Measurement of oscillatory flow pressure gradient in an elastic artery model

In vitro experiments were conducted to measure the oscillatory flow pressure gradient along an elastic tube in order to assess the recent nonlinear theory of Wang and Tarbell. According to this theory, in an elastic tube with oscillatory flow, the mean (time-averaged) pressure gradient cannot be calculated using Poiseuille's law. The effect of wall motion creates a nonlinear convective acceleration, and an induced mean pressure gradient is required to balance the convective acceleration. The induced mean pressure gradient depends on the diameter variation over a cycle, the pulsatility and unsteadiness of the flow, and the phase difference between the pressure wave form and the flow wave form. The amplitude of the pressure gradient also depends on these parameters and may deviate significantly from Womersley's rigid tube theory. A flow loop was constructed to produce oscillatory flow in an elastic tube. Flow wave forms were measured with an ultrasonic flow probe, and ultrasonic diameter crystals were used to measure wall movement. A special device for pressure drop measurement was constructed using Millar catheter tip transducers to obtain both forward and backward pressure drops that were then averaged. This averaging method eliminated the static error of the pressure transducers. The pressure-flow phase angle was varied by clamping a distal elastic section at various locations. Pressure gradients were obtained for a range of phase angles between −55 ° and +49 °. The mean and amplitude of the measured pressure gradient were compared to theoretical values. Both positive and negative induced mean pressure gradients were measured over the range of phase angles. The measured pressure gradient amplitudes were always lower than predicted by Womersley's rigid tube theory. The experimental means and amplitudes are in good agreement with the elastic tube theoretical values. Thus, the experiments verify the theory of Wang and Tarbell.     

Mucus transport in the airways by two-phase gas-liquid flow mechanism: continuous flow model

Mucus transport speed induced by two-phase gas-liquid interaction was measured in the continuous two-phase annular flow tube models, and factors influencing the transport speed were assessed in conjunction with rheological properties of mucus. The flow model was made with 1.0-cm-ID glass tubes and positioned either vertically or horizontally. During a continuous passage of airflow through the model tube, mucus stimulants were supplied into the tube at a rate of 0.5-2.0 ml/min. The advancing speed of the leading edge of the mucous layer and mean mucous layer thickness were then measured. The transport speed in the vertical tube model ranged from 1.1 to 3.1 cm/min with a mucus feed rate of 0.5 ml/min at airflow rates of 0.33-1.17 l/s and increased with increasing airflow rates but decreased rapidly with increasing viscosity of mucus. The transport speed increased almost proportionally with increasing mucus feed rate. Elasticity of mucus did not affect the transport speed itself. However, more elastic mucus caused lower flow resistance and thereby could be transported with a much reduced work load. The transport speed in the horizontal tube model was 5-60% faster than that in the vertical tube model. The mean mucous layer thickness in the vertical tube model was found to be in the range of 0.5-1.5 mm in the experimental conditions used, and decreased rapidly with increasing airflow rate and decreasing viscosity of mucus. From these data the transport speed could be functionally related to airway diameter, mucous layer thickness, and mucus production rate.     

Contributions to the mathematical biophysics of the cardiovascular system

The reflection of pressure waves in a fluid enclosed within a tube with an elastic wall is studied for the case of a localized change in diameter of the tube. The concept of impedance is introduced. The relation of the reflection characteristics of the parts of the tube at either side of the change is derived on the basis of the continuity of pressure and mass flow at the site of the change. This relations is used to derive the expression for the ratio of the pressure oscillations measured in front of, and behind, the constriction in terms of the constants of the system. As a result, a method is indicated to locate the coarctation from measurements of the pressures in front of, and behind it.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.     

Freezing by a flat, circular surface cryoprobe of a tissue phantom with an embedded cylindrical heat source simulating a blood vessel

