Patterns and Stability of Coupled Multi-Stable Nonlinear Oscillators.

Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and stability of coupled driven-damped Helmholtz-Duffing oscillators in bi-stability regimes. We find that despite the fact that the system parameters and the driving force are identical, the stability of the two states to spatially non-uniform perturbations is very different. Moreover, the final stable states, resulting from these spatial perturbations, are not solely dictated by the wavelength of the perturbing mode and take different spatial configurations in terms of the coupled oscillator phases.

Can retrospectively fusing SPECT to CT images reduce radiation doses in myocardial perfusion imaging?

INTRODUCTION: To establish if the CT dataset acquired during the stress element of myocardial perfusion imaging can be fused to the subsequent rest scan to reduce radiation doses from these procedures. METHODS: 86 rest scans were processed and evaluated using a self-designed project specific tool. Recording processing time, the time between the two data sets selected for fusion and assessing radiographic reports to ensure produced images were of diagnostic quality. RESULTS: 70% of fused scans were acquired 6-7 days apart; the mean (SD) processing time was calculated as 2.03 (0.36) minutes. The Pearson's correlation between these two variables was determined to be 0.22, showing a slight positive correlation although not statistically significant. 100% of the images produced were of diagnostic quality. CONCLUSION: Rest scans can be fused to a previously acquired CT, careful consideration should be given when positioning the patient and to the time interval between acquiring the two data sets, departmental guidelines can assist with this. Staff training may also be beneficial to ensure staff can assess if data sets are fusible prior to completing a scan. IMPLICATIONS FOR PRACTICE: This data provides evidence that retrospective fusion can reduce patient radiation doses in myocardial perfusion imaging without compromising diagnostic outcomes. Dose optimisation is an essential part of the ionising radiation (medical exposure) regulations therefore retrospective fusion should be considered in practice to ensure departmental compliance, although it is noteworthy this study is solely based in a single centred one camera department.

RLSuite: An Integrative R-Loop Bioinformatics Framework.

We recently described the development of a database of 810 R-loop mapping datasets and used this data to conduct a meta-analysis of R-loops. R-loops are three-stranded nucleic acid structures containing RNA:DNA hybrids and we were able to verify that 30% of expressed genes have an associated R-loop in a location conserved manner.. Moreover, intergenic R-loops map to enhancers, super enhancers and with TAD domain boundaries. This work demonstrated that R-loop mapping via high-throughput sequencing can reveal novel insight into R-loop biology, however the analysis and quality control of these data is a non-trivial task for which few bioinformatic tools exist. Herein we describe RLSuite, an integrative R-loop bioinformatics framework for pre-processing, quality control, and downstream analysis of R-loop mapping data. RLSuite enables users to compare their data to hundreds of public datasets and generate a user-friendly analysis report for sharing with non-bioinformatician colleagues. Taken together, RLSuite is a novel analysis framework that should greatly benefit the emerging R-loop bioinformatics community in a rapidly expanding aspect of epigenetic control that is still poorly understood.

Measurement and memory in the periodically driven complex Ginzburg-Landau equation.

In the present work we illustrate that classical but nonlinear systems may possess features reminiscent of quantum ones, such as memory, upon suitable external perturbation. As our prototypical example, we use the two-dimensional complex Ginzburg-Landau equation in its vortex glass regime. We impose an external drive as a perturbation mimicking a quantum measurement protocol, with a given "measurement rate" (the rate of repetition of the drive) and "mixing rate" (characterized by the intensity of the drive). Using a variety of measures, we find that the system may or may not retain its coherence, statistically retrieving its original glass state, depending on the strength and periodicity of the perturbing field. The corresponding parametric regimes and the associated energy cascade mechanisms involving the dynamics of vortex waveforms and domain boundaries are discussed.

Evaluation of the First Contact Physiotherapy (FCP) model of primary care: patient characteristics and outcomes.

