Pulsatile flow and oxygen transport past cylindrical fiber arrays for an artificial lung: computational and experimental studies

The influence of time-dependent flows on oxygen transport from hollow fibers was computationally and experimentally investigated. The fluid average pressure drop, a measure of resistance, and the work required by the heart to drive fluid past the hollow fibers were also computationally explored. This study has particular relevance to the development of an artificial lung, which is perfused by blood leaving the right ventricle and in some cases passing through a compliance chamber before entering the device. Computational studies modeled the fiber bundle using cylindrical fiber arrays arranged in in-line and staggered rectangular configurations. The flow leaving the compliance chamber was modeled as dampened pulsatile and consisted of a sinusoidal perturbation superimposed on a steady flow. The right ventricular flow was modeled to depict the period of rapid flow acceleration and then deceleration during systole followed by zero flow during diastole. Experimental studies examined oxygen transfer across a fiber bundle with either steady, dampened pulsatile, or right ventricular flow. It was observed that the dampened pulsatile flow yielded similar oxygen transport efficiency to the steady flow, while the right ventricular flow resulted in smaller oxygen transport efficiency, with the decrease increasing with Re. Both computations and experiments yielded qualitatively similar results. In the computational modeling, the average pressure drop was similar for steady and dampened pulsatile flows and larger for right ventricular flow while the pump work required of the heart was greatest for right ventricular flow followed by dampened pulsatile flow and then steady flow. In conclusion, dampening the artificial lung inlet flow would be expected to maximize oxygen transport, minimize work, and thus improve performance.     

Flow mixing enhancement from balloon pulsations in an intravenous oxygenator

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.     

Pulsatile blood flow and gas exchange across a cylindrical fiber array

The pulsatile blood flow and gas transport of oxygen and carbon dioxide through a cylindrical array of microfibers are numerically simulated. Blood is modeled as a homogeneous Casson fluid, and hemoglobin molecules in blood are assumed to be in local equilibrium with oxygen and carbon dioxide. It is shown that flow pulsatility enhances gas transport and the amount of gas exchange is sensitive to the blood flow field across the fibers. The steady Sherwood number dependence on Reynolds number was shown to have a linear relation consistent with experimental findings. For most cases, an enhancement in gas transport is accompanied with an increase in flow resistance. Maximum local shear stress is provided as a possible indicator of thrombosis, and the computed shear stress is shown to be below the threshold value for thrombosis formation for all cases evaluated.     

Ventilatory effects of high and pulsatile blood flow in the pulmonary circulation

The mechanism of ventilatory stimulation that accompanies increases in cardiac output is unknown. Previous studies addressing this issue have been inconclusive. However, only steady pulmonary blood flow was used. The effect of flow pulsatility merits consideration, because increasing cardiac output raises not only mean pulmonary arterial pressure but also pulse pressure; mechanoreceptors with an important dynamic component to their responses may cause a response to pulsatile, but not steady, flow. Studies were done on anesthetized cats (n = 4) and dogs (n = 4). The right pulmonary artery was cannulated within the pericardium, and systemic blood was pumped from the left atrium to the right pulmonary artery. The right pulmonary circulation was perfused at different levels of flow, which was either steady or pulsatile. Steady-state flow of up to 150 ml.kg-1.min-1 (270 ml.kg-1.min-1 when corrected for the proportion of lung tissue perfused) did not affect breathing pattern. When high pulmonary flow was made pulsatile (pulse pressure approximately 23 mmHg), breath duration decreased from 3.7 +/- 0.72 to 3.4 +/- 0.81 (SD) s (P less than 0.01), representing a change in frequency of only 9%. There was no change in peak inspiratory activity. It was concluded that pulmonary vascular mechanoreceptors are not likely to contribute significantly to the increase in ventilation in association with increases in cardiac output.     

Gas transport in serpentine microporous tubes under steady and pulsatile blood flow conditions

A serpentine gas exchange unit was built with cylindrical tubular microporous membranes featuring periodic arcs with a fixed curvature ratio (ratio of tube radius to radius of curvature) of 1/14 and circular angles between 30 and 360 deg. Oxygen transfer was measured under steady and pulsatile blood flow conditions in vitro and ex vivo to assess the design features which most effectively augment gas transfer. Under steady blood flow conditions, oxygen transfer increased with circular angles beyond 70 deg. Under pulsatile conditions, a wide range of geometrical and fluid mechanical parameters could be combined to enhance gas transfer performance, which eventually depended upon the secondary Reynolds number and the Womersley parameter.     