The effects of a thermally-significant blood vessel, simulated by an embedded acrylic tube, 4.8 mm outer diameter on the freezing field caused by a surface cryoprobe were studied experimentally in a tissue phantom. The flat, 15 mm diameter, circular cryoprobe was operated at a constant cooling rate of -8 degrees C/min by liquid nitrogen down to -60 degrees C. Water flow rates of 30 and 100 ml/min, at a constant temperature of 32.5 degrees C, were maintained in the embedded tube. The latter flow rate is typical to the lower range of blood flows in large arteries in the human body. The phase changing medium (PCM) used was a 30/70% by volume mashed potatoes flakes-water solution. Temperature measurements inside the PCM were performed in one plane perpendicular to the embedded tube, relative to which the cryoprobe was placed at 5 locations in separate experiments. This novel experimental method reduced the perturbation caused by the thermocouple junctions while facilitating rather detailed measurements of the temperature fields developing in the PCM. Results show the development of two hump-like formations on either side of the embedded tube. Freezing was retarded in the region away from the surface cryoprobe and under the tube. This accentuated the dominance of the axial effects, due to the embedded tube, over the radial ones due to the cryoprobe. Results of this study should be considered in designing protocols of cryosurgical procedures performed in the vicinity of thermally-significant blood vessels.     

A computational study on the influence of catheter-delivered intravascular probes on blood flow in a coronary artery model

Catheter-delivered intravascular probes are widely used in clinical practice to measure coronary arterial velocity and pressure, but the artefactual effect of the probe on the variables being measured is not well characterised. A coronary artery was simulated with a 180 degrees curved tube 3mm in diameter and the effect of catheters of different diameters was modelled numerically under pulsatile flow conditions. The presence of a catheter increased pressure by 1.3-4.3 mmHg depending on its diameter, and reduced velocity-pressure phase-lag. For an ultrasound sample volume 5mm downstream from the probe tip, the underestimation in velocity measurement attributed to catheter blockage is approximately 15-21% for an average inlet velocity of 0.1m/s. The velocity measurement error is lower at higher mean flow velocity. Accuracy of clinical velocity measurements could be improved by moving the sample volume farther downstream from the probe tip, because the centrifugal pressure gradient intrinsic to the curvature promotes re-development of flow.     

Dynamics of Breakdown in a Low-Pressure Argon–Mercury Mixture in a Long Discharge Tube

Breakdown dynamics in the course of glow discharge ignition in a long discharge tube (80 cm in length and 25 mm in diameter) filled with argon at a pressure of 3–4 Torr and mercury vapor at room temperature was studied experimentally. Rectangular voltage pulses with amplitudes from 1 to 2.5 kV were applied to the tube anode, the cathode being grounded. Complex electrical and optical measurements of the breakdown dynamics were carried out. Breakdown begins with a primary discharge between the anode and the tube wall. In this stage, a jump in the anode current and a sharp decrease in the anode voltage are observed and prebreakdown ionization wave arises near the anode. The cathode current appears only after the ionization wave reaches the cathode. The wave propagation velocity was measured at different points along the tube axis. The wave emission spectrum contains Hg, Ar, and Ar⁺ lines. The intensities of these lines measured at a fixed point exhibit very different time behaviors. The effect of the tube shielding on the breakdown characteristics was examined. It is found that, at a sufficiently narrow gap between the shield and the tube, this effect can be substantial.     

Biomechanical properties of decellularized porcine common carotid arteries

To analyze the effects of decellularization on the biomechanical properties of porcine common carotid arteries, decellularization was performed by a detergent-enzymatic procedure that preserves extracellular matrix scaffold. Internal diameter, external diameter, and wall thickness were measured by optical microscopy on neighboring histological sections before and after decellularization. Rupture tests were conducted. Inner diameter and wall thickness were measured by echo tracking during pressure inflation from 10 to 145 mmHg. Distensibility and incremental elastic modulus were computed. At 10 mmHg, mean diameter of decellularized arteries was 5.38 mm, substantially higher than controls (4.1 mm), whereas decellularized and control arteries reached the same internal diameter (6.7 mm) at 145 mmHg. Wall thickness decreased 16% for decellularized and 32% for normal arteries after pressure was increased from 10 to 145 mmHg. Decellularized arteries withstood pressure >2,200 mmHg before rupture. At 145 mmHg, decellularization reduced compliance by 66% and increased incremental elastic modulus by 54%. Removal of cellular elements from media led to changes in arterial dimensions. Collagen fibers engaged more rapidly during inflation, yielding a stiffer vessel. Distensibility was therefore significantly lower (by a factor of 3) in decellularized than in normal vessels: reduced in the physiological range of pressures. In conclusion, decellularization yields vessels that can withstand high inflation pressures with, however, markedly different geometrical and biomechanical properties. This may mean that the potential use of a decellularized artery as a scaffold for the creation of xenografts may be compromised because of geometrical and compliance mismatch.     

