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Particles of two different densities can be continuously and rapidly separated by employing sink-float phenomenon in split-flow thin (SPLITT) cells using both centrifugal and gravitational fields. Separation of a binary mixture of submicron size latex beads differing in densities is achieved by feeding them as a suspension in a carrier liquid of intermediate density into a SPLITT cell subject to a centrifugal field. A steady state condition is rapidly achieved, and two particle types accumulate at opposing channel walls as they are carried by the laminar channel flow to two separate outlets. Similarly, micron size particles of two different densities are separated using a planar channel and the gravitational field. Equations are developed to predict throughput in terms of the number fractions of the separated particles determined by scanning electron microscopy. Experimental results from three SPLITT cell systems under different field and flow conditions are compared with theoretical predictions.

Emerging microfluidic-based cell assays favor label-free red blood cell (RBC) depletion. Magnetic separation of RBC is possible because of the paramagnetism of deoxygenated hemoglobin but the process is slow for open-gradient field configurations. In order to increase the throughput, periodic arrangements of the unit magnets were considered, consisting of commercially available Nd-Fe-B permanent magnets and soft steel flux return pieces. The magnet design is uniquely suitable for multiplexing by magnet tessellation, here meaning the tiling of the magnet assembly cross-sectional plane by periodic repetition of the magnet and the flow channel shapes. The periodic pattern of magnet magnetizations allows a reduction of the magnetic material per channel with minimal distortion of the field cylindrical symmetry inside the magnet apertures. A number of such magnet patterns are investigated for separator performance, size and economy with the goal of designing an open-gradient magnetic separator capable of reducing the RBC number concentration a hundred-fold in 1 mL whole blood per hour.

The enumeration of circulating tumor cells (CTCs) in the peripheral bloodstream of metastatic cancer patients has contributed to improvements in prognosis and therapeutics. There have been numerous approaches to capture and counting of CTCs. However, CTCs have potential information beyond simple enumeration and hold promise as a liquid biopsy for cancer and a pathway for personalized cancer therapy by detecting the subset of CTCs having the highest metastatic potential. There is evidence that epithelial cell adhesion molecule (EpCAM) expression level distinguishes these highly metastatic CTCs. The few previous approaches to selective CTC capture according to EpCAM expression level are reviewed. A new two-stage microfluidic device for separation, enrichment and release of CTCs into subpopulations sorted by EpCAM expression level is presented here. It relies upon immunospecific magnetic nanoparticle labeling of CTCs followed by their field- and flow-based separation in the first stage and capture as discrete subpopulations in the second stage. To fine tune the separation, the magnetic field profile across the first stage microfluidic channel may be modified by bonding small Vanadium Permendur strips to its outer walls. Mathematical modeling of magnetic fields and fluid flows supports the soundness of the design.

Asymmetrical flow field-flow fractionation (As-FlFFF) has become the most commonly used of the field-flow fractionation techniques. However, because of the interdependence of the channel flow and the cross flow through the accumulation wall, it is the most difficult of the techniques to optimize, particularly for programmed cross flow operation. For the analysis of polydisperse samples, the optimization should ideally be guided by the predicted fractionating power. Many experimentalists, however, neglect fractionating power and rely on light scattering detection simply to confirm apparent selectivity across the breadth of the eluted peak. The size information returned by the light scattering software is assumed to dispense with any reliance on theory to predict retention, and any departure of theoretical predictions from experimental observations is therefore considered of no importance. Separation depends on efficiency as well as selectivity, however, and efficiency can be a strong function of retention. The fractionation of a polydisperse sample by field-flow fractionation never provides a perfectly separated series of monodisperse fractions at the channel outlet. The outlet stream has some residual polydispersity, and it will be shown in this manuscript that the residual polydispersity is inversely related to the fractionating power. Due to the strong dependence of light scattering intensity and its angular distribution on the size of the scattering species, the outlet polydispersity must be minimized if reliable size data are to be obtained from the light scattering detector signal. It is shown that light scattering detection should be used with careful control of fractionating power to obtain optimized analysis of polydisperse samples. Part I is concerned with isocratic operation of As-FlFFF, and part II with programmed operation.