Physiological flow simulation in residual human stenoses after coronary angioplasty

To evaluate the local hemodynamic implications of coronary artery balloon angioplasty, computational fluid dynamics (CFD) was applied in a group of patients previously reported by [Wilson et al. (1988), 77, pp. 873-885] with representative stenosis geometry post-angioplasty and with measured values of coronary flow reserve returning to a normal range (3.6 +/- 0.3). During undisturbed flow in the absence of diagnostic catheter sensors within the lesions, the computed mean pressure drop delta p was only about 1 mmHg at basal flow, and increased moderately to about 8 mmHg for hyperemic flow. Corresponding elevated levels of mean wall shear stress in the midthroat region of the residual stenoses, which are common after angioplasty procedures, increased from about 60 to 290 dynes/cm2 during hyperemia. The computations (Ree approximately equal to 100-400; alpha e = 2.25) indicated that the pulsatile flow field was principally quasi-steady during the cardiac cycle, but there was phase lag in the pressure drop-mean velocity (delta p - u) relation. Time-averaged pressure drop values, delta p, were about 20 percent higher than calculated pressure drop values, delta ps, for steady flow, similar to previous in vitro measurements by Cho et al. (1983). In the throat region, viscous effects were confined to the near-wall region, and entrance effects were evident during the cardiac cycle. Proximal to the lesion, velocity profiles deviated from parabolic shape at lower velocities during the cardiac cycle. The flow field was very complex in the oscillatory separated flow reattachment region in the distal vessel where pressure recovery occurred. These results may also serve as a useful reference against catheter-measured pressure drops and velocity ratios (hemodynamic endpoints) and arteriographic (anatomic) endpoints post-angioplasty. Some comparisons to previous studies of flow through stenoses models are also shown for perspective purposes.     

Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube

The effect of pulsatile flow on peristaltic transport in a circular cylindrical tube is analysed. The flow of a Newtonian viscous incompressible fluid in a flexible circular cylindrical tube on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The initial flow in the tube is induced by an arbitrary periodic pressure gradient. A perturbation solution with amplitude ratio (wave amplitude/tube radius) as a parameter is obtained when the frequency of the travelling wave and that of the imposed pressure gradient are equal. The interaction effects of periodic wall induced flow and periodic pressure imposed flow are visualized through the presence of substantially different components of steady and higher harmonic oscillating flow in the first order flow solution. Numerical results show a strong variation of steady state velocity profiles with boundary wave number and Reynolds number and a strong phase shift behaviour of the flow in the radial direction.     

Pressure drop and flow rate measurements in a human aortic bifurcation cast for steady and pulsatile flow

Pressure drop and flow rate measurements in a rigid cast of a human aortic bifurcation under both steady and physiological pulsatile flow conditions are reported. Integral momentum and mechanical energy balances are used to calculate impedance, spatially averaged wall shear stress and viscous dissipation rate from the data. In the daughter branches, steady flow impedance is within 30% of the Poiseuille flow prediction, while pulsatile flow impedance is within a factor of 2 of fully developed, oscillatory, straight tube flow theory (Womersley theory). Estimates of wall shear stress are in accord with measurements obtained from velocity profiles. Mean pressure drop and viscous dissipation rate are elevated in pulsatile flow relative to steady flow at the mean flow rate, and the exponents of their Reynolds number dependence are in accord with available theory.     

The central axis prosthetic cardiac valve: an in vitro study of pressure drop assessment under steady-state flow conditions

In this work, a new mechanical prosthetic heart valve, the central axis valve, is presented. This new prosthesis has been tested in vitro, and compared with four other common prosthetic cardiac valves (Starr-Edwards 6120, Bjork-Shiley monostrut, Medtronic-Hall, and St Jude Medical valves). All valves studied have the same orifice diameter of 22 mm. The prostheses were installed inside a transparent mitral test chamber, which enables pressure drop measurement to be made under steady-state flow conditions using a blood analogue fluid. Pressure drop loss is one important factor affecting the overall performance of a prosthetic heart valve. Steady-state flow tests are essential to predict certain flow characteristics and pressure gradient loss before more complicated, expensive, and difficult-to-interpret pulsatile flow tests are conducted. All experiments were performed in vitro and at steady volumetric flow rates of 10 to 30 l/min. The Starr-Edwards SE 6120 showed the highest values for pressure drop. The St Jude Medical valve offers the minimum resistance to flow. The central axis valve comes second to the Starr-Edwards valve for this type of measurement. The new valve is promising. A complete valve evaluation programme, covering initial conceptional design through to clinical use, is in progress. Materials for the fabrication of the new valve are also under consideration.     

