Pulsatile Flow and Mass Transport Over an Array of Cylinders: Gas Transfer in a Cardiac-Driven Artificial Lung

Computational Pulsatile Flow and Efficiency Analysis of Biocompatible Microfluidic Artificial Lungs for Different Fiber Configurations

Average-sized microfluidic artificial lungs consisting of rows and columns of fiber bundles with different column to row aspect ratios (AR) are numerically analyzed for flow characteristics, maximum gas transfer performance, minimum pressure drop, and proper wall shear stress (WSS) values in terms of biocompatibility. The flow is fully laminar and assumed to be incompressible and Newtonian. The transport analysis is performed using a combined convection-diffusion model, and the numerical simulations are carried out with the finite element method. The inlet volumetric flow is modeled as a sinusoidal wave function to simulate the cardiac cycle and its effect on the device performance. The model is first validated with experimental studies in steady-state condition and compared with existing correlations for transient conditions. Then, the validated model is used for a parametric study in both steady and pulsatile flow conditions. The results show that increasing the aspect ratio in fiber configuration leads to converging gas transfer, higher pressure drop, and higher WSS. While determining the optimum configuration, the acceptable shear stress levels play a decisive role to ensure biocompatibility. Also, it is observed that the steady analysis underestimates the gas transfer for higher aspect ratios.

Numerical modeling of pulsatile blood flow through a mini-oxygenator in artificial lungs

While previous in vitro studies showed divergent results concerning the influence of pulsatile blood flow on oxygen advection in oxygenators, no study was done to investigate the uncertainty affected by blood flow dynamics. The aim of this study is to utilize a computational fluid dynamics model to clarify the debate concerning the influence of pulsatile blood flow on the oxygen transport. The computer model is based on a validated 2D finite volume approach that predicts oxygen transfer in pulsatile blood flow passing through a 300-micron hollow-fiber membrane bundle with a length of 254 mm, a building block for an artificial lung device. In this study, the flow parameters include the steady Reynolds number (Re = 2, 5, 10 and 20), Womersley parameter (Wo = 0.29, 0.38 and 0.53) and sinusoidal amplitude (A = 0.25, 0.5 and 0.75). Specifically, the computer model is extended to verify, for the first time, the previously measured O₂ transport that was observed to be hindered by pulsating flow in the Biolung, developed by Michigan Critical Care Consultants. A comprehensive analysis is carried out on computed profiles and fields of oxygen partial pressure (P_O2) and oxygen saturation (S_O2) as a function of Re, Wo and A. Based on the present results, we observe the positive and negative effects of pulsatile flow on P_O2 at different blood flow rates. Besides, the S_O2 variation is not much influenced by the pulsatile flow conditions investigated. While being consistent with a recent experimental study, the computed O₂ volume flow rate is found to be increased at high blood flow rates operated with low frequency and high amplitude. Furthermore, the present study qualitatively explains that divergent outcomes reported in previous in vitro experimental studies could be owing to the different blood flow rates adopted. Finally, the contour analysis reveals how the spatial distributions of P_O2 and S_O2 vary over time.

Hemodynamic Assessment of Hollow-Fiber Membrane Oxygenators Using Computational Fluid Dynamics in Heterogeneous Membrane Models

Extracorporeal membrane oxygenation (ECMO) has been used clinically for more than 40 years as a bridge to transplantation, with hollow-fiber membrane (HFM) oxygenators gaining in popularity due to their high gas transfer and low flow resistance. In spite of the technological advances in ECMO devices, the inevitable contact of the perfused blood with the polymer hollow-fiber gas-exchange membrane, and the subsequent thrombus formation, limits their clinical usage to only 2-4 weeks. In addition, the inhomogeneous flow in the device can further enhance thrombus formation and limit gas-transport efficiency. Endothelialization of the blood contacting surfaces of ECMO devices offers a potential solution to their inherent thrombogenicity. However, abnormal shear stresses and inhomogeneous blood flow might affect the function and activation status of the seeded endothelial cells (ECs). In this study, the blood flow through two HFM oxygenators, including the commercially available iLA® MiniLung Petite Novalung (Xenios AG, Germany) and an experimental one for the rat animal model, was modeled using computational fluid dynamics (CFD), with a view to assessing the magnitude and distribution of the wall shear stress (WSS) on the hollow fibers and flow fields in the oxygenators. This work demonstrated significant inhomogeneity in the flow dynamics of both oxygenators, with regions of high hollow-fiber WSS and regions of stagnant flow, implying a variable flow-induced stimulation on seeded ECs and possible EC activation and damage in a biohybrid oxygenator setting.

