Magnetic Bead Separation from Flowing Blood in a Two-Phase

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Magnetic Bead Separation from Flowing Blood in a Two-Phase Continuous-Flow Magnetophoretic Microdevice: Theoretical Analysis through CFD Simulation Jenifer Gómez-Pastora, Ioannis H Karampelas, Xiaozheng Xue, Eugenio Bringas, Edward P. Furlani, and Inmaculada Ortiz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12835 • Publication Date (Web): 13 Mar 2017 Downloaded from http://pubs.acs.org on March 15, 2017

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The Journal of Physical Chemistry

Magnetic Bead Separation from Flowing Blood in a Two-Phase Continuous-Flow Magnetophoretic Microdevice: Theoretical Analysis through CFD Simulation

Jenifer Gómez-Pastora1, Ioannis H. Karampelas2,3, Xiaozheng Xue2, Eugenio Bringas1, Edward P. Furlani2,4 and Inmaculada Ortiz1*

1. Department of Chemical and Biomolecular Engineering, ETSIIT, University of Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain 2. Department of Chemical and Biological Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USA 3. Flow Science, Inc. Santa Fe, New Mexico, 87505, USA 4. Department of Electrical Engineering, University at Buffalo (SUNY), Buffalo, New York, 14260, USA

*

Correspondence to: Dept. Chemical and Biomolecular Engineering, ETSIIT,

University of Cantabria, Avda Los Castros s/n, 39005 Santander, Spain. E-mail: [email protected]; Phone: +34 942201585; Fax: +34 942201591

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ABSTRACT The use of magnetic particles has recently expanded for a process known as detoxification in which different toxins and microorganisms are captured from the bloodstream of septic patients. Due to the magnetic properties of the particles, once the capture of the pathogens is complete, their separation from the patient’s blood can be performed in a continuous process using an external magnetic field. In this work, we introduce a design for a two-phase continuous-flow microseparator and present an optimization study for the separation of magnetic beads using state-of-the-art computational modeling. The developed numerical method includes a combination of magnetic

and

fluidic

computational

models

that

accurately

describe

the

magnetophoretic motion of the beads. To the best of our knowledge, this is the first computational study of the interaction between two different fluids flowing simultaneously in the device (blood-water) that takes into account two-way coupled particle-fluid interactions in the flow field as well as the effects of the particle motion as they cross the interface between the fluids under various magnetic field intensities. For optimization purposes, a dimensionless number J is introduced and our results show that complete and safe separation is achieved only for a certain range of this parameter (0.20.3). Overall, the modeling effort enables understanding of the fundamental physical phenomena involved in the separation process, while offering an ideal parametric analysis and optimization platform, thereby facilitating the development of novel magnetophoretic microsystems not only for blood detoxification processes but also for many other biomedical applications that involve multiple confined liquid phases.

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1. INTRODUCTION In recent years, there has been a proliferation of applications of superparamagnetic beads in a diverse range of fields due to the outstanding properties of these materials. Specifically, novel processes have been designed in which these materials have been employed as catalytic materials,1,2 adsorbents3,4 or photocatalysts5 for environmental remediation, sensors (detection of specific compounds in fluids),6 magnetic recording and magnetic data storage devices,7 etc. Nonetheless, the majority of their applications have been in the field of biomedicine and have involved their use as magnetic carriers for the capture of different molecules (i.e. bioanalysis, medical diagnosis or therapy).8-11 Indeed, some of the most recent works have addressed the use of magnetic beads for the extracorporeal removal of toxic substances (biotoxins,12 microorganisms,13,14 toxic chemicals15 or drugs16) from blood. In fact, for a number of clinical conditions such as intoxication, bacteraemia or autoimmune diseases, the removal of the disease-causing agents from blood can be considered as the most direct conceivable treatment.17,18 Following this assumption, the scientific community has focused on the use of functionalized magnetic materials that are tailored to recognize a large variety of hazardous substances. Interest in this technology also stems from the limitations of the existing methods (hemodialysis, hemofiltration, plasmapheresis, extracorporeal imunoadsorption, direct injection of chelators and antibodies, etc.) for removing toxic compounds either for patient treatment or diagnosis.19,20 Furthermore, the sequestration of toxins from blood by functionalized magnetic particles can improve the effectiveness of the treatment while reducing its side effects.21,22 Blood detoxification using magnetic beads is an extracorporeal process wherein the patient’s blood is infused with magnetic materials. The ultimate goal of this process is the selective removal of toxins while maintaining healthy functionality of blood



