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Frequency–response curves of the first harmonic A1 calculated from Eq. (4a-c) with the first-order instability zone (light grey zone) and the second-order instability zone (dark grey zone) for different values of the constant force. ... (a) Frequency–response curve for A1/2 calculated from Eq. (11a-e), thin lines-first-order instability, thicker lines-second-order instability (triangles down ‘’ – boundaries of this zone on the left branch, triangles up ‘’ – boundaries of this zone on the right branch) and the thickest lines-stable solutions; (b) bifurcation diagram for decreasing frequency, where yn=y(2πn/Ω). Both parts are plotted for f0=0.02, ζ=0.025, γ=0.0783 and f1=0.1. ... A numerically computed saddle-node bifurcation set in the (Ω,f0) plane for Eq. (1) with ζ=0.025, γ=0.0783 and f1=0.1 [11]. Regions labelled by I–V are characterised by five distinguishable shapes of the frequency–response curves of the first harmonic, which are shown on the right-hand side. ... (a) Frequency–response curve for A1/2 calculated from Eq. (11a-e), thin lines-first-order instability, thick lines-stable solutions; (b) bifurcation diagram for decreasing frequency, where yn=y(2πn/Ω). Both parts are plotted for f0=0.07, ζ=0.025, γ=0.0783 and f1=0.1. ... Frequency–response curves of the first harmonic A1 (black lines) and the second harmonic A2 (gray lines) for the solution given by Eq. (20) obtained by the harmonic balance method; unstable parts are plotted as thin lines and stable parts as thick lines for different values of the constant force and ζ=0.025, γ=0.0783, f1=0.1.
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Airway pressure (Paw) curves during a respiratory cycle under high-frequency percussive ventilation. Upper tracing: inspiration percussive phase (I) and expiration passive phase (E) are indicated. ΔPaw, value of pressure oscillation of the latest percussions before the transition phase between I and E. Lower tracing: expanded tracing contained in the box in the upper tracing, showing the mini-bursts delivered by the ventilator. i, duration of pulse flow administration; e, duration of flow non-administration during a single pulse. Please note the different time scales in the tracings. ... Model, high-frequency ventilation... Techniques, high-frequency ventilator... Mechanics of breathing, high-frequency ventilation
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Representative power spectra for the spontaneous oscillations of capillary blood flow in the artificial microvascular network. For each sample, the graph shows the power density spectrum (normalized to the total power of the signal) computed using 5minute recordings (at 100Hz sampling frequency) of the blood flow through the capillary specified in Fig. 3b. ... The spontaneous oscillations of blood flow in capillaries of the artificial microvascular network. Panels (b) and (c) illustrate the oscillatory behavior in two capillaries exhibiting distinct dynamics (position of the capillaries is marked in panel (a)). For each capillary, representative RBC velocity traces are shown for three samples: (i) purified RBCs suspended in GASP buffer, (ii) purified RBCs suspended in autologous plasma, and (iii) whole blood. Interruptions in the velocity traces shown in panel (c) are due to the temporary absence of RBCs in that particular capillary microchannel (see Supplementary movie SM-5). ... The effect of leukocyte traffic on capillary blood flow oscillations. (a) A representative sequence of images depicting the passage of several leukocytes (arrowheads) through a part of the artificial microvascular network (see Supplementary movie SM-2). Scale bar is 10μm; arrows indicate the direction of flow. (b) A trace of RBC velocity for the capillary microchannel specified in the dotted box in panel (a). Panels (c) shows a magnified view of the velocity traces for the capillary corresponding to images in panel (a). ... Fig. 5 illustrates the effect of leukocyte passage on RBC velocity in the capillary identified as ‘b’ in Fig. 5a (and also in Fig. 3a). We captured the sequence of events associated with the passage of two leukocytes through the capillary and simultaneously measured the RBC velocity (Fig. 5b). The arrival of the first leukocyte in to the capillary (Fig. 5a, 1) resulted in a significant decline of RBC velocity (Fig. 5b, 1–2). The initial stages of its passage through the capillary were associated with a drastic deformation of the leukocyte conforming to the narrow cross-section of the capillary, the formation of a cell-free zone directly in front of the slowly moving leukocyte and the accumulation of a densely