Prochlorococcus is of interest to diverse branches of science. For the past 30 years, research on this minimal phototroph has led to a growing understanding of biological organization across multiple scales, from the genome to the global ocean ecosystem. Progress in understanding drivers of its diversity and ecology, as well as molecular mechanisms underpinning its streamlined simplicity, has been hampered by the inability to manipulate these cells genetically. Multiple attempts have been made to develop an efficient genetic transformation method for Prochlorococcus over the years; all have been unsuccessful to date, despite some success with their close relative, Synechococcus. To avoid the pursuit of unproductive paths, we report here what has not worked in our hands, as well as our progress developing a method to screen the most efficient electroporation parameters for optimal DNA delivery into Prochlorococcus cells. We also report a novel protocol for obtaining axenic colonies and a new method for differentiating live and dead cells. The electroporation method can be used to optimize DNA delivery into any bacterium, making it a useful tool for advancing transformation systems in other genetically recalcitrant microorganisms.As the smallest and most abundant primary producer in the oceans, the cyanobacterium  While environmental microbiology has been revolutionized by the rapid pace of improved sequencing technologies , the numCountless attempts have demonstrated that the creation of successful genetic transformation protocols requires tedious trial and error, and methods developed for one strain are often unsuccessful in close relatives (for a few examples see: ). There Prochlorococcus is the most abundant cyanobacterium worldwide, dominating vast regions of the global oceans [Prochlorococcus biology and ecology has been greatly facilitated by the rise of metagenomic, metatranscriptomic, and metaproteomic studies of ocean samples over the past decade [Prochlorococcus is a perfect example of the imbalance between the availability of genomic data and the dearth of genetic tools.l oceans . It may l oceans  and is rl oceans . Our undt decade . Becauset decade , and hast decade . ProchlProchlorococcus’ numerical dominance in oligotrophic oceans is attributed to its small size (hence high surface/volume ratio), which enhances its ability to compete for limiting nutrients [Prochlorococcus meta-population [Prochlorococcus strain isolated, or wild single-cell sequenced, roughly 100 new genes are added to the Prochlorococcus pangenome – the vast majority of which are of unknown function [utrients , and itsutrients , which epulation . Ecologipulation . Althougfunction .Prochlorococcus is of interest because of its potential as a chassis for synthetic biology applications [Prochlorococcus strains as the top candidates [In addition to its ecological and biogeochemical relevance, the biology of ications . This ceications . It has ications . Indeed,ndidates . Furtherndidates .Prochlorococcus from these different perspectives has been hampered by our inability to develop a robust genetic system. Although we and others have worked on this over many years, very limited progress has been made. Possible reasons behind these failures include the cell’s slow growth rate , their reluctance to grow axenically on solid media, specific media requirements [Progress in studying irements , sensitiirements  and reacirements , unusualirements , and theirements .Prochlorococcus genetic transformation method, based on conjugation from an E. coli donor strain [Prochlorococcus cells – developing a method that should be applicable to a wide range of microorganisms. The next step will be to develop genetic tools compatible with the host that will also bypass the cell’s defences against exogenous DNA, which are abundant in cyanobacteria [Prochlorococcus cells.From our perspective, a significant impediment to rapid progress is that investigators generally do not publish negative results or partial progress; as a result, considerable time is wasted by others in rediscovering what does not work. Thus, before describing our progress, we first report experiments that failed. We initially tried to build upon the only reported successful  r strain . This mebacteria . We repoProchlorococcus strains to various common antibiotics in order to find their minimum inhibitory concentration (MIC), revealing that some antibiotics were more effective than others  [Prochlorococcus strain [E. coli conjugation with Prochlorococcus via a filter mating procedure which did not yield any conjugants in our hands, even after incubating for two months. We next used a liquid mating procedure, testing different E. coli donor strains carrying plasmids with distinct antibiotic resistance genes on various Prochlorococcus and Synechococcus recipient strains , but again obtained no conjugants.coccus)  and has  strain . We firsProchlorococcus during filter mating. Indeed, while a Synechococcus strain could readily recover after the mating procedure, Prochlorococcus strains were often lost at this step. The switch to a liquid mating procedure (see Methods) improved survivability but still did not yield transconjugants. In an effort to find an alternative route to conjugation with Prochlorococcus, we developed a mixed approach where mating was performed inside an agar stab (see Methods for details). Briefly, concentrated cultures of the donor and receiver strains were mixed and injected together inside 1 ml of polymerized agar - the ‘agar stab’ . We reasoned that this agar stab environment would provide a solid medium favoring conjugation while mitigating the drawback of desiccation on top of a filter. After 24 h incubation, the cells were removed from the agar with a pipet tip, resuspended in liquid medium, and plated on antibiotic selection plates.One of the limitations of our mating experiments was the low survival frequency of Synechococcus strain WH8102 [et al. in Prochlorococcus strain MIT9313 [Prochlorococcus. In addition, we cloned the Prochlorococcus promoter for Rubisco protein, P ccmk, in front of a fluorescent reporter gfp or yfp gene to facilitate the characterization of conjugants (see Methods for details). Using this ‘agar stab’ procedure, a Synechococcus strain and two Prochlorococcus strains survived and were able to grow on plates in the absence of antibiotics. After 30 days, we obtained transconjugant colonies of Synechococcus WH8102, but did not obtain transconjugants for either Prochlorococcus strain (SB and NATL2A). We thus abandoned conjugation as a feasible mechanism of genetic transfer and moved on to electroporation. This required the development of a method to assess DNA delivery into live cells.We attempted this procedure with a conjugative plasmid - pBAMD1-4  - contain WH8102  and by T MIT9313 . Though Prochlorococcus, we decided to focus on optimizing the initial step required for any genetic system: DNA delivery. A screening procedure for DNA entry must be able to differentiate between live and dead cells since the delivery of DNA inside dead cells would yield false positives. We needed a dead cell stain that emitted in the blue/violet wavelength range (between 400–500 nm wavelength) so that it could be differentiated from chlorophyll autofluorescence (650–700 nm), and fluorescein-labelled oligonucleotide fluorescence (495–555 nm). While Sytox green (ThermoFisher Scientific) has been used successfully with Prochlorococcus [Prochlorococcus cells in a robust and highly reproducible way . Cells washed in glycerol or PEG8000 did not survive any better than cells washed with MilliQ water, while sorbitol allowed cells to recover as fast as the seawater media control . The colonies typically took 2–3 months to become visible to the naked eye , and could then be picked and transferred into small (~5 ml) volumes of liquid Pro99 medium; they grew as expected and were verified as axenic. This combination of microwave sterilization of the agar and addition of pyruvate to the plating medium allowed us to reproducibly obtain axenic colonies for all the Prochlorococcus strains tested so far .Assuming that mutants will one day be generated, we will need a procedure for selecting them on solid media. To date, the only way to grow romonas . Prochlg growth . Since t species , we sterensities . With thProchlorococcus cells, which are under intense selective pressure for genome minimization [Synechococcus strains [Prochlorococcus [The vast majority of genetic systems developed for bacteria rely on the use of replicative plasmids. Replicative plasmids offer a versatile platform to introduce and express exogenous genes in the target bacterial strain, allowing the development of further technologies for gene knockouts, such as Lambda Red recombineering or CRISPR-Cas9 . Howevermization . Further strains  and haveococcus .Synechococcus strains [Prochlorococcus [in vitro and delivered inside the host by electroporation [An alternative strategy is to use integrative plasmids to serve as delivery vectors, relying on the target cell’s homologous recombination machinery to recombine the exogenous DNA into the host genome . This pr strains  but requococcus , which wococcus  used in poration .Prochlorococcus, such as the strong Rubisco promoter P ccmk [aadA) and chloramphenicol resistance (cat) (see Methods for details). Each of these constructs was tested in two Prochlorococcus strains (MED4 and MIT9313), as well as in several other strains selected for a lower likelihood of degrading incoming DNA by means of a restriction-modification system . However, no transformants were obtained in any of these attempts, despite growth of electroporated strains on the no-antiobiotic control plates.We used the EZ-Tn5 transposition system (Lucigen), which has worked successfully for several challenging bacteria . Transpor P ccmk  or the cProchlorococcus. Among the remaining hurdles are overcoming host defences against foreign genetic material such as restriction-modification systems, and optimizing expression of the antibiotic selection marker and the stable integration of foreign DNA inside the chromosome. We are confident, however, that effective solutions can be found to overcome these hurdles. Solutions might come from new transposome systems [While suitable DNA delivery conditions is a significant step forward, we have not yet achieved a successful genetic transformation of  systems , which c systems ; from us systems ; through systems  that areProchlorococcus MED4 cells were grown under constant light flux (30–40 μmol photons m−2 s−1) at 24 °C in natural seawater-based Pro99 medium containing 0.2-µm-filtered Sargasso Sea water, amended with Pro99 nutrients  prepared as previously described [Axenic escribed . Growth −2 s−1. Growth was monitored