Theoretical analysis of pressure pulse propagation in arterial vessels.

An original mathematical model of viscous fluid motion in a tapered and distensible tube is presented. The model equations are deduced by assuming a two-dimensional flow and taking into account the nonlinear terms in the fluid motion equations, as well as the nonlinear deformation of the tube wall. One distinctive feature of the model is the formal integration with respect to the radial coordinate of the Navier-Stokes equations by power series expansion. The consequent computational frame allows an easy, accurate evaluation of the effects produced by changing the values of all physical and geometrical tube parameters. The model is employed to study the propagation along an arterial vessel of a pressure pulse produced by a single flow pulse applied at the proximal vessel extremity. In particular, the effects of the natural taper angle of the arterial wall on pulse propagation are investigated. The simulation results show that tapering considerably influences wave attenuation but not wave velocity. The substantially different behavior of pulse propagation, depending upon whether it travels towards the distal extremity or in the opposite direction, is observed: natural tapering causes a continuous increase in the pulse amplitude as it moves towards the distal extremity; on the contrary, the reflected pulse, running in the opposite direction, is greatly damped. For a vessel with physical and geometrical properties similar to those of a canine femoral artery and 0.1 degree taper angle, the forward amplification is about 0.9 m-1 and the backward attenuation is 1.4 m-1, so that the overall tapering effect gives a remarkably damped pressure response. For a natural taper angle of 0.14 degrees the perturbation is almost extinct when the pulse wave returns to the proximal extremity.     

High frequency characteristics of the arterial system

Pressure, flow and diameter were measured in the abdominal aorta of five anesthetized dogs during normal heart beats and heart beats with a superimposed impulse (generated by rapidly injecting a small volume of saline into the system). From Fourier analysis it was found that the impulse enhanced the amplitudes of the higher harmonics so that frequencies up to 80 Hz could be studied. Both the input impedance and apparent phase velocity above 20 Hz were independent of frequency and their average values were designated as characteristic impedance and true phase velocity. Average characteristic impedance for all five animals was 2.0 +/- 0.1 X 10(8) Nsm-5 and average phase velocity was 8.3 +/- 0.6 ms-1. Phase velocities calculated from characteristic impedance (1.76-2.39 X 10(8) Nsm-5) and from the slope of the pressure-diameter relation (0.102-0.25 X 10(-8) Nm-3) were similar to the true phase velocity as defined above (6.79-9.85 ms-1). It may be concluded that the input impedance converges to characteristic impedance and apparent phase velocity converges to phase velocity for high frequencies.     

Velocity field of pulsatile flow in a porous tube

This paper describes velocity fields for fully developed periodic laminar flow in a rigid tube with a porous wall. We obtained an analytical solution of the flow by the linear approximation of the Navier-Stokes equation. Unlike the previous works with a constant seepage rate along the axis, we used a wall velocity which contained hydraulic permeation constant Lp. The axial velocity profile shows a local maximum velocity near the wall at a large Womersley number alpha. This suggests that concentration polarization in porous tubular membrane may be reduced at high frequencies if a membrane device is operated under pulsatile flow conditions. The magnitude of wall permeation velocity decreases linearly along the tube axis because the damping of the pressure difference between the inside and the outside of the tube is very small.     

不同添加物对文心兰原球茎增殖及试管苗生长的影响

以文心兰切花品种‘南茜’原球茎(PLB)及试管苗为材料,在培养基MS＋6-BA 2 mg/L＋Ad 1 mg/L＋NAA 0.1 mg/L＋蔗糖30 g/L基础上,利用增殖系数及不同形态指标加权分析研究马铃薯、芋头、南瓜、香蕉及活性炭(AC)5种培养基添加物及其组合对‘南茜’PLB增殖及试管苗生长的影响。结果表明,适宜文心兰PLB增殖培养的添加物为马铃薯泥50 g/L,培养45 d后,PLB增殖系数是对照的3.64倍;适宜无菌小苗(约1.5 cm)增殖及生长的添加物为香蕉泥50 g/L＋AC 1 g/L,加权总分是对照的1.53 倍;适宜无菌中苗(约2.5 cm)增殖及生长的添加物为马铃薯泥25 g/L＋香蕉泥25 g/L,加权总分是对照的1.55倍。     

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.     

