Unidirectional Transport of Superparamagnetic Beads and Biological Cells along an Oval Shaped Magnetic Element Path

Abstract

Achieving new possibilities of cell manipulation or of other microbiological species is one of the most important tasks of the latest lab-on-a-chip devices [1-3]. High throughput and precise movement control are the figures of merit for new tools or chip designs. Common concepts consist of labeling biological cells or other biological entities with magnetic nanoparticles to achieve transport by timely and spatially varying magnetic field gradients [4]. In this context, superparamagnetic microbeads (MB) are widely used to imitate the properties of tagged cells or act as carriers for smaller biological species like DNA-strings or proteins. The particles or MBs can be manipulated on top of hard magnets [5] or soft magnetic thin film structures [6]. Recent research has shown many differently designed patterned thin film structures, featuring multiple advantages for the transport of MBs.One of the transport concepts relies on the interaction of their magnetic moment with a stray magnetic field gradient of arranged soft-magnetic thin film elements. Magnetic field sequences create varying potential states, enabling specific MB trajectories. In narrow soft magnetic tracks, magnetic microstructures that exhibit strong local stray field gradients are moved to drag the MBs along certain directions. For example, two-dimensional arrays of soft magnetic elements with various magnetization states varying with applied magnetic fields enable complex MB manipulation [2]. In every case, the maximum speed of the MB is limited by the hydrodynamic drag force, the surface friction, and by the magnetic force. This links the magnetic moments of the thin film elements and the MB, the friction coefficients, and the MB size.Beneficial and applicable unidirectional movement of a MB and a magnetically labeled rat embryonic fibroblast cell is demonstrated. We show the unidirectional transport of MBs and cells independent of the sign of the magnetic stimuli. Oval shaped elements made from a soft magnetic amorphous iron-based alloy are arranged in a one-dimensional chain, allowing MB transport whether clockwise or counter-clockwise in-plane rotating magnetic fields are applied. A directional motion scheme is achieved by exploiting the stray field dependence of the curvature radius of the facing magnetic elements.Three dimensional simulations [7] are used to forecast the motion of a particle along a chain of ovals and provide the theoretical background to the experimental results. Magnetic potential energy landscapes are calculated between the MB anticipated as magnetic dipoles and the micromagnetic structure of the oval elements simulated using mumax3 [8]. We find that an overlap of the potential minima of two neighboring elements for a spacing similar to the diameter of the MB enables a handover of MBs between magnetic elements. The agreement between the numerical simulated bead trajectories and the experimental movement path is shown in Fig. 1. The unidirectional motion scheme of the beads is demonstrated for different starting conditions for clockwise and counterclockwise rotating fields. The motion is independent of the sense of field rotation. The same manipulation options are obtained with a MB engulfed rat embryonic fibroblast cell as shown in Fig. 2.The robust diode-like particle guidance along predefined tracks, formed by chains of elements, holds also great potential for lab-on-a-chip applications, including cell sorting or highly controllable manipulation of biological carriers. The diode-like behavior of the oval elements leaves the direction of magnetic field rotation as a degree of freedom unexploited, permitting its usage for adding-on other application relevant manipulation schemes. Various aspects and options of the motion rectifying magnetic structures will be discussed.J.M., F.B., and U.S. acknowledge funding through the Deutsche Forschungsgemeinschaft grants DFG MC 9/13-1 and MC 9/13-2. C.A. and C.S. thank the Volkswagen Foundation for funding the project "Molecularly controlled, stimuli-sensitive hydrogels for dynamically adjustable biohybrid actuators". S.S. and C.S. acknowledge funding of the Research Training Group RTG 2154 "Material for Brain" through the Deutsche Forschungsgemeinschaft. J.M. thanks S. Gutekunst for stimulating discussions. The authors thank L. Thormählen for magnetic thin film deposition. **