In vitro flow dynamics of four prosthetic aortic valves: a comparative analysis

The velocity fields downstream of four prosthetic heart valves were mapped in vitro over the entire cross-section of a model aortic root using laser Doppler anemometry. THe Bj?rk-Shiley 60 degrees convexo-concave tilting disc valve, the Smeloff-Cutter caged ball valve, the St. Jude Medical bileaflet valve, and the Ionescu-Shiley standard bioprosthesis were examined under both steady and pulsatile flows. Velocity profiles under steady flow conditions were a good approximation for pulsatile profiles only during midsystole. The pulsatile flow characteristics of the four valves showed variation in large scale flow structures. Comparison of the valves according to pressure drop, shear stress and maximum velocities are also provided.     

Pressure and flow in the umbilical cord

A fluid dynamic study of blood flow within the umbilical vessels of the human maternal-fetal circulatory system is considered. It is found that the umbilical coiling index (UCI) is unable to distinguish between cords of significantly varying pressure and flow characteristics, which are typically determined by the vessel curvature, torsion and length. Larger scale geometric non-uniformities superposed over the inherent coiling, including cords exhibiting width and/or local UCI variations as well as loose true knots, typically produce a small effect on the total pressure drop. Crucially, this implies that a helical geometry of mean coiling may be used to determine the steady vessel pressure drop through a more complex cord. The presence of vessel constriction, however, drastically increases the steady pressure drop and alters the flow profile. For pulsatile-flow within the arteries, the steady pressure approximates the time-averaged value with high accuracy over a wide range of cords. Furthermore, the relative peak systolic pressure measured over the period is virtually constant and approximately 25% below the equivalent straight-pipe value for a large range of non-straight vessels. Interestingly, this suggests that the presence of vessel helicity dampens extreme pressures within the arterial cycle and may provide another possible evolutionary benefit to the coiled structure of the cord.     

The use of a single-fiber reactor for the enzymatic removal of amino acids from solutions

In this article we describe the use of bench-scale single-fiber dialyzers for the development and testing of an immobilized enzyme reactor for the treatment of leukemia. The treatment is based on the enzymatic removal of specific amino acids from the blood of leukemia patients. L-Lysine alpha-oxidase and catalase were coimmobilized within the void space of the porous region of asymmetric hollow-fiber membranes for the removal of L-lysine from simulated human plasma solutions. Hollow-fiber reactor performance was evaluated using a small single-fiber dialyzer (SFD) consisting of a single fiber encased in a protective glass shell. This small reactor affords ease of use, requires small amounts of chemicals and biochemicals, and gives useful reactor performance data. Single-fiber dialyzers were constructed using polyamide fibers with a molecular weight cutoff of 10,000 (PA10 fibers); these fibers demonstrated the best compatibility with and retention of the enzymes. The SFD performance in removing L-lysine from solution was evaluated under both steady and pulsatile flow operation. Pulsatile flow was tested for two reasons: (1) to enhance the radial mass transfer of lysine within the SFD and (2) to simulate the pulsatile flow of blood in dialysis treatment. The use of pulsatile flow increased lysine conversion by 15% over the steady-flow case. Approximately 40% of the lysine was removed from simulated plasma by the SFD in a 4-h experiment using pulsatile flow in the recycle mode.     

Pulmonary capillaries are recruited during pulsatile flow.

Capillaries recruit when pulmonary arterial pressure rises. The duration of increased pressure imposed in such experiments is usually on the order of minutes, although recent work shows that the recruitment response can occur in <4 s. In the present study, we investigate whether the brief pressure rise during cardiac systole can also cause recruitment and whether the recruitment is maintained during diastole. To study these basic aspects of pulmonary capillary hemodynamics, isolated dog lungs were pump perfused alternately by steady flow and pulsatile flow with the mean arterial and left atrial pressures held constant. Several direct measurements of capillary recruitment were made with videomicroscopy. The total number and total length of perfused capillaries increased significantly during pulsatile flow by 94 and 105%, respectively. Of the newly recruited capillaries, 92% were perfused by red blood cells throughout the pulsatile cycle. These data provide the first direct account of how the pulmonary capillaries respond to pulsatile flow by showing that capillaries are recruited during the systolic pulse and that, once open, the capillaries remain open throughout the pulsatile cycle.     