Influence of a downstream narrowing on the flow profile in a tube

The distance over which the upstream flow conditions in a tube are disturbed by a stenosis downstream, i.e. the outlet length, was investigated for Reynolds numbers in the range 210-2900. Two methods were used, the Navier-Stokes equations were solved with a computer and a physical model was constructed and maximal velocities were measured with an ultrasound Doppler system. The computer model showed that Re number does not influence the outlet length, varying the stenosis area from 25% to 90% has an effect. However, the outlet length remained small, below 70% of the diameter of the tube. The physical model confirmed for a 75% stenosis that the outlet length is small, this method set the limit at not more than 1.2 times the tube diameter.     

A simple model describing the elastic properties of human umbilical arterial smooth muscle

Elastic properties of cylindrical segments of 71 normal double and 4 single human umbilical arteries were studied. This specimen is rich in vascular smooth muscle in comparison with other great arteries. Outer diameter versus intraluminal pressure characteristic curves were taken with decreasing pressures in vitro in different contraction states. Tangential force and circumferential incremental elastic modulus were computed. A sum of 222 curves was analysed. The investigations showed that if we take tangential force and outer radius values measured at the same pressure levels but in different contraction states, then a similar proportional change in tangential force will induce a similar proportional passive change in the outer radius, to some extent independently of the degree of active tangential shortening of the segment. For example to induce a 10% passive decrease of the outer radius from values measured at 100 mm Hg intraluminal pressure, tangential force had to be decreased by 76.7 +/- 9.9% in single relaxed arteries, and by 79.6 +/- 0.8% in normal double relaxed segments. These values corresponded to intraluminal pressure levels of 26.4 +/- 4.9 mm Hg and 23.1 +/- 0.9 mm Hg, respectively. In 30% active spontaneous shortening to reach the same 10% passive decrease in outer radius from the value measured at 100 mm Hg, tangential force had to be decreased by 75.2 +/- 1.9% which corresponded to 29.6 +/- 20 mm Hg. The same values in 5-HT induced contraction, 30% active shortening were 76.7 +/- 2.0% and 28.4 +/- 2.6 mm Hg, respectively. In addition to the similarity of relative changes in tangential force, the pressure levels were to some extent also similar. These data suggest that elastic elements in the human umbilical arterial smooth muscle may be organized in such a way as to ensure similar prestretch of similar elastic elements at similar pressures independently of the degree of active shortening of the circumference.     

Growth of a pogonophore: a study of Polybrachia canadensis with a discussion of the development of taxonomic characters

Heptabrachia canadensis , previously known from one juvenile specimen, has been redescribed from new material and transferred to the genus Polybrachia. About 1400 specimens were available for study, including a series of developmental stages ranging from juveniles less than 0.1 mm in diameter to adults 0.6 mm in diameter. The smallest juveniles have one tentacle while most adults have 30 to 40 tentacles. Juveniles differ from adults in diameter, length, number of tentacles and type of tube. The most important observation to emerge is the variability of characters hitherto thought to distinguish different genera, and the need for care in the diagnosis of new species from limited material.     

Learning in Stentor

SYNOPSIS. When placed in a vertical capillary tube of 0.5 mm inner diameter opening at the bottom end into a reservoir, Stentor coeruleus learns to escape; that is, on the 1st trial it takes a long time to find its way out and much less time on the 2nd and succeeding trials. It was found that learning did not occur in a horizontal tube, or in a vertical tube with the open end above, or in tubes of 1 or 2 mm inner diameter. To explain the results it is suggested that the response is actually a delayed geotaxis released only after a definite period of mechanical stimulation from bumping into the walls of the tube. Possibly the phenomenon is related to the process of habituation to mechanical stimuli which has been elucidated by other authors.     

