Tarsal intersegmental reflex responses in the locust hind leg

Locomotion is vital for vertebrates and invertebrates to survive. However, the mechanisms for locomotion are partially unknown. Central Pattern Generators and reflex systems have been shown to be the basis of most movements performed by arthropods. Much has been investigated lately on Central Pattern Generators, but little work has been done in reflex systems. Locomotion and motor output in feet (or tarsus in arthropods) has also been disregarded in research. Despite that feet are responsible for stability and agility in most animals, research on feet movements is scarce.In this thesis the tarsal intersegmental reflex of the locust hind leg is investigated. The tarsal reflex consists of a response in the tarsus when there is a change in the femoro-tibial joint. The main objective of the thesis is to describe the system and to develop mathematical and experimental methods to study, model and analyse it. Through a set of experiments is shown that as the knee joint is extended, the tarsus is depressed, and as the knee joint flexes, the tarsus levates. The experiments demonstrated that there is a purely neuronal link between the femoro-tibial joint position and the tibio-tarsal joint position. Moreover, it also reveals the effect of neuromodulatory compounds, such as dopamine, serotonin or octopamine. The tarsal reflex responses are fairly consistent across individuals, although significant variability across animals was found.To model a system where variability is an issue, a mathematical model with strong generalisation abilities is used: Artificial Neural Networks (ANNs). To design the ANNs, a metaheuristic algorithm has been implemented. The resulting ANNs are shown to be as accurate as other mathematical models used in physiology when used in a well known reflex system, the FETi responses. This results showed that ANNs are as good as Wiener methods in predicting responses and they outperform them in prediction of Gaussian inputs. Furthermore, they are able to predict responses in different animals, independently of the variability, with a more limited performance.New experimental methods are also designed to obtain accurate recordings of tarsal movements in response to knee joint changes. These experimental methods facilitate the data acquisition and its accuracy, reducing measurement errors. Using the mathematical methods validated, these responses are modelled and studied, showing responses to Gaussian and sinusoidal inputs, variability across individuals and effects of neuromodulators.With the tarsal reflex described and modelled, it can be used as a tool for further research in disciplines such as medicine, in the diagnose and treatment of euromuscular dysfunction or design of prosthesis and orthoses. This model can also be implemented in robotics to aid in stability when walking on irregular terrain

Integrative Biomimetics of Autonomous Hexapedal Locomotion

Dürr V, Arena PP, Cruse H, et al. Integrative Biomimetics of Autonomous Hexapedal Locomotion. Frontiers in Neurorobotics. 2019;13: 88.Despite substantial advances in many different fields of neurorobotics in general, and biomimetic robots in particular, a key challenge is the integration of concepts: to collate and combine research on disparate and conceptually disjunct research areas in the neurosciences and engineering sciences. We claim that the development of suitable robotic integration platforms is of particular relevance to make such integration of concepts work in practice. Here, we provide an example for a hexapod robotic integration platform for autonomous locomotion. In a sequence of six focus sections dealing with aspects of intelligent, embodied motor control in insects and multipedal robots—ranging from compliant actuation, distributed proprioception and control of multiple legs, the formation of internal representations to the use of an internal body model—we introduce the walking robot HECTOR as a research platform for integrative biomimetics of hexapedal locomotion. Owing to its 18 highly sensorized, compliant actuators, light-weight exoskeleton, distributed and expandable hardware architecture, and an appropriate dynamic simulation framework, HECTOR offers many opportunities to integrate research effort across biomimetics research on actuation, sensory-motor feedback, inter-leg coordination, and cognitive abilities such as motion planning and learning of its own body size

Locomotor Network Dynamics Governed By Feedback Control In Crayfish Posture And Walking

