Steering control of magnetic helical swimmers in swirling flows due to confinement

Artificial microswimmers are prospective robotic agents especially in biomedical applications. A rotating magnetic field can actuate a magnetized swimmer with a helical tail and enable propulsion. Such swimmers exhibit several modes of instability. Inside conduits, for example, hydrodynamic interactions with the boundaries lead to helical paths for pusher-mode swimmers; in this mode the helical tail pushes a rotating magnetic head. State-of-the-art in controlled navigation of microswimmers is based on aligning the swimmer orientation according to a reference path, thereby requiring both swimmer orientation and position to be known. Object-orientation is hard to track especially in in vivo scenarios which render orientationbased methods practically unfeasible. Here, we show that the kinematics for a confined swimmer can be linearized by assuming a low wobbling angle. This allows for a control law solely based on the swimmer position. The approach is demonstrated through experiments and two different numerical models: the first is based on the resistive force theory for a swimmer inside a swirling flow represented by a forced vortex and the second is a computational fluid dynamics model, which solves Stokes equations for a swimmer inside a circular channel. Helical pusher-mode trajectories are suppressed significantly for the straight path following problem. The error in real-life experiments remains comparable to those in the state-of-the-art methods

Doctor of Philosophy

dissertationThis dissertation presents results documenting advancements on the control of untethered magnetic devices, such as magnetic \microrobots" and magnetically actuated capsuleendoscopes, motivated by problems in minimally invasive medicine. This dissertationfocuses on applying rotating magnetic elds for magnetic manipulation. The contributions include advancements in the way that helical microswimmers (devices that mimicthe propulsion of bacterial agella) are controlled in the presence of gravitational forces, advancements in ways that groups of untethered magnetic devices can be dierentiated and semi-independently controlled, advancements in the way that untethered magnetic device can be controlled with a single rotating permanent magnet, and an improved understanding in the nature of the magnetic force applied to an untethered device by a rotating magnet

Optimal Microswimming

Contrasting the well explored problem on how to steer a macroscopic agent like an airplane or a moon lander to optimally reach a target, ``optimal microswimming'', i.e. the quest for the optimal navigation strategy for microswimmers, remains unsolved. Here, we systematically explore this problem and show that the characteristic flow field of microswimmers crucially influences the required navigation strategy to reach a target fastest. The resulting optimal trajectories can have remarkable and non-intuitive shapes, which qualitatively differ from those of dry active particles or motile macroagents. Our results provide generic insights into the role of hydrodynamics and fluctuations on optimal navigation at the microscale and suggest that microorganisms might have survival advantages when strategically controlling their distance to remote walls. In particular, when fluctuations are present, choosing the optimal strategy, which appropriately respects hydrdynamics, can halve the time to reach the target compared to cases microswimmers head straight towards it.Comment: 10 pages, 8 figures, 68 reference

Design, Actuation, and Functionalization of Untethered Soft Magnetic Robots with Life-Like Motions: A Review

Soft robots have demonstrated superior flexibility and functionality than conventional rigid robots. These versatile devices can respond to a wide range of external stimuli (including light, magnetic field, heat, electric field, etc.), and can perform sophisticated tasks. Notably, soft magnetic robots exhibit unparalleled advantages among numerous soft robots (such as untethered control, rapid response, and high safety), and have made remarkable progress in small-scale manipulation tasks and biomedical applications. Despite the promising potential, soft magnetic robots are still in their infancy and require significant advancements in terms of fabrication, design principles, and functional development to be viable for real-world applications. Recent progress shows that bionics can serve as an effective tool for developing soft robots. In light of this, the review is presented with two main goals: (i) exploring how innovative bioinspired strategies can revolutionize the design and actuation of soft magnetic robots to realize various life-like motions; (ii) examining how these bionic systems could benefit practical applications in small-scale solid/liquid manipulation and therapeutic/diagnostic-related biomedical fields

