Traveling wave magnetophoresis for high resolution chip based separations

Stray Magnetic Field Variations and Micromagnetic Simulations: Models for Ni0.8Fe0.2 Disks Used for Microparticle Trapping

Patterned micro-scale thin-film magnetic structures, in conjunction with weak (~few tens of Oe) applied magnetic fields, can create energy landscapes capable of trapping and transporting fluid-borne magnetic microparticles. These energy landscapes arise from magnetic field magnitude variations that arise in the vicinity of the magnetic structures. In this study, we examine means of calculating magnetic fields in the local vicinity of permalloy (Ni0.8Fe0.2) microdisks in weak (~tens of Oe) external magnetic fields. To do this, we employ micromagnetic simulations and the resulting calculations of fields. Because field calculation from micromagnetic simulations is computationally time-intensive, we discuss a method for fitting simulated results to improve calculation speed. Resulting stray fields vary dramatically based on variations in micromagnetic simulations-vortex vs. non-vortex micromagnetic results-which can each appear despite identical simulation final conditions, resulting in field strengths that differ by about a factor of two.

Optimum transport in systems with time-dependent drive and short-ranged interactions

We consider a one-dimensional lattice gas model of hardcore particles with nearest-neighbor interaction in presence of a time-periodic external potential. We investigate how attractive or repulsive interaction affects particle transport and determine the conditions for optimum transport, i.e., the conditions for which the maximum dc particle current is achieved in the system. We find that the attractive interaction in fact hinders the transport, while the repulsive interaction generally enhances it. The net dc current is a result of the competition between the current induced by the periodic external drive and the diffusive current present in the system. When the diffusive current is negligible, particle transport in the limit of low particle density is optimized for the strongest possible repulsion. But when the particle density is large, very strong repulsion makes particle movement difficult in an overcrowded environment and, in that case, the optimal transport is obtained for somewhat weaker repulsive interaction. Our numerical simulations show reasonable agreement with our mean-field calculations. When the diffusive current is significantly large, the particle transport is still facilitated by repulsive interaction, but the conditions for optimality change. Our numerical simulations show that the optimal transport occurs at the strongest repulsive interaction for large particle density and at a weaker repulsion for small particle density.

Magnetophoretic circuits: A review of device designs and implementation for precise single-cell manipulation

Lab-on-a-chip tools have played a pivotal role in advancing modern biology and medicine. A key goal in this field is to precisely transport single particles and cells to specific locations on a chip for quantitative analysis. To address this large and growing need, magnetophoretic circuits have been developed in the last decade to manipulate a large number of single bioparticles in a parallel and highly controlled manner. Inspired by electrical circuits, magnetophoretic circuits are composed of passive and active circuit elements to offer commensurate levels of control and automation for transporting individual bioparticles. These specifications make them unique compared to other technologies in addressing crucial bioanalytical applications and answering fundamental questions buried in highly heterogeneous cell populations. In this comprehensive review, we describe key theoretical considerations for manufacturing and simulating magnetophoretic circuits. We provide a detailed tutorial for operating magnetophoretic devices containing different circuit elements (e.g., conductors, diodes, capacitors, and transistors). Finally, we provide a critical comparison of the utility of these devices to other microchip-based platforms for cellular manipulation, and discuss how they may address unmet needs in single-cell biology and medicine.

Design and Development of a Traveling Wave Ferro-Microfluidic Device and System Rig for Potential Magnetophoretic Cell Separation and Sorting in a Water-Based Ferrofluid

The timely detection and diagnosis of diseases and accurate monitoring of specific genetic conditions require rapid and accurate separation, sorting, and direction of target cell types toward a sensor device surface. In that regard, cellular manipulation, separation, and sorting are progressively finding application potential within various bioassay applications such as medical disease diagnosis, pathogen detection, and medical testing. The aim of this paper is to present the design and development of a simple traveling wave ferro-microfluidic device and system rig purposed for the potential manipulation and magnetophoretic separation of cells in water-based ferrofluids. This paper details in full: (1) a method for tailoring cobalt ferrite nanoparticles for specific diameter size ranges (10–20 nm), (2) the development of a ferro-microfluidic device for potentially separating cells and magnetic nanoparticles, (3) the development of a water-based ferrofluid with magnetic nanoparticles and non-magnetic microparticles, and (4) the design and development of a system rig for producing the electric field within the ferro-microfluidic channel device for magnetizing and manipulating nonmagnetic particles in the ferro-microfluidic channel. The results reported in this work demonstrate a proof of concept for magnetophoretic manipulation and separation of magnetic and non-magnetic particles in a simple ferro-microfluidic device. This work is a design and proof-of-concept study. The design reported in this model is an improvement over existing magnetic excitation microfluidic system designs in that heat is efficiently removed from the circuit board to allow a range of input currents and frequencies to manipulate non-magnetic particles. Although this work did not analyze the separation of cells from magnetic particles, the results demonstrate that non-magnetic (surrogates for cellular materials) and magnetic entities can be separated and, in some cases, continuously pushed through the channel based on amperage, size, frequency, and electrode spacing. The results reported in this work establish that the developed ferro-microfluidic device may potentially be used as an effective platform for microparticle and cellular manipulation and sorting.