Connective tissue progenitors (CTPs) are a promising therapeutic agent for bone repair. Hyaluronan, a high molecular mass glycosaminoglycan, has been shown by us to be a suitable biomarker for magnetic separation of CTPs from bone marrow aspirates in a canine model. For the therapy to be applicable in humans, the magnetic separation process requires scale-up without compromising the viability of the cells. The scaled-up device presented here utilizes a circular Halbach array of diametrically-magnetized, cylindrical permanent magnets. This allows precise control of the magnetic field gradient driving the separation, with theoretical analysis favoring a hexapole field. The separation vessel has the external diameter of a 50 mL conical centrifuge tube, and has an internal rod that excludes cells from around the central axis. The magnet and separation vessel (collectively dubbed the hexapole magnet separator, or HMS) was tested on four human and four canine bone marrow aspirates. Each CTP-enriched cell product was tested using cell culture bioassays as surrogates for in vivo engraftment quality. The magnetically enriched cell fractions showed statistically significant, superior performance compared to the un-enriched and depleted cell fractions for all parameters tested, including CTP prevalence (CTPs per 106 nucleated cells), proliferation by colony forming unit (CFU) counts, and differentiation by staining for the presence of osteogenic and chondrogenic cells. The simplicity and speed of the HMS operation could allow both CTP isolation and engraftment during a single surgical procedure, minimizing trauma to patients and lowering cost to health care providers.

A theoretical and experimental study of continuous two-dimensional thermal field-flow fractionation (2D-ThFFF) is presented. Separation takes place in radial flow between two closely spaced discs, one of which is heated and the other cooled in order to maintain a temperature gradient across the channel. The cooled disc, which serves as the accumulation wall, is rotated relative to the other to create a shear component to the fluid flow. Under the influence of the thermal gradient and flow components, the sample components spiral outwards along different paths to the outer rim of the channel to be collected. The general principle of operation is described and an approximate theoretical model formulated for predicting the outlet position for the path of each sample component. The influence of the principal operational parameters, such as radial and angular flow rates and thermal gradient, on the deflection angle of the sample trajectory is investigated. Fractionation is demonstrated for polystyrene polymer standards in a binary solvent consisting of cyclohexane and ethylbenzene. Experimental results are compared with theoretical predictions.

The Quadrupole Magnetic Sorter (QMS), employing an annular flow channel concentric with the aperture of a quadrupole magnet, is well established for cell and particle separations. Here we propose a magnetic particle separator comprising a linear array of cylindrical magnets, analogous to the array proposed by Klaus Halbach, mated to a substantially improved form of a parallel plate SPLITT channel, known as the step-SPLITT channel. While the magnetic force and throughput are generally lower than for the QMS, the new separator has advantages in ease of fabrication and the ability to vary the magnetic force to suit the separands. Preliminary experiments yield results consistent with prediction and show promise regarding future separations of cells of biomedical interest.

Gravitational field-flow fractionation (GrFFF) is a useful technique for fast separation of micrometer-sized particles. Different sized particles are carried at different velocities by a flow of fluid along an unobstructed thin channel, resulting in a size-based separation. They are confined to thin focused layers in the channel thickness where force due to gravity is exactly opposed by hydrodynamic lift forces (HLF). It has been reported that the HLF are a function of various parameters including the flow rate (or shear rate), the size of the particles, and the density and viscosity of the liquid. The dependence of HLF on these parameters offers a means of altering the equilibrium transverse positions of the particles in GrFFF, and hence their elution times. In this study, the effect of the viscosity of the carrier fluid on the elution behavior (retention, zone broadening, and resolution) of micrometer-sized particles in GrFFF was investigated using polystyrene (PS) latex beads as model particles. In order to change the carrier liquid viscosity without affecting its density, various amounts of (hydroxypropyl) methyl cellulose (HPMC) were added to the aqueous carrier liquid. It was found that particles migrate at faster rates as the carrier viscosity is increased, which confirms the dependence of HLF on viscosity. At the same time, particle size selectivity decreased but peak shape and symmetry for the more strongly retained particles improved. As a result, separation was improved in terms of both the separation time and resolution with increase of carrier viscosity. A theoretical model for plate height in GrFFF is also presented, and its predictions are compared to experimentally measured values.