by measuring bulk chlorophyll fluorescence and was compared to a no-drug control culture.MED4 cells were grown in Pro99 medium with a Sargasso seawater base, at a light level of 25 μmol photons met al. [E. coli 1100–2 carrying plasmid pRK2 (as the conjugation vector) and pRL153 (kanamycin-resistant), as well as E. coli BW19851 carrying BAC conjugation plasmid pMBD14 [Synechococcus 8102, and Prochlorococcus strains MIT9313 and MED4. As described above, in our hands, the method did not yield any conjugants after incubation of exconjugants for two months. For conjugation via liquid mating, we used the same donor and receiver strains, and the following procedure: 1 ml of log-phase donor E. coli was added to 25 ml of log-phase Synechococcus or Prochlorococcus receiver strain and the co-culture was left to grow overnight. Antibiotic was then directly added to the co-culture at the same concentration used on solid media . The addition of nalidixic acid at 50 µg ml−1 was also attempted to remove the E. coli donor strain. Cultures were then grown for 45–60 days but did not yield conjugants.For conjugation via filter mating, we followed the procedure described by Tolonen et al. . Conjugad pMBD14  . After 24 h incubation, cells were sucked out of the agar using a pipet tip, resuspended in liquid Pro99 medium, and plated for selection with 5 µg ml−1 of spectinomycin and streptomycin .For conjugation via ‘agar stab mating’, we used Prochlorococcus genomes. Genes encoding the GFPmutII and YFP reporters, shown to fluoresce efficiently in a wide range of cyanobacteria [Prochlorococcus P ccmk promoter for Rubisco protein [Prochlorococcus and Synechococcus strains [ccmk promoter was amplified from Prochlorococcus MED4 genomic DNA using primers RL015 and RL016 for the P ccmk-gfpmutII construct, and RL015 and RL019 for the P ccmk-yfp construct. The three-part assembly reaction (plasmid-promoter-insert) was performed using the Gibson assembly master mix 2x (New England Biolabs #E2611S), following the manufacturer’s instructions. The mixture was transformed in One Shot PIR1 Chemically Competent E. coli (Thermofisher #C101010). For the construction of pBAMD1-4-Pccmk  P ccmk was amplified from Prochlorococcus MED4 genomic DNA using primers RL121 and RL122, which contain EcoRI and SwaI restriction sites, respectively. Both pBAMD1-4 and the insert were digested with EcoRI-HF and SwaI-HF (New England Biolabs #R0604S and # R3101S), ligated, and transformed in PIR1 E. coli as described above.We used plasmid mini-Tn5 pBAMD1-4  to constbacteria  were clo protein , well co strains . The pBAg for 5 min at 20 °C and resuspended in 0.5 ml of fresh Pro99. Samples were then serially diluted and immediately run on the flow cytometer. A positive control  and negative control (1 ml of cells from the same culture heated to 80 °C for 5 min) were included with each run to gate the live and dead cell populations.For each sample labelled, 100 µl of culture were transferred to an Eppendorf tube containing 900 µl of filtered Pro99 medium. Then 1 µl of reconstituted LIVE/DEAD Fixable Violet Dead Cell Stain (Thermo Fisher Scientific) was added to the 1 ml cell suspension and incubated for 30 min at room temperature in the dark. Cells were pelleted by centrifugation at 10 000 Prochlorococcus cells were counted by a defined gate on the red fluorescence (chlorophyll) versus forward scatter (size) plot. (2) From these selected events, viable cells were counted by a defined threshold on the blue fluorescence (violet dead cell stain). The threshold was adjusted for each run using the positive (untreated cells) and negative (heat-shocked cells) control. (3) From the ‘viable cell’ subset of events, the cells into which DNA was delivered were counted by a defined threshold on the green fluorescence (fluorescein-labelled oligonucleotides). The threshold was adjusted so that <1 % of events from the negative control (cells that did not enter into contact with the oligonucleotides) were included. The dead cell control comprised cells killed by heat treatment at 80 °C for 5 min. The flow cytometry plots were generated using FlowJo.Cell abundances, viability (Live/Dead violet staining and chlorophyll fluorescence), and fluorescein-labelled oligonucleotide delivery were measured on a Guava easyCyte 12HT flow cytometer . Cells were excited with a blue 488 nm laser for measuring chlorophyll fluorescence (692/40 nm), size (forward scatter) and fluorescein fluorescence (525/30 nm); and with a violet 405 nm laser to measure the violet dead stain fluorescence (448/50 nm). All flow cytometry files were analysed using FlowJo software version 7.6.5  and the following workflow: (1) g for 10 min. Under sterile conditions, pellets were resuspended by gently pipetting up and down in a volume of 100 µl of either solutions 10 % (v/v) glycerol in water; 18.2 % (w/v) sorbitol in water (1M); 5 % (w/v) PEG8000 in water; Pro99 medium (positive control); or MilliQ water (negative control). The washing was repeated once before cells were centrifuged again, resuspended into 1 ml of Pro99 medium, and inoculated in 5 ml of Pro99. The tubes were placed back in the incubator, and recovery was monitored by measuring bulk culture fluorescence. Of note, all osmoprotectant solutions were filter sterilized through 0.2 µm supor membrane filters. Cultures that recovered were checked for the presence of heterotrophic contamination using purity broths, as previously described [For each osmoprotectant tested, 2 ml of triplicate exponentially growing MED4 culture were harvested by centrifugation at 13 000 escribed  to ensurescribed .g for 15 min at 20 °C. Then 50 ml culture pellets were washed three times in 5 ml (1 M sorbitol solution) by centrifugation at 5000 g for 8 min at 20 °C. The final resuspension volume was calculated so that cells were concentrated 1000 times compared to the initial culture volume. Then 500 ng of 90 bp fluorescein-labelled oligonucleotides (sequence: cctcataacaagcagcgctcatagtattaggaatatcgtgaaattcaagatctaagaatatttttttatttaaatttttcaaaattttta) were added to 50 µl of the washed cells and electroporated in 2 mm gap cuvettes at variable electric fields and time constants while keeping the capacitance and resistance fixed at 25 µF and 200 ohms. One ml of fresh Pro99 medium at room temperature was immediately added to the cuvette, and cells were transferred to a culture tube containing 4 ml Pro99 supplemented with 5 mM glucose and 5 mM pyruvate for recovery. Samples were then directly stained with Live/Dead violet and analysed by flow cytometry. We initially tried to deliver a fluorescently labelled pUC19 plasmid , but the signal to noise ratio was not sufficient to detect the plasmid.Exponentially growing cultures were harvested by centrifugation at 7000 in vitro-assembled transposomes were added to the 50 µl cell suspension in sorbitol before electroporation. Addition of DOTAP liposomal transfection reagent (Millipore Sigma) and Type One Inhibitor (Lucigen), following the manufacturer’s instructions, were also attempted, as they were shown to favour successful transposome transformation in the cyanobacterium Arthrospira platensis C1 [For transposome delivery, 2 µl of EZ-Tn5 (Lucigen) ensis C1 . After tProchlorococcus growth [−1, and aminoglycoside resistance (encoded by aadA) selected with a combination of streptomycin and spectinomycin at 5 µg ml−1 total concentration (2.5 µg ml−1 each). Individual colonies typically became visible after 40–60 days. They were picked using a sterile pipet tip and inoculated into 5 ml of fresh Pro99 medium. The efficiency of colony formation from a diluted culture is variable and generally low (~1 %), an effect that seems alleviated by plating a higher number of cells, as an axenic lawn of cells would grow significantly faster, typically visible after 15–30 days.To obtain single colonies from an axenic culture, serial dilutions of an exponentially growing cyanobacterial culture grown in Pro99 medium (as described above) were pour-plated in the plating medium (Pro99 medium supplemented with 0.05 % (wt/vol) Pyruvate and 3.75 mM TAPS (pH 8) and containing 0.3 % low melting point (LMP) agarose. To prepare the plating medium, we first sterilized a 3 % LMP agar solution in ultrapure water independently by three rounds of boiling in a microwave . We then added the melted LMP agar 1 : 10 in the Pro99 medium base supplemented with pyruvate and TAPS. The mixture was maintained at ~28 °C in a water bath to cool before plating. Of importance, the LMP agarose was microwave sterilized and not autoclaved to avoid creating reactive oxygen species likely to inhibit  growth . Microwacat and the spectinomycin/streptomycin resistance gene aadA were codon-optimized for Prochlorococcus using the codon usage table from the Kazusa database, and the OPTIMIZER online tool [ccmk promoter and flanked by the Tn5 mosaic end, and were synthesized through the Genscript gene synthesis service (see sequence in supplementary data).The chloramphenicol resistance gene ine tool . The codTransposome DNA containing the antibiotic resistance cassette and the mosaic ends were amplified using the template plasmids and primers  listed in Transposome T1 amplified using RL005 and RL006 primers from pCV0001 template DNATransposome T2 amplified using RL007 and RL008 primers from pCV0021 template DNATransposome T3 amplified using RL079 and RL080 primers from pBAMD1-4-GFP template DNATransposome T4 amplified using RL079 and RL080 primers from pBAMD1-4-YFP template DNATransposome T5 amplified using RL081 and RL080 primers from the synthesized codon-optimized chloramphenicol resistance cassette template DNATransposome T7 amplified using RL079 and RL080 primers from the pBAMD1-4-Pccmk template DNATransposome T8 amplified using RL140 and RL080 primers from the synthesized codon-optimized Spectinomycin/streptomycin resistance cassette template DNA.−1 plus 2 µl of 100 % glycerol and the mixture was incubated for 30 min at room temperature. The transposomes were either electroporated immediately or frozen at −20 °C for later use. The commercial transposome R6Kγori/KAN-2 from Lucigen kit #TSM08KR was used according to the manufacturer’s instructions.PCR mixtures were digested for 1 h at 37 °C with DpnI (New England Biolabs) to remove the template plasmids. PCR products were then purified using the QIAquick PCR Purification Kit (Qiagen), eluted in TE buffer at pH 7.5, and DNA purity was assessed using a NanoDrop ND8000 spectrophotometer. Using the same kit, samples were often purified a second time to remove detectable impurities. Transposomes were formed using the EZ-Tn5 Transposase (Lucigen) following the manufacturer’s instruction. Then 4 µl of EZ-Tn5 transposase preparation was mixed with 2 µl of transposon DNA at 100 µg µlClick here for additional data file.


