The synchronization of superparamagnetic beads driven by a micro-magnetic ratchet

Design of micromagnetic arrays for on-chip separation of superparamagnetic bead aggregates and detection of a model protein and double-stranded DNA analytes

Magnetically actuated lab-on-a-chip (LOC) technologies have enabled rapid, highly efficient separation of specific biomarkers and cells from complex biological samples. Nonlinear magnetophoresis (NLM) is a technique that uses a microfabricated magnet array (MMA) and a time varying external magnetic field to precisely control the transport of superparamagnetic (SPM) beads on the surface of a chip based on their size and magnetization. We analyze the transport and separation behavior of SPM monomers and dimers on four MMA geometries, i.e., circular, triangular, square and rectangular shaped micromagnets, across a range of external magnetic field rotation frequencies. The measured critical frequency of the SPM beads on an MMA, i.e., the velocity for which the hydrodynamic drag on a bead exceeds the magnetic force, is closely related to the local magnetic flux density landscape on a micromagnet in the presence of an external magnetic field. A set of design criteria has been established for the optimization of MMAs for NLM separation, with particular focus on the shape of the micromagnets forming the array. The square MMA was used to detect a model protein biomarker and gene fragment based on a magnetic bead assembly (MBA) assay. This assay uses ligand functionalized SPM beads to capture and directly detect an analyte through the formation of SPM bead aggregates. These beads aggregates were detected through NLM separation and microscopic analysis resulting in a highly sensitive assay that did not use carrier fluid.

Magnetic microparticle concentration and collection using a mechatronic magnetic ratcheting system

Magnetic ratcheting cytometry is a promising approach to separate magnetically-labeled cells and magnetic particles based on the quantity of magnetic material. We have previously reported on the ability of this technique to separate magnetically-labeled cells. Here, with a new chip design, containing high aspect ratio permalloy micropillar arrays, we demonstrate the ability of this technique to rapidly concentrate and collect superparamagnetic iron oxide particles. The platform consists of a mechatronic wheel used to generate and control a cycling external magnetic field that impinges on a “ratcheting chip.” The ratcheting chip is created by electroplating a 2D array of high aspect ratio permalloy micropillars onto a glass slide, which is embedded in a thin polymer layer to create a planar surface above the micropillars. By varying magnetic field frequency and direction through wheel rotation rate and angle, we direct particle movement on chip. We explore the operating conditions for this system, identifying the effects of varying ratcheting frequency, along with time, on the dynamics and resulting concentration of these magnetic particles. We also demonstrate the ability of the system to rapidly direct the movement of superparamagnetic iron oxide particles of varying sizes. Using this technique, 2.8 μm, 500 nm, and 100 nm diameter superparamagnetic iron oxide particles, suspended within an aqueous fluid, were concentrated. We further define the ability of the system to concentrate 2.8 μm superparamagnetic iron oxide particles, present in a liquid suspension, into a small chip surface area footprint, achieving a 100-fold surface area concentration, and achieving a concentration factor greater than 200%. The achieved concentration factor of greater than 200% could be greatly increased by reducing the amount of liquid extracted at the chip outlet, which would increase the ability of achieving highly sensitive downstream analytical techniques. Magnetic ratcheting-based enrichment may be useful in isolating and concentrating subsets of magnetically-labeled cells for diagnostic automation.

Bioinspired Soft Microrobots with Precise Magneto-Collective Control for Microvascular Thrombolysis

New-era soft microrobots for biomedical applications need to mimic the essential structures and collective functions of creatures from nature. Biocompatible interfaces, intelligent functionalities, and precise locomotion control in a collective manner are the key parameters to design soft microrobots for the complex bio-environment. In this work, a biomimetic magnetic microrobot (BMM) inspired by magnetotactic bacteria (MTB) with speedy motion response and accurate positioning is developed for targeted thrombolysis. Similar to the magnetosome structure in MTB, the BMM is composed of aligned iron oxide nanoparticle (MNP) chains embedded in a non-swelling microgel shell. Linear chains in BMMs are achieved due to the interparticle dipolar interactions of MNPs under a static magnetic field. Simulation results show that, the degree and speed of assembly is proportional to the field strength. The BMM achieves the maximum speed of 161.7 µm s^-1 and accurate positioning control under a rotating magnetic field with less than 4% deviation. Importantly, the locomotion analyses of BMMs demonstrate the frequency-dependent synchronization under 8 Hz and asynchronization at higher frequencies due to the increased drag torque. The BMMs can deliver and release thrombolytic drugs via magneto-collective control, which is promising for ultra-minimal invasive thrombolysis.

