Pulsatile flow and mass transport over an array of cylinders: gas transfer in a cardiac-driven artificial lung

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.     

Some flow visualization and laser-Doppler-velocity measurements in a true-to-scale elastic model of a human aortic arch--a new model technique.

Flow studies were done in an elastic true-to-scale silicone rubber model of an aortic arch to study further hemodynamic influences on atherosclerosis. The model was prepared from a cast of a young woman. A revised model technique was used. The model had a compliance similar to that of the human aortic arch. Velocity measurements were done in the model with a two component laser-Doppler-anemometer in steady and pulsatile flow using a calcium chloride solution with a viscosity of eta = 3.18 mPas and density of rho = 1.28 kg/m3 at 20 degrees C. The time average Reynolds numbers over a whole cycle in the ascending aorta was Re = 1350. The Womersley parameter for pulsatile flow was a = 20. The pulse wave velocity in the ascending aorta was about c = 5.4 m/sec. The secondary flow behavior was discussed for steady and pulsatile flow. Reverse flows were found, especially along the inner radius of the aortic arch in the descending aorta in steady and pulsatile flow and also in small areas of the ascending aorta and at the branches of the aortic arch. The formation of atherosclerotic plaques at preferred local flow regions is discussed.     

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.     

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.     

Disorder distal to modeled stenoses in steady and pulsatile flow

Measurements of the velocity and energy spectra were made in the distal region of modeled stenoses in a rigid tube with both steady and pulsatile water flows. Reynolds numbers of 318–2540 and a pulsatile flow frequency parameter of 15 were employed. The effects of the degree of stenosis, the stenosis geometry and the presence or absence of the downstream confining wall on the development of flow disturbances were investigated. Visualization of the distal flow patterns in stenotic and free jets illustrated the existence of complex fields which included vortex shedding, highly turbulent regions, and recirculation zones. Significant flow disorder was created by a mild stenosis in pulsatile, but not in steady, flow. Nondimensionalization employing the stenosis diameter and flow velocity in the throat of the constriction correlates the vortex shedding frequency and energy spectra within a limited postestenotic region.     

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.     

Experimental study of pulsatile and steady flow through a smooth tube and an atherosclerotic coronary artery casting of man

In vitro investigation of pulsatile and steady flows through a smooth, straight circular tube and a diseased human coronary artery cast was conducted with sugar-water solutions simulating the viscosity of blood. Time averaged pressure drops for pulsatile flows measured in the circular tube over a Reynolds number ranging from 50 to 1,000 were found to be identical to those for steady flows in the same tube, both of which were in excellent agreement with the Poiseuille flow prediction. For the polyurethane case (# 124) made from a human main coronary with significant but 'non obstructive' diffuse atherosclerotic disease, pressure drops for steady flows were found to be greater than Poiseuille flow predictions by a factor of 3-8 in the physiological Reynolds number range from about 100 to 400. Pulsatile flows in the same artery cast resulted in additional 30% increases in time averaged pressure drops, and thus flow resistance, compared to the steady flow data. Steady and pulsatile flow data measured in a straight, axisymmetric model of cast # 124 showed considerably smaller increases in flow resistance than those observed in # 124 casting.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

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.     

Model of oxygen transport limitations in hollow fiber bioreactors

Axial and radial oxygen depletion are believed to be critical scale-limiting factors in the design of cell culture hollow fiber bioreactors. A mathematical analysis of oxygen depletion has been performed in order to develop effectiveness factor plots to aid in the scaling of hollow fiber bioreactors with cells immobilized in the shell-side. Considerations of the lumen mass transport resistances and the axial gradients were added to previous analyses of this immobilization geometry. An order of magnitude analysis was used to evaluate the impact of the shell-side convective fluxes on the oxygen transport. A modified Thiele modulus and a lumen and membrane resistance factor have been derived from the model. Use of these terms in the effectiveness factor plots results in a considerable simplification of the presentation and use of the model. Design criteria such as fiber dimensions and spacing, reactor lengths, and recycle flow rates can be selected using these plots. Model predictions of the oxygen limitations were compared to experimental measurements of the axial cell distributions in a severely oxygen limited hollow fiber bioreactor. Despite considerable uncertainty in our parameters and nonidealities in hollow fiber geometry, the cell distribution correlated well with the modeling results.     