Continuous Flow Separation of Red Blood Cells and Platelets in a Y-Microfluidic Channel Device with Saw-Tooth Profile Electrodes via Low Voltage Dielectrophoresis

Cell counting and sorting is a vital step in the purification process within the area of biomedical research. It has been widely reported and accepted that the use of hydrodynamic focusing in conjunction with the application of a dielectrophoretic (DEP) force allows efficient separation of biological entities such as platelets from red blood cell (RBC) samples due to their size difference. This paper presents computational results of a multiphysics simulation modelling study on evaluating continuous separation of RBCs and platelets in a microfluidic device design with saw-tooth profile electrodes via DEP. The theoretical cell particle trajectory, particle cell counting, and particle separation distance study results reported in this work were predicted using COMSOL v6.0 Multiphysics simulation software. To validate the numerical model used in this work for the reported device design, we first developed a simple y-channel microfluidic device with square “in fluid” electrodes similar to the design reported previously in other works. We then compared the obtained simulation results for the simple y-channel device with the square in fluid electrodes to the reported experimental work done on this simple design which resulted in 98% agreement. The design reported in this work is an improvement over existing designs in that it can perform rapid separation of RBCs (estimated 99% purification) and platelets in a total time of 6–7 s at a minimum voltage setting of 1 V and at a minimum frequency of 1 Hz. The threshold for efficient separation of cells ends at 1000 kHz for a 1 V setting. The saw-tooth electrode profile appears to be an improvement over existing designs in that the sharp corners reduced the required horizontal distance needed for separation to occur and contributed to a non-uniform DEP electric field. The results of this simulation study further suggest that this DEP separation technique may potentially be applied to improve the efficiency of separation processes of biological sample scenarios and simultaneously increase the accuracy of diagnostic processes via cell counting and sorting.

Computational Assessment of Magnetic Nanoparticle Targeting Efficiency in a Simplified Circle of Willis Arterial Model

This paper presents the methodology and computational results of simulated medical drug targeting (MDT) via induced magnetism intended for administering intravenous patient-specific doses of therapeutic agents in a Circle of Willis (CoW) model. The multi-physics computational model used in this work is from our previous works. The computational model is used to analyze pulsatile blood flow, particle motion, and particle capture efficiency in a magnetized region using the magnetic properties of magnetite (Fe₃O₄) and equations describing the magnetic forces acting on particles produced by an external cylindrical electromagnetic coil. A Eulerian-Lagrangian technique is implemented to resolve the hemodynamic flow and the motion of particles under the influence of a range of magnetic field strengths (B_r = 2T, 4T, 6T, and 8T). Particle diameter sizes of 10 nm to 4 µm in diameter were assessed. Two dimensionless numbers are also investigated a priori in this study to characterize relative effects of Brownian motion (BM), magnetic force-induced particle motion, and convective blood flow on particle motion. Similar to our previous works, the computational simulations demonstrate that the greatest particle capture efficiency results for particle diameters within the micron range, specifically in regions where flow separation and vortices are at a minimum. Additionally, it was observed that the capture efficiency of particles decreases substantially with smaller particle diameters, especially in the superparamagnetic regime. The highest capture efficiency observed for superparamagnetic particles was 99% with an 8T magnetic field strength and 95% with a 2T magnetic field strength when analyzing 100 nm particles. For 10 nm particles and an 8T magnetic field strength, the particle capture efficiency was 48%, and for a 2T magnetic field strength the particle capture efficiency was 33%. Furthermore, it was found that larger magnetic field strengths, large particle diameter sizes (1 µm and above), and slower blood flow velocity increase the particle capture efficiency. The key finding in this work is that favorable capture efficiencies for superparamagnetic particles were observed in the CoW model for weak fields (B_r < 4T) which demonstrates MDT as a possible viable treatment candidate for cardiovascular disease.

Three-dimensional close-to-substrate trajectories of magnetic microparticles in dynamically changing magnetic field landscapes

The transport of magnetic particles (MPs) by dynamic magnetic field landscapes (MFLs) using magnetically patterned substrates is promising for the development of Lab-on-a-chip (LOC) systems. The inherent close-to-substrate MP motion is sensitive to changing particle-substrate interactions. Thus, the detection of a modified particle-substrate separation distance caused by surface binding of an analyte is expected to be a promising probe in analytics and diagnostics. Here, we present an essential prerequisite for such an application, namely the label-free quantitative experimental determination of the three-dimensional trajectories of superparamagnetic particles (SPPs) transported by a dynamically changing MFL. The evaluation of defocused SPP images from optical bright-field microscopy revealed a "hopping"-like motion of the magnetic particles, previously predicted by theory, additionally allowing a quantification of maximum jump heights. As our findings pave the way towards precise determination of particle-substrate separations, they bear deep implications for future LOC detection schemes using only optical microscopy.