Wave dissipation in flexible tubes in the time domain: in vitro model of arterial waves

Earlier work of wave dissipation in flexible tubes and arteries has been carried out predominantly in the frequency domain and most of the studies used the measured pressure waveform for presenting the results. In this work we investigate the pattern of wave dissipation in the time domain using the separated forward and backward travelling waves in flexible tubes. We tested four sizes of latex tubes of 2m in length each, where a single semi-sinusoidal in shape, pressure wave, was produced at the inlet of each tube. Simultaneous measurements of pressure and flow waveforms were recorded every 5cm along the tubes and wave speed was determined using the pressure-velocity loop method (PU-loop). The measured data and wave speed were used to separate the pressure waveform and wave intensity, into their forward and backward directions, using wave intensity analysis (WIA). Also, the energy carried by the wave was calculated by integrating the relevant area under the wave intensity curve. The peak of the measured pressure waveform increased downstream, however, the peak of the separated forward pressure waveform decreased exponentially along the tube. Wave intensity and energy also dissipated exponentially along the travelling distance. The peaks of the separated pressure and wave intensity decreased in the forward in a similar exponential way to that in the backward direction in all four tube sizes. Also, the smaller the size of the tube the greater wave dissipation it caused. We conclude that wave separation is useful in studying wave dissipation in elastic tubes, and WIA provides a convenient method for determining the dissipation of the energy carried by the wave along the travelled distance. The separated pressure waveform, wave intensity and wave energy dissipate exponentially with the travelling distance, and wave dissipation varies conversely with the diameter of elastic tubes.     

Initial hydrodynamic study on a new intraaortic axial flow pump: Dynamic aortic valve

Rotary blood pumps have been researched as implantable ventricular assist devices for years. To further reduce the complex of implanted axial pumps, the authors proposed a new concept of intraaortic axial pump, termed previously as "dynamic aortic valve (DAV)". Instead of being driven by an intraaortic micro-electric motor, it was powered by a magnetic field from outside of body. To ensure the perfusion of coronary artery, the axial flow pump is to be implanted in the position of aortic valve. It could serve as either a blood pump or a mechanical valve depending on the power input. This research tested the feasibility of the new concept in model study. A column, made from permanent magnet, is jointed to an impeller in a concentric way to form a "rotor-impeller". Supported by a hanging shaft cantilevered in the center of a rigid cage, the rotor-impeller can be turned by the magnetic field in the surrounding space. In the present prototype, the rotor is 8 mm in diameter and 15 mm in length, the impeller ha     

Erythrocyte sedimentation rate III tube diameter dependence in saline solution

Erythrocyte sedimentation rate was measured in a physiological saline solution as a function of both the tube diameter d and the initial suspension length iota 0. All the sedimentation curves in the vertical tubes were found to overlap over the range 1 mm less than d less than 7 mm and 100 mm less than iota 0 less than 330 mm, within the precision of 8 %. The sedimentation curves in the tilted tubes fit well to an exponential equation of iota = a [1 - exp (-bt)], where iota and t are the medium length along the tube and the elapsed time from sample injection respectively: At fixed tilt angle theta and iota 0, a was roughly constant and b was roughly proportional to l/d, while at fixed theta and d, a was linearly proportional to iota 0 and b was constant. The initial slope ESR (theta) = (d iota/dt) t----0 = ab was represented by a unique straight line as a function of iota 0/d for each fixed tilt angle. The experimental results were compared with some recent theories.     

Hydrodynamics and mixing in down flow jet loop bioreactor with a non-Newtonian fluid

Gas holdup and liquid circulation time were measured in a down flow jet loop bioreactor with a non-Newtonian fluid. It was observed that the circulation time decreases with increase in nozzle diameter, draft tube to column diameter ratio and shear thinning of the media. The gas holdup increases with increase in gas and liquid velocities. The optimum draft tube to column diameter ratio was found to be 0.438. Correlations for gas holdup and circulation time involving operational and geometrical variables were presented.     

Departures from the physical optimality in the bronchial tree of rats (Rattus norvegicus)

We studied the departure from the physical optimality of the bronchial tree of rats using both i) the minimum volume and power and ii) the minimum surface and drag criteria, considering the bronchial junction as the unit study based on Zamir's model for vascular trees. Our results show deviations of the junctions of the bronchial tree from the expected optimums in the proximal airway that can be explained by both, the turbulent or transitional flow regime, and the airway's necessity to distribute its terminal branches in the alveolar surface filling the thoracic volume. The departures of the observed values at the optimum for the minimum volume and power were significantly different than the obtained departure values for the minimum surface and drag criteria. The departure from the optimum was directly related to the diameter of the smallest branch. The slopes of the regressions for the two criteria were different. The regression lines intercept at a bronchial diameter d2 = 0.129 mm. This result agreed with the idea that the tube diameter is limited at small values by the increasing flow resistance with decreasing tube diameter while at large values is limited by the increasing tube volume and dead space with increasing tube diameter.     