OBJECTIVE: First Contact Physiotherapy (FCP) is a primary care model where expert musculoskeletal (MSK) physiotherapists undertake the first patient consultation, to enhance MSK-patient care and free-up GP capacity. The authors report the quantitative findings from the FCP National Evaluation (Phase 3) which evaluated the FCP model against success criteria. DESIGN AND SETTING: A mixed-methods 24-month service evaluation involving 40 FCP sites and 240 FCPs across England. METHODS: An online platform collected patient-reported experience and outcomes following the FCP consultation and at 1, 2 and 3-months follow-up. These included the Keele STarT MSK Tool, pain intensity (0-10 NRS scale), Musculoskeletal Health Questionnaire (MSK-HQ, range 0-56), and Friends-and-Family Test. RESULTS: Over 13 months, 2825 patients were invited by email and 24% (n=680) completed their initial questionnaire. Their mean age was 56.2 (SD 14.9), 61% were female, ethnicity was 97% white, mean pain intensity was 6.1 (SD 2.13) and mean MSK-HQ score was 33.8 (SD 9.5). At 3-months follow-up (n=370) there was a 2.8 (CI 2.5 to 3.1) mean pain intensity reduction from baseline, a mean 7.1 (6.0 to 8.2) score improvement in MSK-HQ and 64% reporting overall improvement (much better/better) since seeing the FCP. One of the six success criteria was not met; 29% of those in employment reported receiving specific work advice from the FCP (target ≥75%). CONCLUSION: Ahead of the planned scale-up of the FCP primary care model across the UK, this evaluation provides useful data on patients who access this service, their short-term clinical outcomes and whether key success criteria are being met.

Bubble lifetimes in DNA gene promoters and their mutations affecting transcription.

Relative lifetimes of inherent double stranded DNA openings with lengths up to ten base pairs are presented for different gene promoters and corresponding mutants that either increase or decrease transcriptional activity in the framework of the Peyrard-Bishop-Dauxois model. Extensive microcanonical simulations are used with energies corresponding to physiological temperature. The bubble lifetime profiles along the DNA sequences demonstrate a significant reduction of the average lifetime at the mutation sites when the mutated promoter decreases transcription, while a corresponding enhancement of the bubble lifetime is observed in the case of mutations leading to increased transcription. The relative difference in bubble lifetimes between the mutated and wild type promoters at the position of mutation varies from 20% to more than 30% as the bubble length decreases.

Evaluation of the First Contact Physiotherapy (FCP) model of primary care: a qualitative insight.

OBJECTIVE: First Contact Physiotherapy (FCP) is a primary care model where expert musculoskeletal (MSK) physiotherapists undertake the first patient consultation, to enhance MSK-patient care and free-up GP capacity. The authors report the qualitative findings from the FCP National Evaluation (Phase 3) which evaluated the FCP model against pre-agreed success criteria. DESIGN AND SETTING: A mixed-methods 24-month service evaluation involving FCP sites across England. METHODS: Data were collected at 2 time points, year 1 and year 2. Data were collected using individual interviews and focus groups, transcribed verbatim and analysed using a hybrid inductive and deductive thematic analysis. Participants were recruited from all stakeholder groups; patients, physiotherapists, general practitioners and administration staff. RESULTS: A total of 6 sites were recruited over both rounds of data collection demonstrating a wide range of service models. Thirty-nine participants were recruited including fourteen patients. All six qualitative success criteria were met. GPs' discourse reflected confidence in the FCP service and competence of the FCPs. Patient discourse reflected self-efficacy and confidence in self-management techniques and reported FCP as a positive experience. FCPs saw providing advice about work related issues as integral to their role and patient discourse reflected perceived benefit from the advice offered. Staff discourse reflected a positive experience of working with, and in, the FCP services. CONCLUSION: Ahead of the planned scale-up of the FCP primary care model across the UK, this evaluation provides useful insights and recommendations to facilitate successful FCP implementation in terms of patient outcome and experience, and staff experience.

Delegation by Allied Health Professionals to Allied Health Assistants: a mixed methods systematic review.