Onset of pulsatile pressure causes transiently increased filtration through artery wall

Convective fluid motion through artery walls aids in the transvascular transport of macromolecules. Although many measurements of convective filtration have been reported, they were all obtained under constant transmural pressure. However, arterial pressure in vivo is pulsatile. Therefore, experiments were designed to compare filtration under steady and pulsatile pressure conditions. Rabbit carotid arteries were cannulated and excised from male New Zealand White rabbits anesthetized with pentobarbitol sodium (30 mg/kg i.v. administered). Hydraulic conductance was measured in cannulated excised rabbit carotid arteries at steady pressure. Next, pulsatile pressure trains were applied within the same vessels, and, simultaneously, arterial distension was monitored using Optical coherence tomography (OCT). For each pulse train, the volume of fluid lost through filtration was measured (subtracting volume change due to residual distension) and compared with that predicted from steady pressure measurements. At 60- and 80-mmHg baseline pressures, the experimental filtration volumes were significantly increased compared with those predicted for steady pressure (P < 0.05). OCT demonstrated that the excess fluid volume loss was significantly greater than the volume that would be lost through residual distension (P < 0.05). After 30 s, the magnitude of the excess of fluid loss was reduced. These results suggest that sudden onset of pulsatile pressure may cause changes in arterial interstitial hydration.     

On the physics of CNS memory

The effects of geometry, type of fluid and properties of the desmotubule membrane on the fluid transport in plasmodesma are discussed from a hydrodynamics viewpoint. It is shown that the “necking” of the ends of plasmodesma has a profound effect on the volume flow rates reducing them by several orders of magnitude. Most of the pressure drop occurs across the “neck” regions. There appears to be little significant difference in the volume flow rates if we consider a Newtonian or powerlaw fluid or if we allow the desmotubule membrane to be permeable or slightly flexible, at least in comparison to the dominating feature of plasmodesma geometry.     

Blood flow multiscale phenomena

The cardiovascular disease is one of most frequent cause deaths in modern society. The objective of this work is analyse the effect of dynamic vascular geometry (curvature, torsion, bifurcation) and pulsatile blood nature on secondary flow, wall shear stress and platelet deposition. The problem was examined as multi-scale physical phenomena using perturbation analysis and numerical modelling. The secondary flow determined as influence pulsatile pressure, vascular tube time-dependent bending and torsion on the main axial flow. Bifurcation and branching phenomena are analysed experimentally through, blood-like fluid pulsatile flow across elastic rubber-like Y-model model. The problem complex geometry near branching in platelet deposit modelling is resolved numerically as Falker-Skan flow.     

Three Dimensional Modeling of the Cerebrospinal Fluid Dynamics and Brain Interactions in the Aqueduct of Sylvius

A computational fluid dynamics (CFD) method is presented to investigate the flow of cerebro-spinal fluid (CSF) in the cerebral aqueduct. In addition to former approaches exhibiting a rigid geometry, we propose a model which includes a deformable membrane as the wall of this flow channel. An anatomical shape of the aqueduct was computed from magnetic resonance images (MRI) and the resulting meshing was immersed in a marker-and-cell (MAC) staggered grid for to take into account fluid–structure interactions. The time derivatives were digitized using the Crank–Nicolson scheme. The equation of continuity was modified by introducing an artificial compressibility and digitized by a finite difference scheme.

Calculations were validated with the simulation of laminar flow in a rigid tube. Then, comparisons were made between simulations of a rigid aqueduct and a deformable one. We found that the deformability of the walls has a strong influence on the pressure drop for a given flow.     