Laminar and turbulent flow in the mammalian aorta: Reynolds number

Laminar to turbulent flow transition in the mammalian aorta is generally characterized by Reynolds number. When dimensional analysis is applied to obtain the Reynolds number in allometric form, it is found that this number is not invariant of body weight but is approximately proportional to body length dimensions. This implies that flow in the aorta of large mammals is turbulent and laminar in smaller mammals during most of ventricular ejection. Since Reynolds number is defined for steady flow through rigid tubes, it may not reflect the actual fluid behavior of pulsatile flow in compliant vessels such as the aorta. In addition, turbulence is frequency dependent. The larger compliance of the aorta and the slower heart rate in larger mammals and the shorter entrance length and higher heart rate in smaller mammals lead to equal prevalence of turbulence. The consequence is that the aortic flow waveforms remain similar in all mammals.     

Influence of pulsatility on the development of intracardiac jets: an in vitro laser Doppler study.

So far, it has been hypothesized that numerical data obtained in steady flow conditions apply to pulsatile flows. In order to study the modifications of the velocity fields due to pulsatility, jets were produced by 8 orifices (with a diameter "D" of 4.4 to 11.3 mm) included in a chamber of 50 mm. The velocity was measured using laser Doppler anemometry with a pulsatile flow ("pf") and compared to the values obtained in steady ("sf"): at maximum velocity, the longitudinal velocity profile is qualitatively similar to this observed in steady flow: it is made of a plateau followed by an hyperbolic velocity decay in the turbulent area. The length of the core ("Lpf") is strongly related to "D" (Lpf = 3.72 D + 5.49, r = .99) and the velocity decay depends on the ratio between the distance "x" from the orifice and "D" (V/Vo = 2.83D/x + 3.46, r = .85, where V is the velocity at "x" and Vo the initial velocity). During the acceleration and the deceleration, the laminar core is disturbed by turbulences. The comparison of "pf" data with "sf" data demonstrated similar diameters at the origin of the jets (Dpf = 0.96 Dsf + .12, r = .99), but significant (p less than .0001) differences both for "L" and "V/Vo": Lpf = .91Lsf + 6.58, r = .97, V/Vopf = .63 V/Vosf + .34, r = .76. Thus, pulsatility modifies velocity fields and the results obtained in steady flow conditions do not apply to pulsatile jets.     

Comparison of steady and pulsatile flow near the ventral and dorsal walls of casts of human aortic bifurcations

Steady and pulsatile flows were passed through casts of human aortic bifurcations and, by means of a laser Doppler anemometer, fluid velocities were measured at selected sites near the ventral and dorsal walls. At these sites, in the vicinity of the bifurcation, the influence of secondary flow is significant and therefore an appreciation of the phasic variation of secondary flow patterns is important. Results are presented comparing the flow direction in both steady and pulsatile flow at sites in three casts. The common features of the flow at these sites were the persistence of the flow direction during the accelerating and decelerating phases of the pulsatile cycle, and the consistently smaller angle (measured from the inlet centerline) of the pulsatile flow direction as compared to the angle of the flow direction in steady flow.     

Numerical simulations of pulsatile blood flow using a new constitutive model

In the present paper we use a new constitutive equation for whole human blood [R.G. Owens, A new microstructure-based constitutive model for human blood, J. Non-Newtonian Fluid Mech. (2006), to appear] to investigate the steady, oscillatory and pulsatile flow of blood in a straight, rigid walled tube at modest Womersley numbers. Comparisons are made with the experimental results of Thurston [Elastic effects in pulsatile blood flow, Microvasc. Res. 9 (1975), 145-157] for the pressure drop per unit length against volume flow rate and oscillatory flow rate amplitude. Agreement in all cases is very good. In the presentation of the numerical and experimental results we discuss the microstructural changes in the blood that account for its rheological behaviour in this simple class of flows. In this context, the concept of an apparent complex viscosity proves to be useful.     

Right bundle branch block pattern during right ventricular permanent pacing: Is it safe or not?

The present case report describes a patient with dual chamber pacemaker whose surface ECG demonstrated paced right bundle branch block pattern suggesting a malpositioned ventricular lead in the left ventricle. However, diagnostic work-up revealed that the lead was appropriately located in the right ventricular apex. Diagnostic maneuvers and clues for differentiating safe right bundle branch block pattern during permanent pacing are thoroughly revisited and discussed within the article.     