BACKGROUND: Delegation by Allied Health Professionals (AHPs) to Allied Health Assistants (AHAs) was introduced in response to various challenges affecting modern health care delivery. However, the clinical and cost-effectiveness of using AHAs is relatively unexplored. OBJECTIVES: The aim of this review was to synthesise the available evidence on; firstly, the clinical and cost-effectiveness of interventions delegated by AHPs to AHAs and secondly, AHPs', AHAs' and patients' attitudes and beliefs towards delegation. DATA SOURCES: MEDLINE, AMED, CINAHL, Cochrane Library, PsycINFO, PEDro, OTseeker and Web of Science databases were searched from inception until January 2019 without restrictions. STUDY SELECTION: Primary studies investigating the clinical and cost-effectiveness of any intervention delegated by an AHP, across the spectrum of clinical areas in relation to adult patients, as well as AHPs', AHAs' and patients' attitudes and beliefs about delegation. DATA EXTRACTION & SYNTHESIS: Data were extracted by pairs of reviewers. Thematic analysis and synthesis of descriptive and analytical themes was conducted. RESULTS: Thirteen publications of variable methodological quality were included. Three studies reported quantitative research and ten qualitative research. No study explored the cost-effectiveness. Only one study investigated clinical effectiveness. Training for both AHPs and AHAs and having clear processes in place were identified as important facilitators of delegation. CONCLUSION AND IMPLICATIONS OF KEY FINDINGS: Delegation is not standardised across AHPs or within each profession. There are clear knowledge gaps regarding the clinical and cost-effectiveness of delegation by AHPs and patients' attitudes and preferences. Further research is needed to facilitate the standardisation of delegation. SYSTEMATIC REVIEW REGISTRATION NUMBER: PROSPERO CRD42019119557.

Microcomputed analysis of nerve angioarchitecture after combined stem cell delivery and surgical angiogenesis to nerve allograft.

INTRODUCTION: A detailed three-dimensional (3D) evaluation of microvasculature is evolving to be a powerful tool, providing mechanistic understanding of angiomodulating strategies. The aim of this study was to evaluate the microvascular architecture of nerve allografts after combined stem cell delivery and surgical angiogenesis in a rat sciatic nerve defect model. MATERIALS AND METHODS: In 25 Lewis rats, sciatic nerve gaps were repaired with (i) autografts, (ii) allografts, (iii) allografts wrapped in a pedicled superficial inferior epigastric artery fascia (SIEF) flap to provide surgical angiogenesis, combined with (iv) undifferentiated mesenchymal stem cells (MSC) and (v) MSCs differentiated into Schwann cell-like cells. At two weeks, vascular volume was measured using microcomputed tomography, and percentage and volume of vessels at different diameters were evaluated and compared with controls. RESULTS: The vascular volume was significantly greatest in allografts treated with undifferentiated MSCs and surgical angiogenesis combined as compared to all experimental groups (P<0.01 as compared to autografts, P<0.0001 to allografts, and P<0.05 to SIEF and SIEF combined with differentiated MSCs, respectively). Volume and diameters of vessel segments in nerve allografts were enhanced by surgical angiogenesis. These distributions were further improved when surgical angiogenesis was combined with stem cells, with greatest increase found when combined with undifferentiated MSCs. CONCLUSIONS: The interaction between vascularity and stem cells remains complex, however, this study provides some insight into its synergistic mechanisms. The combination of surgical angiogenesis with undifferentiated MSCs specifically, results in the greatest increase in revascularization, size of vessels, and stimulation of vessels to reach the middle longitudinal third of the nerve allograft.

Distributions of bubble lifetimes and bubble lengths in DNA.

We investigate the distribution of bubble lifetimes and bubble lengths in DNA at physiological temperature, by performing extensive molecular dynamics simulations with the Peyrard-Bishop-Dauxois (PBD) model, as well as an extended version (ePBD) having a sequence-dependent stacking interaction, emphasizing the effect of the sequences' guanine-cytosine (GC)/adenine-thymine (AT) content on these distributions. For both models we find that base pair-dependent (GC vs AT) thresholds for considering complementary nucleotides to be separated are able to reproduce the observed dependence of the melting temperature on the GC content of the DNA sequence. Using these thresholds for base pair openings, we obtain bubble lifetime distributions for bubbles of lengths up to ten base pairs as the GC content of the sequences is varied, which are accurately fitted with stretched exponential functions. We find that for both models the average bubble lifetime decreases with increasing either the bubble length or the GC content. In addition, the obtained bubble length distributions are also fitted by appropriate stretched exponential functions and our results show that short bubbles have similar likelihoods for any GC content, but longer ones are substantially more likely to occur in AT-rich sequences. We also show that the ePBD model permits more, longer-lived, bubbles than the PBD system.

Transcutaneous electrical nerve stimulation improves fatigue performance of the treated and contralateral knee extensors.