Peristaltic transport of blood: Casson model--II

The problem of peristaltic transport of blood in a uniform and non-uniform tube has been investigated, under zero Reynolds number and long wavelength approximation. Blood is represented by a two-layered fluid model consisting of a central layer of suspension of all erythrocytes, etc., assumed to be a Casson fluid, and a peripheral layer of plasma as a Newtonian fluid. A comparison of results with those without peripheral layer shows that the magnitude of the pressure rise, under a given set of conditions is smaller in the case of model with peripheral layer. It is found that, for a given flow rate, the pressure rise decreases as the viscosity of the peripheral layer decreases, and for a given non zero pressure drop, the flow rate increases as the viscosity of the peripheral layer decreases. However, the flow is independent of the presence of the peripheral layer, for zero pressure rise. Further, the pressure rise in the case of non-uniform geometry is found much smaller than the corresponding value in the uniform geometry.     

Comparison of steady and pulsatile flow in a double branching arterial model

Data are presented to compare fluid flow parameters for steady flow with those for time-varying flow in a simplified two branch model which simulates the region of the abdominal aorta near the celiac and superior mesenteric branches of the dog. Measurements in the model included laser doppler anemometry velocity profiles during steady flow, sinusoidal flow with a superimposed mean flow (referred to as simple oscillatory flow) and arterial pulsatile flow. Shear rate measurements were made by an electrochemical technique during steady flow. Flow visualization studies were done during steady and pulsatile flow. Fluid flow effects in the simplified model during steady flow showed many similarities to the results from previous steady flow studies in a canine aortic cast. Shear rates in the region of the proximal (first, or celiac) branch were independent of flow rates in the distal (second, or mesenteric) branch, but the shear pattern within the proximal branch changed significantly as flow in the proximal branch increased. Shear rates on the proximal flow divider (leading edge into the distal branch) depended primarily on the flow rate to the proximal branch, but not on flow to the distal branch. At certain daughter branch flow ratios (approximately 2:1, proximal to distal), flow separation was promoted at the outer wall of the second branch, but flow separation did not occur in the first branch. In contrast to the canine aortic case results, flow separation was never detected on the distal (mesenteric) flow divider of the simplified model. This observation reflects the subtle effects of geometry on flow since the mesenteric flow divider in the canine cast protrudes into the main flow whereas the distal flow divider in the simplified model does not. There were distinct differences in the flow phenomena between steady, simple oscillatory and arterial pulsatile flow. Peak shear rates during pulsatile flow were as much as 10--100 times greater than steady flow shear rates at comparable mean flow rates. Particularly noteworthy for the pulsatile flow with a Womersley parameter of sixteen were very blunt velocity profiles throughout systole, and the absence of flow separation or reversal in those regions of the model that exhibited flow separation during steady flow. The shape of the waveform influences the nature of the flow during time-varying flows. Future studies of fluid dynamics in model systems must consider the pulsatile nature of the flow if a true interpretation of arterial flow phenomena is to be made.     

Three-dimensional cerebrospinal fluid flow within the human ventricular system

Cerebrospinal fluid (CSF) is a Newtonian fluid and can, therefore, be modelled using computational fluid dynamics (CFD). Previous modelling of the CSF has been limited to simplified geometric models. This work describes a geometrically accurate three dimensional (3D) computational model of the human ventricular system (HVS) constructed from magnetic resonance images (MRI) of the human brain. It is an accurate and full representation of the HVS and includes appropriately positioned CSF production and drainage locations. It was used to investigate the pulsatile motion of CSF within the human brain. During this investigation CSF flow rate was set at a constant 500 ml/day, to mimic real life secretion of CSF into the system, and a pulsing velocity profile was added to the inlets to incorporate the effect of cardiac pulsations on the choroid plexus and their subsequent influence on CSF motion in the HVS. Boundary conditions for the CSF exits from the ventricles (foramina of Magendie and Lushka) were found using a “nesting” approach, in which a simplified model of the entire central nervous system (CNS) was used to examine the effects of the CSF surrounding the ventricular system (VS). This model provided time varying pressure data for the exits from the VS nested within it. The fastest flow was found in the cerebral aqueduct, where a maximum velocity of 11.38 mm/s was observed over five cycles. The maximum Reynolds number recorded during the simulation was 15 with an average Reynolds number of the order of 0.39, indicating that CSF motion is creeping flow in most of the computational domain and consequently will follow the geometry of the model. CSF pressure also varies with geometry with a maximum pressure drop of 1.14 Pa occurring through the cerebral aqueduct. CSF flow velocity is substantially slower in the areas that are furthest away from the inlets; in some areas flow is nearly stagnant.