Sensorimotor circuits integrate biomechanical feedback with ongoing motor activity to produce behaviors that adapt to unpredictable environments. Reflexes are critical in modulating motor output by facilitating rapid responses. During posture, resistance reflexes generate negative feedback that opposes perturbations to stabilize a body. During walking, assistance reflexes produce positive feedback that facilitates fast transitions between swing and stance of each step cycle. Until recently, sensorimotor networks have been studied using biomechanical feedback based on external perturbations in the presence or absence of intrinsic motor activity. Experiments in which biomechanical feedback driven by intrinsic motor activity is studied in the absence of perturbation have been limited. Thus, it is unclear whether feedback plays a role in facilitating transitions between behavioral states or mediating different features of network activity independent of perturbation. These properties are important to understand because they can elucidate how a circuit coordinates with other neural networks or contributes to adaptable motor output. Computational simulations and mathematical models have been used extensively to characterize interactions of negative and positive feedback with nonlinear oscillators. For example, neuronal action potentials are generated by positive and negative feedback of ionic currents via a membrane potential. While simulations enable manipulation of system parameters that are inaccessible through biological experiments, mathematical models ascertain mechanisms that help to generate biological hypotheses and can be translated across different systems. Here, a three-tiered approach was employed to determine the role of sensory feedback in a crayfish locomotor circuit involved in posture and walking. In vitro experiments using a brain-machine interface illustrated that unperturbed motor output of the circuit was changed by closing the sensory feedback loop. Then, neuromechanical simulations of the in vitro experiments reproduced a similar range of network activity and showed that the balance of sensory feedback determined how the network behaved. Finally, a reduced mathematical model was designed to generate waveforms that emulated simulation results and demonstrated how sensory feedback can control the output of a sensorimotor circuit. Together, these results showed how the strengths of different approaches can complement each other to facilitate an understanding of the mechanisms that mediate sensorimotor integration

Identification of the optimal parameters for electrical stimulation to generate locomotor patterns in the rat isolated spinal cord

Recently, an innovative protocol of electrical stimulation, named \u201cfictive locomotion induced stimulation\u201d (FListim), which consists of an intrinsically variable noisy waveform, has been obtained from a segment of chemically-induced fictive locomotion (FL) sampled from the ventral root (VR) of an in vitro preparation of neonatal rat spinal cord. FListim delivered at sub-threshold intensities to a dorsal root (DR) has been shown to optimally activate the central pattern generators (CPGs) for locomotion (Taccola, 2011). In an attempt to introduce novel and improved protocols of stimulation in combination with neurochemicals, the current PhD project aims to identify the features that make sub-threshold noisy waveforms effective in activating locomotor patterns. In an attempt to introduce novel and improved protocols of stimulation in combination with neurochemicals, the current PhD project aims to identify the features that make sub-threshold noisy waveforms effective in activating locomotor patterns. To reach this aim, locomotor-like patterns in response to different noisy waveforms were compared. In order to obtain a wide palette of noisy protocols electromyographic (EMG) recordings were performed from leg muscles of adult volunteers during walking. These recordings were then delivered as stimulating patterns called real locomotion-induced stimulation (ReaListim). To reach this aim, locomotor-like patterns in response to different noisy waveforms were compared. In order to obtain a wide palette of noisy protocols electromyographic (EMG) recordings were performed from leg muscles of adult volunteers during walking. These recordings were then delivered as stimulating patterns called real locomotion-induced stimulation (ReaListim). ReaListim protocols, sampled during different motor behaviours, are equally able to induce an epoch of locomotor-like oscillations. Conversely, smooth kinematic profiles and non-phasic noisy patterns such as standing and isometric contraction, are unable to activate the locomotor CPGs. The complexity of noisy waveforms was then reduced at motoneuronal level, by recording electrical activity of a single motoneuron during FL. Long-lasting episode of FL, were evoked in response to intracellular patterns delivered at sub-threshold intensities. The analysis of motoneuronal firing during FL was used to identify four recurrent frequency values that optimally activated the locomotor CPGs when applied simultaneously in a multifrequency protocol. Different permutations were tried to further simplify the multifrequency protocol while isolating the most effective components of the four identified frequencies. The simplest asynchronous paradigm that can induce locomotor-like episodes consists of a train of rectangular pulses that contain two frequencies: 35 and 172 Hz. This protocol resulted already effective at subthreshold intensity even when delivered for a very short time (500 ms). The role of oxytocin in the modulation of neuronal networks is explored here on spinal networks. Intracellular recordings demonstrate that oxytocin dosedependently depolarizes single motoneurons with the appearance of sporadic bursts with superimposed firing. By applying the selective blocker of sodium channels, tetrodotoxin (TTX), the effects of oxytocin can be completely abolished, which suggest a premotoneuronal-level origin. The neuropeptide is capable to induce VRs depolarization with superimposed synchronous bursts of activity, while reflex responses induced by single pulses are depressed depending on the stimulus strength and peptide-concentration. The disinhibited bursting evoked by the pharmacological blockade of glycine and GABAA receptors blockers, strychnine and bicuculline, respectively, is accelerated by oxytocin, an effect that is suppressed by the selective oxytocin receptor antagonist atosiban. On spinal locomotor networks oxytocin facilitates the emergence of FL episodes in response either to weak noisy waveforms protocols or to the conjoint application of NMDA and 5HT at sub-threshold concentrations, even if the periodicity of a stable FL is not significantly affected by the neuropeptide. Interestingly, the facilitation of the locomotor CPGs by oxytocin is dependent on the endogenous release of 5HT, as is demonstrated by incubation with the inhibitor of 5HT synthesis, pchlorophenilalanine (PCPA). Low-frequency trains of stereotyped pulses (0.33 and 0.67Hz) delivered with a controlled time interval (delays 0.5 to 2 s) to multiple DRs converged on spinal locomotor circuits to generate locomotor rhythm. The same finding is confirmed by the phase resetting that is induced by single afferent stimuli during a simultaneous train of pulses delivered to another DR. Staggered protocols fail to elicit FL when simultaneously applied to multiple DRs, while a multi-site randomized pulse train is still effective in eliciting locomotor-like patterns. This thesis outlines new strategies for optimizing the reactivation of spinal locomotor networks after spinal damage. Though the technology that is currently available in clinics does not allow for the delivery of highly-variable stimulating patterns, experiments reported here indicate a way to overcome these limitations. Indeed, protocols that contain few distinct frequencies that are isolated from the spectrum of noisy waves can activate the CPGs even when delivered with a multisite approach. This suggests that it may be possible to separately supply multiple trains of pulses to several cord sites using different electrostimulators. The yield of stimulation in activating locomotor circuits will be further improved by the association with the neuropeptide oxytocin