The separation efficiencies of three different asymmetrical flow field-flow fractionation (AF4) channel designs were evaluated using polystyrene latex standards. Channel breadth was held constant for one channel (rectangular profile), and was reduced either linearly (trapezoidal profile) or exponentially (exponential profile) along the length for the other two. The effective void volumes of the three channel types were designed to be equivalent. Theoretically, under certain flow conditions, the mean channel flow velocity of the exponential channel could be arranged to remain constant along the channel length, thereby improving separation in AF4. Particle separation obtained with the exponential channel was compared with particle separation obtained with the trapezoidal and rectangular channels. We demonstrated that at a certain flow rate condition (outflow/inflow rate = 0.2), the exponential channel design indeed provided better performance with respect to the separation of polystyrene nanoparticles in terms of reducing band broadening. While the trapezoidal channel exhibited a little poorer performance than the exponential, the strongly decreasing mean flow velocity in the rectangular channel resulted in serious band broadening, a delay in retention time, and even failure of larger particles to elute.

Magnetic field-flow fractionation (MgFFF) is a technique for the separation and characterization of magnetic nanoparticles. It is explained that the analysis of polydisperse samples requires a programmed decay of field and field gradient during sample elution. A procedure for achieving reproducible field decay with asymptotic approach to zero field using a quadrupole electromagnet is described. An example of an analysis of a polydisperse sample under programmed field decay is given.

Superparamagnetic iron oxide (SPIO) particles have been used successfully as an intracellular contrast agent for nuclear MRI cell tracking in vivo. We present a method of detecting intracellular SPIO colloid uptake in live cells using cell magnetophoresis, with potential applications in measuring intracellular MRI contrast uptake. The method was evaluated by measuring shifts in mean and distribution of the cell magnetophoretic mobility, and the concomitant changes in population frequency of the magnetically positive cells when compared to the unmanipulated negative control. Seven different transfection agent (TA) -SPIO complexes based on dendrimer, lipid, and polyethylenimine compounds were used as test standards, in combination with 3 different cell types: mesenchymal stem cells, cardiac fibroblasts, and cultured KG-1a hematopoietic stem cells. Transfectol (TRA) -SPIO incubation resulted in the highest frequency of magnetically positive cells (>90%), and Fugene 6 (FUG) -SPIO incubation the lowest, below that when using SPIO alone. A highly regular process of cell magnetophoresis was amenable to intracellular iron mass calculations. The results were consistent in all the cell types studied and with other reports. The cell magnetophoresis depends on the presence of high-spin iron species and is therefore expected to be directly related to the cell MRI contrast level.—Jing, Y., Mal, N., Williams, P. S., Mayorga, M., Penn, M. S., Chalmers, J. J., Zborowski, M. Quantitative intracellular magnetic nanoparticle uptake measured by live cell magnetophoresis.

Poly(lactic acid) (PLA) nanoparticles were synthesized using a modified evaporation method, testing two different surfactants (sodium cholate and Pluronic F68) for the process. During their formulation the prodrug 5'-octanoyl-CPA (Oct-CPA) of the anti-ischemic N(6)-cyclopentyladenosine (CPA) was encapsulated. Three different purification methods were compared with respect to the influence of surfactant on the size characteristics of the final nanoparticle product. Flow and sedimentation field-flow fractionation techniques (FlFFF and SdFFF, respectively) were used to size characterize the five poly(lactic acid) particle samples. Two different combinations of carrier solution (mobile phase) were employed in the FlFFF analyses, while a solution of poly(vinyl alcohol) was used as mobile phase for the SdFFF runs. The separation performances of the two techniques were compared and the particle size distributions (PSDs), derived from the fractograms, were interpreted with the support of observations by scanning electron microscopy. Some critical aspects, such as the carrier choice and the channel thickness determination for the FlFFF, have been investigated. This is the first comprehensive comparison of the two FFF techniques for characterizing non-standard particulate materials. The two FFF techniques proved to be complementary and gave good, congruent and very useful information on the size distributions of the five poly(lactic acid) particle samples.

Quadrupole magnetic field-flow fractionation (MgFFF) is an analytical separation and characterization technique for nano- and micro-sized magnetic particles. It fractionates particles according to their content of magnetite or other magnetic material. The potential and versatility of MgFFF for separation and characterization of magnetic nanoparticles, such as those used for immunospecific labeling of biological cells for magnetic separation, is demonstrated. A broadly polydisperse sample of dextran-coated magnetite nanoparticles was eluted under programmed field decay conditions, and quantitative data concerning the distribution of magnetite content were determined from the elution profile using a data reduction method.

