Navigation of mini swimmers in channel networks with magnetic fields

Controlled navigation of swimming micro robots inside fluid filled channels is necessary for applications in living tissues and vessels. Hydrodynamic behavior inside channels and interaction with channel walls need to be understood well for successful design and control of these surgical-tools-to-be. In this study, two different mechanisms are used for forward and lateral motion: rotation of helices in the direction of the helical axis leads to forward motion in the viscous fluid, and rolling due to wall traction results with the lateral motion near the wall. Experiments are conducted using a magnetic helical swimmer having 1.5 mm in length and 0.5 mm in diameter placed inside two different glycerol-filled channels with rectangular cross sections. The strength, direction and rotational frequency of the externally applied rotating magnetic field are used as inputs to control the position and direction of the micro swimmer in Y- and T-shaped channels

Bio-inspired Magnetic Systems: Controlled Swimming, Fluid Pumps, and Collective Behaviour

This thesis details the original experimental investigations of magnetically actuated and controlled microscopic systems enabling a range of actions at low Reynolds number. From millimetre-robots and self-propelled swimmers to microfluidic and lab-on-a-chip technology applications. The main theme throughout the thesis is that the systems reply on the interactions between magnetic and elastic components. Scientists often take inspiration from nature for many aspects of science. Millimetre to micrometre machines are no exception to this. Nature demonstrates how soft materials can be used to deform in a manner to create actuation at the microscale in biological environments. Nature also shows the effectiveness of using beating tails known as flagella and the apparent enhancements in flow speeds of collective motion. To begin with, a swimmer comprised of two ferromagnetic particles coupled together with an elastic link (the two-ferromagnetic particle swimmer), was fabricated. The system was created to mimic the swimming mechanism seen by eukaryotic cells, in which these cells rely on morphological changes which allows them to propel resulting in approximate speeds of up to 2 body lengths per second. The aim of this system was to create a net motion and control the direction of propagation by manipulating the external magnetic field parameters. It was shown that the direction of swimming has a dependence on both the frequency and amplitude of the applied external magnetic field. A key factor discovered was that the influence of a small bias field, in this case, the Earth’s magnetic field (100 orders of magnitude smaller than the external magnetic field) resulted in robust control over the speed (resulting in typical swimming speeds of 4 body lengths per second) and direction of propulsion. Following this work, swimmers with a hard ferromagnetic head attached to an elastic tail (the torque driven ferromagnetic swimmer) were investigated. These systems were created to be analogous to the beating flagella of many natural microscopic swimmers, two examples would be sperm cells and chlamydomonas cells. These biological cells have typical speeds of 10s of body lengths per second. The main focus of this investigation was to understand how the tail length affects the swimming performance. An important observation was that there is an obvious length tail (5.7 times the head length) at which the swimming speed is maximised (approximately 13 body lengths per second). The experimental results were compared to a theoretical model based on three beads, one of which having a fixed magnetic moment and the other two non-magnetic, connected via elastic filaments. The model shows sufficient complexity to break time symmetry and create a net motion, giving good agreement with experiment. Portable point-of-care systems have the potential to revolutionise medical diagnostics. Such systems require active pumps with low power (USB powered devices) external triggers. Due to the wireless and localisation of magnetic fields could possibly allow these portable point-of-care devices to come to life. The main focus of this investigation was to create fluid pump systems comprising from the previously investigated two-ferromagnetic particle swimmer and the torque driven ferromagnetic swimmer. Building on the fact that if a system can generate a net motion it would also be able to create a net flow. Utilising the geometry of the systems, it has been demonstrated that a swimmer-based system can become a fluid pump by restricting the translational motion. The flow structure generated by a pinned swimmer in different scenarios, such as unrestricted flow around it as well as flow generated in straight, cross-shaped, Y-shaped and circular channels were investigated. This investigation demonstrated the feasibility of incorporating the device into a channel and its capability of acting as a pump, valve and flow splitter. As well as a single pump system, networks of the previously mentioned pump systems were fabricated and experimentally investigated. The purpose of this investigation was to utilise the behaviour of the collective motion. Such networks could also be attached to the walls or top of the channel to create a less invasive system compared to pump based within the channel system. The final investigation involved creating collective motion systems which could mimic the beating of cilia - known as a metachronal wave. Two methods were used to create an analogous behaviour. The first was using arrays of identical magnetic rotors, which under the influence of an external magnetic field created two main rotational patterns. The rotational patterns were shown to be controllable producing useful flow fields at low Reynolds numbers. The second system relied on the magnetic components having different fixed magnetisation to create a phase lag between oscillations. The magnetic components were investigated within a channel and the separation between the components was shown to be a key parameter for controlling the induced flow. In both cases, a simple model was produced to help understand the behaviour. Finally, a selection of preliminary investigations into possible applications were conducted experimentally. These investigations included, measuring the effective surface viscosity of lipid monolayers, created cell growth microchannels, as well as systems which could be used for blood plasma separation. The properties of lipid monolayers vary with the surface density, resulting on distinct phase transitions. Slight differences in the molecular lattice are often accompanied by significant changes in the surface viscosity and elasticity. The idea was to use a swimmer as a reporter of the monolayer viscosity, resulting in a less invasive method compared to current techniques to monitor monolayer viscosity, for example torsion pendulums and channel viscometers. The reported effective surface viscosity closely matched the typical Langmuir trough measurements (with a systematic shift of approximately 17 Ų/molecule). The blood plasma separation preliminary work shows the previously investigated two-ferromagnetic particle swimmer mixing a typical volume (100 μm) blood sample with a buffer solution in 21 seconds. The system was also able to create locations with a high population of red blood cells. This resulted in a separation between the blood plasma and red blood cells. Two other preliminary results of future investigations were presented; the collective motion of free swimmers, and the fabrication of ribbon-like structures with fixed magnetic moment patterns.European CommissionEngineering and Physical Sciences Research Council (EPSRC