Structured light has revolutionized optical particle manipulation, nano-scaled material processing, and high-resolution imaging. In particular, propagation-invariant light fields such as Bessel, Airy, or Mathieu beams show high robustness and have a self-healing nature. To generalize such beneficial features, these light fields can be understood in terms of caustics. However, only simple caustics have found applications in material processing, optical trapping, or cell microscopy. Thus, these technologies would greatly benefit from methods to engineer arbitrary intensity shapes well beyond the standard families of caustics. We introduce a general approach to arbitrarily shape propagation-invariant beams by smart beam design based on caustics. We develop two complementary methods, and demonstrate various propagation-invariant beams experimentally, ranging from simple geometric shapes to complex image configurations such as words. Our approach generalizes caustic light from the currently known small subset to a complete set of tailored propagation-invariant caustics with intensities concentrated around any desired curve. Propagation-invariant beams have been up to now only available in a few realizations or for specific applications. Here, the authors demonstrate two methods for generating propagation-invariant beams with fully customizable intensity profiles in a comprehensive way inspired by geometrical optics. This growth stemmed both from increased theoretical understanding and from the advent of new optical devices such as spatial light modulators (SLMs). This area of research has now transcended optics, leading to a range of applications in fundamental physics3, telecommunications6, security9, micromachining11, imaging15, and the manipulation of cells and microorganisms17. In particular, the fact that phase-structured light carries orbital angular momentum (OAM)18 allows the exertion not only of forces but also of torques onto atoms, bacteria, or micromachines2.The field of structured light has grown significantly since the early studies of Laguerre- and Hermite-Gaussian modes in laser cavities19. Propagation-invariant beams have a transverse angular spectrum confined to a ring20 whose radius is proportional to their numerical aperture. The best-known examples are Bessel22, Mathieu24, and Weber25 beams, which are described by closed-form expressions that are separable in polar, elliptic and parabolic coordinates, respectively. The intensity maxima of these beams are therefore localized around the corresponding conic section shapes, characterized by their caustics28. Some of these propagation-invariant beams have been used in advanced optical trapping setups29, imaging with high resolution15, and ultrafast nanoscale material processing with high aspect ratios30. However, having only a limited set of beams of this type restricts significantly their usefulness. All the applications mentioned earlier would greatly benefit from the ability to tailor the shapes of propagation-invariant beams for the purpose at hand.A class of structured optical field that has received considerable attention is that of the so-called propagation-invariant or non-diffracting beams, whose transverse intensity distribution remains essentially invariant over a significant propagation distanceThe achievement of our work is propagation-invariant beams with customizable intensity profiles. To design the respective beams, we develop two methods for shaping the corresponding caustics. These methods are illustrated with the experimental implementation of beams whose intensity features trace a range of geometrical shapes as well as more complex patterns such as words, which remain essentially invariant over a significant propagation distance.31. Within the ray picture, propagation invariance requires that all rays travel at the same angle θ with respect to the propagation direction (chosen as the z axis), and that the two-parameter ray family is composed of one-parameter subfamilies of parallel rays constrained to planes parallel to z. This structure guarantees that the caustics themselves are invariant in z, since they correspond to the envelopes of these planes. The fact that all rays have equal angle with respect to the z axis implies that the transverse Fourier spectrum of the wave field is restricted to a ring19 (whose radius is k is the wavenumber). The azimuthal angle ϕ of each subfamily of rays indicates the point along the ring to which they correspond.The conceptual basis for this work is the relation between these wave solutions and the simpler ray model, for which the intensity maxima follow the shapes of the caustics, which are the envelopes of the two-parameter family of rays associated with the fieldA(ϕ) and Φ(ϕ), and the beam’s transverse field is given by Whittaker’s integral20:r =  is the transverse position vector and 31 to Eq. (rc(ϕ):A and Φ appropriately, different caustic shapes can be achieved. The beam’s intensity maxima are localized within the vicinity of these caustics. For example, Bessel beams (for which A is constant and Φ(ϕ) = ℓϕ for integer ℓ) have caustics with circular  cross-sections34, while Mathieu beams have caustics with elliptic or hyperbolic cross-sections24.The mathematical correspondence between the ring’s amplitude and phase distributions, ℓ = 1. The transition between the Fourier plane in Fig. z  for a given rc(ϕ). For simplicity we keep the amplitude A(ϕ) constant. The details of this approach are given in the ‘Methods’ section, and some results are shown in Fig. π on the Fourier ring shown in Fig. ℓ.) From the Fourier phase function, we calculate the transverse ray picture of the beam shown in Fig. q = 5), present a square lattice at the center, surrounded by several rings. This beam interpolates between Bessel beams (q = 0) and four interfering plane waves (q → ∞): we call this light field a Bessel-lattice beam λ0 = 2π/k0 = 532 nm, shaped by a SLM, for their experimental realization. All beams demonstrated here have the same real space structure size a = 2π/k⊥ = 15 μm related to the propagation constant kz via xz-cross-section of the measured intensity volume  would have the largest effect on improving the distance of invariant propagation. Figure ℓ = 2 has the effect of making the square lattice rectangular. An interesting effect can be explored in which the Bessel-lattice beam ℓ = 2 phase vortex plate, resulting in the diffracting field ze and acquires the shape corresponding to 35.Our goal, however, is to solve the inverse problem: find the phase distribution Φ that produces any desired propagation-invariant caustic. The first approach is the solution of Eq.  for Φ(ϕ)entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaThe first approach described above allows finding the phase functions that produce different caustic shapes. However, a limitation of this approach becomes evident from the example of a cardioid caustic in Fig. 38, but without the propagation invariance achieved here. Figure ze, is shown in the top row of Fig. The second method for producing propagation-invariant intensity features in the transverse plane that follow any desired curve is based on ‘drawing’ this curve using a 0th-order Bessel beam (whose caustic is a point) as a pencil. That is, the desired pattern is generated by superimposing coherently a continuum of 0th-order Bessel beams whose foci trace the anticipated curve. The ‘Methods’ section describes this algorithm in detail. Related approaches to create 3D high-intensity curves based on superimposing Gaussian beams or for lower-dimensional accelerating fields were demonstrated in11. 2D caustic light, e.g., with centered periodic lattices and well-defined curvilinear borders, enables fabricating refractive index modulations in (nonlinear) materials for novel topological structures. Imaging systems like light sheet microscopy benefit from the robust long-focus propagation of high-intensity caustics with phase singularities15. Similar to the alphabet of orthogonal states of Bessel beams with different order, the presented propagation-invariant caustics can be used to construct other families of orthogonal states with particular self-healing features, thus are highly important for secure high-dimensional (quantum) communication40.Caustics can be shaped into propagation-invariant light that presents any desired high-intensity curve in its transverse profile. We present methods to tailor the light’s wavefront, forming translation invariant, customized caustics as the envelope of families of rays. The two approaches presented here are illustrated by experimentally implementing propagation-invariant beams whose caustics trace fundamental forms like astroids, deltoids, cardioids, and nephroids, as well as more sophisticated structures such as letters or words. These self-healing beams propagate robustly in the presence of perturbations. We demonstrate the properties of an astroid-shaped Bessel-lattice beam that interpolates between the sum of four plane waves and a Bessel beam. Propagation-invariant caustics satisfy the need for customized high-energy transfer in nano-fabrication applications with light or electron beams for ultrafast cutting and deep drilling in transparent materials4 laser beam with wavelength λ0 = 532 nm is expanded in a plane wave, illuminating a phase-only full HD SLM ‘Holoeye HEO.’ We address a pre-calculated phase pattern to the SLM that allows encoding the real space amplitude and phase simultaneously on a single phase-only modulator41. Therefore, in the common focal plane of the lenses L1 (f = 385 mm) and L2 (f = 38 mm) an appropriate filter in Fourier space is necessary (FF). The desired light field forms in the image plane of the modulator. A movable microscope objective (MO), Olympus MPLN with a magnification of 10 and numerical aperture of 0.25, together with a camera, iDS UI-3370CP-M-GL, constitute the imaging system, capable of observing the propagation of a light field. A second expanded beam, a plane wave, serves as a reference beam and can be switched on for phase measurements using a shutter (S). To recover the spatial phase, a standard digital holographic method is applied, that is based on the superposition of the signal beam with a slightly tilted reference beam42.  Figure ϕ, are located at the points r for which the first and second derivatives of the phase of the integral in Eq. (ϕ vanish:u and ϕ in the Fourier ring is not an angular coordinate in the caustic space. A parametrization of the caustic with ϕ as the parameter may be found by considering the derivative of both sides of the previous equation:ϕ for which ψ(r) from Eq. r(ϕ).The caustics, parametrized by l in Eq.  with resℓ = 0, its caustic is a point. In accordance with Eq. rc is ψ(r) is to construct the angular spectrum by coherent integration of this expression along the desired path rc(τ) and choosing the phase γB(τ) and amplitude AB(τ) appropriately along the curve. Note that the parameter τ is not necessarily the azimuthal angle ϕ, but the arc length of the curve. Since the phase of the field along the curve should grow with the curve’s arc length τ, it is given as:rc(τ), parametrized by τ, between two points A and B can then be calculated via the angular spectrum as:A second approach to realize a desired curve is to use the most localized propagation-invariant light spot we can achieve, a 0th-order Bessel beam, as a pencil to draw the curve. Since Supplementary InformationDescription of Additional Supplementary filesSupplementary Movie 1Supplementary Movie 2Supplementary Movie 3


