatase (ALP)-positive areas, Type I collagen immunopositive areas, mRNA levels of ALP, Runt-related transcription factor 2 (Runx2) and Type I collagen, Runx2 and insulin-like growth factor-1 protein levels, the number of osteoclasts and the surface in callus tissues in Pthrp(+/-) compared with wild-type mice. These results demonstrate that endogenous PTHrP haploinsufficiency impairs the fracture repair process by reducing cartilaginous and bony callus formation, with downregulation of osteoblastic gene and protein expression and a reduction in endochondral bone formation, osteoblastic bone formation and osteoclastic bone resorption. Together, the results indicate that endogenous PTHrP plays an important role in fracture healing.

Early application of pulsed electromagnetic field in the treatment of postoperative delayed union of long-bone fractures: a prospective randomized controlled study.

BACKGROUND: Pulsed electromagnetic field (PEMF) is reported to be an effective adjunct for the management of nonunion long-bone fractures. Most studies implement PEMF treatment after 6 months or longer of delayed union or nonunion following fracture treatment. Despite these variations in treatment, the early application of PEMF following a diagnosis of a postoperative delayed union has not been specifically analyzed. In this study, the outcomes of postoperative delayed union of long-bone fractures treated with an early application of PEMF were evaluated as compared with a sham-treated control group. METHODS: In this prospective, randomized controlled study, a total of 58 long-bone fracture patients, who presented with delayed union of between 16 weeks and 6 months, were randomly split into two groups and subjected to an early application of PEMF or sham treatment. Clinical and radiological assessments were performed to evaluate the healing status. Treatment efficacy was assessed at three month intervals. RESULTS: Patients in the PEMF group showed a higher rate of union than those in the control group after the first three months of treatment, but this difference failed to achieve statistical significance. At the end of the study, PEMF treatment conducted for an average of 4.8 months led to a success rate of 77.4%. This was significantly higher than the control, which had an average duration of 4.4 months and a success rate of 48.1%. The total time from operation to the end of the study was a mean of 9.6 months for patients in the PEMF group. CONCLUSIONS: Fracture patients treated with an early application of PEMF achieved a significantly increased rate of union and an overall reduced suffering time compared with patients that receive PEMF after the 6 months or more of delayed union, as described by others.