Computation of aortic pulse wave velocity and aortic pulse wave velocity and aortic extensibility from pressure gradient measurements.

This study is concerned with the computation of aortic pulse wave velocity based on simultaneous recordings of the aortic pressure gradient and first-time derivative of aortic pressure. These variables were recorded by means of a double-lumen catheter introduced in the aorta of four anesthetized closed chest dogs, and connected to critically damped manometer systems. Results of aortic pulse wave velocity were then compared: (i) to the true phase velocity obtained from spectra of apparent phase velocity, and (ii) to the pulse wave velocity computed from the time shift between maximum slopes of the pressure wave. From the aortic valves to 37 cm down the aortic trunk, pulse wave velocity increased from 410-460 cm/s to approximately 600-800 cm/s. Based on the wave propagation equation presented of Bramwell and Hill (Bramwell, J.C., and Hill, A. V. 1922. Proc. R. Soc. 93, 298-306), volumetric extensibility coefficients were computed from pulse wave velocity data. Results indicated that, from the aortic valves to 37 cm down to the aorta, the mean volumetric extensibility decreased from 0.43-0.56% deltaV/cm H2O to 0.16-0.25% deltaV/cm H2O (1 cm H2O = 94.1 N/m2).     

Frequency dependence of dynamic curvature effects on flow through coronary arteries

The flow through a curved tube model of a coronary artery was investigated computationally to determine the importance of time-varying curvature on flow patterns that have been associated with the development of atherosclerosis. The entry to the tube was fixed while the radius of curvature varied sinusoidally in time at a frequency of 1 or 5 Hz. Angiographic data from other studies suggest that the radius of curvature waveform contains significant spectral content up to 6 Hz. The overall flow patterns were similar to those observed in stationary curved tubes; velocity profile skewed toward the outer wall, secondary flow patterns, etc. The effects of time-varying curvature on the changes in wall shear rate were expressed by normalizing the wall shear rate amplitude with the shear rate calculated at the static mean radius of curvature. It was found that the wall shear rate varied as much as 94 percent of the mean wall shear rate at the mid wall of curvature for a mean curvature ratio of 0.08 and a 50 percent change in radius of curvature. The effects of 5 Hz deformation were not well predicted by a quasi-static approach. The maximum values of the normalized inner wall shear rate amplitude were found to scale well with a dimensionless parameter equivalent to the product of the mean curvature ratio (delta), normalized change in radius of curvature (epsilon), and a Womersley parameter (alpha). This parameter was less successful at predicting the amplitudes elsewhere in the tube, thus additional studies are necessary. The mean wall shear rate was well predicted with a static geometry. These results indicate that dynamic curvature plays an important role in determining the inner wall shear rates in coronary arteries that are subjected to deformation levels of epsilon delta alpha > 0.05. The effects were not always predictable with a quasi-static approach. These results provide guidelines for constructing more realistic models of coronary artery flow for atherogenesis research.     

Characterization of a pilot plant airlift tower loop bioreactor. I: evaluation of the phase properties with model media

Investigations were carried out in a 9 m high, 4 m(3) volume, pilot plant airlift tower loop bioreactor with a draft tube. The reactor was characterized by measuring residence time distributions of the gas phase using pseudostochastic tracer signals and a mass spectrometer and by evaluating the mixing in the liquid phase with single-pulse tracer inputs. The local gas holdup and the bubble size (piercing length) were measured with two-channel electrical conductivity probes. The mean residence times and the intensities of the axial mixing in the riser and downcomer and the circulation times of the phases as well as the fraction of the recirculated gas phase were evaluated. The gas holdup in the riser is nearly uniform along the reactor. In the downcomer, it diminishes from top to bottom. The liquid phase dispersion coefficients, D(L), are smaller than those measured in the corresponding bubble columns. In the pilot plant with tap water the following relationship was found: D(Lr) = cw(SG) (n); with c = 203.4; n = 0.5;D(Lr)(cm(2) s(-1);) and W(SG)(cm s(-1)) where D(Lr) is the longitudinal dispersion coefficient in the riser and W(SG) is the superficial gas velocity. The gas phase dispersion coefficients in the riser of the pilot plant, D(Gr), are also enlarged with increasing superficial gas velocity, W(SG), however, no simple relationship exists. Parameter D(Gr) is the highest in the presence of antifoam agents, intermediate in tap water, and the smallest in ethanol solution.     

