Rotational magnetic particles microrheology: the Maxwellian case

Dynamic response of a ferromagnetic nanofilament under rotating fields: effects of flexibility, thermal fluctuations and hydrodynamics

Using nonequilibrium computer simulations, we study the response of ferromagnetic nanofilaments, consisting of stabilized one dimensional chains of ferromagnetic nanoparticles, under external rotating magnetic fields. In difference with their analogous microscale and stiff counterparts, which have been actively studied in recent years, nonequilibrium properties of rather flexible nanoparticle filaments remain mostly unexplored. By progressively increasing the modeling details, we are able to evidence the qualitative impact of main interactions that can not be neglected at the nanoscale, showing that filament flexibility, thermal fluctuations and hydrodynamic interactions contribute independently to broaden the range of synchronous frequency response in this system. Furthermore, we also show the existence of a limited set of characteristic dynamic filament configurations and discuss in detail the asynchronous response, which at finite temperature becomes probabilistic.

tPA-anchored nanorobots for in vivo arterial recanalization at submillimeter-scale segments

Micro/nanorobots provide a promising approach for intravascular therapy with high precision. However, blood vessel is a highly complex system, and performing interventional therapy in those submillimeter segments remains challenging. While micro/nanorobots can enter submillimeter segments, they may still comprise nonbiodegradable parts, posing a considerable challenge for post-use removal. Here, we developed a retrievable magnetic colloidal microswarm, composed of tPA-anchored Fe3O4@mSiO2 nanorobots (tPA-nbots), to archive tPA-mediated thrombolysis under balloon catheter-assisted magnetic actuation with x-ray fluoroscopy imaging system (CMAFIS). By deploying tPA-nbot transcatheter to the vicinity of the thrombus, the tPA-nbot microswarms were magnetically actuated to the blood clot at the submillimeter vessels with high precision. After thrombolysis, the tPA-nbots can be retrieved via the CMAFIS, as demonstrated in ex vivo organ of human placenta and in vivo carotid artery of rabbit. The proposed colloidal microswarm provides a promising robotic tool with high spatial precision for enhanced thrombolysis with low side effects.

Small-Scale Robotics with Tailored Wettability

Small-scale robots (SSRs) have emerged as promising and versatile tools in various biomedical, sensing, decontamination, and manipulation applications, as they are uniquely capable of performing tasks at small length scales. With the miniaturization of robots from the macroscale to millimeter-, micrometer-, and nanometer-scales, the viscous and surface forces, namely adhesive forces and surface tension have become dominant. These forces significantly impact motion efficiency. Surface engineering of robots with both hydrophilic and hydrophobic functionalization presents a brand-new pathway to overcome motion resistance and enhance the ability to target and regulate robots for various tasks. This review focuses on the current progress and future perspectives of SSRs with hydrophilic and hydrophobic modifications (including both tethered and untethered robots). The study emphasizes the distinct advantages of SSRs, such as improved maneuverability and reduced drag forces, and outlines their potential applications. With continued innovation, rational surface engineering is expected to endow SSRs with exceptional mobility and functionality, which can broaden their applications, enhance their penetration depth, reduce surface fouling, and inhibit bacterial adhesion.

Unveiling the Rolling to Kayak Transition in Propelling Nanorods with Cargo Trapping and Pumping

Magnetic nanorods driven by rotating fields in water can be rapidly steered along any direction while generating strong and localized hydrodynamic flow fields. Here we show that, when raising the frequency of the rotating field, these nanopropellers undergo a dynamic transition from a rolling to a kayak-like motion due to the increase in viscous drag and acquire a finite inclination angle with respect to the plane perpendicular to the bottom surface. We explain these experimental observations with a theoretical model which considers the nanorod as a pair of ferromagnetic particles hydrodynamically interacting with a close stationary surface. Further, we quantify how efficiently microscopic cargoes can be trapped or expelled from the moving nanorod and use numerical simulations to unveil the generated hydrodynamic flow field. These propulsion regimes can be implemented in microfluidic devices to perform precise operations based on the selective sorting of microscopic cargoes.

Passive and Active Microrheology for Biomedical Systems

Microrheology encompasses a range of methods to measure the mechanical properties of soft materials. By characterizing the motion of embedded microscopic particles, microrheology extends the probing length scale and frequency range of conventional bulk rheology. Microrheology can be characterized into either passive or active methods based on the driving force exerted on probe particles. Tracer particles are driven by thermal energy in passive methods, applying minimal deformation to the assessed medium. In active techniques, particles are manipulated by an external force, most commonly produced through optical and magnetic fields. Small-scale rheology holds significant advantages over conventional bulk rheology, such as eliminating the need for large sample sizes, the ability to probe fragile materials non-destructively, and a wider probing frequency range. More importantly, some microrheological techniques can obtain spatiotemporal information of local microenvironments and accurately describe the heterogeneity of structurally complex fluids. Recently, there has been significant growth in using these minimally invasive techniques to investigate a wide range of biomedical systems both in vitro and in vivo. Here, we review the latest applications and advancements of microrheology in mammalian cells, tissues, and biofluids and discuss the current challenges and potential future advances on the horizon.