Moreover, this simple strategy could be well extended to other 2D materials such as WS2 or WSe2, leading to enhanced bandgap modulation.Strain engineering is a promising method to manipulate the electronic and optical properties of two-dimensional (2D) materials. However, with weak van der Waals interaction, severe slippage between 2D material and substrate could dominate the bending or stretching processes, leading to inefficiency strain transfer. To overcome this limitation, we report a simple strain engineering method by encapsulating the monolayer 2D material in the flexible PVA substrate through spin-coating approach. The strong interaction force between spin-coated PVA and 2D material ensures the mechanical strain can be effectively transferred with negligible slippage or decoupling. By applying uniaxial strain to monolayer MoS Strain engineering is a promising method to manipulate properties of two-dimensional (2D) materials but slippage between material and substrate makes strain transfer inefficient. Here the authors overcome slipping effects by encapsulating a 2D material in a polymer substrate. From mechanical point of view, 2D materials could withstand deformations over 10% before rupture, which is over one order of magnitude higher than that of typical bulk semiconductors with a break value typically <1% (refs. 9). The naturally high flexibility has stimulated considerable efforts in further controlling and modulating the electrical and optical properties of 2D semiconductors through strain engineering. For example, by applying tension strains, the bandgap of typical TMD  can be reduced, offering additional degree of freedom to improve the performance of TMD based devices such as strain-induced strong light emission in bilayer WSe2 (ref. 10), and the greatly enhanced carrier mobilities in strained MoS2 transistors12.The two-dimensional (2D) materials have attracted considerable attention in recent years, owing to their unique electrical, optical, and mechanical properties at the single atomic thickness13. The larger germanium atom provides compression strain to silicon channel with much-enhanced hole carrier mobility, and similarly, smaller carbon atom creates tension strain and is used to increase the electron carrier mobility of silicon. Applying existing state-of-the-art strain approaches to 2D materials is not straightforward because there is little physical space for impurity dopants in such atomically thin semiconductors14. Alternatively, in 2D research community, the strain engineering is typically achieved by mechanically exfoliating 2D materials on the surface of flexible polymer substrate that can be mechanically bended or stretched19. However, with weak van der Waals (vdW) force in between20, the strain applied on the polymer may not be effectively transferred to the lattice of 2D materials where the decoupling  and interlayer slippage are unavoidable18, leading to insufficient bandgap modulation. For example, by applying uniaxial strain to monolayer MoS2 on PMMA (polymethyl methacrylate) substrate, small bandgap change (ΔEg) of 38 meV and low bandgap modulation rate  ~70 meV/% are observed21.In modern microelectronics, the strain engineering of silicon channel is achieved by doping the source and drain regions with lattice-mismatched atoms such as germanium and carbonEg and SEgΔ, considerable efforts have been devoted to increase the strain transfer efficiency from polymer substrate to 2D materials. The early attempt used Ti metal as a clamp to fix the MoS2 on the surface of flexible PET  substrate to avoid the slippage22. However, within this structure, the majority strain may be largely accumulated in the metal–MoS2 junction, resulting in nonhomogeneous strain distribution and small bandgap modulation ΔEg of 110 meV (with SEgΔ ~ 45 meV/%) before MoS2 rapture. Alternatively, improved strain transfer efficiency can be achieved by using polymers with higher Young’s modulus EYoung, which have been theoretically predicted and experimentally verified24. For example, by changing the flexible substrate from polydimethylsiloxane (PDMS) (EYoung ~ 430 kPa) to polyvinyl alcohol (PVA) (EYoung ~ 650 MPa), the strain transfer efficiency could be improved over 6 fold18. However, although increasing the substrate EYoung could mitigate the Young’s modulus mismatch between 2D materials and substrate, their vdW interaction is still too weak to prevent slippage and interfacial decoupling during straining process, especially at relatively large strain level. Hence using uniaxial strain, the highest bandgap modulation reported for monolayer MoS2, WSe2, and WS2 are limited to 140 meV, 90 meV, 50 meV, respectively25. The non-optimized bandgap modulation achieved poses a key challenge for investigating fundamental physics of 2D materials through strain engineering, as well as for the practical application of high-performance strain engineered 2D devices and flexible electronics.To enhance the ΔEYoung ~ 10 GPa)26, ensure the mechanical strain applied on the PVA substrate can be effectively transferred to the lattice of 2D materials during the mechanical bending process. By applying uniaxial strain to monolayer MoS2, we observed a higher bandgap change of ~300 meV and a highest modulation rate of ~136 meV/%, approximate two times improvement compared to previous best results  using uniaxial strain and is approaching the energy required for direct-to-indirect bandgap transition in MoS2 (refs. 21). Furthermore, tape peeling test, thermal expansion measurement, multiple cycles straining-relaxing, and load-unload experiments are conducted to verify the efficient bandgap modulation is the result of strong interaction between MoS2 and PVA substrate with negligible slippage in between. Finally, we demonstrate this simple PVA spin-coating approach could be well extended to other TMD such as WS2 or WSe2, and much higher ΔEg and SEgΔ are observed compared to previous reports. Our study not only breaks the limit of TMD bandgap modulation value using strain engineering, but also provides a general approach for efficient strain engineering of other layered 2D materials and conventional 3D thin films.Here, we report a simple strain engineering approach to efficiently modulate the bandgap of 2D materials, by encapsulating them in the flexible PVA through spin-coating method. The strong interaction force between the spin-coated PVA and 2D materials, together with the high Young’s modulus of PVA used here  with 300 nm SiO2 on top  spectrum, as shown in Supplementary Fig. 2 underneath, as shown in Fig. 2 . The relationship between peak position and the strain value is summarized in Fig. EgΔ reaches 125 meV/%, which is consistent with 136 meV/% of our density functional theory (DFT) simulation and the previous simulation results28, as detailed in Supplementary Fig. 2 and the substrate may eventually break, leading to the strain relaxation and the device failure, as schematically illustrated and experimentally demonstrated in Supplementary Fig. We investigate the evolution of the band structure of monolayer MoSgap Fig. , and wit2 ΔEg ~ 10 meV. Th22. Moreover, in order to probe the limit of bandgap modulation and strain tuning capability, we also measure the PL spectrum of the device under compression strain, where highest ΔEg ~ 300 meV and SEgΔ ~ 136 meV/% are demonstrated, as shown in Supplementary Fig. 2 device under strain, as shown in Fig. A′ peak (out-of-plane vibration) keeps relatively constant, and the E′ peak (in-plane vibration) redshift towards lower wavenumber, which is expected and consisted with the previous reports22. Importantly, as the lattice symmetry is gradually broken, we observe a pronounced E′ peak split behavior 29.Besides the peak position, the peak intensity also reduces with increasing strain, owning to the direct-to-indirect band transition with applying tension strain2 on top of pre-fabricated PVA substrate , both of which are less than half of the PVA-encapsulated samples and are consistent with previous reports22, further suggesting the decoupling between sample and substrate, as well as the inefficient strain transfer using conventional approach. We note the slippage or decoupling effect may not only exist in uniaxial experiment (through substrate bending), but could also happen for biaxial straining of 2D materials using AFM tip based or micro-chamber based blister or balloon experiments owning to the weak vdW interaction between 2D material and the anchor substrate during the chamber pressure change, as have been reported in previous literatures32.To highlight the efficiency of our PVA-encapsulation method, the same bending and spectrums measurements are also applied to our control sample with conventional strain engineering approach, by exfoliating monolayer MoSte Figs.  and 2e. 2 samples fabricated through both our spin-coated encapsulation method, as well as conventional exfoliation approach. As shown in Supplementary Fig. 2–PVA interaction, the PL peaks show visible peak fluctuation (~30 meV), consistent with previous literature16 and the highest bandgap modulation is ~60 meV under strain of 1.28%. In contrast, the device fabricated through our PVA encapsulation approach shows more uniform PL peak (with negligible variation) and the bandgap modulation value is ~120 meV, which is around two times improvement compared to conventional exfoliation method. Furthermore, we have also measured multiple devices to show the consistency of our data, and to produce the confidence interval for the measured parameters. As shown in Supplementary Fig. Furthermore, the demonstrated effective strain modulation is a robust behavior within different locations of given sample, as well as between different samples. To demonstrate this, we have applied PL mapping to monolayer MoS33, and therefore could provide a stronger adhesion force towards the MoS2 than typical PDMS or PET substrate used. In fact, PVA itself has been widely used as adhesive glue in the textile industry owing to its excellent adhesion properties35. Secondly, the spin-coating method ensures the conformal contact between PVA and MoS2 and the possible chemical bonds at the defects points and edge sidewall of MoS2 . Thirdly, the PVA used here have a larger EYoung ~ 10 GPa, which is much higher than typical used PDMS with EYoung of 430 KPa. The high EYoung here is essential for efficient strain transfer to MoS2, as have been theoretically analyzed using finite element simulation  and high substrate EYoung, the simple spin-coated PVA encapsulation method used here could provide near unity strain transfer efficiency, as can also be quantitively and directly measured using optical microscope through thermal expansion experiment  shows much smaller ΔEg with applying same level of strain, as shown in Fig. 38, which may be attributed to the finite in-plane compression during the unloading process, as shown in Supplementary Fig. To further confirm the high strain transfer efficiency and negligible material slippage, multiple cycles straining-relaxing test is conducted. Figure ine Fig. . In grea2 slippage and inefficient strain transfer during bending process.Furthermore, the