Multiplexing superparamagnetic beads driven by multi-frequency ratchets

Efficient flowless separation of mixed microbead populations on periodic ferromagnetic surface structures

The simultaneous separational control of motion of individual objects is vital to achieve high efficiency separation for biological analytes in biomedical applications. Here, we show the selective and directed movement of different populations of microbeads depending on their size in a flowless environment by means of a hexagonally structured soft-magnetic microchip platform. By adjusting strength and asymmetry of a modulated in-plane magnetic field, discrete and switchable movement patterns of two different types of beads above a magnetic surface structure are achieved. Starting from a heterogeneous mixture of bead populations and depending on the type of field sequences, directional forward transport of one type of beads is achieved, while the other bead population is immobilized. Despite significant size and magnetic content distributions within each population of microbeads, high separation efficiencies are demonstrated. The selection and movement processes are supported by full-scale magnetofluidic numerical simulations. The magnetic platform allowing multidirectional and selective microbead movement can greatly contribute to the progress of functional lab-on-chip and future diagnostics devices.

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.

Scalable Electronic Ratchet with Over 10% Rectification Efficiency

Electronic ratchets use a periodic potential with broken inversion symmetry to rectify undirected (electromagnetic, EM) forces and can in principle be a complement to conventional diode-based designs. Unfortunately, ratchet devices reported to date have low or undetermined power conversion efficiencies, hampering applicability. Combining experiments and numerical modeling, field-effect transistor-based ratchets are investigated in which the driving signal is coupled into the accumulation layer via interdigitated finger electrodes that are capacitively coupled to the field effect transistor channel region. The output current-voltage curves of these ratchets can have a fill factor >> 0.25 which is highly favorable for the power output. Experimentally, a maximum power conversion efficiency well over 10% at 5 MHz, which is the highest reported value for an electronic ratchet, is determined. Device simulations indicate this number can be increased further by increasing the device asymmetry. A scaling analysis shows that the frequency range of optimal performance can be scaled to the THz regime, and possibly beyond, while adhering to technologically realistic parameters. Concomitantly, the power output density increases from ≈4 W m-2 to ≈1 MW m-2. Hence, this type of ratchet device can rectify high-frequency EM fields at reasonable efficiencies, potentially paving the way for actual use as energy harvester.

Lab-on-a-chip electrical multiplexing techniques for cellular and molecular biomarker detection

Signal multiplexing is vital to develop lab-on-a-chip devices that can detect and quantify multiple cellular and molecular biomarkers with high throughput, short analysis time, and low cost. Electrical detection of biomarkers has been widely used in lab-on-a-chip devices because it requires less external equipment and simple signal processing and provides higher scalability. Various electrical multiplexing for lab-on-a-chip devices have been developed for comprehensive, high throughput, and rapid analysis of biomarkers. In this paper, we first briefly introduce the widely used electrochemical and electrical impedance sensing methods. Next, we focus on reviewing various electrical multiplexing techniques that had achieved certain successes on rapid cellular and molecular biomarker detection, including direct methods (spatial and time multiplexing), and emerging technologies (frequency, codes, particle-based multiplexing). Lastly, the future opportunities and challenges on electrical multiplexing techniques are also discussed.

Lattice symmetries and the topologically protected transport of colloidal particles

The topologically protected transport of colloidal particles on top of periodic magnetic patterns is studied experimentally, theoretically, and with computer simulations. To uncover the interplay between topology and symmetry we use patterns of all possible two dimensional magnetic point group symmetries with equal lengths lattice vectors. Transport of colloids is achieved by modulating the potential with external, homogeneous but time dependent magnetic fields. The modulation loops can be classified into topologically distinct classes. All loops falling into the same class cause motion in the same direction, making the transport robust against internal and external perturbations. We show that the lattice symmetry has a profound influence on the transport modes, the accessibility of transport networks, and the individual transport directions of paramagnetic and diamagnetic colloidal particles. We show how the transport of colloidal particles above a two fold symmetric stripe pattern changes from universal adiabatic transport at large elevations via a topologically protected ratchet motion at intermediate elevations toward a non-transport regime at low elevations. Transport above four-fold symmetric patterns is closely related to the two-fold symmetric case. The three-fold symmetric case however consists of a whole family of patterns that continuously vary with a phase variable. We show how this family can be divided into two topologically distinct classes supporting different transport modes and being protected by proper and improper six fold symmetries. We discuss and experimentally demonstrate the topological transition between both classes. All three-fold symmetric patterns support independent transport directions of paramagnetic and diamagnetic particles. The similarities and the differences in the lattice symmetry protected transport of classical over-damped colloidal particles versus the topologically protected transport in quantum mechanical systems are emphasized.

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.

Topological protection of multiparticle dissipative transport

Topological protection allows robust transport of localized phenomena such as quantum information, solitons and dislocations. The transport can be either dissipative or non-dissipative. Here, we experimentally demonstrate and theoretically explain the topologically protected dissipative motion of colloidal particles above a periodic hexagonal magnetic pattern. By driving the system with periodic modulation loops of an external and spatially homogeneous magnetic field, we achieve total control over the motion of diamagnetic and paramagnetic colloids. We can transport simultaneously and independently each type of colloid along any of the six crystallographic directions of the pattern via adiabatic or deterministic ratchet motion. Both types of motion are topologically protected. As an application, we implement an automatic topologically protected quality control of a chemical reaction between functionalized colloids. Our results are relevant to other systems with the same symmetry.