Dynamic magnetic birefringence in a viscoelastic ferrocolloid

A model is developed to describe the oscillations of optical anisotropy induced in a viscoelastic ferrocolloid (nanodispersion of magnetic particles) by an AC magnetic field. The viscoelasticity of the matrix (carrier medium) is assumed to obey the Jeffreys rheological scheme, whose advantage is that with the aid of just two viscous parameters and a single one for elasticity it enables one to vary the retarded mechanical response of the carrier from a weakly Maxwellian fluid to a medium with the rheology of a Kelvin gel. As the orientational motion of the particles driven by the AC field is always strongly affected by thermal motion, the occurring process is described with the aid of a kinetic (Fokker-Planck type) equation that combines diffusional and drift terms. On this basis, an exact evolution equation for the macroscopic optical anisotropy of a ferrocolloid is derived that is, however, just one link in an infinite chain of equations for statistical moments. The solution is obtained by applying effective field approximation: reducing the number of moment equations to their minimum and closing the chosen set. This solution is substituted to the scheme of a standard polarimetric set-up, and it is demonstrated how the peculiarities imparted by viscoelasticity should manifest themselves on the intensity of the light transmitted through the set up containing a ferrocolloid sample. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Collision and separation of nickel particles embedded in a polydimethylsiloxan matrix under a rotating magnetic field: A strong magneto active function

In order to function as soft actuators, depending on their field of use, magnetorheological elastomers (MREs) must fulfill certain criteria. To name just a few, these can include rapid response to external magnetic fields, mechanical durability, mechanical strength, and/or large deformation. Of particular interest are MREs which produce macroscopic deformation for small external magnetic field variations. This work demonstrates how this can be achieved by just a small change in magnetic field orientation. To achieve this, (super)paramagnetic nickel particles of size ≈ 160 μm were embedded in a non-magnetic polydimethylsiloxan (PDMS) (661–1301 Pa) and their displacement in a stepwise rotated magnetic field (170 mT) recorded using a video microscope. Changes in particle aggregation resulting from very small variations in magnetic field orientation led to the observation of a new strongly magneto-active effect. This configuration is characterized by an interparticle distance in relation to the angle difference between magnetic field and particle axis. This causes a strong matrix deformation which in turn demonstrates hysteresis on relaxation. It is shown that the occurrence strongly depends on the particle size, particle distance, and stiffness of the matrix. Choosing the correct parameter combination, the state can be suppressed and the particle-matrix system demonstrates no displacement or hysteresis. In addition, evidences of non-negligible higher order magnetization effects are experimentally ascertained which is qualitatively in agreement with similar, already theoretically described, particle systems. Even at larger particle geometries, the new strongly magneto-active configuration is preserved and could create macroscopic deformation changes.

Independent Pattern Formation of Nanorod and Nanoparticle Swarms under an Oscillating Field

Natural swarms can be formed by various creatures. The swarms can conduct demanded behaviors to adapt to their living environments, such as passing through harsh terrains and protecting each other from predators. At micrometer and nanometer scales, formation of a swarm pattern relies on the physical or chemical interactions between the agents owing to the absence of an on-board device. Independent pattern formation of different swarms, especially under the same input, is a more challenging task. In this work, a swarm of nickel nanorods is proposed and by exploiting its different behavior with the nanoparticle swarm, independent pattern formation of diverse microrobotic swarms under the same environment can be conducted. A mathematical model for the nanorod swarm is constructed, and the mechanism is illustrated. Two-region pattern changing of the nanorod swarm is discovered and compared with the one-region property of the nanoparticle swarm. Experimental characterization of the nanorod swarm pattern is conducted to prove the concept and validate the effectiveness of the theoretical analysis. Furthermore, independent pattern formation of different microrobotic swarms was demonstrated. The pattern of the nanorod swarm could be adjusted while the other swarm was kept unchanged. Simultaneous pattern changing of two swarms was achieved as well. As a fundamental research on the microrobotic swarm, this work presents how the nanoscale magnetic anisotropy of building agents affects their macroscopic swarm behaviors and promotes further development on the independent control of microrobotic swarms under a global field input.

Hierarchical assemblies of superparamagnetic colloids in time-varying magnetic fields

Magnetically-guided colloidal assembly has proven to be a versatile method for building hierarchical particle assemblies. This review describes the dipolar interactions that govern superparamagnetic colloids in time-varying magnetic fields, and how such interactions have guided colloidal assembly into materials with increasing complexity that display novel dynamics. The assembly process is driven by magnetic dipole-dipole interactions, whose strength can be tuned to be attractive or repulsive. Generally, these interactions are directional in static external magnetic fields. More recently, time-varying magnetic fields have been utilized to generate dipolar interactions that vary in both time and space, allowing particle interactions to be tuned from anisotropic to isotropic. These interactions guide the dynamics of hierarchical assemblies of 1-D chains, 2-D networks, and 2-D clusters in both static and time-varying fields. Specifically, unlinked and chemically-linked colloidal chains exhibit complex dynamics, such as fragmentation, buckling, coiling, and wagging phenomena. 2-D networks exhibit controlled porosity and interesting coarsening dynamics. Finally, 2-D clusters have shown to be an ideal model system for exploring phenomena related to statistical thermodynamics. This review provides recent advances in this fast-growing field with a focus on its scientific potential.