Decomposition of 3D joint kinematics of walking in Drosophila melanogaster

Animals exhibit a rich repertoire of locomotive behaviors. In the context of legged locomotion, i.e. walking, animals can change their heading direction, traverse diverse substrates with different speeds, or can even compensate for the loss of a leg. This versatility emerges from the fact that biological limbs have more joints and/or more degrees of freedom (DOF), i.e. independent directions of motions, than required for any single movement task. However, this further entails that multiple, or even infinitely many, joint configuration can result in the same leg stepping pattern during walking. How the nervous system deals with such kinematic redundancy remains still unknown. One proposed hypothesis is that the nervous system does not control individual DOFs, but uses flexible combinations of groups of anatomical or functional DOFs, referred to as motor synergies. Drosophila melanogaster represents an excellent model organism for studying the motor control of walking, not least because of the extensive genetic toolbox available, which, among others, allows the identification and targeted manipulation of individual neurons or muscles. However, their tiny size and ability for relatively rapid leg movements hampered research on the kinematics at the level of leg joints due to technical limitations until recently. Hence, the main objective of this dissertation was to investigate the three-dimensional (3D) leg joint kinematics of Drosophila during straight walking. For this, I first established a motion capture setup for Drosophila which allowed the accurate reconstruction of the leg joint positions in 3D with high temporal resolution (400 Hz). Afterwards, I created a kinematic leg model based on anatomical landmarks, i.e. joint condyles, extracted from micro computed-tomography scan data. This step was essential insofar that the actual DOFs of the leg joints in Drosophila were currently unknown. By using this kinematic model, I have found that a mobile trochanter-femur joint can best explain the leg movements of the front legs, but is not mandatory in the other leg pairs. Additionally, I demonstrate that rotations of the femur-tibia plane in the middle legs arise from interactions between two joints suggesting that the natural orientation of joint rotational axes can extent the leg movement repertoire without increasing the number of elements to be controlled. Furthermore, each leg pair exhibited distinct joint kinematics in terms of the joint DOFs employed and their angle time courses during swing and stance phases. Since it is proposed that the nervous system could use motor synergies to solve the redundancy problem, I finally aimed to identify kinematic synergies based on the obtained joint angles from the kinematic model. By applying principal component analysis on the mean joint angle sets of leg steps, I found that three kinematic synergies are sufficient to reconstruct the movements of the tarsus tip during stepping for all leg pairs. This suggests that the problem of controlling seven to eight joint DOFs can be in principle reduced to three control parameters. In conclusion, this dissertation provides detailed insights into the leg joint kinematics of Drosophila during forward walking which are relevant for deciphering motor control of walking in insects. When combined with the extensive genetic toolbox offered by Drosophila as model organism, the experimental platform presented here, i.e. the 3D motion capture setup and the kinematic leg model, can facilitate investigations of Drosophila walking behavior in the future

Kinematická analýza rytmických pohybů: aplikace na třes rukou člověka a kmit křídel mušky octomilky.