Hydrodynamic synchronization and clustering in ratcheting colloidal matter

Ratchet transport systems are widespread in physics and biology; however, the effect of the dispersing medium in the collective dynamics of these out-of-equilibrium systems has been often overlooked. We show that, in a traveling wave magnetic ratchet, long-range hydrodynamic interactions (HIs) produce a series of remarkable phenomena on the transport and assembly of interacting Brownian particles. We demonstrate that HIs induce the resynchronization with the traveling wave that emerges as a "speed-up" effect, characterized by a net raise of the translational speed, which doubles that of single particles. When competing with dipolar forces and the underlying substrate symmetry, HIs promote the formation of clusters that grow perpendicular to the driving direction. We support our findings both with Langevin dynamics and with a theoretical model that accounts for the fluid-mediated interactions. Our work illustrates the role of the dispersing medium on the dynamics of driven colloidal matter and unveils the growing process and cluster morphologies above a periodic substrate.

The Origins and the Current Applications of Microfluidics-Based Magnetic Cell Separation Technologies

The magnetic separation of cells based on certain traits has a wide range of applications in microbiology, immunology, oncology, and hematology. Compared to bulk separation, performing magnetophoresis at micro scale presents advantages such as precise control of the environment, larger magnetic gradients in miniaturized dimensions, operational simplicity, system portability, high-throughput analysis, and lower costs. Since the first integration of magnetophoresis and microfluidics, many different approaches have been proposed to magnetically separate cells from suspensions at the micro scale. This review paper aims to provide an overview of the origins of microfluidic devices for magnetic cell separation and the recent technologies and applications grouped by the targeted cell types. For each application, exemplary experimental methods and results are discussed.

Translatory and rotatory motion of exchange-bias capped Janus particles controlled by dynamic magnetic field landscapes

Magnetic Janus particles (MJPs), fabricated by covering a non-magnetic spherical particle with a hemispherical magnetic in-plane exchange-bias layer system cap, display an onion magnetization state for comparably large diameters of a few microns. In this work, the motion characteristics of these MJPs will be investigated when they are steered by a magnetic field landscape over prototypical parallel-stripe domains, dynamically varied by superposed external magnetic field pulse sequences, in an aqueous medium. We demonstrate, that due to the engineered magnetization state in the hemispherical cap, a comparably fast, directed particle transport and particle rotation can be induced. Additionally, by modifying the frequency of the applied pulse sequence and the strengths of the individual field components, we observe a possible separation between a combined or an individual occurrence of these two types of motion. Our findings bear importance for lab-on-a-chip systems, where particle immobilization on a surface via analyte bridges shall be used for low concentration analyte detection and a particle rotation over a defined position of a substrate may dramatically increase the immobilization (and therefore analyte detection) probability.

Short- and Long-Range Microparticle Transport on Permalloy Disk Arrays in Time-Varying Magnetic Fields

We investigate maneuvering superparamagnetic microparticles, or beads, in a remotely-controlled, automated way across arrays of few-micron-diameter permalloy disks. This technique is potentially useful for applying tunable forces to or for sorting biological structures that can be attached to magnetic beads, for example nucleic acids, proteins, or cells. The particle manipulation method being investigated relies on a combination of stray fields emanating from permalloy disks as well as time-varying externally applied magnetic fields. Unlike previous work, we closely examine particle motion during a capture, rotate, and controlled repulsion mechanism for particle transport. We measure particle velocities during short-range motion—the controlled repulsion of a bead from one disk toward another—and compare this motion to a simulation based on stray fields from disk edges. We also observe the phase-slipping and phase-locked motion of particles engaging in long-range transport in this manipulation scheme.

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.

Transport Efficiency of Biofunctionalized Magnetic Particles Tailored by Surfactant Concentration

Controlled transport of surface-functionalized magnetic beads in a liquid medium is a central requirement for the handling of captured biomolecular targets in microfluidic lab-on-chip biosensors. Here, the influence of the physiological liquid medium on the transport characteristics of functionalized magnetic particles and on the functionality of the coupled protein is studied. These aspects are theoretically modeled and experimentally investigated for prototype superparamagnetic beads, surface-functionalized with green fluorescent protein immersed in buffer solution with different concentrations of a surfactant. The model reports on the tunability of the steady-state particle substrate separation distance to prevent their surface sticking via the choice of surfactant concentration. Experimental and theoretical average velocities are discussed for a ratchet-like particle motion induced by a dynamic external field superposed on a static locally varying magnetic field landscape. The developed model and experiment may serve as a basis for quantitative forecasts on the functionality of magnetic particle transport-based lab-on-chip devices.

