Fabrication and magnetic control of alginate-based rolling microrobots

Today one of the most exciting frontiers in robotics is the development of untethered micro- and nanorobotic systems, which hold the potential to revolutionize the fields of bio-manufacturing and medicine. Over the past decade, scientists and engineers have shown the ability to produce very large populations (10²-10¹⁴) of small scale (10^-9-10^-6 m) robots using a diverse array of materials and techniques.^1–4 Swarms of these tiny robots may be ideal for on-site construction of high resolution macroscale biomaterials and devices without the need of specialized surfaces.⁵ While these types of large population, small sized, robotic systems have many advantages over their larger scale counterparts, they also present a set of unique challenges in terms manufacturing and control.⁶ In an effort to overcome these challenges, this work explores a simple and rapid fabrication method for generating soft particle based microrobots, as well as demonstrating feedback motion control of these microrobots.

Thus far, there have been a number of fabrication methods developed to construct small scale robots including direct laser writing,^7,8 template-directed electrodeposition,⁹ and glancing angle deposition.⁴ However most of these fabrication methods require highly specialized equipment and complex processing steps that preclude the inclusion of biological materials, such as living cells, within their constructs. Alternatively, there have been a number of microfluidic methods, including flow focusing^10,11 and electrohydrodynamic co-jetting,^12,13 developed to generate spherical microparticles capable of encapsulating materials. However, these methods often require some form of lithography to fabricate microfluidic channels and also have large sample volumes (>0.1 cm³) due to dead volumes within their systems. This can be prohibitive when the targeted materials for encapsulation are only available in low quantities (e.g. primary cells), and in many cases involve the use of processes or materials, such as an immiscible liquid phase^14–16 or ultra violet light,¹⁷ which can be incompatible with live cells.

Of the wide variety of microfluidic fabrication methods reported thus far, centrifugally induced particle generation using polysaccharides has been demonstrated to be one of the most efficient methods to encapsulate viable cells.^18–20 Polysaccharide based hydrogels, due in part to their biocompatibility, have been widely used for encapsulating and transporting a number of organic and inorganic particles. In particular, alginates have garnered a significant amount of investigations due to their ability to rapidly crosslink in the presence of divalent cations.²¹ By combining alginate with single or multiple species, for example stem cells or drugs, loaded-alginate microspheres can be formed, providing protection for the encapsulated species en route to targeted locations. Furthermore, the contents of these microgels can be controllably released using chemical,²² mechanical,²³ optical,²⁴ or biological²⁵ methods. Many groups have termed these loaded-alginate particles as artificial cells,^26–28 in that they mimic the basic structure of living cells (i.e. membrane, cytoplasm, organelles, etc.). These cell-like particles have the potential to be used for on-demand assembly of high resolution biological materials;²⁹ yet they are limited by the fact that it is difficult to precisely control their movement, assembly times depend on manual skill, and have low throughput.³⁰ Also, while magnetic navigation of biomaterials has been extensively studied,^31–33 to our knowledge no particle based microrobot encapsulating mammalian cells and magnetic particles has been reported. Towards this end we have fabricated alginate Janus microparticles (i.e. artificial cells) that encapsulate both magnetic nanoparticles and living cells and demonstrate the ability to actuate these microparticles autonomously through vision based feedback control utilizing the magnetic field generated by a three-axis electromagnetic coil system. In comparison to the work of S. Fusco et.al.,³³ our control method is very similar, however the main difference in this work is the method of fabrication and that we demonstrate control our robot using rolling on a solid plane versus in bulk fluid.

