Flow and Oxygen Transfer Characteristics of an Intravenous Membrane Oxygenator: A Computational Study

Spectral element computational simulations of the conservation of mass, momentum and species equations are performed to investigate the flow and oxygen transfer characteristics of an Intravenous Membrane Oxygenator (IMO). The simulations consider a three-dimensional IMO computational model consisting of equally-spaced fibers, an elastic balloon with non-permeable walls positioned longitudinally within the vena cava, and a Newtonian and time-dependent incompressible flow. Flow characteristics and oxygen transfer parameters are determined for operating conditions of a stationary and a pulsating balloon. For the stationary balloon configuration the flow is two-dimensional, parallel, laminar and without secondary flows for the Reynolds number range of 5.7-455.2. Evaluations of the oxygen transfer characteristics for the stationary balloon indicate that the main transport mechanisms are diffusion and convection in the crosswise and streamwise directions, respectively. Additionally, evaluations of oxygen transfer rates and Sherwood numbers in this Reynolds number range indicate that the oxygen transfer rate reaches an asymptotic limit at relatively moderate Reynolds numbers. For the pulsating balloon, flow characteristic results demonstrate the existence of a strong secondary flow around the fiber, and between the balloon and the fiber. This secondary flow induces oscillatory crosswise and streamwise velocities and a seemingly random spanwise flow which enhances the flow mixing as well as the transport of oxygen from the fiber surface to the bulk flow.     

Flow and Oxygen Transfer Characteristics of an Intravenous Membrane Oxygenator: A Computational Study

Abstract

Spectral element computational simulations of the conservation of mass, momentum and species equations are performed to investigate the flow and oxygen transfer characteristics of an Intravenous Membrane Oxygenator (IMO). The simulations consider a three-dimensional IMO computational model consisting of equally-spaced fibers, an elastic balloon with non-permeable walls positioned longitudinally within the vena cava, and a Newtonian and time-dependent incompressible flow. Flow characteristics and oxygen transfer parameters are determined for operating conditions of a stationary and a pulsating balloon. For the stationary balloon configuration the flow is two-dimensional, parallel, laminar and without secondary flows for the Reynolds number range of 5.7-455.2. Evaluations of the oxygen transfer characteristics for the stationary balloon indicate that the main transport mechanisms are diffusion and convection in the crosswise and streamwise directions, respectively. Additionally, evaluations of oxygen transfer rates and Sherwood numbers in this Reynolds number range indicate that the oxygen transfer rate reaches an asymptotic limit at relatively moderate Reynolds numbers. For the pulsating balloon, flow characteristic results demonstrate the existence of a strong secondary flow around the fiber, and between the balloon and the fiber. This secondary flow induces oscillatory crosswise and streamwise velocities and a seemingly random spanwise flow which enhances the flow mixing as well as the transport of oxygen from the fiber surface to the bulk flow.     

Methodology for predicting oxygen transport on an intravenous membrane oxygenator combining computational and analytical models

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.     

Oscillatory flow and gas transport through a symmetrical bifurcation

Axial gas transport due to the interaction between radial mixing and radially nonuniform axial velocities is responsible for gas transport in thick airways during High-frequency oscillatory ventilation (HFO). Because the airways can be characterized by a bifurcating tube network, the secondary flow in the curved portion of a bifurcating tube contributes to cross-stream mixing. In this study the oscillatory flow and concentration fields through a single symmetrical airway bifurcating tube model were numerically analyzed by solving three-dimensional Navier-Stokes and mass concentration equations with the SIMPLER algorithm. The simulation conditions were for a Womersley number, alpha = 9.1 and Reynolds numbers in the parent tube between 200 and 1000, corresponding to Dn2/alpha 4 in the curved portion between 2 and 80, where Dn is Dean number. For comparison with the results from the bifurcating tube, we calculated the velocity and concentration fields for fully developed oscillatory flow through a curved tube with a curvature rate of 1/10, which is identical to the curved portion of the bifurcating tube. For Dn2/alpha 4 < or = 10 in the curved portion of the bifurcating tube, the flow divider and area changes dominate the axial gas transport, because the effective diffusivity is greater than in either a straight or curved tube, in spite of low secondary velocities. However, for Dn2/alpha 4 > or = 20, the gas transport characteristics in a bifurcation are similar to a curved tube because of the significant effect of secondary flow.     