Mattertronics for programmable manipulation and multiplex storage of pseudo-diamagnetic holes and label-free cells

Manipulating and separating single label-free cells without biomarker conjugation have attracted significant interest in the field of single-cell research, but digital circuitry control and multiplexed individual storage of single label-free cells remain a challenge. Herein, by analogy with the electrical circuitry elements and electronical holes, we develop a pseudo-diamagnetophoresis (PsD) mattertronic approach in the presence of biocompatible ferrofluids for programmable manipulation and local storage of single PsD holes and label-free cells. The PsD holes conduct along linear negative micro-magnetic patterns. Further, eclipse diode patterns similar to the electrical diode can implement directional and selective switching of different PsD holes and label-free cells based on the diode geometry. Different eclipse heights and junction gaps influence the switching efficiency of PsD holes for mattertronic circuitry manipulation and separation. Moreover, single PsD holes are stored at each potential well as in an electrical storage capacitor, preventing multiple occupancies of PsD holes in the array of individual compartments due to magnetic Coulomb-like interaction. This approach may enable the development of large programmable arrays of label-free matters with high throughput, efficiency, and reliability as multiplex cell research platforms.

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.

Nanonewton Magnetophoretic Microtrap Array for Microsystems

Here we report on the development of a lab-on-chip that integrates a dense array of micrometer-sized magnetic traps, with each individual trap generating a magnetic force as high as a few nN on standard superparamagnetic beads. The composite materials embedding traps are prepared from the microstructural engineering of a mixture between iron microparticles and polydimethylsiloxane. This approach breaks with standard microfabrication technologies: it is inexpensive, relatively easy to implement, and offers the ability to modulate the magnetic properties of the composites on a customized basis. The magnetic forces acting on the superparamagnetic beads have been measured following two approaches: first, on-chip through the hydrodynamic determination of the holding magnetic force, simultaneously on a large population of traps; and second, ex situ, by atomic force microscopy equipped with a colloidal probe, on individual traps. The experimental results have been compared with calculations from finite element modeling. Despite the geometrical simplification of the modeled system, both experiments and calculations give consistent values of force, ranging from 0.5 to 5 nN. These findings show that in operando determination of forces is a robust method that gives a high throughput overview of the forces acting in the device. It further demonstrates that the use of such functional composite materials can be a relevant alternative to standard microfabrication technologies, as it leads to competitive magnetophoretic performances.

Static array of droplets and on-demand recovery for biological assays

Microfluidics has revolutionized several research areas by providing compact yet powerful microanalytical devices that in many cases outperform conventional systems. Among different microfluidics technologies, droplet microfluidics has emerged as a powerful platform to enable analyses of biological samples and phenomena because of its simplicity and versatility. Droplet microfluidics enables high-throughput encapsulation, manipulation, and analysis of single cells while drastically reducing the cost and time required by conventional technologies. For many of these microanalysis systems, manipulation of individual droplets is extremely important as it enables multiplexed high dimensional phenotyping of the targets, going beyond surface phenotyping. One of the key manipulation steps that needs to be implemented with high precision is enabling long-term observation of droplets and recovery of a subset of these droplets for further analysis. This Perspective highlights the recent advances and provides an outlook on future developments that will enable highly complex analyses of biological samples.

Optical detection of the magnetophoretic transport of superparamagnetic beads on a micromagnetic array

Micromagnetic arrays (MMAs) have proven to be powerful tools for controlling the transport and separation of bioanalytes, i.e., they allow bioanalyte-superparamagnetic (SPM) bead complexes of specific size and magnetization to be moved in a synchronized manner that is precisely controlled with the orientation of an external magnetic field. This article presents a laser-photodetector system for the simple detection of individual SPM beads moving on a specific region of an MMA. This system detects the SPM beads through the change in intensity of reflective light as they move from the highly reflective micromagnetics to the supporting substrate. We demonstrate that this opti-MMA system allowed the size, number, and magnetic and optical properties of the SPM beads to be rapidly determined for regions > 49 µm² in size. The response of the opti-MMA system was characterized in several optical configurations to develop a theoretical description of its sensitivity and dynamic range. The speed, low-cost, and sensitivity of this system promises to allow MMAs to be readily applied in in vitro diagnostics and biosensing.

Evaluating and forecasting movement patterns of magnetically driven microbeads in complex geometries

The manipulation of superparamagnetic microbeads for lab-on-a-chip applications relies on the steering of microbeads across an altering stray field landscape on top of soft magnetic parent structures. Using ab initio principles, we show three-dimensional simulations forecasting the controlled movement of microbeads. Simulated aspects of microbead behaviour include the looping and lifting of microbeads around a magnetic circular structure, the flexible bead movement along symmetrically distributed triangular structures, and the dragging of magnetic beads across an array of exchange biased magnetic microstripes. The unidirectional motion of microbeads across a string of oval elements is predicted by simulations and validated experimentally. Each of the simulations matches the experimental results, proving the robustness and accuracy of the applied numerical method. The computer experiments provide details on the particle motion not accessible by experiments. The simulation capabilities prove to be an essential part for the estimation of future lab-on-chip designs.