To fabricate artificial cells, a 5% sodium alginate solution was combined with 50 nm diameter iron oxide nanoparticles (5% (w/w)), thoroughly mixed, sonicated, and subsequently autoclaved. Human breast carcinoma cells (MDA-MB-231, ATCC), cultured to 70% confluency in Dulbecco’s modified eagle medium (DMEM) supplemented with 10% fetal bovine serum and 1% penicillin/streptomycin, were trypsinized and washed in fresh media and then gently resuspended in a separate autoclaved 5% sodium alginate solution (without nanoparticles). The two alginate solutions, containing cells and magnetic microparticles, were then carefully loaded on opposing sides of a 34 gauge needle that was fixed in a 1.5 mL microtube (Fig. 1(a)) containing 1.2 mL of calcium chloride (2.5% (w/w)). Janus particles, containing superparamagnetic particles in one hemisphere and living cells in the other, were formed as droplets were ejected from the needle into the calcium chloride solution during centrifugation at 1000 G for thirty seconds.

The diameter, $dp$⁠, of the particle ejected from the needle nozzle during quasi-static droplet formation can be written as,¹⁸ 

where $dn$⁠, $σp$⁠, $ρp$⁠, and $g$⁠, are the diameter of the nozzle, surface tension of the alginate solution, density of alginate solution, and the applied gravitational force, respectively. Using a nozzle diameter of 100 $μm$⁠, and an alginate solution with a surface tension¹⁸ of 65.45 mN m^-1, a measured density of 1.1 g cm^-3, Eq. (1) yields a particle diameter of 154 $μm$ for an applied centrifugal force of 1000 G. From digital imaging the average size of the artificial cell Janus particles was found to be 150 ± 9.3 $μm$ (Fig. 1b). In addition, florescence imaging revealed encapsulation of labelled MDA-MB-231 breast cancer cells in the hemisphere without magnetic nanoparticles (Fig. 1d).

To characterize the magnetic responsiveness and to actuate their motion, a custom-built approximate Helmholtz coil system, consisting of three pairs of electromagnetic coils, was used to generate a uniform rotating magnetic field, as previously described.³⁴ The coil system was powered using three programmable power supplies that were controlled via a National Instruments data acquisition (NIDAQ) controller.³⁵ This system was embedded inside of a motorized stage connected to an invert microscope (Leica DMIRB) equipped with a high speed camera. The rotational frequency, orientation (i.e. clockwise or counterclockwise), and strength of the generated magnetic field were controlled through a LabVIEW program. Experiments took place within a polydimethylsiloxane (PDMS) chamber (8 mm in diameter and 5 mm in height) sandwiched between two glass coverslips, filled with phosphate buffered saline, that was positioned at the center of the magnetic controller.

To quantify their magnetic responsiveness, artificial cells were rotated in plane at various external field frequencies, and their motion recorded at 500 frames per second. The optical asymmetry of the particles enabled the use of image processing to determine rotational rate, as previously described.³⁶ Experiments were conducted at least three times for three different artificial cells; the maximum standard deviation of measured rotation rates was 2 Hz. At low external frequencies the artificial cells were able to synchronously follow the external rotating field, up until a critical point. Above this critical point there was a non-linear decrease in rotational speed (Fig. 2(a)). It has been established that this behavior occurs when the phase-lag between the dipole moment of the particle and the external field becomes larger than 90°.³⁷ When the phase lag becomes greater than 90° the particle slows down, and can no longer follow the applied field synchronously because of viscous drag. The particles then begin rotating in the opposite direction as they try to realign themselves with the external field. From the rotational response obtained for two different external field strengths, it was determined that the maximum rotational speed of the artificial cells was approximately 60 Hz for a 15 mT field and 30 Hz for a 5 mT field. This data was used to set the rotational frequency range during translational control experiments, to avoid asynchronous rotation and limit Joule heating of the coil system.

For translational motion control of the artificial cells, we applied rotating magnetic fields, which were used to control the heading direction. Specifically, the xy motion of the artificial cell was controlled by manipulating the strength (mT), orientation (rad), and frequency (Hz) of the rotating fields generated by the approximate Helmholtz coil system. The resultant magnetic field used for two-dimensional control can be expressed as

where $B$⁠, $ω$⁠, $θ$⁠, and $t$ represent the amplitude of the rotating magnetic field, rotational frequency of the field, direction of motion, and time, respectively (Fig. 2(b)). The direction of the velocity vector of the rolling artificial cell coincides with the vector orthogonal to the plane of the rotating field, which can be described by

NIDAQ controllers were used to manipulate the voltage and sinusoidal signals generated by the power supplies connected to the electromagnetic coils.