Cell Injection Millirobot Development and Evaluation in Microfluidic Chip

We propose an innovative design of millirobot, which can achieve donor cell suction, delivery, and injection in a mammalian oocyte on a microfluidic chip. The millirobot body contains a hollow space that produces suction and ejection forces for the injection of cell nuclei using a nozzle at the tip of the robot. Specifically, a controller changes the hollow volume by balancing the magnetic and elastic forces of a membrane along with the motion of stages in the XY plane. A glass capillary attached to the tip of the robot contains a nozzle that is able to absorb and inject cell nuclei. The millirobot provides three degrees of freedom and generates micronewton forces. We demonstrate the effectiveness of the proposed millirobot through an experiment of the absorption and ejection of 20-µm particles from the nozzle using magnetic control in a microfluidic chip.

Magnetophoretic lensing by concentric topographic cylinders of perpendicular magnetic anisotropy multilayers

Colloidal magnetophoretic lensing of water suspended micrometer-sized superparamagnetic beads (SPBs) above a topographically patterned magnetic thin film system with perpendicular magnetic anisotropy is demonstrated. The magnetic pattern consisting of concentric annuli of micron-sized widths has been superimposed with a rotating external magnetic field, and it is shown that the trajectories of the SPBs above this structure are similar to light rays in an optical focusing lens. SPB trajectories converge towards the central region and have divergent trajectories while passing the center. The experimental findings are corroborated by a quantitative model for the SPB trajectories. The magnetophoretic lensing effect leads to a high SPB concentration in the center of the pattern and may be useful for applications where SPBs have to approach each other in a controlled way.

Micromagnet arrays enable precise manipulation of individual biological analyte-superparamagnetic bead complexes for separation and sensing

In this article, we review lab on a chip (LOC) devices that have been developed for processing magnetically labelled biological analytes, e.g., proteins, nucleic acids, viruses and cells, based on micromagnetic structures and a time-varying magnetic field. We describe the methods that have been developed for fabricating micromagnetic arrays and the bioprocessing operations that have been demonstrated using superparamagnetic (SPM) beads, i.e., programmed transport, switching, separation of specific analytes, and pumping and mixing of fluids in microchannels. The primary advantage of micromagnet devices is that they make it possible to develop systems that control individual SPM beads, enabling high-efficiency separation and analysis. These devices do not require hydrodynamic control and lend themselves to parallel processing of large arrays of SPM beads with modest levels of power consumption. Micromagnet devices are well suited for bioanalytical applications that require high-resolution separation, e.g., detection of rare cell types such as circulating tumour cells, or biosensor applications that require multiple magnetic bioprocessing operations on a single chip.

Dynamic trajectory analysis of superparamagnetic beads driven by on-chip micromagnets

We investigate the non-linear dynamics of superparamagnetic beads moving around the periphery of patterned magnetic disks in the presence of an in-plane rotating magnetic field. Three different dynamical regimes are observed in experiments, including (1) phase-locked motion at low driving frequencies, (2) phase-slipping motion above the first critical frequency f_c1, and (3) phase-insulated motion above the second critical frequency f_c2. Experiments with Janus particles were used to confirm that the beads move by sliding rather than rolling. The rest of the experiments were conducted on spherical, isotropic magnetic beads, in which automated particle position tracking algorithms were used to analyze the bead dynamics. Experimental results in the phase-locked and phase-slipping regimes correlate well with numerical simulations. Additional assumptions are required to predict the onset of the phase-insulated regime, in which the beads are trapped in closed orbits; however, the origin of the phase-insulated state appears to result from local magnetization defects. These results indicate that these three dynamical states are universal properties of bead motion in non-uniform oscillators.