minimized material slippage can also be confirmed by load-unload test, where continuous strain is applied and withdrawn from the sample. As shown in Fig. 2, but could be well-extended to other 2D semiconductors to achieve higher bandgap modulation than typical exfoliation approach. To demonstrate this, we have applied this simple method to mechanically exfoliated monolayer WSe2, CVD  grown monolayer WSe2, as well as CVD grown monolayer WS2. As shown in Fig. 2 and previous reports. The peak position can be further extracted and plotted as a function of the strain applied. As shown in Fig. Eg of 176 meV (SEgΔ = 109 meV/%), 137 meV (SEgΔ = 53 meV/%), 253 meV (SEgΔ = 43 meV/%) are observed for exfoliated WSe2, CVD WSe2, and CVD WS2, respectively. The difference between exfoliated WSe2 and CVD grown WSe2 could be attributed to the inferior quality of CVD grown samples, with possible dopants, defects, or pre-strains. Nevertheless, the observed ΔEg values are much higher than previous reports44, indicating our method is a general approach for effective strain transfer with negligible slippage.The simple spin-coated PVA encapsulation approach is not only limited to MoSEg and SEgΔ. As shown in Fig. Eg and SEgΔ, as highlighted by blue area, and is much higher than various strain engineering methods in previous reports (highlighted by the gray area). This suggests that our simple strain engineering approach may be further extended to other emerging 2D materials or thin film semiconductors, with another degree of freedom to further manipulate their band structures, as well as electronic transport properties . Furthermore, we note the efficient straining of vdW heterostructures would be an interesting topic for future investigation. However, our spin-coating encapsulation method only provide strong interaction between the PVA substrate and one layer of 2D material, while the heterostructures are still bonded through weak vdW interaction and the interlayer slippage may dominate the overall device straining behavior.At last, we compare the performance of our PVA-encapsulation approach with previous strain engineering methods in terms of ΔEYoung of PVA ensure the mechanical strain can be effectively transferred to the lattice of 2D materials. By applying uniaxial strain to monolayer MoS2, we observed a higher bandgap modulation ΔEg ~ 300 meV and SEgΔ ~ 136 meV/%, which is approximately two times enhancement compared to previous best results, and is consistent with our DFT calculations. Furthermore, we confirmed the negligible slippage (between TMD and spin-coated PVA) in our system through detailed tape peeling test, multiple cycles straining-relaxing, thermal expansion measurement, and load-unload bending experiments. Our simple method offers a general strain engineering approach beyond the limit conventional direct-exfoliating method, providing another degree-of-freedom to discover and to investigate the fundamental physics in 2D layered materials as well as conventional 3D thin film materials. It may also provide exciting implications for electronic, optoelectronics, nanoelectromechanical systems, and other devices that can benefit from the flexible, transparent nature of atomic monolayers.In summary, we report a simple and efficient strain engineering approach to modulate the bandgap of monolayer 2D materials by using PVA encapsulation through a spin-coating method. The strong adhesion force  and high 2 is first mechanically exfoliated on the surface of the silicon substrate (p++) with 300 nm SiO2 on top (substrate size: 30 × 10 mm2). Next, 10 wt% PVA  solution is spin-coated on the surface of SiO2 (with MoS2) at a speed of 1000 rpm for 40 s, and baked at 70 °C (1 min) to remove water solvent. Subsequently, a PET  film is glued onto the upper surface of the PVA film using adhesive glue  to increase the thickness for easily handling of flexible substrate. Next, the entire flexible substrate (PVA/glue/PET) with the encapsulated MoS2 can be slowly peeled off from SiO2 substrate using tweezer, as shown in the Fig. For PVA encapsulation method, monolayer MoSε = τ/R, where 2τ and R are the substrate thickness and curvature radius, respectively. The thickness 2τ of the entire flexible substrate is accurately measured to be ~185 μm through the cross-section optical image, as shown in Supplementary Fig. R, we have imaged the curvature radius through both the cross-sectional optical image and photograph, and directly measured the accurate curvature radius R under the device, as shown red dash line in Supplementary Fig. In general, the strain applied on flexible substrate can be expressed through the simple equation 46. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional with semi-empirical DFT-D3 vdW correction method is adopted47 and the plane-wave cut-off energy is 1115 eV. To avoid mirror interactions, a vacuum space of 15 Å is added between adjacent cells in the thickness direction. The Brillouin zone k-point sampling is 10 × 10 × 1 for electronic ground-state computations. The crystal structures are fully relaxed until the force on each atom and total energy variations are smaller than 2.6 × 10−2 eV/Å and 1.4 × 10−3 eV (ref. 48). The strains are achieved by varying the relaxed cell parameters and the atom positions are optimized again after the variations.The first-principles calculation is carried out by the open-source QUANTUM ESPRESSO plane-wave density functional theory (DFT) package2 and PVA were modeled using perfect bonding. The calculations were performed using commercial FE package COMSOL Multiphysics (version 5.2). Young’s modulus and Poisson’s ratio are 10 GPa and 0.3 for PVA substrate, 170 GPa and 0.27 for MoS2 nanosheet, respectively.The discretized FE models contain about 12,099 units with very fine meshes in the contact region. The final mesh density was determined through a series of convergence studies. Appropriate boundary conditions were used along two edges of the PVA to simulate the loading strain. The interface between MoS−1 grating is used, where laser power is 500 μW (MoS2), 50 μW (WSe2) and 500 μW (WS2), respectively. For Raman spectrum measurement, 488 nm laser is used with 250 μW power and a grating levels of 2400 lines mm−1.The entire mechanical device and flexible substrate are placed on a confocal microscope (Renishaw invia-reflex) to measure Raman and photoluminescence spectrums. For PL spectrum measurement, 532 nm laser with 1800 lines mmSupplementary Information


Clinical data suggest that efficacious vagus nerve stimulation (VNS) is limited by side effects such as cough and dyspnea that have stimulation thresholds lower than those for therapeutic outcomes. VNS side effects are putatively caused by activation of nearby muscles within the neck, via direct muscle activation or activation of nerve fibers innervating those muscles. Our goal was to determine the thresholds at which various VNS-evoked effects occur in the domestic pig—an animal model with vagus anatomy similar to human—using the bipolar helical lead deployed clinically.Intrafascicular electrodes were placed within the vagus nerve to record electroneurographic (ENG) responses, and needle electrodes were placed in the vagal-innervated neck muscles to record electromyographic (EMG) responses.Contraction of the cricoarytenoid muscle occurred at low amplitudes (~0.3 mA) and resulted from activation of motor nerve fibers in the cervical vagus trunk within the electrode cuff which bifurcate into the recurrent laryngeal branch of the vagus. At higher amplitudes (~1.4 mA), contraction of the cricoarytenoid and cricothyroid muscles was generated by current leakage outside the cuff to activate motor nerve fibers running within the nearby superior laryngeal branch of the vagus. Activation of these muscles generated artifacts in the ENG recordings that may be mistaken for compound action potentials representing slowly conducting Aδ-, B-, and C-fibers.Our data resolve conflicting reports of the stimulation amplitudes required for C-fiber activation in large animal studies (>10 mA) and human studies (<250 μA). After removing muscle-generated artifacts, ENG signals with post-stimulus latencies consistent with Aδ- and B-fibers occurred in only a small subset of animals, and these signals had similar thresholds to those that caused bradycardia. By identifying specific neuroanatomical pathways that cause off-target effects and characterizing the stimulation dose-response curves for on- and off-target effects, we hope to guide interpretation and optimization of clinical VNS All procedures described were performed on either the left or right vagus nerve, and only one side per animal. All procedures were performed in an acute terminal study lasting between 10 and 12 h.2.1.−1), xylazine (2 mg/kg−1), and glycopyrrolate (0.006 mg/kg−1), then intubated and anesthetized using isoflurane (1.5%–3% isoflurane in room air). Saline (0.9%) was administered continuously with analgesia . Heart rate, respiration, blood pressure, and end-tidal CO2 were used to assess depth of anesthesia, and isoflurane dosage was adjusted as needed. Animals were euthanized using pentobarbital (100 mg kg−1 i.v.).All animals were sedated using an intramuscular injection of telazol  using a thermal wire stripper to create an electrode contact. A suture tie was placed near the location of the electrode contact to assist in tracking the electrode contact during the surgical procedure. A suture needle  was attached to one end of the platinum wire by threading the wire through the needle eyelet and twisting the wire, and an insulated copper extension wire with touchproof connector  was soldered to the other end. The needle was used to introduce each LIFE into the vagus nerve, and the needle was removed prior to recordings. Three to five LIFEs were implanted per animal in a staggered cluster (Bipolar stainless steel needle electrodes were used for measurement of electromyograms (EMG) in the cricothyroid and cricoarytenoid muscles. Custom longitudinal intrafascicular electrodes (LIFEs) were built in-house for measuring electroneurograms (ENG) . These recordings were collected continuously  before, during, and after application of each stimulation pulse. One of the LIFEs was used as the reference electrode for all electrophysiology recordings.Heart rate (HR) and blood pressure were monitored using a pressure catheter  placed into the femoral artery, then digitized and saved using a PowerLab and Bridge Amplifier .2.4.μs per phase and amplitudes from 50 to 3000 μA evaluated in a random order. Stimulation was typically delivered for 30 s at each amplitude with at least 1 min rest between trials to allow cardiac responses to return to baseline; in some cases, stimulation was delivered for 3 s at each amplitude with at least 10 s rest due to time constraints. Stimulation parameters were chosen to approximate the parameters used in the clinic  for both cathode cranial and cathode caudal configurations. To verify the source of EMG and ENG recordings, some stimulation amplitudes—typically 1000, 2000, and 3000 μA—were repeated following a series of perturbations including administration of a neuromuscular blocking agent , transection of the recurrent and superior laryngeal vagus nerve branches, and transection of the vagus trunk between the stimulation electrode and LIFEs.Input-output curves were generated for ENG, EMG, and HR from 50 to 3000 2.5.All signal processing was performed in Matlab R2018b . ENG and EMG recordings were filtered using a 400 sample median high-pass filter (y = x − medfilt1(x)) and a gaussian low-pass filter (gaussfiltcoef and filtfilt) with corner frequency of 5 kHz; these filters were applied in order to lessen filter ringing near the stimulation artifact that may obscure recording of the fastest compound action potentials. Stimulation-triggered median traces of evoked LIFE and EMG recordings were calculated for each stimulation amplitude. The activation threshold and latency for each feature were visually identified in the compound action potential and EMG traces .