Investigation of fluid flow patterns in a hollow fiber module using magnetic resonance velocity imaging

Summary Magnetic Resonance Imaging (MRI) was used to obtain new information about fluid flow patterns in hollow fiber reactors. Significant changes in inlet flow distribution were observed as a function of Reynolds number. Images taken at the tube bundle entrance and exit showed that maldistribution of flow persists throughout the module. Furthermore, the results suggest that individual fibers act in a mixed degree as feeders or collectors depending upon radial position. These effects must be considered when modelling or designing hollow fiber reactors.     

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.     

Distribution of mass transfer rate and wall shear stress behind simple rectangular stenosis in pulsating flow

The distributions of mass transfer rate and wall shear stress in sinusoidal laminar pulsating flow through a two-dimensional asymmetric stenosed channel have been studied experimentally and numerically. The distributions are measured by the electrochemical method. The measurement is conducted at a Reynolds number of about 150, a Schmidt number of about 1000, a nondimensional pulsating frequency of 3.40, and a nondimensional flow amplitude of 0.3. It is suggested that the deterioration of an arterial wall distal to stenosis may be greatly enhanced by fluid dynamic effects.     

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.     

Oscillatory flow in a cone-and-plate bioreactor

Motivated by biometric applications, we analyze oscillatory flow in a cone-and-plate geometry. The cone is rotated in a simple harmonic way on a stationary plate. Based on assuming that the angle between the cone and plate is small, we describe the flow analytically by a perturbation method in terms of two small parameters, the Womersley number and the Reynolds number, which account for the influences of the local acceleration and centripetal force, respectively. Working equations for the shear stresses induced both by laminar primary and secondary flows on the plate surface are presented.     

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.     

Improved performance in viscous mycelial fermentations by agitator retrofitting

For viscous mycelial fermentations it was demonstrated at the pilot-plant scale that the replacement of standard radial flow Rushton turbines with larger diameter axial-flow Prochem hydrofoil impellers significantly improved oxygen transfer efficiency. It was also determined that the Streptomyces broth under evaluation is highly shear thinning. Separate experiments using a Norcardia broth with similar Theological properties demonstrated that the oxygen transfer coefficient, K(L)a, can be greatly increased by use of water additions to reduce broth viscosity. These observations are consistent with the hypothesis that the improvement in oxygen transfer by changing agitator types is primarily due to an improvement in bulk mixing. A model is presented, based on the concepts of Bajpai and Reuss, which explains this improvement in performance in terms of enlargement of the well mixed micromixer region for viscous mycelial broths.     

Mass transfer to fluids flowing through rotating nonaligned straight tubes

Relatively inefficient heat/mass transfer is characteristic of tubular devices if the Reynolds number is low. One method of improving the heat/mass transfer efficiency of such devices is by inducing transverse laminar secondary circulations that are superimposed on the primary flow field; the resulting transverse velocity components lead to fluid mixing and hence augmented mass transfer in the tube lumen. The present work is a theoretical and experimental investigation of the enhanced transport in rotating, nonaligned, straight tubes, a method of transport enhancement that utilizes Coriolis acceleration to create transverse fluid mixing. This technique couples the transport advantages of coiled tubes with the design advantages of straight tubes. The overall mass balance equation is numerically solved for transfer into fluids flowing steadily through rotating nonaligned straight tubes. This solution, for small Coriolis disturbances, incorporates a third order perturbation solution for the primary and secondary flow fields. For sufficiently small Coriolis disturbances the bulk concentration increase is found to be uniquely determined by the value of a single similarity parameter. As the Coriolis disturbance is increased, however, two additional parameters are required to accurately characterize the mass transfer. In general, increasing the Coriolis accelerations results in an increase in mass transfer. There are solution regimens, however, in which increasing this acceleration can lead to a decrease in mass transfer efficiency. This interesting phenomena, which has important design implications, appears to result from velocity-weighting effects on the exiting sample. Experiments, involving the measurement of oxygen transferred into water and blood, produced data that agree with the theoretical predictions.     