Formulation of Generalized Mass Transfer Correlations for Blood Oxygenator Design

This paper numerically investigates non-Newtonian blood flow with oxygen and carbon dioxide transport across and along an array of uniformly square and staggered arranged fibers at various porosity (ε) levels, focussing on a low Reynolds number regime (Re < 10). The objective is to establish suitable mass transfer correlations, expressed in the form of Sherwood number (Sh = f(ε, Re, Sc)), that identifies the link from local mass transfer investigations to full-device analyses. The development of a concentration field is initially investigated and expressions are established covering the range from a typical deoxygenated condition up to a full oxygenated condition. An important step is identified where a cut-off point in those expressions is required to avoid any under- or over-estimation on the Sherwood number. Geometrical features of a typical commercial blood oxygenator is adopted and results in general show that a balance in pressure drop, shear stress, and mass transfer is required to avoid potential blood trauma or clotting formation. Different definitions of mass transfer correlations are found for oxygen/carbon dioxide, parallel/transverse flow, and square/staggered configurations, respectively. From this set of correlations, it is found that transverse flow has better gas transfer than parallel flow which is consistent with reported literature. The mass transfer dependency on fiber configuration is observed to be pronounced at low porosity. This approach provides an initial platform when one is looking to improve the mass transfer performance in a blood oxygenator without the need to conduct any numerical simulations or experiments.

Computational study of the blood flow in three types of 3D hollow fiber membrane bundles

The goal of this study is to develop a computational fluid dynamics (CFD) modeling approach to better estimate the blood flow dynamics in the bundles of the hollow fiber membrane based medical devices (i.e., blood oxygenators, artificial lungs, and hemodialyzers). Three representative types of arrays, square, diagonal, and random with the porosity value of 0.55, were studied. In addition, a 3D array with the same porosity was studied. The flow fields between the individual fibers in these arrays at selected Reynolds numbers (Re) were simulated with CFD modeling. Hemolysis is not significant in the fiber bundles but the platelet activation may be essential. For each type of array, the average wall shear stress is linearly proportional to the Re. For the same Re but different arrays, the average wall shear stress also exhibits a linear dependency on the pressure difference across arrays, while Darcy's law prescribes a power-law relationship, therefore, underestimating the shear stress level. For the same Re, the average wall shear stress of the diagonal array is approximately 3.1, 1.8, and 2.0 times larger than that of the square, random, and 3D arrays, respectively. A coefficient C is suggested to correlate the CFD predicted data with the analytical solution, and C is 1.16, 1.51, and 2.05 for the square, random, and diagonal arrays in this paper, respectively. It is worth noting that C is strongly dependent on the array geometrical properties, whereas it is weakly dependent on the flow field. Additionally, the 3D fiber bundle simulation results show that the three-dimensional effect is not negligible. Specifically, velocity and shear stress distribution can vary significantly along the fiber axial direction.

Biplane angiography for experimental validation of computational fluid dynamic models of blood flow in artificial lungs

This article presents an investigation into the validation of velocity fields obtained from computational fluid dynamic (CFD) models of flow through the membrane oxygenators using x-ray digital subtraction angiography (DSA). Computational fluid dynamic is a useful tool in characterizing artificial lung devices, but numerical results must be experimentally validated. We used DSA to visualize flow through a membrane oxygenator at 2 L/min using 37% glycerin at 22°C. A Siemens Artis Zee system acquired biplane x-ray images at 7.5 frames per second, after infusion of an iodinated contrast agent at a rate of 33 ml/s. A maximum cross-correlation (MCC) method was used to track the contrast perfusion through the fiber bundle. For the CFD simulations, the fiber bundle was treated as a single momentum sink according to the Ergun equation. Blood was modeled as a Newtonian fluid, with constant viscosity (3.3 cP) and density (1050 kg/m3). Although CFD results and experimental pressure measurements were in general agreement, the simulated 2 L/min perfusion did not reproduce the flow behavior seen in vitro. Simulated velocities in the fiber bundle were on average 42% lower than experimental values. These results indicate that it is insufficient to use only pressure measurements for validation of the flow field because pressure-validated CFD results can still significantly miscalculate the physical velocity field. We have shown that a clinical x-ray modality, together with a MCC tracking algorithm, can provide a nondestructive technique for acquiring experimental data useful for validation of the velocity field inside membrane oxygenators.