packed ‘tail’ of RBCs behind it (Fig. 5a, 1–2, also Supplementary movie SM-2). Once this process was complete, the ‘comet tail’ continued to move through the capillary as a unified, high-resistance plug (Fig. 5a, 2–3) and had little further effect on the overall RBC velocity in the capillary (Fig. 5b, 2–3) (the low-amplitude oscillations of RBC velocity during this period are likely due to the changes in nodal pressure caused by leukocyte traffic outside of the frame of view). The entry of the second leukocyte initially did not have a significant effect on RBC velocity, because the ‘comet tail’ associated with the first leukocyte was still occupying most of the capillary, thus creating the plug flow conditions in the microchannel (Fig. 5a, 3). The RBC velocity increased because the subsequent outflow of the first leukocyte and its densely packed RBC ‘tail’ significantly reduced the local hematocrit within the capillary and thus reduced its fluidic resistance. The exit of the first ‘comet tail’ effectively unplugged the capillary, and thus enabled the gradual accumulation of densely packed RBC ‘tail’ behind the second leukocyte (Fig. 5a, 4). The formation of this second ‘comet tail’ increased the fluidic resistance of the capillary, consequently reducing the RBC velocity (Fig. 5b, 4–5). The RBC velocity recovered to its time-average level (Fig. 5b, 5–6) upon the exit of the second leukocyte and its RBC ‘tail’ from the capillary (Fig. 5a, 6), and the dynamics of blood flow in the capillary returned to its leukocyte-free state (Fig. 5b).... Unlike the re-constituted blood samples in this study (and in most computational simulations investigating the origin of capillary blood flow oscillations) (Carr and Lacoin, 2000; Carr et al., 2005; Gardner et al., 2010; Geddes et al., 2010a; Kiani et al., 1994; Pries et al., 1990), real blood contains leukocytes. Although experiments with the purified RBC samples provide a valuable insight into the underlying mechanisms, they completely overlook the phenomena associated with traffic of leukocytes in the microvasculature and thus carry limited relevance to the dynamics of capillary blood flow in vivo. Leukocytes and leukocyte-related phenomena have been often neglected in modeling studies in part because in the absence of experimental studies their contribution was not fully appreciated (perhaps due to their relative rarity — in normal healthy blood, leukocytes are about 1000-times less abundant than RBCs). The traffic of leukocytes through the artificial microvascular network, however, has a very significant impact on the distribution of RBCs in bifurcations and the spatiotemporal heterogeneity of hematocrit throughout the network (Fig. 2), and the effect of leukocytes on the overall fluidic resistance of the microvasculature has been previously affirmed in vivo (Helmke et al., 1997; Lasta et al., 2011). The movement of leukocytes in narrow capillaries is associated with the formation of characteristic ‘comet tails’ — relatively large, multi-cellular aggregates preceded by a volume of cell-free plasma (Figs. 2b–c, 5a, 6a). The abrupt, transient fluctuations in local hematocrit (and therefore apparent viscosity) due to the passage of these ‘comet tails’ through the network result in very large amplitude oscillations of capillary blood flow (Fig. 4) and even a complete reversal of the flow direction in some capillaries (Fig. 5). The large-amplitude oscillations due to leukocyte traffic are generated via a mechanism independent from the effect of plasma skimming and occur within a distinct range of frequencies (Fig. 4). Our results suggest that the dominant frequency of these large-amplitude oscillations will likely depend on the concentration of leukocytes and on the architecture of the microvascular network (particularly the presence of narrow capillaries of a sufficient length to enable the formation of fully developed ‘comet tails’). This mechanism is not unique to leukocytes and can involve other similarly sized cells (e.g. circulating tumor cells, stem cells), RBCs with impaired deformability or platelet aggregates to yield similar consequences for the capillary blood flow dynamics (see Supplementary movie SM-4). Importantly, the prevalence of large-amplitude oscillations generated through this mechanism may significantly increase in pathological circumstances, when the presence of elevated numbers of activated leukocytes and platelets as well as RBCs with impaired deformability or aggregability is known to cause redistribution of blood flow by retarding or even obstructing the flow in smaller capillaries (Barshtein et al., 2011; Carr et al., 2005; Lasta et al., 2011; Miele et al., 2009).