Criteria for mucus transport in the airways by two-phase gas-liquid flow mechanism

The critical conditions for mucous layer transport in the respiratory airways by two-phase gas-liquid flow mechanism were investigated by using 0.5- and 1.0-cm-ID tube models. Several test liquids with rheological properties comparable to human sputum were supplied continuously into the vertically positioned tube models in such a way that the liquid could form a uniform layer while traveling upward through the tube with a continuous upward airflow. The critical airflow rate and critical liquid layer thickness required for the upward transport of the liquids were determined. The critical airflow rate was in the Reynolds number (Re) range of 142-1,132 in the 0.5-cm-ID tube model and 708-2,830 in the 1.0-cm-ID tube model depending on the types of liquids tested. In both models, the critical airflow rate was lower with viscoelastic liquids than with viscous oils. The critical liquid layer thickness ranged from 0.2 to 0.5 mm in the 0.5-cm-ID tube model and 0.8 to 1.4 mm in the 1.0-cm-ID tube model at Re of 2,800. These values decreased rapidly with increasing airflow rate. The critical thickness relative to the tube diameter ranged from 3 to 15% of the respective tube diameter and was lower by approximately 30-50% in the 0.5-cm-ID tube model than in the 1.0-cm-ID tube model over the entire Re range tested. The results indicate that the critical conditions for the mucus transport by two-phase gas-liquid flow mechanism are within the range that can be achieved in patients with bronchial hypersecretions during normal breathing.     

Initial hydrodynamic study on a new intraaortic axial flow pump: Dynamic aortic valve

Rotary blood pumps have been researched as implantable ventricular assist devices for years. To further reduce the complex of implanted axial pumps, the authors proposed a new concept of intraaortic axial pump, termed previously as “dynamic aortic valve (DAV)”. Instead of being driven by an intraaortic micro-electric motor, it was powered by a magnetic field from outside of body. To ensure the perfusion of coronary artery, the axial flow pump is to be implanted in the position of aortic valve. It could serve as either a blood pump or a mechanical valve depending on the power input. This research tested the feasibility of the new concept in model study. A column, made from permanent magnet, is jointed to an impeller in a concentric way to form a “rotor-impeller”. Supported by a hanging shaft cantilevered in the center of a rigid cage, the rotor-impeller can be turned by the magnetic field in the surrounding space. In the present prototype, the rotor is 8 mm in diameter and 15 mm in length, the impeller has 3 vanes with an outer diameter of 18 mm. The supporting cage is 22 mm in outer diameter and 20 mm in length. When tested, the DAV prototype is inserted into the tube of a mock circuit. The alternative magnetic field is produced by a rotating magnet placed side by side with the rotor-impeller at a distance of 30 mm. Once the alternative magnetic field is presented in the surrounding space, the DAV starts to turn, leading to a pressure difference and liquid flow in the tube. The flow rate or pressure difference is proportioned to rotary speed. At the maximal output of hydraulic power, the flow rate reached 5 L/min against an afterload of 100 mmHg. The maximal pressure difference generated by DAV at a rotation rate of 12600 r/min was 147 mmHg. The preliminary results demonstrated the feasibility of “DAV”, further research on this concept is justifiable.     

Effect of vessel compliance on the in-vitro performance of a pulsating respiratory support catheter

Intravena caval respiratory support (or membrane oxygenation) is a potential therapy for patients with acute respiratory insufficiency. A respiratory support catheter is being developed that consists of a bundle of hollow fiber membranes with a centrally positioned pulsating balloon to enhance gas exchange. This study examined the influence of vessel compliance on the gas exchange performance of the pulsating respirator, support catheter. Polyurethane elastic tubes were fabricated with compliance comparable to that measured in bovine vena cava specimens. The gas exchange performance of the respiratory catheter was studied in an in-vitro flow loop using either the model compliant tube or a rigid tube as a "mock" vena cava. Balloon pulsation enhanced gas exchange comparably in both rigid and model compliant vessels up to 120 bpm pulsation frequency. Above 120 bpm gas exchange increased with further pulsation in the rigid tube, but no additional increase in gas exchange was seen in the compliant tube. The differences above 120 bpm may reflect differences in the compliance of the elastic tube versus the natural vena cava.