Physics of Microswimmers - Single Particle Motion and Collective Behavior

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics (to appear

Design and Implementation of Electromagnetic Actuation System to Actuate Micro/NanoRobots in Viscous Environment

The navigation of Micro/Nanorobots (MNRs) with the ability to track a selected trajectory accurately holds significant promise for different applications in biomedicine, providing methods for diagnoses and treatments inside the human body. The critical challenge is ensuring that the required power can be generated within the MNR. Furthermore, ensuring that it is feasible for the robot to travel inside the human body with the necessary power availability. Currently, MNRs are widely driven either by exogenous power sources (light energy, magnetic fields, electric fields, acoustics fields, etc.) or by endogenous energy sources, such as chemical interaction energy. Various driving techniques have been established, including piezoelectric as a driving source, thermal driving, electro-osmotic force driven by biological bacteria, and micro-motors powered by chemical fuel. These driving techniques have some restrictions, mainly when used in biomedicine. External magnetic fields are another potential power source of MNRs. Magnetic fields can permeate deep tissues and be safe for human organisms. As a result, magnetic fields’ magnetic forces and moments can be applied to MNRs without affecting biological fluids and tissues. Due to their features and characteristics of magnetic fields in generating high power, they are naturally suited to control the electromagnetically actuated MNRs in inaccessible locations due to their ability to go through tiny spaces. From the literature, it can be inferred from the available range of actuation technologies that magnetic actuation performs better than other technologies in terms of controllability, speed, flexibility of the working environment, and far less harm may cause to people. Also, electromagnetic actuation systems may come in various configurations that offer many degrees of freedom, different working mediums, and controllability schemes. Although this is a promising field of research, further simulation studies, and analysis, new smart materials, and the development and building of new real systems physically, and testing the concepts under development from different aspects and application requirements are required to determine whether these systems could be implemented in natural clinical settings on the human body. Also, to understand the latest development in MNRs and the actuation techniques with the associated technologies. Also, there is a need to conduct studies and comparisons to conclude the main research achievements in the field, highlight the critical challenges waiting for answers, and develop new research directions to solve and improve the performance. Therefore, this thesis aims to model and analyze, simulate, design, develop, and implement (with complete hardware and software integration) an electromagnetic actuation (EMA) system to actuate MNRs in the sixdimensional (6D) motion space inside a relatively large region of interest (ROI). The second stage is a simulation; simulation and finite element analysis were conducted. COMSOL multi-physics software is used to analyze the performance of different coils and coil pairs for Helmholtz and Maxwell coil configurations and electromagnetic actuation systems. This leads to the following.: • Finite element analysis (FEA) demonstrates that the Helmholtz coils generate a uniform and consistent magnetic field within a targeted ROI, and the Maxwell coils generate a uniform magnetic gradient. • The possibility to combine Helmholtz and Maxwell coils in different space dimensions. With the ability to actuate an MNR in a 6D space: 3D as a position and 3D as orientation. • Different electromagnetic system configurations are proposed, and their effectiveness in guiding an MNR inside a mimicked blood vessel environment was assessed. • Three pairs of Helmholtz coils and three pairs of coils of Maxwell coils are combined to actuate different size MNRs inside a mimicked blood vessel environment and in 6D. Based on the modeling results, a magnetic actuation system prototype that can control different sizes MNRs was conceived. A closed-loop control algorithm was proposed, and motion analysis of the MNR was conducted and discussed for both position and orientation. Improved EMA location tracking along a chosen trajectory was achieved using a PID-based closed-loop control approach with the best possible parameters. Through the model and analysis stage, the developed system was simulated and tested using open- and closed-loop circumstances. Finally, the closedloop controlled system was concluded and simulated to verify the ability of the proposed EMA to actuate an MN under different trajectory tracking examples with different dimensionality and for different sizes of MNRs. The last stage is developing the experimental setup by manufacturing the coils and their base in-house. Drivers and power supplies are selected according to the specifications that actuate the coils to generate the required magnetic field. Three digital microscopes were integrated with the electromagnetic actuation system to deliver visual feedback aiming to track in real-time the location of the MNR in the 6D high viscous fluidic environment, which leads to enabling closed-loop control. The closed-loop control algorithm is developed to facilitate MNR trajectory tracking and minimize the error accordingly. Accordingly, different tests were carried out to check the uniformity of the magnetic field generated from the coils. Also, a test was done for the digital microscope to check that it was calibrated and it works correctly. Experimental tests were conducted in 1D, 2D plane, and 3D trajectories with two different MNR sizes. The results show the ability of the proposed EMA system to actuate the two different sizes with a tracking error of 20-45 µm depending on the axis and the size of the MNR. The experiments show the ability of the developed EMA system to hold the MNR at any point within the 3D fluidic environment while overcoming the gravity effects. A comparison was made between the results achieved (in simulation and physical experiments) and the results deduced from the literature. The comparison shows that the thesis’s outcomes regarding the error and MNR size used are significant, with better performance relative to the MNR size and value of the error