When placed in a uniform magnetic field the dipole moment of an artificial cell aligns with the applied magnetic field, and as the external field begins to rotate the artificial cell also begins to turn in order to maintain dipole alignment. Assuming that sliding does not occur and that damping forces, including surface adhesion with the substrate, are much weaker than the magnetic torque generated between the dipole moment of the particle and external field, the artificial cell maintains a constant rotational speed. Furthermore, if the rotational angle of the applied field is not equal to 90° or 180°,³⁸ then the cell experiences a non-zero net force and torque that causes rotation and translation.^39,40 This mode of surface motion, or rolling locomotion, was used to manipulate the artificial cell’s translation. To model the kinematics of the microrobots we applied a wheeled vehicle model⁴¹ and fit the model to the experimental data as,

where $v$ is the velocity and $u$ is the turning rate of the rotational magnetic field (Fig. 2(c)). To steer the artificial cells using the kinematic equation in Eq. (4) we implemented the following control law

where $k$ is a tunable parameter and $α$ is the angle difference between the heading angle of the microrobot and the angle to the target position. This controller was used to steer the artificial cell, but does not control rotation frequency.

To demonstrate controllability using our feedback control system, we autonomously steered the artificial cell to travel in a predefined ‘‘DU’’ path. In Fig. 3(a), the predefined waypoints of the microrobots ‘‘DU’’ path are shown as open white circles, and the actual trajectory of the artificial cell is shown as the white solid line. The rotation frequency was maintained at 0.2 Hz and the average velocity was 53.66 $μm/s$⁠. As shown in Fig. 3(b), the velocity profile oscillates significantly. This is due to the near-spherical shape and the soft nature of the artificial cells; this is similar to trying to move a wheel that is not perfectly circular and prone to deformation. This effect is especially apparent during sharp turns where the artificial cells can overshoot the position of the next waypoint.

In this paper we have demonstrated a rapid method for fabrication of alginate based rolling microrobots, containing both living cells and superparamagnetic particles, using commercially available parts. The ability to compartmentalize living cells in a separate compartment from iron oxide particles can effectively limit the cytotoxicity associated with cellular uptake of nanoparticles,¹⁹ while also imparting sufficient magnet material for motion control using low power magnetic fields. Characterization of the magnetic responsiveness of these Janus microparticles showed that they display distinct regimes of synchronously and asynchronously motion when exposed to an external uniform rotating magnetic field. Using a single global magnetic input signal and a simple feedback control law, we demonstrated autonomous control of the artificial cell by causing it to move in a predefined path. Here, control over only a single artificial cell was shown, however multiple artificial cells present within an experimental chamber are all exposed to and actuated by the magnetic field, and thus global control over a group of particles can be accomplished using the described system. Yet, to achieve biomedical or biological applications a global magnetic field must be able to guide an arbitrary number of artificial cells located in n number of initial positions to m number of goal locations. This can be accomplished in two ways: (1) by exploiting differences in the magnetic composition of artificial cells so that heterogeneous populations of cells behave differently under the same applied field⁴² (2) using obstacles within the workspace, which are sufficient to make positions of particles fully controllable.⁴³ We envision that this microrobotic system can be used to study biological phenomena, such as cell signaling, and also be use as tool for mask-less biomanufacturing. By using stimuli-responsive artificial cell based microrobots to assemble larger structures, this system could potentially be used for many biomedical applications. For example, assemblies of stimuli-responsive artificial cell could be used for tissue engineering, pharmaceutical research, and regenerative medicine, depending on the contents (human cells, drugs, etc.) and design of the assembly. Furthermore, the control and design strategies developed for this microscale fabrication system could be used to aid in advancing current additive bio-manufacturing methodologies.