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constituents. Magnetic beads with different surface chemistries are currently being tested for the selective removal of biological, chemical or radioactive toxic compounds that might be present in the bloodstream of intoxicated patients. Some of these materials have shown to have high affinity to different toxins and have enabled high removal capacities and very fast kinetics (less than 1 minute)23 in various experimental studies. Once the adsorption of the toxins onto the beads surface is completed, the magnetic separation stage takes place and the toxins are removed along with the material, leading to a toxin-free blood solution that returns to the circulatory system of the patient. Numerous microfluidic magnetic separator designs have been proposed in the last years for carrying out the recovery of magnetic beads from different biological fluids, including blood.17,24,25 These are usually batch separators where the particles are separated due to a magnet located next to a channel. This magnet generates local field gradients that trap the beads on the walls of the channel in proximity to the magnet, which results in a particle-clean solution at the outlet. After the blood to be treated passes through the channel, the permanent magnet is removed and the particles are retrieved from the walls. However, in several recent studies continuous separators have been introduced, where the particles are deflected from the blood stream and collected into a flowing buffer solution by a magnetic gradient applied perpendicular to the flow direction.23,26,27 The concept of continuous separators is illustrated in Figure 1. The use of continuous microfluidic systems poses several advantages compared to batch magnetic separators. First, the accumulation of beads on the walls is minimized because the beads are continuously removed along with the buffer suspension. Thus, the flow is not restricted and the efficiency and capacity of the separator do not change with time.28 This issue becomes particularly important when large volumes of blood have to be treated. Batch separators may also enable the non-specific entrapment of blood


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components in the capturing regions, which degrades the quality of the treated solution. The effect might even be deleterious in certain cases of excessive blood cell entrapment. This adverse effect can be avoided by the use of continuous separators. An additional advantage of continuous separators is that the nature of the process itself enables a high level of the integration with established processes such as the adsorption of toxins, leading to a continuous detoxification process.26 This not only increases separation efficacy and throughput, but also allows the integration of both stages into a continuous treatment process.

Figure 1. Schematic diagram of the continuous-flow magnetic separation.

The application of continuous magnetic separators in this process must meet two fundamental requirements: i) the complete recovery of the magnetic beads from the blood solution and, ii) the elimination or minimization of intermixing between the blood and buffer streams inside the device. As far as the first requirement is concerned, all the magnetic beads have to be recovered post-treatment, since there exists an underlying uncertainty concerning their biotoxicity. Although some materials have been approved



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by the US Federal Drug Administration,19 an extracorporeal process that enables the full recovery of all the particles before returning the treated blood to the patient is preferred at this stage of development. In this regard, previous research has shown that magnetic beads can be easily manipulated with simple permanent magnets, reaching bead recoveries in excess of 99% in both batch and continuous separators.25,26,29 The ability to recover beads with permanent magnets is, perhaps, the most attractive characteristic of this technology since they are powerful, small and low-cost sources, facilitating the design of portable devices for low infrastructure settings, without requiring any power or electricity compared to microelectromagnetic devices. Also, the use of electrical currents for the generation of magnetic fields is not suitable for bioapplications due to the generation of Joule heating, and substantial effort may be required for their design and fabrication due to complex circuitry.28 Hence, the use of rare-earth permanent magnets is considered the best alternative due to their easy setup and because they provide the field and gradients required for the separation in an economical and immediate manner. As far as the second requirement is concerned, the colaminar streams should flow independently along the length of the channel and be separated at their respective outlets, avoiding possible loss or dissolution. This type of fluid behavior may be particularly difficult to achieve, especially when both the feed suspension (blood) and the buffer solution have different flow characteristics i.e. flow rates or fluid properties. It should be noted that blood is a complex fluid composed by a suspension of red and white cells (erythrocytes and leukocytes) and platelets in plasma, with variable rheological properties depending on the patient and the flow conditions,30 which increases the complexity of the bioseparator design. Also, the possible diffusion of


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blood components between phases should be studied and minimized due to the detrimental effect that it may have by altering the blood composition. While the requirement i), of complete particle recovery from blood solutions, has been the subject of study in previous works,25,30 the requirement ii), of the complete separation of phases inside the two-phase separators, has received minimal attention and no numerical analyses of the process have been reported so far. Furthermore, relatively few experimental results addressing this issue are available.23,26,27 Hence, magnetic bioseparator design parameters such as the flow conditions of both phases and the flow perturbation due to particle-fluid interactions, which might affect the composition of the two streams or their separation at the outlets, are issues that remain unresolved and have never been described before, to the best of our knowledge. Advancing this novel technology to the next stage requires the reliable removal of the magnetic beads by appropriately studied magnetic fields and the independent flow of both solutions without any intermixing inside the device. The aim of the current article is to provide an in-depth analysis of the design details of liquid-liquid two-phase magnetic bioseparators and apply these new principles in the recovery of magnetic beads from flowing blood. In order to achieve this goal, we introduce a combination of magnetic and fluidic computational models that describe the bead trajectory inside a symmetric microchannel under the influence of an external permanent magnet along with the potential mixing or modification between fluid streams. These models provide a rational design guide in this field of research since they can be used to predict the separation performance by taking into account key operational variables and impact parameters, such as the bead and fluid properties, the characteristics of the magnet and the selected flow rates. This approach is well-suited for parametric analysis and optimization, thereby facilitating the development of novel