Magnetophoretic Transport Line System for Rapid On-Chip Attomole Protein Detection

A lab-on-a-chip traveling wave magnetophoresis approach for sensitive and rapid protein detection is reported. In this method, a chip-based magnetic microarray comprising lines of micrometer-sized thin film magnetic elements was used to control the movement of magnetic beads (MBs). The MBs and the chip were functionalized, forming a sandwich-type assay. The MBs were transported across a detection area, and the presence of target molecules resulted in the immobilization of MBs within this area. Target quantification was accomplished by MB counting in the detection area using an optical microscope. In order to demonstrate the versatility of the microarray, biotinylated antiavidin was selected as the target protein. In this case, avidin-functionalized MBs and an avidin-functionalized detection area were used. With a total assay time of 1 to 1.5 h (depending on the labeling approach used), a limit of detection in the attomole range was achieved. Compared to on-chip surface plasmon resonance biodetection systems, our method has a larger dynamic range and is about a factor of 500 times more sensitive. Furthermore, our MB transportation system can operate in any chip-based biosensor platform, thereby significantly improving traditional biosensors.

Geometrical optimization of microstripe arrays for microbead magnetophoresis

Manipulation of magnetic beads plays an increasingly important role in molecular diagnostics. Magnetophoresis is a promising technique for selective transportation of magnetic beads in lab-on-a-chip systems. We investigate periodic arrays of exchange-biased permalloy microstripes fabricated using a single lithography step. Magnetic beads can be continuously moved across such arrays by combining the spatially periodic magnetic field from microstripes with a rotating external magnetic field. By measuring and modeling the magnetophoresis properties of thirteen different stripe designs, we study the effect of the stripe geometry on the magnetophoretic transport properties of the magnetic microbeads between the stripes. We show that a symmetric geometry with equal width of and spacing between the microstripes facilitates faster transportation and that the optimal period of the periodic stripe array is approximately three times the height of the bead center over the microstripes.

Two-dimensional spatial manipulation of microparticles in continuous flows in acoustofluidic systems

We report a modeling and experimental study of techniques to acoustically focus particles flowing through a microfluidic channel. Our theoretical model differs from prior works in that we solve an approximate 2-D wave transmission model that accounts for wave propagation in both the solid and fluid phases. Our simulations indicate that particles can be effectively focused at driving frequencies as high as 10% off of the resonant condition. This conclusion is supported by experiments on the acoustic focusing of particles in nearly square microchannels, which are studied for different flow rates, driving frequencies and placements of the lead zirconate titanate transducer, either underneath the microchannel or underneath a parallel trough. The relative acoustic potential energy and the resultant velocity fields for particles with positive acoustic contrast coefficients are estimated in the 2-D limit. Confocal microscopy was used to observe the spatial distribution of the flowing microparticles in three dimensions. Through these studies, we show that a single driving frequency from a single piezoelectric actuator can induce the 2-D concentration of particles in a microchannel with a nearly square cross section, and we correlate these behaviors with theoretical predictions. We also show that it is possible to control the extent of focusing of the microparticles, and that it is possible to decouple the focusing of microparticles in the vertical direction from the lateral direction in rectangular channels with anisotropic cross sections. This study provides guidelines to design and operate microchip-based acoustofluidic devices for precise control over the spatial arrangement of microparticles for applications such as flow cytometry and cellular sorting.

Tunable interactions between paramagnetic colloidal particles driven in a modulated ratchet potential

We study experimentally and theoretically the interactions between paramagnetic particles dispersed in water and driven above the surface of a stripe patterned magnetic garnet film. An external rotating magnetic field modulates the stray field of the garnet film and generates a translating potential landscape which induces directed particle motion. By varying the ellipticity of the rotating field, we tune the inter-particle interactions from net repulsive to net attractive. For attractive interactions, we show that pairs of particles can approach each other and form stable doublets which afterwards travel along the modulated landscape at a constant mean speed. We measure the strength of the attractive force between the moving particles and propose an analytically tractable model that explains the observations and is in quantitative agreement with experiment.