External Power-Driven Microrobotic Swarm: From Fundamental Understanding to Imaging-Guided Delivery

Untethered micro/nanorobots have been widely investigated owing to their potential in performing various tasks in different environments. The significant progress in this emerging interdisciplinary field has benefited from the distinctive features of those tiny active agents, such as wireless actuation, navigation under feedback control, and targeted delivery of small-scale objects. In recent studies, collective behaviors of these tiny machines have received tremendous attention because swarming agents can enhance the delivery capability and adaptability in complex environments and the contrast of medical imaging, thus benefiting the imaging-guided navigation and delivery. In this review, we summarize the recent research efforts on investigating collective behaviors of external power-driven micro/nanorobots, including the fundamental understanding of swarm formation, navigation, and pattern transformation. The fundamental understanding of swarming tiny machines provides the foundation for targeted delivery. We also summarize the swarm localization using different imaging techniques, including the imaging-guided delivery in biological environments. By highlighting the critical steps from understanding the fundamental interactions during swarm control to swarm localization and imaging-guided delivery applications, we envision that the microrobotic swarm provides a promising tool for delivering agents in an active, controlled manner.

Magnetic torque-driven deformation of Ni-nanorod/hydrogel nanocomposites

Nickel (Ni) nanorods were prepared by the anodized aluminum oxide (AAO) template method and dispersed in poly(acrylamide) (PAM) hydrogels. The deformation of the magnetoresponsive composites was studied with particular attention to the consequences of finite magnetic shape anisotropy as compared to rigid dipoles on the field-dependent torque. For comparison with experiments, the composite was described as an elastic continuum with a local magnetic torque density, applied by discrete particles and determined by the local orientation of their magnetic anisotropy axis with respect to the magnetic field. The mean magnetic moment of the single domain particles m and their volume density in the composite φ vol were derived from the static field-dependent optical transmission (SFOT) of linear polarized light. The mechanical coupling between the particles and their viscoelastic environment was retrieved from the rotational dynamics of the nanorods using oscillating field-dependent optical transmission (OFOT) measurements. Field- and orientation-dependent magnetization measurements were analyzed using the Stoner–Wohlfarth (SW) model and a valid parameter range was identified by introducing an effective anisotropy constant K A as a new empirical model parameter. This adapted SW-model for quantitative description of the field- and orientation dependence of the magnetic torque was validated by measuring the local rotation of nanorods in a soft elastic hydrogel. Finally, torsional and bending deformation of thin magnetically textured composite filaments were computed and compared with experiments.

Real-Time Magnetic Navigation of a Rotating Colloidal Microswarm Under Ultrasound Guidance

OBJECTIVE

Untethered microrobots hold great promise for applications in biomedical field including targeted delivery, biosensing, and microsurgery. A major challenge of using microrobots to perform in vivo tasks is the real-time localization and motion control using medical imaging technologies. Here we report real-time magnetic navigation of a paramagnetic nanoparticle-based microswarm under ultrasound guidance.

METHODS

A three-axis Helmholtz electromagnetic coil system integrated with an ultrasound imaging system is developed for generation, actuation, and closed-loop control of the microswarm. The magnetite nanoparticle-based microswarm is generated and navigated using rotating magnetic fields. In order to localize the microswarm in real time, the dynamic imaging contrast has been analyzed and exploited in image process to increase the signal-to-noise ratio. Moreover, imaging of the microswarm at different depths are experimentally studied and analyzed, and the minimal dose of nanoparticles for localizing a microswarm at different depths is ex vivo investigated. For real-time navigating the microswarm in a confined environment, a PI control scheme is designed.

RESULTS

Image differencing-based processing increases the signal-to-noise ratio, and the microswarm can be ex vivo localized at depth of 2.2-7.8 cm. Experimental results show that the microswarm is able to be real-time navigated along a planned path in a channel, and the average steady-state error is 0.27 mm (  ∼ 33.7% of the body length).

SIGNIFICANCE

The colloidal microswarm is real-time localized and navigated using ultrasound feedback, which shows great potential for biomedical applications that require real-time noninvasive tracking.