Transport of a collection of classical particles involves thermal ratchet effect or adiabatic motion, which brings complexity to control multiparticle transport. Here, Loehr et al. show topologically protected multiparticle transport of diamagnetic and paramagnetic colloids, driven by periodic modulation loops of an external magnetic field.

Quantitative Magnetic Separation of Particles and Cells Using Gradient Magnetic Ratcheting

Extraction of rare target cells from biosamples is enabling for life science research. Traditional rare cell separation techniques, such as magnetic activated cell sorting, are robust but perform coarse, qualitative separations based on surface antigen expression. A quantitative magnetic separation technology is reported using high-force magnetic ratcheting over arrays of magnetically soft micropillars with gradient spacing, and the system is used to separate and concentrate magnetic beads based on iron oxide content (IOC) and cells based on surface expression. The system consists of a microchip of permalloy micropillar arrays with increasing lateral pitch and a mechatronic device to generate a cycling magnetic field. Particles with higher IOC separate and equilibrate along the miropillar array at larger pitches. A semi-analytical model is developed that predicts behavior for particles and cells. Using the system, LNCaP cells are separated based on the bound quantity of 1 μm anti-epithelial cell adhesion molecule (EpCAM) particles as a metric for expression. The ratcheting cytometry system is able to resolve a ±13 bound particle differential, successfully distinguishing LNCaP from PC3 populations based on EpCAM expression, correlating with flow cytometry analysis. As a proof-of-concept, EpCAM-labeled cells from patient blood are isolated with 74% purity, demonstrating potential toward a quantitative magnetic separation instrument.

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.

Micromagnet arrays for on-chip focusing, switching, and separation of superparamagnetic beads and single cells

Nonlinear magnetophoresis (NLM) is a novel approach for on-chip transport and separation of superparamagnetic (SPM) beads, based on a travelling magnetic field wave generated by the combination of a micromagnet array (MMA) and an applied rotating magnetic field. Here, we present two novel MMA designs that allow SPM beads to be focused, sorted, and separated on-chip. Converging MMAs were used to rapidly collect the SPM beads from a large region of the chip and focus them into synchronised lines. We characterise the collection efficiency of the devices and demonstrate that they can facilitate on-chip analysis of populations of SPM beads using a single-point optical detector. The diverging MMAs were used to control the transport of the beads and to separate them based on their size. The separation efficiency of these devices was determined by the orientation of the magnetisation of the micromagnets relative to the external magnetic field and the size of the beads and relative to that of micromagnets. By controlling these parameters and the rotation of the external magnetic field we demonstrated the controlled transport of SPM bead-labelled single MDA-MB-231 cells. The use of these novel MMAs promises to allow magnetically-labelled cells to be efficiently isolated and then manipulated on-chip for analysis with high-resolution chemical and physical techniques.

Microscopic dynamics of synchronization in driven colloids

Synchronization of coupled oscillators has been scrutinized for over three centuries, from Huygens' pendulum clocks to physiological rhythms. One such synchronization phenomenon, dynamic mode locking, occurs when naturally oscillating processes are driven by an externally imposed modulation. Typically only averaged or integrated properties are accessible, leaving underlying mechanisms unseen. Here, we visualize the microscopic dynamics underlying mode locking in a colloidal model system, by using particle trajectories to produce phase portraits. Furthermore, we use this approach to examine the enhancement of mode locking in a flexible chain of magnetically coupled particles, which we ascribe to breathing modes caused by mode-locked density waves. Finally, we demonstrate that an emergent density wave in a static colloidal chain mode locks as a quasi-particle, with microscopic dynamics analogous to those seen for a single particle. Our results indicate that understanding the intricate link between emergent behaviour and microscopic dynamics is key to controlling synchronization.

Synchronization may occur when naturally oscillating systems are driven by an external modulation, for example, in charge density waves. Here, Juniper et al. visualize the locked modes of synchronization at a microscopic level using a colloidal system.

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.

High-efficiency dielectrophoretic ratchet

Brownian ratchets enable the use of thermal motion in performing useful work. They typically employ spatial asymmetry to rectify nondirected external forces that drive the system out of equilibrium (cf. running marbles on a shaking washboard). The major application foreseen for Brownian ratchets is high-selectivity fractionation of particle or molecule distributions. Here, we investigate the functioning of an important model system, the on/off ratchet for water-suspended particles, in which interdigitated finger electrodes can be switched on and off to create a time-dependent, spatially periodic but asymmetric potential. Surprisingly, we find that mainly dielectrophoretic rather than electrophoretic forces are responsible for the ratchet effect. This has major implications for the (a)symmetry of the ratchet potential and the settings needed for optimal performance. We demonstrate that by applying a potential offset the ratchet can be optimized such that its particle displacement efficiency reaches the theoretical upper limit corresponding to the electrode geometry and particle size. Efficient fractionation based on size selectivity is therefore not only possible for charged species, but also for uncharged ones, which greatly expands the applicability range of this type of Brownian ratchet.

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.