Nonlinear dynamics and fluctuations in biological systems

The present habilitation thesis in theoretical biological physics addresses two central dynamical processes in cells and organisms: (i) active motility and motility control and (ii) self-organized pattern formation. The unifying theme is the nonlinear dynamics of biological function and its robustness in the presence of strong fluctuations, structural variations, and external perturbations. We theoretically investigate motility control at the cellular scale, using cilia and flagella as ideal model system. Cilia and flagella are highly conserved slender cell appendages that exhibit spontaneous bending waves. This flagellar beat represents a prime example of a chemo-mechanical oscillator, which is driven by the collective dynamics of molecular motors inside the flagellar axoneme. We study the nonlinear dynamics of flagellar swimming, steering, and synchronization, which encompasses shape control of the flagellar beat by chemical signals and mechanical forces. Mechanical forces can synchronize collections of flagella to beat at a common frequency, despite active motor noise that tends to randomize flagellar synchrony. In Chapter 2, we present a new physical mechanism for flagellar synchronization by mechanical self-stabilization that applies to free-swimming flagellated cells. This new mechanism is independent of direct hydrodynamic interactions between flagella. Comparison with experimental data provided by experimental collaboration partners in the laboratory of J. Howard (Yale, New Haven) confirmed our new mechanism in the model organism of the unicellular green alga Chlamydomonas. Further, we characterize the beating flagellum as a noisy oscillator. Using a minimal model of collective motor dynamics, we argue that measured non-equilibrium fluctuations of the flagellar beat result from stochastic motor dynamics at the molecular scale. Noise and mechanical coupling are antagonists for flagellar synchronization. In addition to the control of the flagellar beat by mechanical forces, we study the control of the flagellar beat by chemical signals in the context of sperm chemotaxis. We characterize a fundamental paradigm for navigation in external concentration gradients that relies on active swimming along helical paths. In this helical chemotaxis, the direction of a spatial concentration gradient becomes encoded in the phase of an oscillatory chemical signal. Helical chemotaxis represents a distinct gradient-sensing strategy, which is different from bacterial chemotaxis. Helical chemotaxis is employed, for example, by sperm cells from marine invertebrates with external fertilization. We present a theory of sensorimotor control, which combines hydrodynamic simulations of chiral flagellar swimming with a dynamic regulation of flagellar beat shape in response to chemical signals perceived by the cell. Our theory is compared to three-dimensional tracking experiments of sperm chemotaxis performed by the laboratory of U. B. Kaupp (CAESAR, Bonn). In addition to motility control, we investigate in Chapter 3 self-organized pattern formation in two selected biological systems at the cell and organism scale, respectively. On the cellular scale, we present a minimal physical mechanism for the spontaneous self-assembly of periodic cytoskeletal patterns, as observed in myofibrils in striated muscle cells. This minimal mechanism relies on the interplay of a passive coarsening process of crosslinked actin clusters and active cytoskeletal forces. This