Direct measurement of the ballistic motion of a freely floating colloid in Newtonian and viscoelastic fluids

A thermal colloid suspended in a liquid will transition from a short-time ballistic motion to a long-time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure of the particular liquid. We directly observe a free floating tracer particle's ballistic motion and its transition to the long-time regime in both a Newtonian fluid and a viscoelastic Maxwell fluid. We examine the motion of the free particle in a Newtonian fluid and demonstrate a high degree of agreement with the accepted Clercx-Schram model for motion in a dense fluid. Measurements of the functional form of the ballistic-to-diffusive transition provide direct measurements of the temperature, viscosity, and tracer radius. We likewise measure the motion in a viscoelastic Maxwell fluid and find a significant disagreement between the theoretical asymptotic behavior and our measured values of the microscopic properties of the fluid. We observe a greatly increased effective mass for a freely moving particle and a decreased plateau modulus.

Passive and Active Microrheology of the Intestinal Fluid of the Larval Zebrafish

The fluids of the intestine serve as a physical barrier to pathogens, a medium for the diffusion of nutrients and metabolites, and an environment for commensal microbes. The rheological properties of intestinal mucus have therefore been the subject of many investigations, thus far limited to in vitro studies due to the difficulty of measurement in the natural context of the gut. This limitation especially hinders our understanding of how the gut microbiota interact with the intestinal space, since examination of this calls not only for in vivo measurement techniques, but for techniques that can be applied to model organisms in which the microbial state of the gut can be controlled. We have addressed this challenge with two complementary approaches. We performed passive microrheological measurements using thermally driven nanoparticles and active microrheology using micron-scale ellipsoidal magnetic microparticles, in both cases using light-sheet fluorescence microscopy to optically access the intestinal bulb of the larval zebrafish, a model vertebrate. We present viscosity measurements in germ-free animals (devoid of gut microbes), animals colonized by a single bacterial species, and conventionally reared animals, and find that in all cases, the mucin-rich intestinal liquid is well described as a Newtonian fluid. Surprisingly, despite known differences in the number of secretory cells in germ-free zebrafish and their conventional counterparts, the fluid viscosity for these two groups is very similar, as measured with either technique. Our study provides, to our knowledge, the first in vivo microrheological measurements of the intestinal space in living animals, and we comment on its implications for timescales of host-microbe interactions in the gut.

Impact of a mechanical shear stress on intracellular trafficking

Intracellular trafficking mainly takes place along the microtubules, and its efficiency depends on the local architecture and organization of the cytoskeletal network. In this work, the cytoplasm of stem cells is subjected to mechanical vortexing at a frequency of up to 1 Hz, by using magnetic chains of endosomes embedded in the cell body, in order to locally perturb the network structure. The consequences are evaluated on the directionality and processivity of the spontaneous motion of endosomes. When the same chains are used both to shear the cell medium and to probe the intracellular traffic, a substantial decrease in transport efficiency is detected after applying the mechanical shear. Interestingly, when using different objects to apply the shear and to probe the spontaneous motion, no alteration of the transport efficiency can be detected. We conclude that shaking the vesicles mainly causes their unbinding from the cytoskeletal tracks, but has little influence on the integrity of the network itself. This is corroborated by active microrheology measurements, performed with chains actuated by a magnetic field, and showing that the mechanical compliance of the cytoplasm is similar before and after slow vortexing.

Magnetic response of gelatin ferrogels across the sol-gel transition: the influence of high energy crosslinking on thermal stability

As emerging responsive materials, ferrogels have demonstrated significant potential for applications in areas of engineering to regenerative medicine. Promising techniques to study the behavior of magnetic nanoparticles (MNPs) in such matrices include magnetic particle spectroscopy (MPS) and magnetorelaxometry (MRX). This work investigated the magnetic response of gelatin-based ferrogels with increasing temperatures, before and after high energy crosslinking. The particle response was characterized by the nonlinear magnetization using MPS and quasistatic magnetization measurements as well as MRX to discriminate between Néel and Brownian relaxation mechanisms. The effective magnetic response of MNPs in gelatin was suppressed, indicating that the magnetization of the ferrogels was strongly influenced by competing dipole-dipole interactions. Significant changes in the magnetic behavior were observed across the gelatin sol-gel transition, as influenced by the matrix viscosity. These relaxation processes were modeled by Fourier transformation of the Langevin function, combined with a Debye term for the nonlinear magnetic response, for single core MNPs embedded in matrices of changing viscosities. Using high energy electron irradiation as a crosslinking method, modified ferrogels exhibited thermal stability on a range of timescales. However, MRX relaxation times revealed a slight softening around the gelatin sol-gel transition felt by the smallest particles, demonstrating a high sensitivity to observe local changes in the viscoelasticity. Overall, MPS and MRX functioned as non-contact methods to observe changes in the nanorheology around the native sol-gel transition and in crosslinked ferrogels, as well as provided an understanding of how MNPs were integrated into and influenced by the surrounding matrix.