−1, Aβ 40–70 m s−1, Aγ 15–40 m s−1, Aδ 5–15 m s−1, B 3–14 m s−1)  . Aβ-fibe4 m s−1) . Aδ-fibe−1), the faster Aα-fiber evoked compound action potentials could have potentially occurred within the stimulation artifact. Thus, Aα-fiber compound action potentials could not be consistently differentiated from the stimulation artifact. Aα-fibers are larger diameter than Aβ-fibers, and thus Aα-fibers have lower stimulation thresholds than Aβ-fibers; therefore, we made the assumption that measurement of ENGs with post-stimulus latencies consistent with Aβ-fibers was an indication of Aα-fiber activation at a lower threshold. Given this assumption, we treated Aα- and Aβ-fibers as one combined neural response (Aα/Aβ). Aδ- and B-fibers have overlapping conduction velocities and were therefore treated as one combined neural response (Aδ/B). C-fiber components were not evident in any of our recordings with one possible exception (discussed later). For most animals, two EMG responses occurred with distinct stimulation thresholds and distinct latencies. The peak of the first major deflection was used to calculate the latency for each response. Data is presented comparing the left and right vagus responses, as well as between male and female animals, but no statistical comparisons were made due to relatively low number of animals in each group . A summary of all data points is available in stacks.iop.org/JNE/17/046017/mmedia).Given the range of possible Aα-fiber conduction velocities (70–120 m sHeart rate data was pre-processed using a 1000 point moving average filter (smooth Matlab function). Baseline was calculated as the median of the 30 s of data prior to stimulation. The change in heart rate was calculated as the median of the 5 data points surrounding the peak deflection subtracted from the baseline. See Data associated with this study, , were co2.6.μm sections using a Leica Biosystems Rotary Microtome  and stained using Gomori’s trichrome. Slides were imaged using a Motic Slide Scanner  at 20×.Histology dye  was placed along the ventral and lateral edge of the vagus nerve to maintain orientation. The nerve was sampled from just cranial to the nodose ganglion to just caudal to the recurrent laryngeal bifurcation, thus including the region of nerve where the stimulating electrode contacts were placed. The samples were placed in 10% neutral buffered formalin for ~24 h at 4 °C. Samples underwent a series of standard processing steps as previously described  of the vagus and terminate in the cricoarytenoid muscle of the neck. The motor fibers of the superior laryngeal branch (SL) bifurcate from the cervical vagus cranial to the standard VNS electrode placement to terminate in the cricothyroid and cricoarytenoid muscles in both humans and pigs  taken using epineural cuffs placed on the vagus can be contaminated by the activation of nearby muscles . Direct At low levels of stimulation, a long latency response was consistently evident in EMG recordings from the cricothyroid muscle across the cohort ; aggregate data for all animals can be found in 3.2.After dose response curves were obtained in both the intact state and after neuromuscular junction blockade, a subset of stimulation amplitudes were repeated in the intact state (after the effects of vecuronium had abated) to establish baseline EMG responses immediately before transection of the RL and SL branches was performed. These transections were performed to confirm the RL and SL branches were required for activation of the cricothyroid and cricoarytenoid muscles by VNS. Afterwards, the vagus trunk between the bipolar electrode contacts and LIFEs was also transected to determine whether the recorded ENG signals were indeed compound action potentials evoked by VNS, as opposed to additional unanticipated sources of artifact.Example ENG and EMG traces before and after the somatic branch transections are shown in Similar to our earlier comparisons between ENG and EMG for neuromuscular junction blockade experiments, elimination of specific signals in EMGs via branch transection also eliminated signals with identical post-stimulus latencies in ENGs; therefore, these transections confirmed that the ENGs were contaminated by EMG artifacts. In animals where the main vagus trunk was transected between the stimulation electrode and the LIFEs , transection of the main vagus trunk eliminated all ENG signals. This confirms the remaining LIFE electrode recorded signals prior to vagotomy were indeed neural in origin and not some unanticipated additional artifact . The sti3.3.μA for activation of Aα/Aβ-, Aγ-, and Aδ/B-fibers, respectively, for this example animal. Given temporal overlap of Aα/Aβ signals with the larger stimulation artifact, and overlap of Aγ signals with the larger Aα/Aβ signals, automatic calculation of amplitude and subsequent determination of threshold was challenging in multiple animals. We therefore used visual identification to produce the data found in To determine the stimulation threshold for each ENG and EMG response, stimulation-triggered median traces were stacked across stimulation amplitudes to visualize changes in evoked responses . Visual 3.4.μA. This is substantially lower than the threshold for ENGs with conduction velocities most consistent with parasympathetic efferents (B-fibers) and/or mechanoreceptor afferents (Aδ-fibers) which was 1677 ± 289 μA. Aα/Aβ-fiber activation was observed in all animals, while Aδ/B-responses were only observed in 3 of 13 animals despite the use of stimulation amplitudes over twice the average clinically tolerable amplitudes (up to 3 mA vs 1.2–1.3 mA). The short-latency EMG previously demonstrated to be caused by the activation of the SL branch had a higher threshold (1472 μA ± 643 μA). A higher threshold for SL fibers was expected as the SL is located outside the epineural cuff and activated by current leakage outside the cuff. The thresholds for activation of Aα/Aβ-fibers and the long-latency EMG response were generally lower than those thresholds for responses of fiber types associated with desired therapeutic effects, i.e. activation of Aδ/B-fibers . The threshold for the long latency EMG component via the recurrent laryngeal branch was similar (0.295 ± 0.180 mA). Notably, these stimulation levels are much lower than the average tolerable stimulation amplitudes used clinically (1.2–1.3 mA given similar pulse width)  along the length of the nerve. Consequently the LivaNova lead may not prevent current leakage as effectively as other epineural cuff designs that have more insulation such as the BioControl’s CardioFit lead  than the threshold found in a canine study  (μs pulse width) than the threshold in canines . It should also be noted in three of the five dogs tested from Consistent with this hypothesis, the threshold for activation of large diameter A-fibers in the vagal trunks of pigs was smaller  . In thesμs pulse widths and 20–30 Hz. Similarly, our results indicate that the threshold for activation of Aδ- or B-fibers was 1.67 ± 0.29 mA (200 μs pulse width). In these prior studies, C-fiber activation was observed only at stimulation parameters well beyond levels that are tolerable by human patients (17 ± 7.6 mA with 300 μs pulse width in μs pulse width). C-fiber activation was not observed in our study,1 unsurprisingly as 3 mA was the maximal stimulation used. We observed extensive concurrent activation of the neck muscles, which tended to cause electrodes to be displaced from tissue, at amplitudes larger than 3 mA. Considering the previous work exploring higher amplitudes—and the lack of clinical relevance in exploring these values due to generation of intolerable side effects—we concluded that there was limited benefit to exploring higher current amplitudes.Although the latency range used to define B-fibers differed slightly between the aforementioned studies (μs pulse width) . At higher levels of stimulation (~1.4 mA) approaching clinically tolerable limits, current leakage outside of the cuff activated the motor fibers in the nearby superior laryngeal branch, causing contraction of both the cricoarytenoid and cricothyroid muscles. Stimulation at the average tolerable levels derived from clinical studies (~1.3 mA) was often insufficient to activate Aδ- and/or B-fibers and/or evoke bradycardia. Additionally, Aδ-/B-fiber activation and bradycardia were not observed in multiple animals despite stimulation amplitudes as high as 3 mA. Our data also suggest that previously reported C-fiber recordings were due to artifacts arising from EMGs elicited by activation of short and long-latency motor pathways through the superior and recurrent laryngeal branches of the vagus, respectively.Collectively, these data suggest that the superior laryngeal branch of the vagus nerve may be an anatomical landmark that should be avoided during VNS. Moreover, strategies to avoid the therapy-limiting side effect, such as use of high density epineural electrodes to take better advantage of functional organization within the cervical vagus, should be explored. In addition, mechanisms of VNS that do not depend on direct activation of sensory afferents from the visceral organs should be investigated with increased attention.Supplementary Material