A multiphysics approach for modeling early atherosclerosis

This work is devoted to the development of a mathematical model of the early stages of atherosclerosis incorporating processes of all time scales of the disease and to show their interactions. The cardiovascular mechanics is modeled by a fluid–structure interaction approach coupling a non-Newtonian fluid to a hyperelastic solid undergoing anisotropic growth and a change of its constitutive equation. Additionally, the transport of low-density lipoproteins and its penetration through the endothelium is considered by a coupled set of advection–diffusion-reaction equations. Thereby, the permeability of the endothelium is wall-shear stress modulated resulting in a locally varying accumulation of foam cells triggering a novel growth and remodeling formulation. The model is calibrated and applied to an murine-specific case study, and a qualitative validation of the computational results is performed. The model is utilized to further investigate the influence of the pulsatile blood flow and the compliance of the artery wall to the atherosclerotic process. The computational results imply that the pulsatile blood flow is crucial, whereas the compliance of the aorta has only a minor influence on atherosclerosis. Further, it is shown that the novel model is capable to produce a narrowing of the vessel lumen inducing an adaption of the endothelial permeability pattern.     

Finite element simulation of pulsatile flow through arterial stenosis.

The problem of blood flow through a stenosis is solved using the incompressible Navier-Stokes equations in a rigid circular tube presenting a partial occlusion. Calculations are based on a Galerkin finite element method. The time marching scheme employs a predictor-corrector technique using a variable time step. Results are obtained for steady and physiological pulsatile flows. Computational experiments analyse the effect of varying the degree of stenosis, the stricture length, the Reynolds number and Womersley number. The method gives results which agree well with previous computations for steady flows and experimental findings for steady and pulsatile flows.     

Patterns of flow in the left coronary artery

The purpose of this investigation is to describe our preliminary observations of the overall pattern of flow in a mold of the left coronary artery of a pig. Flow in the coronary mold was visualized by the injection of dye into the sinus of Valsalva. Studies were performed during steady flow at rates of 100, 200, 300, 400, and 500 mL/min. Studies were also performed during pulsatile flow, using a pulse duplicator that simulated the magnitude and phasic pattern of coronary flow at rest and during reactive hyperemia. At conditions that simulated rest, mean coronary flow was adjusted to 121 mL/min of which 24 mL/min (20 percent) was systolic. During simulated reactive hyperemia, mean flow was 440 mL/min. Visualization of flow revealed the absence of disturbances of turbulence during both steady and pulsatile flow in the left anterior descending (LAD) and left circumflex (CIRC) coronary arteries throughout the entire range of flow studied. Prominent spiraling of flow occurred during steady and pulsatile flow. Spiraling of flow was not observed in the LAD at rest during pulsatile flow, but developed during simulated reactive hyperemia. Helical flows were observed in the CIRC both during simulated rest and reactive hyperemia. These observations suggest that helical flows may be characteristic features of flow in the left coronary artery; whereas turbulence may not be a feature of this flow field. Whether the spiraling of flow that we observed related to the spiral distribution of early atheroma reported by others, is undetermined.     

Hollow fiber bioreactors with internal aeration circuits

New hollow fiber bioreactors for aerobic culture were introduced and Aspergillus niger for citric acid production was cultivated as a model system. These reactors consisted of a bundle mixed of hydrophilic membranes for liquid nutrient transport and hydrophobic membranes for gaseous nutrient transport. The cells were successfully cultivated. However, the polymeric hollow fiber membranes were compressed and blocked by excessive fungal cell growth. Citric acid was produced with a high volumetric productivity compared with that of shake-flask fermentation, but the long-term operation was not successful due to a rapid decrease of the production rate.     

An experimental study of pressure losses in pulsatile flows through rigid and pulsating stenosis

The time-dependent pressure curves of a pulsatile flow across rigid and pulsating stenoses were investigated experimentally in a laboratory simulator of the outflow tract of the heart right ventricle. The experiments were performed within the range of physiological conditions of frequency and flow rate. The experimental setup consisted of a closed flow system which was operated by a pulsatile pump, and a test chamber which enabled checking different modes of stenosis. Rigid constrictions were simulated by means of axisymmetric blunt-ended annular plugs with moderate-to-severe area reductions. The pulsating stenosis consisted of a short starling resistor device operated by a pulsating external pressure which was synchronized by the pulsatile flow. It was found that the shape of the time-dependent pressure curve upstream of the stenosis was different in the case of rigid stenosis than in the pulsating one. Potential clinical applications of the work may relate to diagnosis of the type of stenosis in the congenital heart disease known as Tetralogy of Fallot.