Microgels at the Water/Oil Interface: In Situ Observation of Structural Aging and Two-Dimensional Magnetic Bead Microrheology

Stimuli-responsive microgels can be used as stabilizers for emulsions. However, the details of structure and the viscoelastic property of the microgel-laden interface are still not well-known. We synthesized fluorescently labeled microgels and used confocal microscopy to observe their arrangement at the water/oil interface. The microgels aggregated spontaneously at the interface, and the aggregated structure reorganized due to thermal motion. The structure of the interfacial layer formed by microgels depended on the microgel concentration at the interface. We suggest that the structure was controlled by the aggregation and adsorption of microgels at the interface. The interparticle separation between microgels at the interface decreased over time, implying a slow aging process of the microgels at the interface. Magnetic beads were introduced at the interface and used to trigger deformation of the microgel layer. Under compression and shear the microgels in the aggregated structure rearranged, leading to plastic deformation, and some elastic responses were also observed.

Magnetic microrods as a tool for microrheology

Dynamics of superparamagnetic rods in crossed constant and alternating magnetic fields as a function of field frequency are studied and it is shown that above the critical value of the amplitude of the alternating field the rod oscillates around the direction of the alternating field. The fit of the experimentally measured time dependence of the mean orientation angle of the rod allows one to determine the ratio of magnetic and viscous torques which act on the rod. The protocol of microrheological measurements consists of recording the dynamics of the orientation of the rod when the magnetic field is applied at an angle to the rod and observing its relaxation due to the accumulated elastic energy after the field is switched off. The microrheological data obtained are in reasonable agreement with the macrorheological measurements.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Rotational microrheology of Maxwell fluids using micron-sized wires

We demonstrate a simple method for rotational microrheology in complex fluids using micrometric wires. The three-dimensional rotational Brownian motion of the wires suspended in Maxwell fluids is measured from their projection on the focal plane of a microscope. We analyze the mean-squared angular displacement of the wires of length between 1 and 40 μm. The viscoelastic properties of the suspending fluids are examined from this analysis and found to be in good agreement with macrorheology data. Viscosities of simple and complex fluids between 10(-2) and 30 Pa s could be measured. As for the elastic modulus, values up to ∼5 Pa could be determined. This simple technique, allowing for a broad range of probed length scales, opens new perspectives in microrheology of heterogeneous materials such as gels, glasses and cells.

Conformational changes of a single magnetic particle string within gels

Magnetorheological (MR) gels consist of micron sized magnetic particles inside a gel matrix. Before physical cross-linking, the suspension is subjected to a small magnetic field which creates a particle string structure. After cross-linking, the string is kept within the gel at room temperature. Under an external homogeneous magnetic field and mechanical deformation, the soft swollen gel matrix allows the string to largely rearrange at microscopic scales. With the help of two homemade magneto cells mounted on an optical microscope, we were able to follow the conformational change and instabilities of a single magnetic particle string under the combined influence of shear (or stretch) and the magnetic field. In the absence of mechanical deformation, an external magnetic field, applied in the perpendicular direction to the string, breaks it into small pieces generating periodic structures like sawteeth. When an external magnetic field is applied parallel to the pre-aligned string, it exhibits a length contraction. However, under shear strain perpendicular to the original pre-structured string (and magnetic field), the string breaks and short string segments tilt, making an angle with the original direction that is smaller than that of the applied shear (non-affine). The difference in tilt angle scales with the inverse length of the small segments L-1 and the magnetic flux density B, reflecting the ability of the gel matrix to expel solvents under local stress.

Impact of photosensitizers activation on intracellular trafficking and viscosity

The intracellular microenvironment is essential for the efficiency of photo-induced therapies, as short-lived reactive oxygen species generated must diffuse through their intracellular surrounding medium to reach their cellular target. Here, by combining measurements of local cytoplasmic dissipation and active trafficking, we found that photosensitizers activation induced small changes in surrounding viscosity but a massive decrease in diffusion. These effects are the signature of a return to thermodynamic equilibrium of the system after photo-activation and correlated with depolymerization of the microtubule network, as shown in a reconstituted system. These mechanical measurements were performed with two intracellular photosensitizing chlorins having similar quantum yield of singlet oxygen production but different intracellular localizations (cytoplasmic for mTHPC, endosomal for TPCS2a). These two agents demonstrated different intracellular impact.

Magnetic wire-based sensors for the microrheology of complex fluids

We propose a simple microrheology technique to evaluate the viscoelastic properties of complex fluids. The method is based on the use of magnetic wires of a few microns in length submitted to a rotational magnetic field. In this work, the method is implemented on a surfactant wormlike micellar solution that behaves as an ideal Maxwell fluid. With increasing frequency, the wires undergo a transition between a steady and a hindered rotation regime. The study shows that the average rotational velocity and the amplitudes of the oscillations obey scaling laws with well-defined exponents. From a comparison between model predictions and experiments, the rheological parameters of the fluid are determined.