Linear propagation of pulsatile waves in viscoelastic tubes

An experimental and theoretical analysis is made of pulsatile wave propagation in deformable latex tubes as a model of the propagation of pressure pulses in arteries. A quasi one-dimensional linear model is used in which, in particular, attention is paid to the viscous phenomena in fluid and tube wall. The agreement between experimental and theoretical results is satisfactory. It appeared that the viscoelastic behaviour of the tube wall dominates the damping of the pressure pulse. Several linear models are used to describe the wall behaviour. No significant differences between the results of these models were found.     

Hydrogen production by photoreactive nanoporous latex coatings of nongrowing Rhodopseudomonas palustris CGA009

Nonuniform light distribution is a fundamental limitation to biological hydrogen production by phototrophic bacteria. Numerous light distribution designs and culture conditions have been developed to reduce self-shading and nonuniform reactivity within bioreactors. In this study, highly concentrated (2.0 x 108 CFU/muL formulation) nongrowing Rhodopseudomonas palustris CGA009 were immobilized in thin, nanoporous, latex coatings. The coatings were used to study hydrogen production in an argon atmosphere as a function of coating composition, thickness, and light intensity. These coatings can be generated aerobically or anaerobically and are more reactive than an equivalent number of suspended or settled cells. Rhodopseudomonas palustris latex coatings remained active after hydrated storage for greater than 3 months in the dark and over 1 year when stored at -80 degrees C. The initial hydrogen production rate of the microphotobioreactors containing 6.25 cm2, 58.4 mum thick Rps. palustris latex coatings illuminated by 34.1 PAR mumol photons m-2 s-1 was 6.3 mmol H2 m-2 h-1 and had a final yield of 0.55 mol H2 m-2 in 120 h. A dispersible latex blend has been developed for direct comparison of the specific activity of settled, suspended, and immobilized Rps. palustris.     

A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree

Using a frequency-domain Womersley-type model, we previously simulated pulsatile blood flow throughout the coronary arterial tree. Although this model represents a good approximation for the smaller vessels, it does not take into account the nonlinear convective energy losses in larger vessels. Here, using Womersley's theory, we present a hybrid model that considers the nonlinear effects for the larger epicardial arteries while simulating the distal vessels (down to the 1st capillary segments) with the use of Womersley's Theory. The main trunk and primary branches were discretized and modeled with one-dimensional Navier-Stokes equations, while the smaller-diameter vessels were treated as Womersley-type vessels. Energy losses associated with vessel bifurcations were incorporated in the present analysis. The formulation enables prediction of impedance and pressure and pulsatile flow distribution throughout the entire coronary arterial tree down to the first capillary segments in the arrested, vasodilated state. We found that the nonlinear convective term is negligible and the loss of energy at a bifurcation is small in the larger epicardial vessels of an arrested heart. Furthermore, we found that the flow waves along the trunk or at the primary branches tend to scale (normalized with respect to their mean values) to a single curve, except for a small phase angle difference. Finally, the model predictions for the inlet pressure and flow waves are in excellent agreement with previously published experimental results. This hybrid one-dimensional/Womersley model is an efficient approach that captures the essence of the hemodynamics of a complex large-scale vascular network. The present model has numerous applications to understanding the dynamics of coronary circulation.     

A general method of determining the frequency-dependent propagation coefficient and characteristic impedance of an artery in the presence of reflections.

An iterative method of calculating propagation parameters at harmonics of heart rate for a uniform vascular segment from a combination of four arterial waveform measurements is presented. Measurements of blood pressure, vascular diameter, and blood flow-rate may be combined arbitrarily provided only that at least one measurement of pressure and one of flow-rate be included; the requirement of four measurements implies at least two measurement sites along the vessel. The analysis is thus a generalization of those associated with previous methods of determining propagation parameters, allowing for instance relaxation of the requirement of equal spacing in the three-point method. Results are presented for the propagation of an impulse along a rubber tube when the measurements are pressure at two sites, flow-rate and diameter.     