mechanism of cytoskeletal pattern formation exemplifies how local interactions can generate large-scale spatial order in active systems. On the organism scale, we present an extension of Turing’s framework for self-organized pattern formation that is capable of a proportionate scaling of steady-state patterns with system size. This new mechanism does not require any pre-pattering clues and can restore proportional patterns in regeneration scenarios. We analytically derive the hierarchy of steady-state patterns and analyze their stability and basins of attraction. We demonstrate that this scaling mechanism is structurally robust. Applications to the growth and regeneration dynamics in flatworms are discussed (experiments by J. Rink, MPI CBG, Dresden).:1 Introduction 10 1.1 Overview of the thesis 10 1.2 What is biological physics? 12 1.3 Nonlinear dynamics and control 14 1.3.1 Mechanisms of cell motility 16 1.3.2 Self-organized pattern formation in cells and tissues 28 1.4 Fluctuations and biological robustness 34 1.4.1 Sources of fluctuations in biological systems 34 1.4.2 Example of stochastic dynamics: synchronization of noisy oscillators 36 1.4.3 Cellular navigation strategies reveal adaptation to noise 39 2 Selected publications: Cell motility and motility control 56 2.1 “Flagellar synchronization independent of hydrodynamic interactions” 56 2.2 “Cell body rocking is a dominant mechanism for flagellar synchronization” 57 2.3 “Active phase and amplitude fluctuations of the flagellar beat” 58 2.4 “Sperm navigation in 3D chemoattractant landscapes” 59 3 Selected publications: Self-organized pattern formation in cells and tissues 60 3.1 “Sarcomeric pattern formation by actin cluster coalescence” 60 3.2 “Scaling and regeneration of self-organized patterns” 61 4 Contribution of the author in collaborative publications 62 5 Eidesstattliche Versicherung 64 6 Appendix: Reprints of publications 66Das Thema der vorliegenden Habilitationsschrift in Theoretischer Biologischer Physik ist die nichtlineare Dynamik funktionaler biologischer Systeme und deren Robustheit gegenüber Fluktuationen und äußeren Störungen. Wir entwickeln hierzu theoretische Beschreibungen für zwei grundlegende biologische Prozesse: (i) die zell-autonome Kontrolle aktiver Bewegung, sowie (ii) selbstorganisierte Musterbildung in Zellen und Organismen. In Kapitel 2, untersuchen wir Bewegungskontrolle auf zellulärer Ebene am Modelsystem von Zilien und Geißeln. Spontane Biegewellen dieser dünnen Zellfortsätze ermöglichen es eukaryotischen Zellen, in einer Flüssigkeit zu schwimmen. Wir beschreiben einen neuen physikalischen Mechanismus für die Synchronisation zweier schlagender Geißeln, unabhängig von direkten hydrodynamischen Wechselwirkungen. Der Vergleich mit experimentellen Daten, zur Verfügung gestellt von unseren experimentellen Kooperationspartnern im Labor von J. Howard (Yale, New Haven), bestätigt diesen neuen Mechanismus im Modellorganismus der einzelligen Grünalge Chlamydomonas. Der Gegenspieler dieser Synchronisation durch mechanische Kopplung sind Fluktuationen. Wir bestimmen erstmals Nichtgleichgewichts-Fluktuationen des Geißel-Schlags direkt, wofür wir eine neue Analyse-Methode der Grenzzykel-Rekonstruktion entwickeln. Die von uns gemessenen Fluktuationen entstehen mutmaßlich durch die stochastische Dynamik molekularen Motoren im Innern der Geißeln, welche auch den Geißelschlag antreiben. Um die statistische Physik dieser Nichtgleichgewichts-Fluktuationen zu verstehen, entwickeln wir eine analytische Theorie der Fluktuationen