Numerical and experimental study of a rotating magnetic particle chain in a viscous fluid

A simple and fast numerical method is developed capable of accurately determining the 3D rotational dynamics of a magnetic particle chain in an infinite fluid domain. The focus is to control the alternating breakup and reformation of the bead chain which we believe is essential to achieve effective fluid mixing at small scales. The numerical scheme makes use of magnetic dipole moments and extended forms of the Oseen-Burgers tensor to account for both the magnetic and hydrodynamic interactions between the particles. It is shown that the inclusion of hydrodynamic interaction between the particles is crucial to obtain a good description of the particle dynamics. Only a small error of deviation is observed when benchmarking the numerical scheme against a more computationally intensive method, the direct simulation method. The numerical results are compared with experiments and the simulated rotational dynamics correspond well with those obtained from video-microscopy experiments qualitatively and quantitatively. In addition, a dimensionless number (R(T)) is derived as the sole control parameter for the rotational bead chain dynamics. Numerically and experimentally, R(T)≈ 1 is the boundary between rigid "rod" and dynamic "breaking and reformation" behaviors.

Magnetic nanomanipulations inside living cells compared with passive tracking of nanoprobes to get consensus for intracellular mechanics

During the last decade, the development of nanomaterials to penetrate inside living cells has been the focus of a large number of studies, with applications for the biomedical field. However, the further dynamics of these nanomaterials inside the cells is dictated by the intracellular environment and in particular its mechanical properties. The mechanical characteristics of the cell interior can be probed with either active or passive microrheological approaches. However, active intracellular microrheology is still in its infancy, owing to the difficulty of inserting probes that can be manipulated by external forces. Here we review recent active microrheology studies using magnetic nanoprobes inserted into endosomes or phagosomes as useful approaches for measuring frequency-dependent viscoelasticity, for mapping the viscoelastic landscape, as well as for identifying the contribution of individual cytoskeleton components and the influence of cell motility. The results of such direct measurements challenge the validity of more typical passive approaches in which the spontaneous displacement of embedded nanoprobes is measured. Here we discuss that one must distinguish probes suitable for use in conditions of thermal equilibrium, whose movements reflect the mechanical environment from probes that interact actively with the cytoplasm and cytoskeleton, in a state of nonequilibrium for which fluctuation-dissipation theorem no longer holds. However, when data on these probes' viscoelastic microenvironment is available, such passive probe movements can yield useful information on the forces responsible for intracellular activity.

Rotational diffusion of magnetic nickel nanorods in colloidal dispersions

Colloidal dispersions of Ni nanorods were synthesized by pulsed electrodeposition of Ni into nanoporous aluminum oxide layers followed by dissolution of the templates. Geometrical characterization of the nanorods by transmission electron microscopy and scanning electron microscopy allowed us to determine the average length (100-250 nm) and diameter (20-40 nm) of the rods and to estimate the thickness of the polyvinylpyrrolidone surfactant layer. Due to their acicular shape, nanorods of the given size are uniaxial ferromagnetic single domain particles and exhibit a distinct anisotropic polarizability. These two characteristic properties are the physical basis for magnetic field-dependent optical transmission and allow us to investigate the rotational diffusion of the nanorods in liquid dispersion. In the present study, we employed AC magnetization measurements, dynamical light scattering and optical transmission measurements in a rotating magnetic field to determine the rotational diffusion coefficient. The results from all three methods were consistent and agree with theory within a factor of 2.

Small-world rheology: an introduction to probe-based active microrheology

We introduce active, probe-based microrheological techniques for measuring the flow and deformation of complex fluids. These techniques are ideal for mechanical characterization either when little sample is available, or when samples show significant spatial heterogeneity. We review recent results, paying particular attention to comparing and contrasting rheological parameters obtained from micro- and macro-rheological techniques.

Aggregation and disaggregation dynamics of sedimented and charged superparamagnetic micro-particles in water suspension

This article presents results on the aggregation and disaggregation kinetics on a 1 μm diameter charged superparamagnetic particles dispersed in water under a constant uniaxial magnetic field in experiments with salt (KCl) added to the suspension in order to observe the behaviour of the system when the electrical properties of the particles have been screened. These particles have an electric charge and are confined between two separated 100 μm thick quartz windows, and sediment near the charged bottom wall. The electrostatic interactions that take place in this experimental setup may affect the micro-structure and colloidal stability of the suspension and thus, the dynamics of aggregation and disaggregation.

Elastic torsion effects in magnetic nanoparticle diblock-copolymer structures

Magnetic properties of thin composite films, consisting of non-interacting polystyrene-coated γ-Fe(2)O(3) (maghemite) nanoparticles embedded into polystyrene-block-polyisoprene P(S-b-I) diblock-copolymer films are investigated. Different particle concentrations, ranging from 0.7 to 43 wt%, have been used. The magnetization measured as a function of external field and temperature shows typical features of anisotropic superparamagnets including a hysteresis at low temperatures and blocking phenomena. However, the data cannot be reconciled with the unmodified Stoner-Wohlfarth-Néel theory. Applying an appropriate generalization we find evidence for either an elastic torque being exerted on the nanoparticles by the field or a broad distribution of anisotropy constants.