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microfluidic systems not only for blood detoxification processes but also for many other biomedical applications that involve two or more confined liquid phases. Finally, it should be noted that although similar scientific research exists in the literature using a similar solution methodology,31,32 a key distinguishing feature of our current work is the detailed study of the interaction between two fluids flowing simultaneously in the device while taking into account the effects of particle-fluid interactions. Based on our analysis, it is possible to predict the change in the flow patterns due to the magnetophoretic motion of beads as they cross the interface between fluid phases.

2. THEORY 2.1. Approach In this section, the model for predicting the magnetophoretic particle transport inside a bioseparator, such as the one shown in Figure 1, is derived. The computational model takes into account the dominant forces acting on the beads i.e. the magnetic and fluidic forces along with two-way momentum transfer between the particles and the flow field. A numerical Computational Fluid Dynamics (CFD) analysis is used to predict the beadfluid transport, whereas an analytical approach is employed for the prediction of both the magnetic field generated by a rectangular magnet and the corresponding magnetic force on the particles. Thus, the model involves a CFD-based Eulerian-Lagrangian approach. The Lagrangian framework is used to model the bead dynamics while the fluid transport, which is predicted by solving the Navier-Stokes equations, is calculated with an Eulerian approach. It should be noted that the magnetic separation of beads is a complex process that involves multiple competing forces acting on the particles in the presence of an external magnetic field (i.e. magnetic force, viscous drag, gravity and buoyancy, inertia, particle-


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fluid interactions, thermal kinetics and interparticle effects, including magnetic dipole interactions, Helmholtz double-layer interactions and Van der Waals forces).28,33 Although some of these contributions might influence the separation process, the development of a rigorous mathematical model that considers all these effects is complex and unnecessary for the purpose of this work. Hence, the model developed here only takes into account the dominant magnetic and drag forces, and also the particle-fluid interactions that are important to analyze the flow perturbation (which might alter the composition of the biofluid at the separator outlets). Other forces different than these ones were neglected since their impact on the separation can be considered of second order in effect. Therefore, according to the Lagrangian approach, particles are modeled as discrete units and the trajectory of each is estimated by applying the classical Newtonian dynamics:28

m

= ∑

(1)

where mp and vp are the mass and velocity of the particle and Fext represents all external force vectors exerted on the particle. In order to solve equation (1), the magnetic and fluidic forces that drive the particle motion must first be developed.

2.2. Magnetic force The magnetic force Fm acting on a particle is obtained using the “effective” dipole moment method in which the magnetized particle is replaced by an “equivalent” point dipole with a moment , .28,34,35 The acting on the dipole can be calculated from:

= μ , · ∇

(2)



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where μ represents the permeability of the free space and is the applied magnetic

field intensity at the center of the particle. The moment , can be determined using a

magnetization model that takes into account self-demagnetization and magnetic saturation of the particles:28,33

, = V fH

(3) where the function f(Ha) is calculated as follows:

fH = (4)

!" #$

" #$ %!

$ |H | < ) ! # *M,, " $

" # %!

" #$ %! .," |H | ≥ ) ! # * M,, |/ | " $ 0

where Vp is the volume of a spherical particle of radius rp, χ and χ are the susceptibilities of the particle and the fluid respectively, and Ms,p represents the saturation magnetization of the particles.

Thus, the expression for takes into account the conditions both below and above the saturation of the particle as a function of the external applied field and can be written as:

= μ V fH · ∇ (5)

As it is derived from the previous equations, the beads motion depends on their properties and the magnetic characteristics of the surrounding fluid. For this work, we assume that the susceptibility of the fluid phases is essentially that of free space, although it is important to note that the susceptibility of the suspension medium can have a significant effect on Fm.30 Also, the magnetophoretic motion of a particle depends on its properties, e.g. its composition and size. Particles used in biological and biomedical studies are usually made by incorporating iron oxide nanoparticles within 9 ACS Paragon Plus Environment

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porous monosized polymer beads.36 In this work, particles with sizes of 5 µm, density of 2000 kg·m-3 and saturation magnetization values of 105 A·m-1 were chosen. These values commonly fall into the range of properties of beads employed in relevant studies.37 The following magnetization model developed for submicron size Fe3O4

particles30,38 was adopted (that is consistent with Eq. (4) when χ >>1):

3, |H |
1) result in bead trapping at the walls, and although all of them are separated from the blood solution, the high perturbation of