Direct identification of the herpes simplex virus UL27 gene through single particle manipulation and optical detection using a micromagnetic array

Magnetophoretic lab on a chip technologies are rapidly evolving into integrated systems for the identification of biomarkers and cells with ultra-high sensitivity. We demonstrate the highly efficient detection of the Human herpes simplex virus type 1 (HSV) UL27 gene through the programmed assembly of superparamagnetic (SPM) nanoparticles based on oligonucleotide hybridization. The state of assembly of the SPM nanoparticles was determined by optical signature of the synchronized motion on the beads on a micromagnetic array (MMA). This technique has been used to identify <200 copies of the HSV UL27 gene without amplification in less than 20 minutes. The MAA can also be used to separate gene-SPM bead aggregates from millions of unreacted SPM beads based on nonlinear magnetophoresis (NLM). The MMA-optical detection system promises to enable highly sensitive, nucleic acid analysis to be performed without amplification and with the consumption of minimal amounts of reagent.

Multifarious Transit Gates for Programmable Delivery of Bio-functionalized Matters

Programmable delivery of biological matter is indispensable for the massive arrays of individual objects in biochemical and biomedical applications. Although a digital manipulation of single cells has been implemented by the integrated circuits of micromagnetophoretic patterns with current wires, the complex fabrication process and multiple current operation steps restrict its practical application for biomolecule arrays. Here, a convenient approach using multifarious transit gates is proposed, for digital manipulation of biofunctionalized microrobotic particles that can pass through the local energy barriers by a time-dependent pulsed magnetic field instead of multiple current wires. The multifarious transit gates including return, delay, and resistance linear gates, as well as dividing, reversed, and rectifying T-junction gates, are investigated theoretically and experimentally for the programmable manipulation of microrobotic particles. The results demonstrate that, a suitable angle of the gating field at a suitable time zone is crucial to implement digital operations at integrated multifarious transit gates along bifurcation paths to trap microrobotic particles in specific apartments, paving the way for flexible on-chip arrays of biomolecules and cells.

Autonomous Magnetic Microrobots by Navigating Gates for Multiple Biomolecules Delivery

The precise delivery of biofunctionalized matters is of great interest from the fundamental and applied viewpoints. In spite of significant progress achieved during the last decade, a parallel and automated isolation and manipulation of rare analyte, and their simultaneous on-chip separation and trapping, still remain challenging. Here, a universal micromagnet junction for self-navigating gates of microrobotic particles to deliver the biomolecules to specific sites using a remote magnetic field is described. In the proposed concept, the nonmagnetic gap between the lithographically defined donor and acceptor micromagnets creates a crucial energy barrier to restrict particle gating. It is shown that by carefully designing the geometry of the junctions, it becomes possible to deliver multiple protein-functionalized carriers in high resolution, as well as MCF-7 and THP-1 cells from the mixture, with high fidelity and trap them in individual apartments. Integration of such junctions with magnetophoretic circuitry elements could lead to novel platforms without retrieving for the synchronous digital manipulation of particles/biomolecules in microfluidic multiplex arrays for next-generation biochips.

Architecture for Directed Transport of Superparamagnetic Microbeads in a Magnetic Domain Wall Routing Network

Directed transport of biological species across the surface of a substrate is essential for realizing lab-on-chip technologies. Approaches that utilize localized magnetic fields to manipulate magnetic particles carrying biological entities are attractive owing to their sensitivity, selectivity, and minimally disruptive impact on biomaterials. Magnetic domain walls in magnetic tracks produce strong localized fields and can be used to capture, transport, and detect individual superparamagnetic microbeads. The dynamics of magnetic microbead transport by domain walls has been well studied. However, demonstration of more complex functions such as selective motion and sorting using continuously driven domain walls in contiguous magnetic tracks is lacking. Here, a junction architecture is introduced that allows for branching networks in which superparamagnetic microbeads can be routed along dynamically-selected paths by a combination of rotating in-plane field for translation, and a pulsed out-of-plane field for path selection. Moreover, experiments and modeling show that the select-field amplitude is bead-size dependent, which allows for digital sorting of multiple bead populations using automated field sequences. This work provides a simple means to implement complex routing networks and selective transport functionalities in chip-based devices using magnetic domain wall conduits.

Collective transport for active matter run-and-tumble disk systems on a traveling-wave substrate

We examine numerically the transport of an assembly of active run-and-tumble disks interacting with a traveling-wave substrate. We show that as a function of substrate strength, wave speed, disk activity, and disk density, a variety of dynamical phases arise that are correlated with the structure and net flux of disks. We find that there is a sharp transition into a state in which the disks are only partially coupled to the substrate and form a phase-separated cluster state. This transition is associated with a drop in the net disk flux, and it can occur as a function of the substrate speed, maximum substrate force, disk run time, and disk density. Since variation of the disk activity parameters produces different disk drift rates for a fixed traveling-wave speed on the substrate, the system we consider could be used as an efficient method for active matter species separation. Within the cluster phase, we find that in some regimes the motion of the cluster center of mass is in the opposite direction to that of the traveling wave, while when the maximum substrate force is increased, the cluster drifts in the direction of the traveling wave. This suggests that swarming or clustering motion can serve as a method by which an active system can collectively move against an external drift.