Colour-barcoded magnetic microparticles for multiplexed bioassays

Encoded particles have a demonstrated value for multiplexed high-throughput bioassays such as drug discovery and clinical diagnostics. In diverse samples, the ability to use a large number of distinct identification codes on assay particles is important to increase throughput. Proper handling schemes are also needed to readout these codes on free-floating probe microparticles. Here we create vivid, free-floating structural coloured particles with multi-axis rotational control using a colour-tunable magnetic material and a new printing method. Our colour-barcoded magnetic microparticles offer a coding capacity easily into the billions with distinct magnetic handling capabilities including active positioning for code readouts and active stirring for improved reaction kinetics in microscale environments. A DNA hybridization assay is done using the colour-barcoded magnetic microparticles to demonstrate multiplexing capabilities.

In vivo determination of fluctuating forces during endosome trafficking using a combination of active and passive microrheology

Background

Regulation of intracellular trafficking is a central issue in cell biology. The forces acting on intracellular vesicles (endosomes) can be assessed in living cells by using a combination of active and passive microrheology.

Methodology/Principal Findings

This dual approach is based on endosome labeling with magnetic nanoparticles. The resulting magnetic endosomes act both as probes that can be manipulated with external magnetic fields to infer the viscoelastic modulus of their surrounding microenvironment, and as biological vehicles that are trafficked along the microtubule network by means of forces generated by molecular motors. The intracellular viscoelastic modulus exhibits power law dependence with frequency, which is microtubule and actin-dependent. The mean square displacements of endosomes do not follow the predictions of the fluctuation-dissipation theorem, which offers evidence for active force generation. Microtubule disruption brings the intracellular medium closer to thermal equilibrium: active forces acting on the endosomes depend on microtubule-associated motors. The power spectra of these active forces, deduced through the use of a generalized Langevin equation, show a power law decrease with frequency and reveal an actin-dependent persistence of the force with time. Experimental spectra have been reproduced by a simple model consisting in a series of force steps power-law distributed in time. This model enlightens the role of the cytoskeleton dependent force exerted on endosomes to perform intracellular trafficking.

Conclusions/Significance

In this work, the influence of cytoskeleton components and molecular motors on intracellular viscoelasticity and transport is addressed. The use of an original probe, the magnetic endosome, allows retrieving the power spectrum of active forces on these organelles thanks to interrelated active and passive measures.

Finally a computational model gives estimates of the force itself and hence of the number of the motors pulling on endosomes.

Combined passive and active microrheology study of protein-layer formation at an air-water interface

We investigate the mechanical properties of layers of the protein beta-lactoglobulin during their formation at the air-water interface using a combination of passive and active microrheological techniques. The passive microrheology, which employs multiple particle tracking measurements using spherical colloids, indicates that the interfacial rheology evolves over time through three stages as protein adsorbs at the interface: (i) an increase in viscosity, (ii) a period of spatial heterogeneity in which the interface contains elastic and viscous regions, and (iii) the development of a uniformly rigid elastic film. Varying solution pH between pH = 5.2, the isoelectric point of beta-lactoglobulin, and pH = 7.0 has no qualitative effect on this mechanical evolution. The active microrheology, which employs ferromagnetic nanowires rotating in response to magnetic torques, similarly shows an increasing interfacial viscosity at early times and evidence of mechanical heterogeneity at intermediate times. However, at late times, the nanowire mobility becomes strongly pH dependent. For pH = 5.2, the layer responds as a rigid elastic film to the stress imposed by the wire. For pH = 7.0, it displays a viscous response that contrasts with the passive measurements. We associate this contrast with a nonlinear response to the wire at late times that reflects a low yield stress of the film at higher pH. This ability to compare passive and active measurements demonstrates the advantage of applying multiple microrheological methods to resolve ambiguity in any single approach.

Magnetic micro-manipulations to probe the local physical properties of porous scaffolds and to confine stem cells

The in vitro generation of engineered tissue constructs involves the seeding of cells into porous scaffolds. Ongoing challenges are to design scaffolds to meet biochemical and mechanical requirements and to optimize cell seeding in the constructs. In this context, we have developed a simple method based on a magnetic tweezer set-up to manipulate, probe, and position magnetic objects inside a porous scaffold. The magnetic force acting on magnetic objects of various sizes serves as a control parameter to retrieve the local viscosity of the scaffolds internal channels as well as the stiffness of the scaffolds pores. Labeling of human stem cells with iron oxide magnetic nanoparticles makes it possible to perform the same type of measurement with cells as probes and evaluate their own microenvironment. For 18 microm diameter magnetic beads or magnetically labeled stem cells of similar diameter, the viscosity was equivalently equal to 20 mPa s in average. This apparent viscosity was then found to increase with the magnetic probes sizes. The stiffness probed with 100 microm magnetic beads was found in the 50 Pa range, and was lowered by a factor 5 when probed with cells aggregates. The magnetic forces were also successfully applied to the stem cells to enhance the cell seeding process and impose a well defined spatial organization into the scaffold.