PURPOSE: Transcutaneous electrical nerve stimulation (TENS) can reduce acute and chronic pain. Unilateral fatigue can produce discomfort in the affected limb and force and activation deficits in contralateral non-exercised muscles. TENS-induced local pain analgesia effects on non-local fatigue performance are unknown. Hence, the aim of the study was to determine if TENS-induced pain suppression would augment force output during a fatiguing protocol in the treated and contralateral muscles. METHODS: Three experiments were integrated for this article. Following pre-tests, each experiment involved 20 min of TENS, sham, or a control condition on the dominant quadriceps. Then either the TENS-treated quadriceps (TENS_Treated) or the contralateral quadriceps (TENS_Contra) was tested. In a third experiment, the TENS and sham conditions involved two\; 100-s isometric maximal voluntary contractions (MVC) (30-s recovery) followed by testing of the contralateral quadriceps (TENS_Contra-Fatigue). Testing involved single knee extensors (KE) MVCs (pre- and post-test) and a post-test 30% MVC to task failure. RESULTS: The TENS-treated study induced greater (p = 0.03; 11.0%) time to KE (treated leg) failure versus control. The TENS_Contra-Fatigue induced significant (p = 0.04; 11.7%) and near-significant (p = 0.1; 7.1%) greater time to contralateral KE failure versus sham and control, respectively. There was a 14.5% (p = 0.02) higher fatigue index with the TENS (36.2 ± 10.1%) versus sham (31.6 ± 10.6%) conditions in the second fatigue intervention set (treated leg). There was no significant post-fatigue KE fatigue interaction with the TENS_Contra. CONCLUSIONS: Unilateral TENS application to the dominant KE prolonged time to failure in the treated and contralateral KE suggesting a global pain modulatory response.

Simple Wave-Optical Superpositions as Prime Number Sieves.

We encode the sequence of prime numbers into simple superpositions of identical waves, mimicking the archetypal prime number sieve of Eratosthenes. The primes are identified as zeros accompanied by phase singularities in a physically generated wave field for integer valued momenta. Similarly, primes are encoded in the diffraction pattern from a simple single aperture and in the harmonics of a single vibrating resonator. Further, diffraction physics connections to number theory reveal how to encode all Gaussian primes, twin primes, and how to construct wave fields with amplitudes equal to the divisor function at integer spatial frequencies. Remarkably, all of these basic diffraction phenomena reveal that the naturally irregular sequence of primes can arise from trivially ordered wave superpositions.

A disclosure gel for visual detection of live Bacillus anthracis spores.

AIMS: To develop a gel formulation to trigger a visual signal for rapid disclosure of the location and extent of surface contamination with viable Bacillus anthracis spores. METHODS AND RESULTS: Methylumbelliferyl-α-d-glucopyranoside was combined with hyaluronic acid to produce a gel that could be applied to a surface as a coating. It remained hydrated for a sufficient time for α-glucosidase activity present in intact B. anthracis spores to cleave the substrate and release the fluorescent product, methylumbelliferone. The presence of B. anthracis spores could be disclosed at 5 × 104 CFU per reaction test well (0·32 cm2 ) both visually and using fluorescence detection equipment. CONCLUSIONS: The disclosure gel provides a rapid, visual response to the presence of B. anthracis spores on a surface. SIGNIFICANCE AND IMPACT OF THE STUDY: The disclosure gel demonstrates the first steps towards the development of a formulation that can provide nonspecialist users with a visual alert to the presence of B. anthracis spores on a surface. It is envisioned that such a formulation would be beneficial in scenarios where exposure to spore release is a risk, and could be used in the initial assessment of equipment to aid prioritization and localized execution of a decontamination strategy.

The signatures of microorganisms and of human and environmental biomes can now be used to provide evidence in legal cases.

The microorganisms with which we share our world go largely unnoticed. We are, however, beginning to be able to exploit their apparently silent presence as witnesses to events that are of legal concern. This information can be used to link forensic samples to criminal events and even perpetrators. Once dead, our bodies are rapidly colonised, internally and externally. The progress of these events can be charted to inform how long and even by what means a person has died. A small number of microbial species could actually be the cause of such deaths as a result of biocrime or bioterrorism. The procedures and techniques to respond to such attacks have matured in the last 20 years. The capability now exists to identify malicious intent, characterise the threat agent to isolate level and potentially link it to perpetrators with a high level of confidence.

Core outcome sets for prevention and treatment of postpartum haemorrhage: an international Delphi consensus study.