Rytmický pohyb, pravidelný nebo nepravidelný, je nedílnou součástí motorického chování a to jak ve zdraví, tak v průběhu nemoci. Hlubší pochopení geneze rytmického pohybu je důležité pro porozumění patofyziologii onemocnění, mezi jejichž projevy rytmický pohyb patří. V disertační práci jsem studovala dva konkrétní aspekty rytmického pohybu: bilaterální koordinaci a modulární řízení. První z nich jsem analyzovala na třesu lidských rukou, druhý na pohybu křídel u modelového organismu Drosophila melanogaster (octomilka obecná). Mnoho typů třesu, včetně fyziologického třesu (PT) a esenciálního tremoru (ET), se vyskytuje v končetinách po obou stranách těla, s podobnou základní frekvencí kmitání. To naznačuje, že kontralaterální třesy mohou mít společný zdroj nebo jsou jinak spojené. Ve své studii jsem prozkoumala vazbu mezi třesem levé a pravé ruky. Pomocí 3D- akcelerometrů jsem změřila časový průběh třesu, a použila stacionární i nestacionární (waveletové) výpočetní metody k vyhodnocení bilaterální koherence. Měření na všech třech prostorových osách umožnilo prozkoumat ucelenější sadu kinematických proměnných, než ve většině předešlých studií. Nestacionární analýza usnadnila identifikaci časově transientní koherence, což je scénář, který se v analýze třesu dříve nebral v úvahu. U většiny subjektů s PT...Rhythmic motions, regular or irregular, are an integral part of motor behavior both in health and in disease. Better understanding of its neural control mechanisms helps in developing methods for controlling the progression of diseases manifesting as rhythmic motions. I studied two specific aspects of rhythmic motions: bilateral coordination of hand tremors in human subjects and modular control of locomotion in invertebrates. Many types of tremors, including the physiological tremor (PT) and the essential tremor (ET) occur in limbs on both the sides of the body, with similar fundamental frequency of the oscillation. This raises the possibility that the contralateral tremors may have a common source or are otherwise coupled. However, while significant contralateral interaction is seen in these two types of tremors, only limited evidence of bilateral coherence has been shown in the previous literature. Therefore, in my study I explored the existence of a weak coupling between the left and right oscillators the may lead to intermittent bilateral coherence. I measured triaxial acceleration of the two hands and systematically assessed their bilateral coherence, using both stationary and non-stationary (wavelet-based) analyses methods. Measuring all three axes allowed examination of a more complete set...Institute of Biophysics and Informatics First Faculty of Medicine Charles University in PragueÚstav biofyziky a informatiky 1. LF UK v PrazeFirst Faculty of Medicine1. lékařská fakult

Characterisation of the biomechanical, passive, and active properties of femur-tibia joint leg muscles in the stick insect Carausius morosus