Magneto-mechanical mixing and manipulation of picoliter volumes in vesicles

Superparamagnetic beads in giant unilamellar vesicles are used to facilitate magnetic manipulation, positioning, agitation and mixing of ultrasmall liquid volumes. Vesicles act as leakproof picoliter reaction vessels in an aqueous bulk solution and can be deliberately conveyed by an external magnetic field to a designated position. Upon application of an external magnetic field the beads align to form extended chains. In a rotating magnetic field chains break up into smaller fragments caused by the interplay of viscous friction and magnetic attraction. This process obeys a simple relationship and can be exploited to enhance mixing of the vesicle content and the outer solution or adjacent vesicle volumes exactly at the position of release.

Electrostatic and hydrodynamics effects in a sedimented magnetorheological suspension

We present experimental results on the equilibrium microstructure of a sedimented magnetorheological suspension, namely, an aqueous suspension of micron-sized superparamagnetic particles. We develop a study of the electrical interactions on the suspension by processing video-microscopy images of the sedimented particles. We calculate the pair distribution function, g(r), which yields the electrostatic pair potential u(r), showing an anomalous attractive interaction for distances on the order of twice the particle diameter, with characteristic parameters whose values show a dependence with the two-dimensional concentration of particles. The repulsive body of the potential is adjusted to a DLVO expression in order to calculate the Debye screening length and the effective surface charge density. Influence of confinement and variations on the Boltzmann sedimentation profile because of the electrostatic interactions appear to be essential for the interpretation of experimental results.

Out-of-equilibrium microrheology inside living cells

Both forced and spontaneous motions of magnetic microbeads engulfed by Dictyostelium cells have served as experimental probes of intracellular dynamics. The complex shear modulus G*(omega), determined from active oscillatory measurements, has a power-law dynamics and increases with the probe size, reflecting intracellular structural complexity. The combined use of passive microrheology allows one to derive the power spectrum of active forces acting on intracellular phagosomes and to test the validity of the fluctuation-dissipation theorem inside living cells.

Transient behaviour of magnetic micro-bead chains rotating in a fluid by external fields

Magnetic micro-beads can facilitate many functions in lab-on-a-chip systems, such as bio-chemical labeling, selective transport, magnetic sensing and mixing. In order to investigate potential applications of magnetic micro-beads for mixing in micro fluidic systems, we developed a pin-jointed mechanism model that allows analysing the behaviour of rotating superparamagnetic bead chains. Our numerical model revealed the response of the chains on a rotating magnetic field over time. We could demonstrate that the governing parameters are the Mason number and number of beads in the chain. The results are in agreement with the simplified analytical model, assuming a straight chain, but also allow prediction of the transient chain shape. The modelled chains develop an anti-symmetric S-shape that is stable, if the Mason number for a given chain length does not surpass a critical value. Above that value, rupture occurs in the vicinity of the chain centre. However, variations in bead susceptibility can shift the location of rupture. Moreover, we performed experiments with superparamagnetic micro-beads in a small fluid volume exposed to a uniform rotating magnetic field. Our simulation could successfully predict the observed transient chain form and the time for chain rupture. The developed model can be used to design optimised bead based mixers in micro fluidic systems.

Scaling in the aggregation dynamics of a magnetorheological fluid

We present experimental results on the aggregation dynamics of a magnetorheological fluid, namely, an aqueous suspension of micrometer-sized superparamagnetic particles, under the action of a constant uniaxial magnetic field using video microscopy and image analysis. We find a scaling behavior in several variables describing the aggregation kinetics. The data agree well with the Family-Vicsek scaling ansatz for diffusion-limited cluster-cluster aggregation. The kinetic exponents z and z' are obtained from the temporal evolution of the mean cluster size S(t) and the number of clusters N(t), respectively. The crossover exponent Delta is calculated in two ways: first, from the initial slope of the scaling function; second, from the evolution of the nonaggregated particles, n1(t). We report on results of Brownian two-dimensional dynamics simulations and compare the results with the experiments. Finally, we discuss the differences obtained between the kinetic exponents in terms of the variation in the crossover exponent and relate this behavior to the physical interpretation of the crossover exponent.

Rotating magnetic particle microrheometry in biopolymer fluid dynamics: Mucus microrheology

The polymer properties of canine mucus were investigated through the method of rotating magnetic particle microrheometry. Mucus is visualized as a physically entangled biopolymer of low polydispersity in a water-based solution. Mucus was modeled according to the constitutive law of a Doi-Edwards fluid. The magnetic-particle equation of rotational motion is analytically solved in the linear viscoelastic limit rendering theoretical flow profiles which are used to fit the experimental trace signals of the particle remanent-magnetic-field decay. The zero-shear-rate viscosity was found to be 18,000 P and the relaxation time at about 42 s. The molecular weight between entanglements for mucins was estimated at 1.7 MDa rendering an estimation of about seven physical cross-links per molecule. Rheological investigations were extended also to diluted and concentrated rations of the normal mucus simulating the conditions found in more physiological extremes.