Turbulent flow of red cells in dilute suspensions. Effect on kinetics of O2 uptake.

The turbulent flow properties of dilute (0.06% by volume) suspensions of human red blood cells in 4-mm-bore glass tubing were estimated by laser anemometry. The flow properties of the dilute red cell suspension were similar to those of a dilute suspension of polystyrene spheres (0.5 micron diameter) in isotonic NaCl solution. Flow was found to be laminar when the Reynolds number was below 2,000, transitional in the range of Reynolds numbers from 2,000 to 3,000, and fully turbulent above Reynolds number 3,000. These results differ from previous studies of more concentrated red cell suspensions. The length scales of the turbulence were also estimated: at a Reynolds number near 4,000 the macroscale is about 1.25 mm, the Taylor microscale is about 0.85 mm, and the Kolmogoroff scale is near 0.075 mm. The results are discussed in relation to previous measurements of the rate of oxygen uptake by dilute red cell suspensions in the flow-type rapid reaction apparatus. Our results suggest that under the conditions of most of these oxygen uptake measurements, the turbulent flow is characterized by eddies about 1 mm across, mixing with each other on a time scale of about 45 ms. Since most of the reported oxygen uptake measurements involve a similar time scale, it is possible that an effective "unstirred layer" influenced the reported rate of oxygen uptake.     

Numerical simulations of the pulsating flow of cerebrospinal fluid flow in the cervical spinal canal of a Chiari patient

The flow of cerebrospinal fluid (CSF) in a patient-specific model of the subarachnoid space in a Chiari I patient was investigated using numerical simulations. The pulsating CSF flow was modeled using a time-varying velocity pulse based on peak velocity measurements (diastole and systole) derived from a selection of patients with Chiari I malformation. The present study introduces the general definition of the Reynolds number to provide a measure of CSF flow instability to give an estimate of the possibility of turbulence occurring in CSF flow. This was motivated by the fact that the combination of pulsating flow and the geometric complexity of the spinal canal may result in local Reynolds numbers that are significantly higher than the commonly used global measure such that flow instabilities may develop into turbulent flow in these regions. The local Reynolds number was used in combination with derived statistics to characterize the flow. The results revealed the existence of both local unstable regions and local regions with velocity fluctuations similar in magnitude to what is observed in fully turbulent flows. The results also indicated that the fluctuations were not self-sustained turbulence, but rather flow instabilities that may develop into turbulence. The case considered was therefore believed to represent a CSF flow close to transition.     

Protein refolding in an oscillatory flow reactor

We demonstrate that an oscillatory flow reactor is a viable reactor for protein refolding via direct dilution. The mixing characteristics of the oscillatory flow reactor are well described and controllable and, importantly, can be scaled-up to process scale without a loss of mixing efficiency. This makes the oscillatory flow reactor an attractive alternative to conventional stirred-tank reactors for process-scale renaturation.     

Augmentation of axial dispersion by intermittent oscillatory flow.

The efficiency of axial gas dispersion during ventilation with high-frequency oscillation (HFO) is improved by manipulating the oscillatory flow waveform such that intermittent oscillatory flow occurs. We therefore measured the velocity profiles and effective axial gas diffusivity during intermittent oscillatory flow in a straight tube to verify the intermittency augmentation effect on axial gas transfer. The effective diffusivity was dependent on the flow patterns and significantly increased with an increase in the duration of the stationary phase. It was also found that the ratio of effective diffusivity to molecular diffusivity is two times greater than that in sinusoidal oscillatory flow. Moreover, turbulence during deceleration or at the beginning of the stationary phase further augments axial dispersion, with the effective diffusivity being over three times as large, thereby proving that the use of intermittent oscillatory flow effectively augments axial dispersion for ventilation with HFO.     