in einem minimalen Modell kollektiver Motor-Dynamik. Zusätzlich zur Regulation des Geißelschlags durch mechanische Kräfte untersuchen wir dessen Regulation durch chemische Signale am Modell der Chemotaxis von Spermien-Zellen. Dabei charakterisieren wir einen grundlegenden Mechanismus für die Navigation in externen Konzentrationsgradienten. Dieser Mechanismus beruht auf dem aktiven Schwimmen entlang von Spiralbahnen, wodurch ein räumlicher Konzentrationsgradient in der Phase eines oszillierenden chemischen Signals kodiert wird. Dieser Chemotaxis-Mechanismus unterscheidet sich grundlegend vom bekannten Chemotaxis-Mechanismus von Bakterien. Wir entwickeln eine Theorie der senso-motorischen Steuerung des Geißelschlags während der Spermien-Chemotaxis. Vorhersagen dieser Theorie werden durch Experimente der Gruppe von U.B. Kaupp (CAESAR, Bonn) quantitativ bestätigt. In Kapitel 3, untersuchen wir selbstorganisierte Strukturbildung in zwei ausgewählten biologischen Systemen. Auf zellulärer Ebene schlagen wir einen einfachen physikalischen Mechanismus vor für die spontane Selbstorganisation von periodischen Zellskelett-Strukturen, wie sie sich z.B. in den Myofibrillen gestreifter Muskelzellen finden. Dieser Mechanismus zeigt exemplarisch auf, wie allein durch lokale Wechselwirkungen räumliche Ordnung auf größeren Längenskalen in einem Nichtgleichgewichtssystem entstehen kann. Auf der Ebene des Organismus stellen wir eine Erweiterung der Turingschen Theorie für selbstorganisierte Musterbildung vor. Wir beschreiben eine neue Klasse von Musterbildungssystemen, welche selbst-organisierte Muster erzeugt, die mit der Systemgröße skalieren. Dieser neue Mechanismus erfordert weder eine vorgegebene Kompartimentalisierung des Systems noch spezielle Randbedingungen. Insbesondere kann dieser Mechanismus proportionale Muster wiederherstellen, wenn Teile des Systems amputiert werden. Wir bestimmen analytisch die Hierarchie aller stationären Muster und analysieren deren Stabilität und Einzugsgebiete. Damit können wir zeigen, dass dieser Skalierungs-Mechanismus strukturell robust ist bezüglich Variationen von Parametern und sogar funktionalen Beziehungen zwischen dynamischen Variablen. Zusammen mit Kollaborationspartnern im Labor von J. Rink (MPI CBG, Dresden) diskutieren wir Anwendungen auf das Wachstum von Plattwürmern und deren Regeneration in Amputations-Experimenten.:1 Introduction 10 1.1 Overview of the thesis 10 1.2 What is biological physics? 12 1.3 Nonlinear dynamics and control 14 1.3.1 Mechanisms of cell motility 16 1.3.2 Self-organized pattern formation in cells and tissues 28 1.4 Fluctuations and biological robustness 34 1.4.1 Sources of fluctuations in biological systems 34 1.4.2 Example of stochastic dynamics: synchronization of noisy oscillators 36 1.4.3 Cellular navigation strategies reveal adaptation to noise 39 2 Selected publications: Cell motility and motility control 56 2.1 “Flagellar synchronization independent of hydrodynamic interactions” 56 2.2 “Cell body rocking is a dominant mechanism for flagellar synchronization” 57 2.3 “Active phase and amplitude fluctuations of the flagellar beat” 58 2.4 “Sperm navigation in 3D chemoattractant landscapes” 59 3 Selected publications: Self-organized pattern formation in cells and tissues 60 3.1 “Sarcomeric pattern formation by actin cluster coalescence” 60 3.2 “Scaling and regeneration of self-organized patterns” 61 4 Contribution of the author in collaborative publications 62 5 Eidesstattliche Versicherung 64 6 Appendix: Reprints of publications 6