OBJECTIVE: To develop core outcome sets (COS) for studies evaluating interventions for (1) prevention and (2) treatment of postpartum haemorrhage (PPH), and recommendations on how to report the COS. DESIGN: A two-round Delphi survey and face-to-face meeting. POPULATION: Healthcare professionals and women's representatives. METHODS: Outcomes were identified from systematic reviews of PPH studies and stakeholder consultation. Participants scored each outcome in the Delphi on a Likert scale between 1 (not important) and 9 (critically important). Results were discussed at the face-to-face meeting to agree the final COS. Consensus at the meeting was defined as ≥ 70% of participants scoring the outcome as critically important (7-9). Lectures, discussion and voting were used to agree how to report COS outcomes. MAIN OUTCOME MEASURES: Outcomes from systematic reviews and consultations. RESULTS: Both Delphi rounds were completed by 152/205 (74%) participants for prevention and 143/197 (73%) for treatment. For prevention of PPH, nine core outcomes were selected: blood loss, shock, maternal death, use of additional uterotonics, blood transfusion, transfer for higher level of care, women's sense of wellbeing, acceptability and satisfaction with the intervention, breastfeeding, and adverse effects. For treatment of PPH, 12 core outcomes were selected: blood loss, shock, coagulopathy, hysterectomy, organ dysfunction, maternal death, blood transfusion, use of additional haemostatic intervention, transfer for higher level of care, women's sense of wellbeing, acceptability and satisfaction with the intervention, breastfeeding, and adverse effects. Recommendations were developed on how to report these outcomes where possible. CONCLUSIONS: These COS will help standardise outcome reporting in PPH trials. TWEETABLE ABSTRACT: Core outcome sets for PPH: nine core outcomes for PPH prevention and 12 core outcomes for PPH treatment.

Models used for case-mix adjustment of patient reported outcome measures (PROMs) in musculoskeletal healthcare: A systematic review of the literature.

BACKGROUND: Case-mix adjustment is an established method to take account of variations across cohorts in baseline patient factors, when comparing health outcomes. Although commonplace, there is a lack of evidence as to the most appropriate case-mix adjustment model to use to enable fair comparisons of PROM data in musculoskeletal services. OBJECTIVES: To conduct a systematic review summarising evidence of the development, validation, and performance of musculoskeletal case-mix adjustment models, and to make recommendations for future methods. DATA SOURCES: Searches included; AMED, CINAHL, EMBASE, HMIC, MEDLINE, and grey literature. ELIGIBILITY CRITERIA: Studies; from January 1992-May 2017, English language, musculoskeletal adult population, developing or validating a case-mix adjustment model, using a relevant PROM, and using patient factors feasible for clinical collection. DATA SYNTHESIS: Two reviewers evaluated selected papers. The CASP Cohort Tool was used to assess quality. RESULTS: Fourteen studies were included; eight US studies on the Focus on Therapeutic Outcomes model (pooled n=546,726 patients (with pre/post treatment data)) and six UK studies related to the UK National PROMs Programme model (pooled n=282,424 patients (with pre/post treatment data)). The majority used retrospective data, restricted to complete datasets. Both US and UK models showed good predictive ability (R2 18-42%). Common model variables were; baseline PROM score, age, sex, comorbidities, symptom duration, and surgical history. Reduced quality scores were mainly due to acceptability of patient recruitment, and completeness and length of patient follow up. CONCLUSION: Significant methodological crossover was found. Further studies are however needed to externally validate and develop models across musculoskeletal settings. PROSPERO database(CRD42017055948).

Intra-luminal gene therapy in the porcine artery using a recombinant adeno-associated virus 9.

The ability to improve or restore blood flow and promote healing in ischemic tissue has many potential clinical applications. Augmentation by direct delivery of growth factors may further enhance results, but requires a method for sustained delivery. In this study, we have tested the ability of adeno-associated virus 9 (AAV9) delivered within the lumen of a porcine artery to transfect the vessel and produce a desired product. The marker chosen was green fluorescent protein (GFP) (Ke et al., 2011). In 4 farm pigs the cranial tibial artery was surgically exposed. The vessel was temporarily clamped proximally, and divided distally. A cannula was placed intraluminally, and the arterial segment was injected with 1×10E13 particles of AAV9.CB7.CI.GFP·WPRE.rBG. At 14days the transfected cranial tibial artery as well as the liver, spleen and kidneys were harvested. ELISA and reverse transcriptase quantitative polymerase chain reaction (RT-qPCR) were used to analyze the artery for GFP production. Significant GFP expression was seen in all transfected cranial tibial vessels, as determined by both GFP protein production (ELISA) and mRNA (RT-qPCR). No GFP was identified in liver, spleen or kidney, nor in the no-GFP control animal artery. Adeno-associated virus 9 is an appropriate vector for gene therapy experiments in the porcine artery model. This vector, and the intraluminal deliver method described result in robust gene expression at 2weeks without evident systemic spill of the virus. The ability to limit delivery of the gene to an isolated segment of vessel is desirable for future research applications.