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Complexity analysis of the epileptiform network time series for reference case without stimulation (REF) and with therapeutic network neuromodulation switched on (CRG). (a) Short-time maximum Lyapunov exponent values. Troughs in the REF signal indicate location of SLEs. (b) Phase coherence time–frequency distribution (left column) and corresponding mean phase coherence time series (right column). Asterisks denote location of SLEs. ... Coupled oscillator... CRG neuromodulation stimulus time–frequency characteristics as determined from application of bandpass filtering and the wavelet transform. ... Complexity measures of different neuromodulation approaches: unstimulated reference (REF), 10 Hz low-frequency stimulation (LFS), 120 Hz high-frequency stimulation (HFS) and closed-loop cognitive rhythm generator neuromodulation (CRG). (a) Normalized maximum Lyapunov exponent, lower 25th percentile (mean ± std. err.). (b) Normalized mean phase coherence, upper 75th percentile (mean ± std. err.). Superscript symbols indicate significance at the 5% level (Wilcoxon rank sum test). ... Cross-frequency coupling within the CRG neuromodulation stimulus signal. (a) Comparison of time series of theta, gamma and phase-shuffled surrogate gamma. (b) Overlay of normalized amplitudes of the gamma envelope (solid) with the reference theta oscillation (segmented) for model and surrogate gamma time series. (c) Autospectra of the respective model and surrogate gamma signals in (a). (d) Mean phase coherence of the envelope of model gamma (solid) and surrogate gamma (segmented) with the theta oscillation. (e) Modulation index map of gamma frequencies with theta frequencies (left) and theta with delta (right) (note the color scales are different).
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Western blot analyses of α-actinin, myogenin, troponin-T, myosin, integrin β1, talin and FAK. (A) C2C12 myoblasts were allowed to reach confluence (Day 0, lane 1) and thereafter differentiated for 8 days followed by 6 h of 1 Hz EPS. Whole cell lysates were prepared and blotted as indicated in the figure. The arrowhead indicates a 190 kDa fragment of the cleaved talin. Representative immunoblots were obtained from 3 independent experiments. (B) Densitometric analysis of digested talin by EPS. Error bars are SEM (n=3–5). *Pfrequency, as confirmed by Western blot analysis (left panel) and densitometric analysis (right panel). *P<0.05. (E) Changes in the amount of digested talin, with EPS, in the absence and presence of 100 μM Verapamil, 10 μM BAPTA–AM or 10 mM EGTA, as confirmed by Western blot analysis (left panel) and densitometric analysis (right panel). ... Ca2+ oscillation... After 2 h of continuous application of EPS at 40 V/60 mm, 24 ms and 1 Hz, contraction of C2C12 myotubes dependent on the frequency of EPS was observed. Cells grown in a 4-well culture plate were imaged for ∼1 min during EPS treatment as described in Materials and methods. ... Differentiated C2C12 myotubes were stimulated with EPS at 40 V/60 mm, 24 ms and 1 Hz. The C2C12 myotubes initially showed no contractility in response to EPS at any of the frequencies. Cells in a 4-well culture plate were imaged for ∼1 min during EPS treatment as described in Materials and methods.
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(a) Results of PSMA detection in diluted bovine serum, with D2B functionalized pillars devices. Full blue circles and blue line are the same already shown in Fig. 3a, empty purple triangles represent data obtained detecting PSMA in diluted bovine serum (1:20 in PBS). Two concentrations, 10nM and 100nM, and a control sample (only bovine serum) were tested. (b) Dark squares show frequency shifts induced by PSMA at 100nM in PBS, containing BSA 0.2%w/v, as a function of the antigen incubation time. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... (a) Results of PSMA detection in PBS, containing BSA 0.2%w/v, with D2B functionalized pillars devices. 7 concentrations, ranging from 300pM to 100nM, were tested, full blue circles. On the left axis, frequency shifts induced at each PSMA concentration are displayed. On the right axis, corresponding values of PSMA density are shown. Green line indicates the initial frequency shift occurring after D2B adsorption, while the orange one indicates the frequency shift induced by BSA passivation. Each value is the mean shift and the error bar is the standard deviation of at least 30 independent pillars detected in parallel. Experimental data are fitted with a second order Langmuir curve (blue line) which provides a KD=18nM. Red empty circles represent data acquired using three different devices to demonstrate the reproducibility of the detection system. (b) Boxplot representation of data obtained detecting PSMA at 10nM in PBS containing BSA 0.2%w/v, with D2B functionalized pillars using three different devices. Statistical analysis, one way ANOVA test provides p=0.1132, means and variances are not significantly different (significance p<0.05). (c) Box plot representation of data obtained detecting PSMA in PBS at 100nM with D2B functionalized pillars using three different devices. Statistical analysis, one way ANOVA test provides p=0.1489, means and variances are not significantly different (significance p<0.05). (d) Box plot representation of data obtained detecting 7 different concentrations of PSMA in PBS containing BSA 0.2%w/v, with D2B functionalized pillars devices; concentrations ranging from 300pM to 100nM. Data distributions are compared by t-test (significance p<0.05). Data at 300pM, assumed as baseline, are compared with all the other concentrations. Data at 3nM and 10nM are also compared. Significance is represented for each couple as (*) significant p≤0.05, (**) very significant p≤0.01, (***) extremely significant p<0.001. