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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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Plots of χM′T vs T (top) and χM″ vs T (bottom) for complex 3 in a 0.3mT ac field oscillating at the indicated frequencies. ... Plots of χM′T vs T (top) and χM″ vs T (bottom) for complex 2 in a 0.3mT ac field oscillating at the indicated frequencies. ... Plots of χM′T vs T (top) and χM″ vs T (bottom) for complex 6 in a 0.3mT ac field oscillating at the indicated frequencies. ... Plots of χM′T vs T (top) and χM″ vs T (bottom) for complex 4 in a 0.3mT ac field oscillating at the indicated frequencies. ... Plots of χM′TvsT (top) and χM″vsT (bottom) for complex 5 in a 0.3mT ac field oscillating at the indicated frequencies.
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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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Large-scale experiments examining spherical-flame propagation of propane–air flames up to a diameter of 1.2m were performed. Throughout these experiments, the growth of the Darrieus–Landau instability was directly observed and detailed measurements show that the increase of flame velocity follows a pattern of self-similar oscillatory growth that has not been previously reported. These oscillations are found to be the result of periodic growth and saturation of a narrow range of length scales that follows each generation of cell formation. Based on these observations, a new method to estimate the fractal-acceleration exponent is proposed based on the amplitude and frequency of these oscillations. Comparisons between the fractal exponents derived by this method and a direct power law fit show reasonable agreement with one another, as well as with values reported by previous studies.
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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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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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Low frequency oscillation amplitudes of oxygenated hemoglobin (oxyHb) and total hemoglobin (totalHb) for 14 obstructive sleep apnea (OSA) patients before and after continuous positive airway pressure (CPAP) treatment for at least two months 23 OSA patients before CPAP treatment were also compared to 13 healthy controls, right sided figure. Error bars are standard error of the mean. μM=micromolar oxyHb or totalHb concentration. Black boxes are OSA patients before CPAP treatment, striped grey boxes are OSA patients after CPAP treatment, and grey boxes are healthy subjects. ∗Indicates a P value=0.022.
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Normalized transverse sphere oscillation frequency as a function of reduced velocity. Present results: +, Sphere dynamics; ◊, PIV. Literature: m⁎=7.87 (Van Hout et al., 2010): □ fN=2.65Hz (represents measured natural frequency in medium). ○ m⁎=0.76; ▵ m⁎=2.83 (Govardhan and Williamson, 1997).
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Dominant frequency... Computer modeling of ICl,vol effects on ventricular fibrillation (VF) dynamics. Wave dynamics in VF were simulated in two dimensions with the canine ventricular myocyte model plus insertion of ICl,vol. A: Snapshot of Vm. Note that a significantly larger spiral occupies most of the central region, where ICl,vol is higher. B: Typical examples of Vm oscillations in VF. Note that the trace from the dominant spiral shows high-frequency regular patterns of Vm oscillations (top trace). C: VF frequency map. Lines are drawn every 2 Hz. Darker colors indicate higher frequency. D: Frequency analysis of Vm. Note that the higher ICl,vol density in the center shows high VF frequencies substantially (6.2 ± 0.2 Hz vs 13.6 ± 0.1 Hz). A movie of transition from complex to stable rotor in the center is provided in the supplementary data (Simulation-VF-IClvol.mpg). ... Time-frequency distribution of ventricular fibrillation (VF) frequencies. Time-frequency domain (TFD) analysis was applied to the right ventricle (RV; left panels) and left ventricle (LV; right panels) to track the time-dependent changes in frequency distribution during iso-osmotic and hypo-osmotic conditions. Spectrograms (i.e., frequencies vs time) and power distributions are displayed as gray-scale maps, such that the darker the pixel, the higher the energy level. Under hypo-osmotic stress, VF frequencies increased gradually (∼20 minutes of hypo-osmotic perfusion) and then reached a stable level, especially in the LV (top and middle panels). Note that hypo-osmotic solution increased VF frequencies in both RV and LV, but LV had marked frequency changes compared with RV. Perfusion with 10 μM indanyloxyacetic acid-94 (IAA-94) first slowed VF frequencies (bottom panels), but then after 20 minutes VF terminated spontaneously (n = 7/9 hearts). ... Effect of hypo-osmotic solution on ventricular fibrillation (VF) frequencies. VF was induced by burst stimulation, and changes in VF frequencies were monitored under normal, hypo-osmotic, and ICl,vol inhibition using indanyloxyacetic acid-94 (IAA-94). Vm was recorded optically during a control VF (A), hypo-osmotic solution (B), and during VF after perfusion with 10 μM IAA-94 (C). In panel B, Vm oscillations were considerably more regular, and VF frequencies gradually shifted to a single high frequency. A movie file (experimental VF-Hypo-osmotic.mpg) in supplementary data depicts the high level of organization of VF in hypo-osmotic conditions. In panel C, inhibition of ICl,vol under hypo-osmotic conditions reversed the changes in VF dynamics. ... Spatial distribution of peak frequencies from TDF analysis. Distribution of ventricular fibrillation (VF) frequencies is represented as a three-dimensional volume plot. A: Orientation. B: Control perfusion. C: Hypo-osmotic perfusion. Here, VF frequencies are distributed in discrete regions with sharp boundary between left ventricle (LV) and right ventricle (RV). D: Perfusion with hypo-osmotic plus indanyloxyacetic acid-94 (IAA-94) resulted in substantially lower VF frequencies and reduced regional heterogeneities in frequency. ... Time-frequency domain analysis
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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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