Preliminary observation on human tubal electrical activity in vivo

The authors have set up a new technique for recording the human tubal electrical activity in vivo. A polyethylene catheter was used with six couples of electrodes placed on the tube of 5 women during simple laparohysterectomy. The slow electrical activity was recorded by means of a 8-channel paper amplifying recorder for 3-5 days from surgery. The fimbria showed frequencies between 1.25 and 3.3 c/min, the ampulla showed higher frequencies (1-5 c/min), the isthmus showed little electrical activity. The propagation signal velocity ranges between 0.25 and 0.5 cm/sec. The amplitude ranges between 50 and 200 V. The propagation occurs mainly in the distal-proximal direction.     

Velocity and Directionality of the Electrohysterographic Signal Propagation

Objective

The initiation of treatment for women with threatening preterm labor requires effective distinction between true and false labor. The electrohysterogram (EHG) has shown great promise in estimating and classifying uterine activity. However, key issues remain unresolved and no clinically usable method has yet been presented using EHG. Recent studies have focused on the propagation velocity of the EHG signals as a potential discriminator between true and false labor. These studies have estimated the propagation velocity of individual spikes of the EHG signals. We therefore focus on estimating the propagation velocity of the entire EHG burst recorded during a contraction in two dimensions.

Study Design

EHG measurements were performed on six women in active labor at term, and a total of 35 contractions were used for the estimation of propagation velocity. The measurements were performed using a 16-channel two-dimensional electrode grid. The estimates were calculated with a maximum-likelihood approach.

Results

The estimated average propagation velocity was 2.18 (±0.68) cm/s. No single preferred direction of propagation was found.

Conclusion

The propagation velocities estimated in this study are similar to those reported in other studies but with a smaller intra- and inter-patient variation. Thus a potential tool has been established for further studies on true and false labor contractions.     

Effects of the ablation of the nucleus pulposus on the vibrational behavior of the lumbosacral hinge

This study was designed to investigate the respective damping properties of the annulus fibrosus and nucleus pulposus of the intervertebral disc during propagation of vibration waves through the osteoligamento-muscular axis of the spine. The study was conducted on a 8-10 kg deeply anesthetized baboon. In the first surgical phase five accelerometers were implanted in the first sacral vertebra and on the anterior side of the four lower lumbar vertebrae. The bioinstrumented animal was placed in a restraining chair and exposed to narrow-bandwidth (0-100 Hz) 0.16 G RMS random vibration. Once data was recorded, the nuclei pulposi of the studied discs were removed by suction, the surrounding annuli remaining intact. The still deeply anesthetized animal was again exposed to the same 0-100 Hz, 0.16 G RMS vibration. Results were analyzed and their reproducibility was tested on three animals.     

Wall shear rate measurements in an elastic curved artery model

Since atherosclerotic lesions tend to be localized at bends and branching points, knowledge of wall shear rate patterns in models of these geometries may help elucidate the mechanism of atherogenesis. This study uses the photochromic method of flow visualization to determine both the mean and amplitude of the wall shear rate waveform in straight and curved elastic arterial models to demonstrate the effects of curvature, elasticity, and the phase angle between the flow and pressure waveforms (impedance phase angle). Under sinusoidal flow conditions characteristic of large arteries, the mean shear rate at the inner wall of the curved tube is reduced 40–56% from its steady flow value, depending on the phase angle. Wall shear rate amplitudes in the curved tube are significantly reduced by wall motion (36–55% of the Womersley amplitude for a straight rigid tube). The shear rate amplitude at the outer wall decreases 30% as the phase angle is reduced from −20° to −66°, while the shear rate amplitude at the inner wall increases 45%. As a result, the oscillatory nature of flow at the outer wall decreases with decreasing negative phase angle, but flow at the inner wall becomes much more oscillatory. At large negative phase angles, characteristic of hypertension or vasoactive agents, the shear rate at the inner wall has a small mean and cycles through positive and negative values; the shear rate at the outer wall remains positive throughout the flow cycle. Thus, the impedance phase angle could affect atherogenesis along the inner wall if temporal and directional changes in wall shear rate play a role.     