These findings suggest thigh angular velocity is strongly related to running speed and lower limb impact kinematics associated with vertical force application.During high-speed running, lower limb vertical velocity at touchdown has been cited as a critical factor needed to generate large vertical forces. Additionally, greater leg angular velocity has also been correlated with increased running speeds. However, the association between these factors has not been comprehensively investigated across faster running speeds. Therefore, this investigation aimed to evaluate the relationship between running speed, thigh angular motion and vertical force determinants. It was hypothesized that thigh angular velocity would demonstrate a positive linear relationship with both running speed and lower limb vertical velocity at touchdown. A total of 40 subjects  from various athletic backgrounds volunteered and completed 40 m running trials across a range of sub-maximal and maximal running speeds during one test session. Linear and angular kinematic data were collected from 31–39 m. The results supported the hypotheses, as across all subjects and trials (range of speeds: 3.1–10.0 m s Summary: This investigation examined running speed, thigh motion and vertical force determinants. Results suggest thigh angular velocity is strongly correlated to speed and the lower limb impact kinematics underlying force application. Whether at sub-maximal or maximal intensity, maintaining a constant forward running speed presents several mechanical challenges. Among these requirements, steady-speed running necessitates that the net three-dimensional acceleration of the center of mass (COM) over an entire stride cycle is zero. Therefore, the horizontal and lateral forces must integrate to zero during each stride, and the average vertical ground reaction force over a complete stride cycle must equal the body's weight . AlthougNearly a half-century of research has examined vertical force application during running , 2010. AIn addition to lower-limb impact mechanics, proximal kinematic inspection (thigh segments) may provide additional insight. Previous publications on bipedal locomotion have suggested that limbs function as harmonic oscillators with torsion springs at the hip and scissor-like thigh angular motion . In thisFurthermore, measurements of leg angular velocity have been positively related to running speed in human sprinting  and citeTherefore, the aim of this study was to examine thigh angular motion and kinematic factors influencing vertical force application across a range of speeds. Our first hypothesis was that thigh angular velocity would demonstrate a positive and linear relationship with running speed across a range of sub-maximal and maximal intensities. Our second hypothesis was that thigh angular velocity would demonstrate a positive and linear correlation with lower limb velocity at touchdown across a range of running speeds, lending insight into the relationship between thigh angular motion and vertical force determinants. These concepts may contribute to the understanding of human running, with practical applications for training interventions aimed at enhancing running performance.The subjects differed greatly in size and athletic background, but demonstrated similar modifications to running mechanics across the range of speeds. Representative data for thigh angular position versus time is presented in Table S2.Spatial–temporal variables and thigh angular kinematic variables are presented for a single subject  across his individual range of speeds in c) decreased with increasing speed for individual subjects =135.1, P<0.001]. Flight time (Tf) was slightly briefer in duration at fast speeds than at slow and intermediate speeds for all subjects and trials , although the differences in Tf between slow and intermediate speeds were not statistically significant (P>0.8). Step rate (SR) increased across the range of speeds for both individual subjects =179.4, P<0.0001]. Step length (SL) increased across speeds for individual subjects =67.1, P<0.0001], although the increases in SL from intermediate to fast speeds were not statistically significant (P=0.17). Across all subjects and trials, the mean distance travelled by the COM during ground contact (Lc) was 0.97±0.01 m. However, Lc increased slightly across speeds , though the increases in Lc from intermediate to fast speeds were not statistically significant (P>0.9). Analysis regarding vertical velocity of the lower limb (ankle marker) at the instant of touchdown (Ankle Vztd) is presented in the last section of the Results.For the spatial–temporal variables, contact time , as illustrated by representative data in total occurred with speed for individual subjects . Increases in θtotal across the range of speeds were due to both increases in thigh flexion (θflex) and increases in thigh extension (θext) (Table S2). Across all subjects and trials, the total excursion angle during contact (θc) approached one radian (mean θc=0.97±0.01 radian). However, there were increases in θc across the range of speeds for individual subjects . Increases in θc across the range of speeds were due to both increases in thigh touchdown (θtd) and in thigh takeoff (θto) (Table S2).With respect to thigh angular kinematics, faster speeds were generally characterized by higher frequency and greater total amplitude of thigh angular motion (θsubjects C and forsubjects C and foravg) and speed for individual subjects =204.2, P<0.0001]. Additionally, the average angular velocity of the stance thigh during ground contact (ωc) increased with speed for all subjects and trials . Per Eqn 4, Tc showed a strong relationship with ωc for all subjects and trials , and Tc also had a strong relationship with ωavg for all subjects and trials . Per Eqn 6, ωc× leg length (L0) showed a direct positive linear relationship with speed for all subjects and trials with the best fit line constrained through the origin . Also, ωretr increased with speed across all subjects and trials . Finally, across all subjects and trials, ωavg was related to the other two measures of thigh angular velocity, as ωavg had a strong positive relationship to both ωc  and ωretr .All measures of thigh angular velocity significantly increased across speeds. There was a positive and linear relationship between absolute average thigh angular velocity during the entire gait cycle . Faster top speeds were significantly related to briefer Tc across all top speed trials . Faster top speeds were also significantly related to greater SR across the entire subject population . Similar relationships were found for SL across all top speed trials . However, top speed was not significantly related to Tf  or Lc, .Kinematic variables were analyzed across all top speed trials and with runners grouped by top speed and sex. There were significant differences in top speed for the fast versus slow subjects when analyzed within sex . For all top speed trials, θc was slightly greater than one radian (mean θc=1.07±0.01 radian). However, θc was negatively and significantly related with speed across all top speed trials  when analyzing fast versus slow runners within sex . Additional top speed data for θtd, θto, θext and θflex are presented in Table S3.For thigh angular kinematics, faster top speeds were characterized by higher frequency and greater θp speeds C, althoud trials C, and diavg was positively and significantly related to faster top speeds . Likewise, ωc was positively and significantly related to faster top speeds across all top speed trials  and when analyzing fast versus slow runners within sex . Finally, ωretr was positively and significantly related to faster top speeds across all top speed trials  and when analyzing fast versus slow runners within sex .Across all top speed trials, ωp speeds D and whetd demonstrated positive and linear relationships with both running speed and with measures of thigh angular velocity (ωavg and ωretr). Ankle Vztd increased across the range of speeds for individual subjects . Faster top speeds were positively and significantly related to greater Ankle Vztd across all top speed trials , although when analyzing fast versus slow top speeds within sex, Ankle Vztd demonstrated significant differences for females but did not reach significance for males . Ankle Vztd was positively and significantly related to ωavg across all subjects and trials . Finally, Ankle Vztd was significantly related to ωretr across all subjects and trials , and when analyzed for top speed trials only .Ankle Vzsubjects D and ford trials B, and wh−1).We undertook this investigation to explore the relationship between thigh angular motion, ground contact mechanics and running speed. Based on our framework, we hypothesized that thigh angular velocity would have a strong positive linear relationship with running speed across the entire range of trials, and across the subjects’ range of top speeds. We also hypothesized that thigh angular velocity would have a strong positive linear relationship with lower limb vertical velocity at touchdown. We recruited a heterogenous group of 40 subjects that included males and females across a range of different sizes , from a variety of athletic backgrounds , and had them run across more than a threefold range of speeds  were nearly identical to the differences in top speed (∼13 to 14%).Individual subjects ran faster by increasing both the frequency and amplitude of thigh angular motion, resulting in an increase in thigh angular velocity  and 2. Tl trials D. Additir and ωc , with 74d trials D. When td trials , the pertd demonstrated a significant positive relationship with speed  across the range of speeds, with 75% shared variance between Ankle Vztd and ωavg  were violated. Based on prior evidence it was assumed that θc≈1.0 radian and that Lc≈L0≈1.0 m . Likewise, Lc increased slightly across speeds . Conceivably, if the θtd angles had deviated further from the expected values, it could have weakened the correlation between thigh angular velocity (ωavg and ωretr) and Ankle Vztd. As it related to thigh flexion and extension during flight, recent evidence . Furthermore, across the top speed trials, fast males and fast females had θtotal that was shifted more front-side, with a greater proportion of θtotal occurring in θflex than in θext, compared to slow males and slow females (Appendix B and Table S3).A second assumption related to symmetrical thigh flexion and extension values about the zero-axis during both ground contact and flight phases. Our assumption of symmetrical θevidence  has suggavg must increase for ωc to increase. Our data supported this premise, as across all subjects and trials, there was 92% shared variance between ωavg and ωc, and 90–91% shared variance between Tc and measures of thigh angular velocity (ωavg and ωc). Therefore, despite some data not fully conforming to simplifying assumptions, the two experimental hypotheses were still supported strongly by the results.Finally, the thigh segment motion was qualitatively oscillatory and reciprocal. Peak flexion of one thigh generally exhibited temporal coordination with peak extension of the other thigh, especially at faster speeds . Althougavg and running speed. Data from this investigation supports these concepts, as results indicated a direct positive linear relationship between increases in ωavg of 1.0 rad s−1 and increases in running speed of ∼1.2 m s−1 , the existing evidence regarding the thigh angular kinematic determinants of speed  suggest Potential applications of these findings for performance improvement in human sprinting are intriguing. Coaching cues such as ‘whip from the hip’ have been popularized by some well-known practitioners, emphasizing a vigorous scissor-like action of the thighs , and theOur findings align with recent research linking faster running speeds to increased hip joint muscular activation, torque, work and power . HoweverHere we investigated thigh motion and lower limb vertical velocity at touchdown across a broad range of runners and speeds. As hypothesized, thigh angular velocity had a direct linear relationship to both running speed and the lower limb kinematics underlying vertical force application. Our results suggest that increases in thigh angular velocity are not only necessary to match the kinematic demands for high-speed running, but also contribute to the larger mass-specific vertical forces necessary to support faster speeds. Therefore, interventions aimed at improving running performance likely need to elicit an increase in thigh angular velocity through all phases of the gait cycle.td or θto in td or θto in c is determined by leg length L0 and θc:c≈1.0 radian, Eqn 1 demonstrates that contact length is approximately equal to leg length (Lc≈L0). Furthermore, since