Bioinspired reorientation strategies for application in micro/nanorobotic control

Engineers have recently been inspired by swimming methodologies of microorganisms in creating micro-/nanorobots for biomedical applications. Future medicine may be revolutionized by the application of these small machines in diagnosing, monitoring, and treating diseases. Studies over the past decade have often concentrated on propulsion generation. However, there are many other challenges to address before the practical use of robots at the micro-/nanoscale. The control and reorientation ability of such robots remain as some of these challenges. This paper reviews the strategies of swimming microorganisms for reorientation, including tumbling, reverse and flick, direction control of helical-path swimmers, by speed modulation, using complex flagella, and the help ofmastigonemes. Then, inspired by direction change in microorganisms,methods for orientation control for microrobots and possible directions for future studies are discussed. Further, the effects of solid boundaries on the swimming trajectories of microorganisms and microrobots are examined. In addition to propulsion systems for artificial microswimmers, swimming microorganisms are promising sources of control methodologies at the micro-/nanoscale

A Novel Propeller Design for Micro-Swimming robot

The applications of a micro-swimming robot such as minimally invasive surgery, liquid pipeline robot etc. are widespread in recent years. The potential application fields are so inspiring, and it is becoming more and more achievable with the development of microbiology and Micro-Electro-Mechanical Systems (MEMS). The aim of this study is to improve the performance of micro-swimming robot through redesign the structure. To achieve the aim, this study reviewed all of the modelling methods of low Reynolds number flow including Resistive-force Theory (RFT), Slender Body Theory (SBT), and Immersed Boundary Method (IBM) etc. The swimming model with these methods has been analysed. Various aspects e.g. hydrodynamic interaction, design, development, optimisation and numerical methods from the previous researches have been studied. Based on the previous design of helix propeller for micro-swimmer, this study has proposed a novel propeller design for a micro-swimming robot which can improve the velocity with simplified propulsion structure. This design has adapted the coaxial symmetric double helix to improve the performance of propulsion and to increase stability. The central lines of two helical tails overlap completely to form a double helix structure, and its tail radial force is balanced with the same direction and can produce a stable axial motion. The verification of this design is conducted using two case studies. The first one is a pipe inspection robot which is in mm scale and swims in high viscosity flow that satisfies the low Reynolds number flow condition. Both simulation and experiment analysis are conducted for this case study. A cross-development method is adopted for the simulation analysis and prototype development. The experiment conditions are set up based on the simulation conditions. The conclusion from the analysis of simulation results gives suggestions to improve design and fabrication for the prototype. Some five revisions of simulation and four revisions of the prototype have been completed. The second case study is the human blood vessel robot. For the limitations of fabrication technology, only simulation is conducted, and the result is compared with previous researches. The results show that the proposed propeller design can improve velocity performance significantly. The main outcomes of this study are the design of a micro-swimming robot with higher velocity performance and the validation from both simulation and experiment

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

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

Elastic Tail Propulsion at Low Re

The use of microswimmers, or microscopic swimming robots, in the medical field is becoming more sought after for applications such as targeted drug delivery and microsurgery. While such microswimmers do not yet exist for use on patients, many researchers are working on this front to make them a reality. One of the main challenges in making these microswimmers a reality is creating propulsion in a low Reynolds number environment. This project aims to create and test a prototype of a swimmer which employs 3D circular movement of its tail for propulsion in a very viscous fluid, mimicking a low Reynolds environment in the macroscale. To create a successful proof of concept of 3D circular propulsion, simulations, prototyping, and experimental evaluation of the prototype were conducted during the course of this project. Finite element analysis using the commercial software COMSOL was conducted to design a swimmer tail that would generate a positive thrust force, and a velocity at an order of magnitude consistent with the analytical prediction. Guided by the simulation results, a prototype was fully realized, and testing was conducted resulting in a speed of 0.5 mm/s, which matched with the order of magnitude of the speed obtained from the simulations. The data collected from testing accompanied by simulations confirmed our proof of concept. Lastly, additional simulations were performed to find optimal parameters that can be implemented in the swimmer design for future testing. In essence, this report will provide an overview of the design, construction, and testing of a scaled-up experimental platform to examine the principle of elastic propulsion in highly viscous fluid