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.

Magnetically Patterned Rolled-Up Exchange Bias Tubes: A Paternoster for Superparamagnetic Beads

We realized a deterministic transport system for superparamagnetic microbeads through micrometer-sized tubes acting as channels. Beads are moved stepwise in a paternoster-like manner through the tube and back on top of it by weak magnetic field pulses without changing the field pulse polarity and taking advantage of the magnetic stray field emerging from the tubular structures. The microtubes are engineered by rolling up exchange bias layer systems, magnetically patterned into parallel stripe magnetic domains. In this way, the tubes possess distinct azimuthally aligned magnetic domain patterns. This transport mechanism features high step velocities and remote control of not only the direction and trajectory but also the velocity of the transport without the need of fuel or catalytic material. Therefore, this approach has the potential to impact several fields of 3D applications in biotechnology, including particle transport related phenomena in lab-on-a-chip and lab-in-a-tube devices.

An on-chip micromagnet frictionometer based on magnetically driven colloids for nano-bio interfaces

A novel method based on remotely controlled magnetic forces of bio-functionalized superparamagnetic colloids using micromagnet arrays was devised to measure frictional force at the sub-picoNewton (pN) scale for bio-nano-/micro-electromechanical system (bio-NEMS/MEMS) interfaces in liquid. The circumferential motion of the colloids with phase-locked angles around the periphery of the micromagnets under an in-plane rotating magnetic field was governed by a balance between tangential magnetic force and drag force, which consists of viscous and frictional forces. A model correlating the phase-locked angles of the steady colloid rotation was formulated and validated by measuring the angles under controlled magnetic forces. Hence, the frictional forces on the streptavidin/Teflon interface between the colloids and the micromagnet arrays were obtained using the magnetic forces at the phase-locked angles. The friction coefficient for the streptavidin/Teflon interface was estimated to be approximately 0.036 regardless of both vertical force in the range of a few hundred pN and velocity in the range of a few tenths of μm s(-1).

Label-Free and Continuous-Flow Ferrohydrodynamic Separation of HeLa Cells and Blood Cells in Biocompatible Ferrofluids

In this study, a label-free, low-cost, and fast ferrohydrodynamic cell separation scheme is demonstrated using HeLa cells (an epithelial cell line) and red blood cells. The separation is based on cell size difference, and conducted in a custom-made biocompatible ferrofluid that retains the viability of cells during and after the assay for downstream analysis. The scheme offers moderate-throughput (≈106 cells h-1 for a single channel device) and extremely high recovery rate (>99%) without the use of any label. It is envisioned that this separation scheme will have clinical applications in settings where rapid cell enrichment and removal of contaminating blood will improve efficiency of screening and diagnosis such as cervical cancer screening based on mixed populations in exfoliated samples.

Magnetophoretic Conductors and Diodes in a 3D Magnetic Field

We demonstrate magnetophoretic conductor tracks that can transport single magnetized beads and magnetically labeled single cells in a 3-dimensional time-varying magnetic field. The vertical field bias, in addition to the in-plane rotating field, has the advantage of reducing the attraction between particles, which inhibits the formation of particle clusters. However, the inclusion of a vertical field requires the re-design of magnetic track geometries which can transport magnetized objects across the substrate. Following insights from magnetic bubble technology, we found that successful magnetic conductor geometries defined in soft magnetic materials must be composed of alternating sections of positive and negative curvature. In addition to the previously studied magnetic tracks taken from the magnetic bubble literature, a drop-shape pattern was found to be even more adept at transporting small magnetic beads and single cells. Symmetric patterns are shown to achieve bi-directional conduction, whereas asymmetric patterns achieve unidirectional conduction. These designs represent the electrical circuit corollaries of the conductor and diode, respectively. Finally, we demonstrate biological applications in transporting single cells and in the size based separation of magnetic particles.

Transport and selective chaining of bidisperse particles in a travelling wave potential

We combine experiments, theory and numerical simulation to investigate the dynamics of a binary suspension of paramagnetic colloidal particles dispersed in water and transported above a stripe-patterned magnetic garnet film. The substrate generates a one-dimensional periodic energy landscape above its surface. The application of an elliptically polarized rotating magnetic field causes the landscape to translate, inducing direct transport of paramagnetic particles placed above the film. The ellipticity of the applied field can be used to control and tune the interparticle interactions, from net repulsive to net attractive. When considering particles of two distinct sizes, we find that, depending on their elevation above the surface of the magnetic substrate, the particles feel effectively different potentials, resulting in different mobilities. We exploit this feature to induce selective chaining for certain values of the applied field parameters. In particular, when driving two types of particles, we force only one type to condense into travelling parallel chains. These chains confine the movement of the other non-chaining particles within narrow colloidal channels. This phenomenon is explained by considering the balance of pairwise magnetic forces between the particles and their individual coupling with the travelling landscape.