Numerical simulations of odorant detection by biologically inspired sensor arrays

The antennules of many marine crustaceans enable them to rapidly locate sources of odorant in turbulent environmental flows and may provide biological inspiration for engineered plume sampling systems. A substantial gap in knowledge concerns how the physical interaction between a sensing device and the chemical filaments forming a turbulent plume affects odorant detection and filters the information content of the plume. We modeled biological arrays of chemosensory hairs as infinite arrays of odorant flux-detecting cylinders and simulated the fluid flow around and odorant flux into the hair-like sensors as they intercepted a single odorant filament. As array geometry and sampling kinematics were varied, we quantified distortion of the flux time series relative to the spatial shape of the original odorant filament as well as flux metrics that may be important to both organisms and engineered systems attempting to measure plume structure and/or identify chemical composition. The most important predictor of signal distortion is the ratio of sensor diameter to odorant filament width. Achieving high peak properties (e.g. sharpness) of the flux time series and maximizing the total number of odorant molecules detected appear to be mutually exclusive design goals. Sensor arrays inspired specifically by the spiny lobster Panulirus argus and mantis shrimp Gonodactylaceus falcatus introduce little signal distortion but these species' neural systems may not be able to resolve plume structure at the level of individual filaments via temporal properties of the odorant flux. Current chemical sensors are similarly constrained. Our results suggest either that the spatial distribution of flux across the aesthetasc array is utilized by P. argus and G. falcatus, or that such high spatiotemporal resolution is unnecessary for effective plume tracking.

An Investigation of Pulsatile Flow Past Two Cylinders as a Model of Blood Flow in an Artificial Lung

Pulsatile flow across two circular cylinders with different geometric arrangements is studied experimentally using the particle image velocimetry method and numerically using the finite element method. This investigation is motivated the need to optimize gas transfer and fluid mechanical impedance for a total artificial lung, in which the right heart pumps blood across a bundle of hollow microfibers. Vortex formation was found to occur at lower Reynolds numbers in pulsatile flow than in steady flow, and the vortex structure depends strongly on the geometric arrangement of the cylinders and on the Reynolds and Stokes numbers.

Pulsatile flow past an oscillating cylinder

A fundamental study to characterize the flow around an oscillating cylinder in a pulsatile flow environment is investigated. This work is motivated by a new proposed design of the total artificial lung (TAL), which is envisioned to provide better gas exchange. The Navier-Stokes computations in a moving frame of reference were performed to compute the dynamic flow field surrounding the cylinder. Cylinder oscillations and pulsatile free-stream velocity were represented by two sinusoidal waves with amplitudes A and B and frequencies ω(c) and ω, respectively. The Keulegan-Carpenter number (K(c)=U(o)∕Dω(c)) was used to describe the frequency of the oscillating cylinder while the pulsatile free-stream velocity was fixed by imposing ω∕K(c)=1 for all cases investigated. The parameters of interest and their values were amplitude (0.5D<A<D), the Keulegan-Carpenter number (0.33<K(c)<1), and the Reynolds number (5<Re<20) corresponding to operating conditions of the TAL. It was observed that an increase in amplitude and a decrease in K(c) are associated with an increase in vorticity (up to 246%) for every Re suggesting that mixing could be enhanced by the proposed TAL design. The drag coefficient was found to decrease for higher amplitudes and lower K(c) for all cases investigated. In some cases the drag coefficient values were found to be lower than the stationary cylinder values (A=0.5, K(c)=0.3, and Re=10 and 20). A lock-in phenomenon (cylinder oscillating frequency matched the vortex shedding frequency) was found when K(c)=1 for all cases. This lock-in condition was attributed to be the cause of the rise in drag observed in that operating regime. For optimal performance of the modified TAL design it is recommended to operate the device at higher fiber oscillation amplitudes and lower K(c) (avoiding the lock-in regime).

Micro-scale Modeling of Flow and Oxygen Transfer in Hollow Fiber Membrane Bundle

The aim of this work was to develop a modeling approach to solve the flow and oxygen transfer when the blood passes through the hollow-fiber membrane bundle. For this purpose, a "two-region" modeling approach was developed regarding the hollow fiber and blood regions. The oxygen transfer in these regions was defined with separate diffusion processes. Two dimensional single and multi-fiber geometries were created and flow solutions were obtained for a non-Newtonian fluid. The convection-diffusion-reaction equation was solved to produce the oxygen partial pressure distributions. As a benefit of coupling the interstitial flow field into the oxygen transfer through the hollow-fiber membrane bundle, the membrane resistance was taken into consideration. Thus, varying oxygen partial pressures were observed on the outer fiber surface, which is contrary to the common simplifying assumptions of negligible membrane resistance and uniform oxygen content on the fiber surface (Traditional approach). It was illustrated that, the current approach can be utilized to predict the mass transfer efficiencies without overestimating as compared to the predictions obtained with the traditional approach. Utilization of the current approach was found to be beneficial for the geometries with lower packing density which allows significant P(O2) variations on the fiber surfaces. For the geometries with dense packings, the above simplifying assumptions could be applicable. The model predictions were validated with the experimental measurements taken from a benchmark device.

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.

Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (α), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O2 and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0≤A≤0.75, α=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and α are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O2 feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh̿, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying α for the ranges investigated. The effect of pulsatility on Sh̿ is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.

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.