The new technique of quadrupole magnetic field-flow fractionation is described. It is a separation and characterization technique for particulate magnetic materials. Components of a sample are eluted from the separation channel at times dependent on the strength of their interaction with the magnetic field. A quadrupole electromagnet allows a programmed reduction of field strength during analysis of polydisperse samples.

Field-flow fractionation (FFF) is an analytical scale separation and characterizatio technique for macromolecules and particles. A quadrupole magnetic FFF device has bee constructed for analyzing magnetic nanoparticles. It is shown to give reproducible results and be capable of distinguishing between different lots of a commercial magnetic nanoparticle material.

With the analytical expression for the magnetophoretic mobility of an ideal, linearly polarizable sphere undergoing creeping motion in viscous medium, we have shown that both attractive and repulsive motions are possible in the magnetic field. We have validated theoretical predictions using magnetic monodisperse microspheres of 5.2-microm diameter and nonmagnetic polystyrene microspheres of 6.99-microm diameter suspended in solutions of paramagnetic ions. The microsphere magnetophoretic mobility was measured using a modified particle tracking velocimetry system, developed in-house and called a cell tracking velocimeter. The product of measured mobility and viscosity agrees well with the theoretical prediction, differing only by approximately 11%. Further, a 26% increase in resolution between magnetic and nonmagnetic particle distributions was evaluated when paramagnetic ion carrier was used instead of water. Continuous particle sorting based on differences in magnetophoretic mobility was performed with another device developed by us, the quadrupole magnetic flow sorter (QMS). In the QMS, the introduction of paramagnetic ions into the carrier was effective in suppressing nonspecific crossover (i.e., the transport of low-mobility particles into the magnetic particle fraction) in particles and in biologically relevant red blood cells and thus showed promise as a means of increasing the purity of the magnetic separation.

The separation performance of a split-flow thin (SPLITT) separation device depends on uniformity of channel thickness and the precise placement of the flow splitters at fixed distances between the channel walls. The observation of nonspecific crossover, that is, the transport of sample materials across the channel thickness without the influence of an applied field, has routinely been taken to indicate the presence of irregularities in splitter shape or placement. Computational fluid dynamics software may be used to predict the influence of splitter imperfections on nonspecific crossover, where it is assumed that sample transport is by convection alone. A previous study has shown how small inlet splitter imperfections can account for the relatively low levels of nonspecific crossover observed with typical annular SPLITT devices. This study, however, could not distinguish between the possible sources of nonspecific crossover; hydrodynamic lift or shear-induced diffusion could have contributed. To confirm the validity of the computational approach, a series of experiments has been carried out on a channel having a deliberately and severely bent splitter. Nonspecific crossover was measured for a range of inlet and outlet flow rate ratios, with the bent splitter placed at both the channel inlet and outlet. The severity of the splitter distortion was sufficient to produce significant nonspecific crossover over a wide range of flow conditions. Good agreement was found between experiment and prediction based on computational fluid dynamics, with experiment generally showing only slightly higher crossover than prediction. The quantitative agreement for this extreme case suggests that the contribution to nonspecific crossover due to geometrical imperfections can be well described using computational fluid dynamics.

In this paper we provide experimental evidence showing that various types of submicrometer-sized particles (latexes, inorganic, and metallic), suspended in either aqueous or nonaqueous carrier liquids to which a temperature gradient dT/dx is applied, experience a force in the direction opposite to that of dT/dx. This behavior is similar to that of small particles such as soot, aerosols, and small bubbles suspended in stagnant gases across which temperature gradients are applied, a phenomenon known as “thermophoresis in gases.” We report the use of a thermal field-flow fractionation (ThFFF) apparatus in two different configurations to establish the direction of particle motion subject to a temperature gradient. The first approach employed the conventional horizontal ThFFF channel orientation. In this case, small electrical potentials were applied across the narrow channel thickness either to augment or to act in opposition to the applied thermal gradient, depending on whether the accumulation wall was maintained at a positive or negative potential relative to the depletion wall. Thus, by observing the changes in the retention behavior of surface-charged latices or silica particles with changes in potential difference across the channel thickness, we were able to ascertain the direction of migration of the particles in the thermal gradient. The second approach involved the use of a ThFFF column oriented vertically in an implementation of a technique known as thermogravitational FFF. In this approach, the convective flow along the channel length (due to density gradients associated with the temperature gradient) couples with the thermal diffusion effect across the channel thickness to result in a combined particle retention mechanism. A retarded upward migration rate is indicative of accumulation of particles at the cold wall, while enhanced upward migration would indicate a hot-wall accumulation. From the results of our investigations, we conclude that submicrometer-sized particles suspended in either aqueous or nonaqueous carrier liquids and subjected to a temperature gradient migrate from the hot wall toward the cold wall of a ThFFF channel.