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.

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.

Manipulation of Superparamagnetic Beads on Patterned Exchange-Bias Layer Systems for Biosensing Applications

A technology platform based on a remotely controlled and stepwise transport of an array arrangement of superparamagnetic beads (SPB) for efficient molecular uptake, delivery and accumulation in the context of highly specific and sensitive analyte molecule detection for the application in lab-on-a-chip devices is presented. The near-surface transport of SPBs is realized via the dynamic transformation of the SPBs’ magnetic potential energy landscape above a magnetically stripe patterned Exchange-Bias (EB) thin film layer systems due to the application of sub-mT external magnetic field pulses. In this concept, the SPB velocity is dramatically influenced by the magnitude and gradient of the magnetic field landscape (MFL) above the magnetically stripe patterned EB substrate, the SPB to substrate distance, the magnetic properties of both the SPBs and the EB layer system, respectively, as well as by the properties of the external magnetic field pulses and the surrounding fluid. The focus of this review is laid on the specific MFL design in EB layer systems via light-ion bombardment induced magnetic patterning (IBMP). A numerical approach is introduced for the theoretical description of the MFL in comparison to experimental characterization via scanning Hall probe microscopy. The SPB transport mechanism will be outlined in terms of the dynamic interplay between the EB substrate’s MFL and the pulse scheme of the external magnetic field.

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.

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.

Directed Magnetic Particle Transport above Artificial Magnetic Domains Due to Dynamic Magnetic Potential Energy Landscape Transformation

An approach for a remotely controllable transport of magnetic micro- and/or nanoparticles above a topographically flat exchange-bias (EB) thin film system, magnetically patterned into parallel stripe domains, is presented where the particle manipulation is achieved by sub-mT external magnetic field pulses. Superparamagnetic core-shell particles are moved stepwise by the dynamic transformation of the particles' magnetic potential energy landscape due to the external magnetic field pulses without affecting the magnetic state of the thin film system. The magnetic particle velocity is adjustable in the range of 1-100 μm/s by the design of the substrate's magnetic field landscape (MFL), the particle-substrate distance, and the magnitude of the applied external magnetic field pulses. The agglomeration of magnetic particles is avoided by the intrinsic magnetostatic repulsion of particles due to the parallel alignment of the particles' magnetic moments perpendicular to the transport direction and parallel to the surface normal of the substrate during the particle motion. The transport mechanism is modeled by a quantitative theory based on the precise knowledge of the sample's MFL and the particle-substrate distance.

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.

Synthesis of brightly PEGylated luminescent magnetic upconversion nanophosphors for deep tissue and dual MRI imaging

A method is developed to fabricate monodispersed biocompatible Yb/Er or Yb/Tm doped β-NaGdF4 upconversion phosphors using polyelectrolytes to prevent irreversible particle aggregation during conversion of the precursor, Gd2 O(CO3 )2.H2 O:Yb/Er or Yb/Tm, to β-NaGdF4 :Yb/Er or Yb/Tm. The polyelectrolyte on the outer surface of nanophosphors also provided an amine tag for PEGylation. This method is also employed to fabricate PEGylated magnetic upconversion phosphors with Fe3 O4 as the core and β-NaGdF4 as a shell. These magnetic upconversion nanophosphors have relatively high saturation magnetization (7.0 emu g(-1) ) and magnetic susceptibility (1.7 × 10(-2) emu g(-1) Oe(-1) ), providing them with large magnetophoretic mobilities. The magnetic properties for separation and controlled release in flow, their optical properties for cell labeling, deep tissue imaging, and their T1 - and T2 -weighted magnetic resonance imaging (MRI) relaxivities are studied. The magnetic upconversion phosphors display both strong magnetophoresis, dual MRI imaging (r1 = 2.9 mM(-1) s(-1) , r2 = 204 mM(-1) s(-1) ), and bright luminescence under 1 cm chicken breast tissue.

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.

On-chip magnetic separation and encapsulation of cells in droplets

Single cell study is gaining importance because of the cell-to-cell variation that exists within cell population, even after significant initial sorting. Analysis of such variation at the gene expression level could impact single cell functional genomics, cancer, stem-cell research, and drug screening. The on-chip monitoring of individual cells in an isolated environment would prevent cross-contamination, provide high recovery yield, and enable study of biological traits at a single cell level. These advantages of on-chip biological experiments is a significant improvement for a myriad of cell analyses methods, compared to conventional methods, which require bulk samples and provide only averaged information on cell structure and function. We report on a device that integrates a mobile magnetic trap array with microfluidic technology to provide the possibility of separation of immunomagnetically labeled cells and their encapsulation with reagents into picoliter droplets for single cell analysis. The simultaneous reagent delivery and compartmentalization of the cells immediately following sorting are all performed seamlessly within the same chip. These steps offer unique advantages such as the ability to capture cell traits as originated from its native environment, reduced chance of contamination, minimal use of the reagents, and tunable encapsulation characteristics independent of the input flow. Preliminary assay on cell viability demonstrates the potential for the device to be integrated with other up- or downstream on-chip modules to become a powerful single-cell analysis tool.