A biohybrid artificial lung prototype with active mixing of endothelialized microporous hollow fibers

Acute respiratory distress syndrome (ARDS) affects nearly 150,000 patients per year in the US, and is associated with high mortality (≈40%) and suboptimal options for patient care. Mechanical ventilation and extracorporeal membrane oxygenation are limited to short‐term use due to ventilator‐induced lung injury and poor biocompatibility, respectively. In this report, we describe the development of a biohybrid lung prototype, employing a rotating endothelialized microporous hollow fiber (MHF) bundle to improve blood biocompatibility while MHF mixing could contribute to gas transfer efficiency. MHFs were surface modified with radio frequency glow discharge (RFGD) and protein adsorption to promote endothelial cell (EC) attachment and growth. The MHF bundles were placed in the biohybrid lung prototype and rotated up to 1,500 revolutions per minute (rpm) using speed ramping protocols to condition ECs to remain adherent on the fibers. Oxygen transfer, thrombotic deposition, and EC p‐selectin expression were evaluated as indicators of biohybrid lung functionality and biocompatibility. A fixed aliquot of blood in contact with MHF bundles rotated at either 250 or 750 rpm reached saturating pO₂ levels more quickly with increased rpm, supporting the concept that fiber rotation would positively contribute to oxygen transfer. The presence of ECs had no effect on the rate of oxygen transfer at lower fiber rpm, but did provide some resistance with increased rpm when the overall rate of mass transfer was higher due to active mixing. RFGD followed by fibronectin adsorption on MHFs facilitated near confluent EC coverage with minimal p‐selectin expression under both normoxic and hyperoxic conditions. Indeed, even subconfluent EC coverage on MHFs significantly reduced thrombotic deposition adding further support that endothelialization enhances, blood biocompatibility. Overall these findings demonstrate a proof‐of‐concept that a rotating endothelialized MHF bundle enhances gas transfer and biocompatibility, potentially producing safer, more efficient artificial lungs. Biotechnol. Bioeng. 2010; 106: 490–500. © 2010 Wiley Periodicals, Inc.     

Secondary velocity fields in the conducting airways of the human lung

An understanding of flow and dispersion in the human respiratory airways is necessary to assess the toxicological impact of inhaled particulate matter as well as to optimize the design of inhalable pharmaceutical aerosols and their delivery systems. Secondary flows affect dispersion in the lung by mixing solute in the lumen cross section. The goal of this study is to measure and interpret these secondary velocity fields using in vitro lung models. Particle image velocimetry experiments were conducted in a three-generational, anatomically accurate model of the conducting region of the lung. Inspiration and expiration flows were examined under steady and oscillatory flow conditions. Results illustrate secondary flow fields as a function of flow direction, Reynolds number, axial location with respect to the bifurcation junction, generation, branch, phase in the oscillatory cycle, and Womersley number. Critical Dean number for the formation of secondary vortices in the airways, as well as the strength and development length of secondary flow, is characterized. The normalized secondary velocity magnitude was similar on inspiration and expiration and did not vary appreciably with generation or branch. Oscillatory flow fields were not significantly different from corresponding steady flow fields up to a Womersley number of 1 and no instabilities related to shear were detected on flow reversal. These observations were qualitatively interpreted with respect to the simple streaming, augmented dispersion, and steady streaming convective dispersion mechanisms.     

Mathematical Model of a Countercurrent Flow Multi-fibre Dialyser

Summary The closed form solution to a distributed parameter mathematical model of a countercurrent flow dialyser is presented. The model consisting of a bundle of hollow fibres in a shell accounts for axial convection and radial diffusion. The proposed model relates the fractional removal of a solute to mass transfer parameters such as Sherwood number, length Peclet number and system geometry. Excellent agreement with experimental beer dialysis data is demonstrated for the removal of alcohol using 8-lm thick 200-lm diameter cuprophane hollow-fibre membrane fibres. Potentially, this model could be very helpful in designing new processes involving dialysis. For example, removal efficiency better than 90% is achievable in systems operating with a Sherwood number of 2.0, length Peclet number of 5 · 105, unit tube-side/shell-side volumetric flow and length-to-diameter ratio of 5000. Results were obtained in this work from only the first eigenvalue and the case of no solute in the incoming dialysate stream.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.