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the fluids generated due to their acceleration to the high field zone makes such operating conditions very unfavorable for the treatment purposes of this device. Therefore, lower magnetic forces are required in order to ensure the phase separation in a continuous operation mode. Although lower magnetic fields (0.001 ≤ J ≤ 0.15) result in a negligible fluid perturbation, these conditions may not be conducive to successful particle removal, as seen in Table 1. As a result, medium magnetic forces (in the order of 300 pN) are required for the complete particle separation while maintaining the biofluid integrity at the outlet and the interface stability. The best case scenario from all the possibilities appears to be achieved for J numbers of approximately 0.2, as seen in Table 1. In this case the particles would be slowly deflected towards the water phase due to the weak intensity of the fields, and thus, they would leave the device without colliding or getting trapped at the walls, which may perturbate the interface height and hinder the fluid separation at outlets. Finally, it should be noted that the range of J numbers required for a complete and safe separation avoiding intermixing of liquid streams (0.2-0.3) might be only valid for channels with similar characteristics to the device employed in this work. Thus, by using different channel geometries or similar devices with different magnetic sources (i.e. different field and gradients distributions inside the device), different separation performance might be obtained with these range of values. However, the channel design employed in this work is simple and similar to the ones employed for this type of applications,28 thus ensuring its applicability for other related future studies. Nonetheless, the mathematical procedure developed here could be implemented in different geometries or magnetic sources in order to obtain the range of values that predict the best performance in different devices.


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Also, in a practical application of this device, higher flowrates would be required. However, this could be easily achieved by employing multiple devices in parallel arrangement, rather than increasing the dimensions of the system, which would increase the magnetic field required for a complete particle recovery (when keeping constant the fluid velocities). Furthermore, microfluidic devices can be manufactured with the use of inexpensive materials and relatively simple manufacturing process. Therefore, the use of multiple microchannels in a parallel configuration would greatly increase the capacity of the process with a negligible increase in capital costs due to the low manufacturing cost.

Table 1. Analysis of particle recovery and fluid perturbation as a function of the magnetic conditions applied inside the device.

Magnet separation distance “d” (mm) 0

Fm,z (nN)

J value

Particle separation

Fluid perturbation

6.71

4.07

Complete

High

1

0.589

0.357

Complete

Medium

1.15

0.356

0.216

Complete

Low

1.25

0.236

0.143

Incomplete

Low

1.5

0.1

0.06

Incomplete

None

2

2.34·10-2

0.014

No separation

None

3

2.35·10-3

0.0014

No separation

None

4. CONCLUSIONS In this work, we have introduced a novel computational model for predicting and optimizing the process of magnetic bead separation from blood in a multiphase 33 ACS Paragon Plus Environment


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continuous-flow microdevice. This model takes into account the dominant forces acting on the particles and can be used to study critical details of the separation process, including the trajectories of individual particles, the time required for the separation and the perturbation of the blood/buffer co-flows (i.e. instability of the blood/buffer interface). A small, low-cost permanent magnet can be used to generate suitable magnetic fields and forces inside the device to implement viable particle separation, which represents a key

advantage

of

this

technology

compared

to,

for

example,

active

microelectromagnetic devices. By varying the position of the magnet, we demonstrate that variable magnetic field gradients are generated, and thus, different separation efficacies are obtained. It is readily observed that high magnetic forces are undesirable for multiphase continuous separators due to the extreme acceleration of the particles which leads to perturbations of the flow patterns and to the disruption of the fluid interface. However, medium magnetic forces appear to be ideal for this kind of processes, because the complete bead separation can be achieved while maintaining the biofluid integrity and interface stability. Thus, we have shown for the first time that by precisely modelling the two-way coupling between the moving particles and the fluids, fluid separation at the outlets can be optimized. Furthermore, the modeling approach described herein is very general and can be applied broadly to various bioseparation processes, promoting fundamental understanding of the underlying mechanisms thus proving useful in the development and rational design of novel applications. Nevertheless, experimental analyses regarding the separation of the fluid phases and the flow perturbation during the particle magnetophoresis are limited as was remarked above, which hinders validation of the


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simulations. Therefore, more experimental works are required in order to validate our theoretical analysis, which will be the focus of our future work.

ACKNOWLEDGEMENTS Financial support from the Spanish Ministry of Economy and Competitiveness under the project and CTQ2015-66078-R (MINECO/FEDER) is gratefully acknowledged. Jenifer Gómez-Pastora also thanks the FPI postgraduate research grant (BES-2013064415). Edward P. Furlani gratefully acknowledges financial support from the U.S. National Science Foundation, through Award CBET-1337860.

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Magnetic Bead Separation from Flowing Blood in a Two-Phase

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