Continuous separation principles using external microaction forces

During the past decade, methods for the continuous separation of microparticles with microaction forces have rapidly advanced. Various action forces have been used in designs of both microchannel and capillary continuous separation systems, which depend on properties such as conductivity, permittivity, absorptivity, refractive index, magnetic susceptibility, and compressibility. Particle migration velocity has been used to characterize the particles. Biological cells have been the most interesting targets of these continuous separation methods.

Depinning and collective dynamics of magnetically driven colloidal monolayers

We study the collective dynamics of interacting paramagnetic colloids transported via a magnetic ratchet effect above a modulated periodic potential. Upon increasing the modulation frequency, the particles undergo a series of dynamic transitions, from a continuous smectic flow to a disorder flow, and later enter into a two phase flow regime, ending in a complete pinned state. In the disordered phase, the system organizes into density waves due to traffic jams, as in granular systems, while the two phase flow regime shows strong similarities with plastic flow in vortex matter. Finally, it is shown that induced attractive interactions between the moving colloids lead to enhancement of the particle current due to formation of condensed chains traveling along the modulated landscape.

Resistive pulse sensing of analyte-induced multicomponent rod aggregation using tunable pores

Resistive pulse sensing is used to monitor individual and aggregated rod-shaped nanoparticles as they move through tunable pores in elastomeric membranes. By comparing particles of similar dimensions, it is demonstrated that the resistive pulse signal of a rod is fundamentally different from that of a sphere. Rods can be distinguished using two measurements: the blockade event magnitude (Δi(p) ), which reveals the particle's size, and the full width at half maximum (FWHM) duration, which relates to the particle's speed and length. While the observed Δi(p) values agree well with simulations, the measured FWHM times are much larger than expected. This increase in dwell time, caused by rods moving through the pore in various orientations, is not observed for spherical particles. These differences are exploited in a new agglutination assay using rod-shaped particles. By controlling the surface chemistry and location of the capture ligand, rods are made to form either long "end-on-end" or wide "side-on" aggregates upon the addition of an analyte. This observation will facilitate multiplexed detection in agglutination assays, as particles with a particular aspect ratio can be distinguished by two measurements. This is first demonstrated with a biotinylated target and avidin capture probe, followed by the detection of platelet-derived growth factor (PDGF-BB) using an aptamer capture probe, with limits of detection down to femtomolar levels.

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.

The application of an optically switched dielectrophoretic (ODEP) force for the manipulation and assembly of cell-encapsulating alginate microbeads in a microfluidic perfusion cell culture system for bottom-up tissue engineering

This study reports the utilisation of an optically switched dielectrophoretic (ODEP) force for the manipulation and assembly of cell-encapsulating alginate microbeads in a microfluidic perfusion cell culture system for bottom-up tissue engineering. One of the key features of this system is the ODEP force-based mechanism, which allows a commercial projector to be coupled with a computer to manipulate and assemble cell-encapsulating microbeads in an efficient, manageable, and user-friendly manner. Another distinctive feature is the design of the microfluidic cell culture chip, which allows the patterned cell-encapsulating microbeads to be cultivated on site under culture medium perfusion conditions. For demonstrating its application in bottom-up cartilage tissue engineering, chondrocyte-encapsulating alginate microbeads varying in encapsulated cell densities were generated. The manipulation forces associated with operating the alginate microbeads were experimentally evaluated. The results revealed that the measured manipulation forces increased with increases in both the applied electric voltage and the number of cells in the alginate microbeads. Nevertheless, the observed manipulation force was found to be independent of the size of the cell-free alginate microbeads. It can be speculated that the friction force may influence the estimation of the ODEP force within the experimental conditions investigated. In this study, chondrocyte-encapsulating alginate microbeads with three different cell densities were manipulated and assembled in the proposed microfluidic system to form a compact sheet-like cell culture construct that imitates the cell distribution in the cross-section of native articular cartilage. Moreover, the demonstration case also showed that the cell viability of the cultured cells in the microfluidic system remained as high as 96 ± 2%. In this study, four sheet-like cell culture constructs were stacked to create a larger assembled cell culture construct. The cell distribution inside the cell culture construct was further confirmed by a confocal microscopy observation, which showed that the distribution was similar to that in native articular cartilage. As a whole, the proposed system holds great promise as a platform for engineering tissue constructs with easily tunable inner cell distributions.