Peripheral pacemakers and patterns of slow wave propagation in the canine small intestine in vivo

In an anesthetized, open-abdomen, canine model, the propagation pattern of the slow wave and its direction, velocity, amplitude, and frequency were investigated in the small intestine of 8 dogs. Electrical recordings were made using a 240-electrode array from 5 different sites, spanning the length of the small intestine. The majority of slow waves propagated uniformly and aborally (84%). In several cases, however, other patterns were found including propagation in the oral direction (11%) and propagation block (2%). In addition, in 69 cases (3%), a slow wave was initiated at a local site beneath the electrode array. Such peripheral pacemakers were found throughout the entire intestine. The frequency, velocity, and amplitude of slow waves were highest in the duodenum and gradually declined along the intestine reaching lowest values in the distal ileum (from 17.4+/-1.7 c/min to 12.2+/-0.7 c/min; 10.5+/-2.4 cm/s to 0.8+/-0.2 cm/s, and 1.20+/-0.35 mV to 0.31+/-0.10 mV, respectively; all p<0.001). Consequently, the wavelength of the slow wave was strongly reduced from 36.4+/-0.8 cm to 3.7 +/- 0.1 cm (p<0.001). We conclude that the patterns of slow wave propagation are usually, though not always, uniform in the canine small intestine and that the gradient in the wavelength will influence the patterns of local contractions.     

Sand as a medium for transmission of vibratory signals of prey in antlions Euroleon nostras (Neuroptera: Myrmeleontidae)

Abstract.  European pit-building antlions ( Euroleon nostras / Geoffroy in Fourcroy/) detect their prey by sensing the vibrations that prey generate during locomotory activity. The behavioural reactions and some of the physical properties of substrate vibrations in sand are measured to observe signal transmission through the substrate. The frequency range of the signals of four arthropod species ( Tenebrio molitor , Pyrrhocoris apterus , Formica sp. and Trachelipus rathkei ) is 0.1–4.5 kHz and acceleration values are in the range 400 μm s⁻² to 1.5 mm s⁻². Substrate particle size and the frequency of prey signals both influence the propagation properties of vibratory signals. The damping coefficient at a frequency 300 Hz varies from 0.26 to 2.61 dB cm⁻¹ and is inversely proportional to the size of the sand particle. The damping coefficient is positively correlated with the frequency of the pulses. Vibrations in finer sand are attenuated more strongly than in coarser sand and, consequently, an antlion detects its prey only at a short distance. The reaction distance is defined as the distance of the prey from the centre of the pit when the antlion begins tossing sand as a reaction to the presence of prey. The mean reaction distance is 3.3 cm in the finest sand (particle size ≤ 0.23 mm) and 12.3 cm in coarser sand (particle size 1–1.54 mm). The most convenient sands for prey detection are considered to be medium particle-sized sands.     

Gas dispersion in volume-cycled tube flow. I. Theory.

A mathematical theory is derived for the dispersion of a contaminant bolus introduced into a fully developed volume-cycled oscillatory pipe flow. The convection-diffusion equation is solved for a tracer gas bolus by expressing the local concentration field as a series expansion of derivatives of the area-averaged concentration. The local, as well as the area-averaged, concentration is determined for a uniform initial slug or Gaussian bolus. The effect of various flow parameters such as Womersley parameter, Schmidt number, and tidal volume is investigated. The overall dispersion is characterized by a time-averaged effective diffusion coefficient, which for long duration coincides with previous dispersion theories based on a constant linear axial concentration profile. The effective diffusion coefficient can be determined from the local time history of concentration, independent of the spatial location or the initial tracer bolus. Furthermore the local peaks of the concentration-time curve follow a decaying curve dictated by the time-averaged effective diffusion coefficient. Thus the theory is directly applicable for dispersion measurements in oscillatory tube flows, a basis for the pulmonary airways application, as shown by Gaver et al. (J. Appl. Physiol. 72: 321-331, 1992).