The understanding of locomotive behaviour of an animal necessitates the knowledge not only about its neural activity but also about the transformation of this activity patterns into muscle activity. The stick insect is a well studied system with respect to its motor output which is shaped by the interplay between sensory signals, the central neural networks for each leg joint and the coordination between the legs. The muscles of the FT (femur-tibia) joint are described in their morphologies and their motoneuronal innervation patterns, however little is known about how motoneuronal stimulation affects their force development and shortening behaviour. One of the two muscles moving the joint is the extensor tibiae, which is particularly suitable for such an investigation as it features only three motoneurons that can be activated simultaneously, which comes close to a physiologically occuring activation pattern. Its antagonist, the flexor tibiae, has a more complex innervation and a biomechanical investigation is only reasonable at full motoneuronal recruitment. Muscle force and length changes were measured using a dual-mode lever system that was connected to the cut muscle tendon. Both tibial muscles of all legs were studied in terms of their geometry: extensor tibiae muscle length changes with the cosine of the FT joint angle, while flexor tibiae length changes with the negative cosine, except for extreme angles (close to 30° and 180°). For all three legs, effective flexor tibiae moment arm length (0.564 mm) is twice that of the extensor tibiae (0.282 mm). Flexor tibiae fibres are 1.5 times longer (2.11 mm) than extensor tibiae fibres (1.41 mm). Active isometric force measurements demonstrated that extensor tibiae single twitch force is notably smaller than its maximal tetanical force at 200 Hz (2-6 mN compared to 100-190 mN) and takes a long time to decrease completely (> 140 ms). Increasing either frequency or duration of the stimulation extends maximal force production and prolongs the relaxation time of the extensor tibiae. The muscle reveals `latch´ properties in response to a short-term increase in activation. Its working range is on the ascending limb of the force-length relationship (see Gordon et al. (1966b)) with a shift in maximum force development towards longer fibre lengths at lower activation. The passive static force increases exponentially with increasing stretch. Maximum forces of 5 mN for the extensor, and 15 mN for the flexor tibiae occur within the muscles´ working ranges. The combined passive torques of both muscles determine the rest position of the joint without any muscle activity. Dynamically generated forces of both muscles can become as large as 50-70 mN when stretch ramps mimick a fast middle leg swing phase. FT joint torques alone (with ablated muscles) do not depend on FT joint angle, but on deflection amplitude and velocity. Isotonic force experiments using physiological activation patterns demonstrate that the extensor tibiae acts like a low-pass filter by contracting smoothly to fast instantaneous stimulation frequency changes. Hill hyperbolas at 200 Hz vary a great deal with respect to maximal force (P0) but much less in terms of contraction velocity (V0) for both tibial muscles. Maximally stimulated flexor tibiae muscles are on average 2.7 times stronger than extensor tibiae muscles (415 mN and 151 mN), but contract only 1.4 times faster (6.05 mm/s and 4.39 mm/s). The dependence of extensor tibiae V0 and P0 on stimulation frequency can be described with an exponential saturation curve. V0 increases linearly with length within the muscle´s working range. Loaded release experiments characterise extensor and flexor tibiae series elastic components as quadratic springs. The mean spring constant of the flexor tibiae is 1.6 times larger than of the extensor tibiae at maximal stimulation. Extensor tibiae stretch and relaxation ramps show that muscle relaxation time constant slowly changes with muscle length, and thus muscle dynamics have a long-lasting dependence on muscle length history. High-speed video recordings show that changes in tibial movement dynamics match extensor tibiae relaxation changes at increasing stimulation duration

Local Positive Velocity Feedback for the movement control of elastic joints in closed kinematic chains : a modelling and simulation study of a 2DoF arm and a 3DoF insect leg