horizontal velocity during the flight phase is constant (negating wind resistance), the runner's forward speed is determined by the time it takes the COM to traverse Lc, where Tc is ground contact time Becaug speeds , increaspeeds (c .c) is equal to the total contact excursion angle divided by ground contact time:c is expressed as a function of θc and ωc:o for Lc yields Eqn 5:c equal to 1.0 radian, running speed is directly related to L0 and ωc:f=1/T, where T is the time period) and amplitude (A). Thigh angular position as a function of time is displayed in Eqn 7:c is equal to the slope of the angular position versus time curve during the ground contact phases .Additionally, leg angular velocity is a crucial determinant of locomotor stability and control . Averagen humans , with con humans . Fig. 7 c is related to the average of the absolute value of thigh angular velocity during ωavg. Because of the continuous harmonic motion of the thighs, it would be expected that a faster ωc would correspond to a proportionately faster ωavg. From a mathematical standpoint, Eqns 7 and 8 imply that ωc and ωavg can be improved by increasing either f or A, or increasing some combination of both (see examples in c and ωavg must both increase for running speed to increase (per hypothesis 1).The figures and equations above indicate that thigh angular velocity must be regulated to maintain a constant forward running speed. It has been suggested that the limbs function as harmonic oscillators , which iavg should be related to an increased lower limb vertical velocity at touchdown. As the front swinging thigh extends and causes limb retraction during the last portion of the flight phase directly prior to impact  prior to touchdown, and both of these measures should be positively related to vertical velocity of the lower limb at touchdown across the range of running speeds (per hypothesis 2).Enhanced ωact e.g. A,B,D,E, n=7), horizontal jumps (n=2)], five intercollegiate team sport athletes  and six recreationally trained subjects. Female subjects included six intercollegiate or post-collegiate track and field athletes , eight intercollegiate team sport athletes , and six recreationally trained subjects. Complete subject descriptive characteristics are listed in Table S1. Per inclusionary criteria, all subjects were healthy and regularly active (defined as exercising three or more times per week) at the time of testing.All testing and data collection were completed in one 90 min testing session at the West Chester University of Pennsylvania laboratory and indoor athletic facility. A total of 40 subjects volunteered and provided written informed consent in accordance with the West Chester University of Pennsylvania Institutional Review Board. This included 20 males  and 20 females . Male subjects included nine intercollegiate or post-collegiate track and field athletes [≤400 m sprints . Subjects were measured for height using a standard measuring tape and weighed on a digital scale . Subjects then performed a full-body warm up including jogging, skipping, dynamic stretches and sub-maximal sprints. Next, for the purposes of motion capture, subjects wore reflective markers placed on the heel and ball of the foot on the lateral aspect of the running shoe, as well as on the lateral aspect of the ankle, knee, hip and shoulder . There were 12 reflective markers total, six on each side of the body. A still frame motion capture recording of each subject standing in the center of the field of view was completed prior to the testing to serve as a reference for kinematic analyses. Measurements of leg length from greater trochanter to ground were determined from the still frame motion capture recording, with an average leg-length value determined using measurements of right and left leg.For the experimental testing, subjects completed 40 m running trials, and data were captured and analyzed on four trials over a range of speeds. Although the subjects were not directly paced by the investigators while running, they were instructed to complete the trials at progressively faster speeds, with the last trial being maximal. All trials were completed in a running lane in an indoor athletic facility with a multi-purpose floor. The running lane was 60 m in total length, allowing the subjects 20 m to safely decelerate and stop after completing each 40 m running trial. Subjects began each trial in an upright, ‘two-point’ stance with the preferred leg forward and started at their own initiative. For the trials completed at less than maximal intensity, subjects were instructed to gradually accelerate to a cone placed at 25 m, and then to run at a constant speed from 25 m through 40 m. For the maximal effort trials , subjects were instructed to perform an all-out acceleration from the beginning of the sprint, and continue at full speed all the way through the finish line at the 40 m mark. Subjects were allowed complete recovery between trials.Three-dimensional kinematic data were recorded using an eight-camera motion capture system collecting at 200 Hz . The field of view captured by the motion capture system was eight meters in length, from 31–39 m in the running lane. This field of view was selected to ensure that data could be collected for one complete gait cycle for even the tallest, fastest subjects with the longest stride lengths. Prior to data collection, the capture volume was dynamically calibrated using a wand with reflective markers at known spacings. After data collection, motion capture files were exported and uploaded to Microsoft Excel, where the data were up-sampled to 1000 Hz using linear interpolation and post-filtered using a low-pass, fourth-order, zero-phase-shift Butterworth filter with a cutoff frequency of 25 Hz . PositioR2=0.99 and mean absolute error <0.15 m s−1, see Fig. S1).In addition to measuring running speed using motion capture data (described below), running speed was verified with a radar gun . The radar data were collected at 47 Hz and exported to Microsoft Excel for analysis. Speed versus time data were fit to a mono-exponential equation using an iterative least-squares regression routine . Speed v−1 from 31–39 m, and all trials satisfied this criterion.With regard to collecting top speed data in the field of view from 31–39 m, prior research has illustrated that team-sport athletes approach peak speed by 30 m into a sprint . Althougc, Tf, SR, SL, Lc and Ankle Vztd. All reported values are trial averages from both right and left limbs during one complete gait cycle.Based on the kinematic data, spatial–temporal and thigh angular kinematic variables were quantified for all trials. Spatial-temporal variables included: running speed, Tc and Tf), all trials were reviewed using the motion capture software , with instances of touchdown and takeoff determined from visual inspection of the heel and ball marker vertical position relative to the running surface. This method was validated compared to an in-ground laboratory force plate using a separate sub-sample of subjects, and demonstrated a high level of agreement with the force plate measurements . SR was calculated as the inverse of the sum of ground contact time and flight time, or SR=1/(Tc+Tf). SL was calculated from running speed and step rate, or SL=Speed/SR. Per Eqn 2 and c was calculated by multiplying running speed and ground contact time, or Lc=Speed×Tc. The absolute value of vertical velocity of the ankle marker at the instant of touchdown (Ankle Vztd) was used as a proxy for lower limb impact velocity , thigh angular position at takeoff (θto), total thigh excursion during the ground contact phase , peak thigh extension during flight (θext), peak thigh flexion during flight (θflex), total thigh excursion from peak extension through peak flexion , average thigh angular retraction velocity measured from peak thigh flexion until touchdown ωretr, average thigh angular velocity during the ground contact phase ωc, and average thigh angular velocity during the entire gait cycle ωavg. Thigh angular kinematics were quantified in an absolute frame of reference, with the thigh angle compared to vertical, and not relative to trunk. Thigh angular velocities  were determined by calculating the derivative of the thigh segment angular position versus time data, with angular velocities measured as absolute values. As with the spatial–temporal variables, reported thigh angular kinematic values were trial averages from one complete gait cycle, with trial averages determined from both right and left limbs.Additionally, several thigh angular kinematic variables were determined, including: thigh angular position at touchdown  to generate a best-fit equation and coefficient of determination (R2), with x representing running speed unless otherwise noted. Furthermore, differences in each of the kinematic variables were analyzed across speeds with trials divided into three categories based on percentage top speed, calculated for each subject as a percentage of his or her fastest trial. These categories were slow , intermediate , and fast . The normality of data was determined using the D'Augustino and Pearson omnibus normality test or the Shapiro–Wilk test. Parametric data were analyzed using 3x1 analysis of variance (ANOVA) and Tukey’s post-hoc tests, and non-parametric data were analyzed using the Kruskal–Wallis test (H statistic) and Dunn's multiple comparisons tests.To examine the relationship between running speed and the kinematic variables of interest, the data were analyzed across all subjects and trials. Six of the 40 subjects had sub-maximal trials with motion capture data that were not usable due to marker occlusions. These trials were discarded, resulting in n=40, one trial per subject) were independently analyzed as a separate sub-set of data, with simple linear regression used to determine the relationship between each kinematic variable and top speed. To provide further insight into these top speed trials, runners were grouped by sex  and top speed (the faster ten subjects versus the slower ten subjects for each sex). For each kinematic variable, separate independent t-tests were used to analyze fast versus slow males and fast versus slow females. This analysis was selected instead of a 2×2 ANOVA (sex by speed) because the primary comparisons of interest were kinematic differences between fast and slow runners analyzed within sex. For each data set, the normality of data was determined using the D'Augustino and Pearson omnibus normality test or the Shapiro–Wilk test. Parametric data were analyzed using unpaired two-tailed t-tests, and non-parametric data were analyzed using Mann–Whitney tests. For the top speed trials, absolute percentage difference was also used to express the magnitude of difference between fast versus slow group means for each variable, calculated as:a priori threshold for all significance tests was set at α=0.05. Statistical analyses of thigh angular kinematics were calculated in units of radians, although for enhanced clarity, units of degrees are also presented where relevant in Figs 2–7 and in S2, S3. Power analyses for regression and ANOVA were completed using G*Power , based on α=0.05, β=0.8 and moderate effect size. All other statistics were completed using Microsoft Excel and GraphPad Prism software .In addition to the aforementioned analysis, top speed trials (