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... (a) Optical image of a “T” shaped pillar array actuated by a piezo at the resonance frequency of one of them, in the middle a pillar is oscillating. (b) A schematic representation of pillar detection: when pillars oscillate, the light reflection path is slightly deviated and the light intensity recorded by the CCD slightly decreased. (c) 53 traces corresponding to 53 different pillars as a function of actuation frequency. (d) Individual actuation mode. (e) Multiple actuation mode is obtained driving separate frequencies in parallel through the same piezo actuator and detecting simultaneously more pillars with separate resonance frequencies. ... Real time video of the dynamic response of pillars during a frequency scan. In the upper part, a real time image of the pillar array is shown. In the lower part, the signals corresponding to the image intensity of the top of pillars are acquired. At the resonance frequency, in the array image, the pillar oscillation is visible, while in the lower part, the corresponding signal of the image intensity decreases and the resonance peak appears. ... The following is the Supplementary material related to this article Movie 1.Movie 1Real time video of the dynamic response of pillars during a frequency scan. In the upper part, a real time image of the pillar array is shown. In the lower part, the signals corresponding to the image intensity of the top of pillars are acquired. At the resonance frequency, in the array image, the pillar oscillation is visible, while in the lower part, the corresponding signal of the image intensity decreases and the resonance peak appears.
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The effect of tail shape on the maximum nondimensional amplitude, Amax, at ξ=0.75 and the nondimensional frequency of oscillations, f˜, for nose A; Λ=0.5 – comparison between theory and experiment. ... Consecutive frames showing the towed flexible cylinder executing a cycle of second-mode flexural oscillation with frequency f=1.58Hz at U=2.4m/s (flow direction: ↓). ... Consecutive frames showing the towed flexible cylinder with Λ=0.25, executing a cycle of essentially criss-crossing oscillations with frequency f=0.25Hz at U=0.3m/s (flow direction: ↓). ... Consecutive frames showing the towed flexible cylinder executing a cycle of essentially second-mode flexural oscillation (the third-mode oscillation not fully developed) with frequency f=1.88Hz at U=3.0m/s (flow direction: ↓). ... The effect of towrope length on the maximum nondimensional amplitude, Amax, at ξ=0.75 and the nondimensional frequency of oscillations, f˜ (nose A; tail A) – comparison between theory and experiment.
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Frequency as a function of Reynolds number. ... h-dependence of the frequency, Re=350, Stage II. ... Oscillating flow... h-dependence of the frequency, Re=350, Stage I.
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Time–frequency map and wavelet power (arbitrary units) of the voltage signal obtained in the location ‘P’. T49, HL=0.235m, N=350rpm. ... Influence of the liquid height, HL, on the free surface frequency, f. The solid line represents the theoretical frequency evaluated using Eq. (2). ... Influence of N on the instability frequency, f. T49 with different liquid heights, HL. ... Frequency spectrum of the voltage signal in the location ‘P’. T49, HL=0.235m in T49. (a) N=300rpm (Re=4.8×104); (b) N=350rpm (Re=5.6×104). ... Frequency spectrum of the pressure signal. HL=0.175m. (a) N=250rpm; (b) N=300rpm.
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Oscillation at outer edge with damping effect for a DEA with λ0=3.5 under harmonic electronic load. (a) ΩR0ρ/μ=0.00145. (b) ΩR0ρ/μ=0.00725. (c) ΩR0ρ/μ=0.0725Hz. (d) ΩR0ρ/μ=0.725. ... Oscillation at outer edge without damping effect for a DEA with λ0=3.5 under harmonic electronic load. (a) ΩR0ρ/μ=0.00145. (b) ΩR0ρ/μ=0.00725. (c) ΩR0ρ/μ=0.0725Hz. (d) ΩR0ρ/μ=0.725. ... Theoretical oscillation amplitudes at various dimensionless excitation frequencies and the dynamic range for a DEA. The inserted figure is a magnification of the measured data and theoretical prediction with actual dimensionless damping coefficient derived from the transient response.
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