Magnetophoretic mobility arises from the motion of an electrically neutral body in a viscous medium when exposed to an inhomogenous magnetic field. Conforming to other types of mobility, which generally have the form of a “reciprocal friction coefficient” (such as electrophoretic mobility), we have defined the magnetophoretic mobility, m, as a ratio of a particle–field interaction parameter, φ m, to the particle friction coefficient, f, so that with the parameter φ m equal to the product of the magnetic susceptibility of the particle relative to that of the medium, Δχ, and its volume, V m, so that The particle mobility is an important factor in predicting separation when a mixture of particles of different mobilities is exposed to an external field. We have combined the information about the particle magnetophoretic mobility, measured by cell tracking velocimetry, and the theory of the split-flow thin channel fractionation, to describe particle and cell separations in a flowing solution through an annular...

In asymmetrical flow field-flow fractionation (As-FlFFF), only the membrane-covered accumulation wall is permeable to fluid; the opposite channel wall is impermeable. Fluid enters the channel at the inlet and exits partly through the membrane-covered accumulation wall and partly through the channel outlet. This means that not only does the volumetric channel flow rate decrease along the channel length as fluid exits through the membrane but also the cross-channel component to fluid velocity must approach zero at the impermeable wall. This dependence of cross-channel fluid velocity on distance across the channel thickness influences the equilibrium concentration profile for the sample components introduced to the channel. The concentration profile departs from the exponential profile predicted for the ideal model of field-flow fractionation. This influences both the retention ratio and the principal contribution to bandspreading—the nonequilibrium contribution. The derivation of an equation for the nonequilibrium bandspreading parameter χ in As-FlFFF is presented, and its numerical solution graphed. At high retention, it is shown that the solutions for both retention ratio R and χ converge on those for the ideal model, as expected. At lower levels of retention, the departures from the ideal model are significant, particularly for bandspreading. For example, at a level of retention corresponding to a retention parameter λ of 0.05, R is almost 4 % higher than for the ideal model (0.28047 as compared to 0.27000) but the value of χ is almost 60 % higher. The equations presented for both R and χ include a first-order correction for the finite size of the particles—the steric exclusion correction. These corrections are shown to be significant for particle sizes eluting well before steric inversion. For example, particles of half the inversion diameter are predicted to elute 25 % slower and to show almost 40 % higher bandspreading when steric effects are not accounted for. The work presented contributes to the fundamental theory of As-FlFFF and allows quantitative prediction of both retention and bandspreading at all levels of retention.

Magnetic microsphere suspensions undergo complex motion when exposed to finite sources of the magnetic field, such as small permanent magnets. The computational complexity is compounded by a difficulty in choosing a suitable choice of visualization tools because this often requires using the magnetic force vector field in three dimensions. Here we present a potentially simpler approach by using the magnetic pressure. It is a scalar quantity, pm = B2/2μ0, and its usefulness has been already demonstrated in applications to magnetohydrodynamics and ferrohydrodynamics (where B is the applied field and μ0 = 4π×10−7 T.m/A). The equilibrium distribution of the magnetic bead plug in aqueous suspension is calculated as an isosurface of the magnitude of the magnetic pressure pm = const, in the field of two permanent magnet blocks calculated from closed formulas. The geometry was adapted from a publication on the magnetic bead suspensions in microsystems and the predicted bead plug distribution is shown to agree remarkably well with the experiment.