Re-aerosolization of Bacillus thuringiensis spores from concrete and turf.

Spores of Bacillus anthracis deposited on surfaces can become airborne again as a result of air currents and mechanical forces. As such, they are a potential source of infection by inhalation. Spores of Bacillus thuringiensis were used to quantify this phenomenon in a simulation of outdoor conditions. Concrete and turf surfaces were inoculated by aerosol to produce high spore densities (greater than 1 × 109  CFU per m2 ) which were then subjected to the passage of air at 10 ms-1 with and without simulated walking. Re-aerosolized spores were sampled by wetted wall cyclone air samplers. The mean total re-aerosolization rate from concrete (m-2  min-1 ) was 1·16 × 10-3 for wind alone and 3·2 × 10-3 for wind and simulated walking while for turf the respective values were 2·7 × 10-4 and 6·7 × 10-4 . SIGNIFICANCE AND IMPACT OF THE STUDY: Following the malicious and/or accidental release of an aerosol of Bacillus anthracis spores, the immediate risk of human inhalation would decrease as the spores were deposited on surfaces or diluted by wind flow. There is, however, a concern that the deposited spores could become re-aerosolized and so present an ongoing hazard. Using an accurate simulant for B. anthracis spores a method is reported here that allowed the enumeration of re-aerosolized spores from concrete and turf by wind flow and footfall. Under the conditions used, the rates of re-aerosolization were low. These findings will need to be verified under real outdoor conditions before the true significance in terms of secondary exposure to pathogenic spores can be assessed.

The outcome and complications of vascularised fibular grafts.

AIMS: Free vascularised fibular grafting has been used for the treatment of large bony defects for more than 40 years. However, there is little information about the risk factors for failure and whether newer locking techniques of fixation improve the rates of union. The purpose of this study was to compare the rates of union of free fibular grafts fixed with locking and traditional techniques, and to quantify the risk factors for nonunion and failure. PATIENTS AND METHODS: A retrospective review involved 134 consecutive procedures over a period of 20 years. Of these, 25 were excluded leaving 109 patients in the study. There were 66 men and 43 women, with a mean age of 33 years (5 to 78). Most (62) were performed for oncological indications, and the most common site (52) was the lower limb. Rate of union was estimated using the Kaplan-Meier method and risk factors for nonunion were assessed using Cox regression. All patients were followed up for at least one year. RESULTS: The rate of union was 82% at two years and 97% at five years. Union was achieved after the initial procedure in 76 patients (70%) at a mean of ten months (3 to 19), and overall union was achieved in 99 patients (91%). No surgical factor, including the use of locked fixation or supplementary corticocancellous bone grafts increased the rate of union. A history of smoking was significantly associated with a risk of nonunion. DISCUSSION: Free vascularised fibular grafting is a successful form of treatment for large bony defects. These results suggest that the use of modern techniques of fixation does not affect the risk of nonunion when compared with traditional forms of fixation, and smoking increases the risk of nonunion following this procedure. Cite this article: Bone Joint J 2017;99-B:134-8.

Speed-of-light pulses in the massless nonlinear Dirac equation with a potential.

We consider the massless nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction g^{2}/2(Ψ[over ¯]Ψ)^{2} in the presence of three external electromagnetic real potentials V(x), a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find different scenarios depending on initial conditions, namely, propagation of the initial pulse along one direction, splitting of the initial pulse into two pulses traveling in opposite directions, and focusing of two initial pulses followed by a splitting. For all considered cases, the final waves travel with the speed of light and are solutions of the massless linear Dirac equation. During these processes the charge and the energy are conserved, whereas the momentum is conserved when the solutions possess specific symmetries. For the case of the constant potential, we derive exact analytical solutions of the massless NLD equation that are also solutions of the massless linearized Dirac equation. Decay or growth of the initial pulse is also predicted from the evolution of the charge for the case of a non-zero imaginary part of the potential.