Flow enhanced non-linear magnetophoretic separation of beads based on magnetic susceptibility

Magnetic separation provides a rapid and efficient means of isolating biomaterials from complex mixtures based on their adsorption on superparamagnetic (SPM) beads. Flow enhanced non-linear magnetophoresis (FNLM) is a high-resolution mode of separation in which hydrodynamic and magnetic fields are controlled with micron resolution to isolate SPM beads with specific physical properties. In this article we demonstrate that a change in the critical frequency of FNLM can be used to identify beads with magnetic susceptibilities between 0.01 and 1.0 with a sensitivity of 0.01 Hz(-1). We derived an analytical expression for the critical frequency that explicitly incorporates the magnetic and non-magnetic composition of a complex to be separated. This expression was then applied to two cases involving the detection and separation of biological targets. This study defines the operating principles of FNLM and highlights the potential for using this technique for multiplexing diagnostic assays and isolating rare cell types.

Microstripes for transport and separation of magnetic particles

We present a simple technique for creating an on-chip magnetic particle conveyor based on exchange-biased permalloy microstripes. The particle transportation relies on an array of stripes with a spacing smaller than their width in conjunction with a periodic sequence of four different externally applied magnetic fields. We demonstrate the controlled transportation of a large population of particles over several millimeters of distance as well as the spatial separation of two populations of magnetic particles with different magnetophoretic mobilities. The technique can be used for the controlled selective manipulation and separation of magnetically labelled species.

Origin of multiplexing capabilities of multifrequency magnetic ratchets

Through a combination of theory, numerical simulation, and experiment, we investigate the motion of magnetic beads on the surface of a magnetic ratchet driven by multifrequency fields. Here, we focus on the influence of static forcing terms, which were not included in previous models, and we derive analytical models that show why the static forcing terms are responsible for inducing beads of two different sizes to move in opposite directions on the same ratchet potential. We begin our analysis with the simplest possible forcing model, and we show that the main effect of the static forcing terms is to delay the phase of flux reversal. From there, we move onto the full analysis and theoretically derive the phase range for which opposite motion among two different bead types is achieved. Based on these theoretical results, we conduct experimental investigations that explore the effects of bead size and static forcing coefficient on the direction of bead motion, which confirm most of the expected trends. These results shed light both on past experimental work both by ourselves and others, as well as elucidate the more general multiplexing capabilities of ratchets.

Multiplexing superparamagnetic beads driven by multi-frequency ratchets

Here, we explore the single particle dynamics of superparamagnetic beads exposed to multifrequency ratchets. Through a combination of theory, simulation, and experiment, we determine the important tuning parameters that can be used to implement multiplexed separation of polydisperse colloidal mixtures. In particular, our results demonstrate that the ratio of driving frequencies controls the transition between open and closed trajectories that allow particles to be transported across a substrate. We also demonstrate that the phase difference between the two frequencies controls not only the direction of motion but also which particles are allowed to move within a polydisperse mixture. These results represent a fundamentally different approach to colloidal separation than the previous methods which are based on controlling transitions between phase-locked and phase-slipping regimes, and have a higher degree of multiplexing capabilities that can benefit the fields of biological separation and sensing as well as provide crucial insights into general ratchet behavior.

Transport of superparamagnetic beads through a two-dimensional potential energy landscape

The nonlinear dynamic behavior of superparamagnetic beads transported through a two-dimensional potential energy landscape is explored empirically and through numerical simulation. The beads are driven through a periodic array of micromagnets by an external rotating field oriented at an angle θ relative to the magnetization direction of the substrate. The bead's motion was highly sensitive to the angle of the driving field near critical angles and to various system parameters, including bead size, rotation frequency, and substrate pole density. Our results suggest the possibility of using this behavior in a highly discriminative colloidal separation system, in which two different bead types can be tuned to move in orthogonal directions.