An algorithm that employs numerical integration for analysis of field-flow fractionation (FFF) data is presented. The algorithm utilizes detector response, field strength, and channel flow rate data, monitored at discrete time intervals during sample elution to generate a distribution of sample components according to particle size or molecular weight. The field strength and channel flow rate may either be held constant or programmed as functions of time, and it is not necessary for these programs to follow specific mathematical functions. If experimental conditions are monitored during a run, the algorithm can account for any deviation from nominal set conditions. The algorithm also allows calculation of fractionating power for the actual conditions as monitored during the run. The method provides greatly increased flexibility in the application of the FFF family of techniques. It removes the limitations on experimental conditions incurred by adherence to analytically available solutions to FFF theory, allowing ad hoc variation of field strength and other experimental parameters as necessary to increase sensitivity and specificity of the method. An implementation of the algorithm is described that is independent of the FFF technique (i.e., independent of field type) and mode of operation. To reduce computation time, it uses mathematical techniques to reduce the required number of numerical integrations. This is of particular importance when the perturbations to ideal FFF theory, such as those due to the effects of hydrodynamic lift forces, particle-wall or particle-particle interactions, and secondary relaxation, necessitate relatively lengthy numerical calculations.

An experimental technique is discussed in which the size distribution of a population of cells is de- termined by calculating each cell's settling velocity. The settling velocity is determined from microscopically ob- tained images which were recorded on SVHS tape. These images are then computer imaged and processed, and the cell's location and velocity are determined using a computer algorithm referred to as cell tracking velocim- etry (CTV). Experimental data is presented comparing the distribution of human lymphocytes and a human breast cancer cell line, MCF-7, determined using a Coulter counter and the CTV approach. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 64: 509-518, 1999.

The quadrupole magnetic cell sorter is a form of split-flow thin-channel (SPLITT) separation device. It employs a quadrupole magnetic field and annular channel geometry. Immunomagnetic labels are used to bind to specific receptors on the surface of the cells of interest. It is the interaction of these labels with the magnetic field that brings about the selective isolation of these cells. The SPLITT separation devices have generally been based on parallel-plate geometry, usually with effectively constant field strength applied across the channel thickness. The nonconstant field strength and annular channel geometry of the magnetic cell sorter require that a new strategy be developed for optimization of inlet and outlet flow rates. We present such a strategy here based on a consideration of certain specific cell trajectories within the system.

Sample relaxation in the frit-inlet asymmetrical flow fieldflow fractionation (FIA-FlFFF) channel is accomplished hydrodynamically. The focusing/relaxation procedure, which is essential to the efficient operation of conventional asymmetrical flow FFF, is therefore avoided. It follows that for FIA-FlFFF there is no requirement for valve switching to achieve convergent (focusing) channel flows, and sample relaxation and separation proceed without interruption. This represents a major advance in the facility of operation of asymmetrical flow FFF. In this work, we present the derivation of equations to describe the variation in mean channel flow velocity along the full length of the frit-inlet asymmetrical channel. Equations for channel void time (the time for a nonretained material to pass through the channel) are also presented. The equations are sufficiently general so as to be applicable to both rectangular and trapezoidal channel designs. On the basis of these equations, the retention time for a sample component can be calculated by applying basic flow FFF theory. Simple equations are also presented to determine conditions consistent with complete relaxation of samples within the frit-inlet region. Such conditions ensure maximization of separation efficiency during subsequent elution. The retention and resolving power of FIA-FlFFF are demonstrated using sets of standard latex spheres and proteins. Experimental data show that retention in FIAFlFFF follows the general principles of field-flow fractionation, provided the variation in flow velocity is correctly accounted for. Finally, effects of sample load and injection volume are also discussed.

Field-flow fractionation (FFF) and split-flow thin cell fractionation (SPLITT fractionation) provide high resolution size- or mass-based separation of particulate samples. FFF is an analytical technique, whereas SPLITT fractionation operates on a preparative scale. In this work, the FFF and SPLITT technologies were applied to the size analysis and separation of magnetic beads. The optimization of operating conditions was investigated.

A laboratory prototype of a flow cell sorter based on magnetic quadrupole field was built and evaluated. The magnetic force acting on magnetically labeled cells in such a field has a `centrifugal’ character which provides a basis for the design of a continuous separation process. The sorter was tested on a model cell system of human peripheral lymphocytes labeled with magnetic colloid.