Schneider A. Local Positive Velocity Feedback for the movement control of elastic joints in closed kinematic chains : a modelling and simulation study of a 2DoF arm and a 3DoF insect leg. Bielefeld (Germany): Bielefeld University; 2006.In der Beinbewegungssteuerung von laufenden Tieren (z.B. in unserem Modellsystem, der indischen Stabheuschrecke Carausius morosus) unterscheidet man Stemm- und Schwingbewegungen. Während einer Schwingbewegung hat das schwingende Bein keinerlei Objektkontakt, da es vom Boden abgehoben duch die Luft nach vorne geführt wird. Das Bein kann als offene kinematische Kette betrachtet und jedes Gelenk der Kette frei bewegt werden. Während der Stemmbewegung haben alle beteiligten Beine Bodenkontakt und bilden somit geschlossene kinematische Ketten. Die Gelenkwinkel derjenigen Beine, die an diesen geschlossenen kinematischen Ketten beteiligt sind, sind nicht mehr frei wählbar. Eine beliebige Einzelbewegung eines Gelenks führt zu Verspannungen in den kinematischen Ketten, die nur durch die aktive (entspannende) Bewegung anderer Gelenke aufgelöst werden können. Ähnliche Probleme treten auch bei Bewegungen mit Armen und Händen auf, wenn diese Manipulationsaufgaben mit Objektkontakt ausführen (z.B. beim Öffnen einer Tür durch einen Menschen). Aufgabenstellungen dieser Art werden in der Robotik unter dem Begriff "compliant motion tasks" zusammengefasst. Beispiele hierfür sind Kontaktschweißen, kooperative Manipulation von Objekten durch mehrere Roboter, Pick-and-Place Aufgaben bei Montagerobotern und, wie erwähnt, auch Stemmbewegungen bei Laufmaschinen. Klassische Lösungsansätze für diese Art von Problemen basieren auf dem "hybrid control" Ansatz von Raibert und Craig (Raibert and Craig, 1981, Trans. of the ASME, 102: 126-133) oder auf dem "impedance control" Ansatz von Hogan (Hogan, 1985, ASME J. Dynam. Syst., Meas., Contr., 107: 1-23). Für die Ansteuerung einer sechsbeinigen Laufmaschine mit insgesamt 18 Gelenken müssen dafür die entsprechenden kinematischen und dynamischen Gleichungen bekannt sein und in jedem Regleraufruf neu berechnet werden. Es scheint unwahrscheinlich, dass Tiere diese Berechnungen explizit durchführen. Cruse und Mitarbeiter (Cruse et al., 1995, Advances in Artificial Life, 668-678) schlugen vor, dass Insekten diese Aufgabe unter Ausnutzung der in der Literatur vielfach beschriebenen Reflexumkehr (auch Unterstützungsreflex) bewältigen (siehe z.B. Bässler, 1976, Biol. Cybernetics, 24: 47-49). Bei der Reflexumkehr unterstützt ein Regelmechanismus, der im ruhenden Tier für die Beibehaltung einer Gelenksposition bei äußeren Störungen sorgt, im aktiven Tier eine passive Bewegung und verstärkt diese aktiv. Nimmt man nun im stemmenden Tier eine aktive Bewegung eines Gelenks an, so wirkt sich diese mechanisch vermittelt über die geschlossenen Ketten auf alle anderen Gelenke aus. Der Unterstützungsreflex in den anderen Gelenken führt dazu, dass diese die angeregte Bewegung mitmachen und verstärken. Das Ergebnis ist eine koordinierte Stemmbewegung, die von den lokal geregelten Gelenken gemeinsam ausgeführt wird, obwohl diese nicht neuronal miteinander kommunizieren und keine zentrale Instanz einen vorausberechneten Bewegungsplan ausgibt. In der vorliegenden Arbeit wird diese Hypothese aufgegriffen und quantitativ überprüft. Es werden verschiedene elastische Gelenkmodelle entwickelt, die als Grundlage für die Implementierung eines Unterstützungsreflex dienen. Der Unterstützungsreflex als solcher wird in Form von Lokaler Positiver Geschwindigkeitsrückkopplung (Local Positive Velocity Feedback, LPVF) hergeleitet und seine Funktionsfähigkeit mit einem Standardtest, dem einarmigen Kurbeln, getestet. Die wichtigste Eigenschaft, nämlich die Fähigkeit, verschiedene Gelenke ohne direkte Kommunikation zu koordinieren, wird damit nachgewiesen. In einem weiteren Schritt wird gezeigt, dass eine Erweiterung des Ansatzes durch Einführung einer Leistungssteuerung dazu führt, dass die Koordinationsfähigkeit selbst dann erhalten bleibt, wenn eine stemmende Gliedmaße große Kräfte, z.B. gegen eine äußere Trägheitskraft, aufbringen muss. Das Regelungskonzept wird auf einer dynamischen Einbeinsimulation getestet, die Funktionsfähigkeit demonstriert und mit den biologischen Daten von aktivierten Tieren verglichen. In einem letzten Schritt wird der LPVF-Regler mit einem Stehregler kombiniert. Der entstandene Gesamtregler erklärt biologische Befunde aus der Lauf- und aus der Stehdomäne

Parameter identification in networks of dynamical systems

Mathematical models of real systems allow to simulate their behavior in conditions that are not easily or affordably reproducible in real life. Defining accurate models, however, is far from trivial and there is no one-size-fits-all solution. This thesis focuses on parameter identification in models of networks of dynamical systems, considering three case studies that fall under this umbrella: two of them are related to neural networks and one to power grids. The first case study is concerned with central pattern generators, i.e. small neural networks involved in animal locomotion. In this case, a design strategy for optimal tuning of biologically-plausible model parameters is developed, resulting in network models able to reproduce key characteristics of animal locomotion. The second case study is in the context of brain networks. In this case, a method to derive the weights of the connections between brain areas is proposed, utilizing both imaging data and nonlinear dynamics principles. The third and last case study deals with a method for the estimation of the inertia constant, a key parameter in determining the frequency stability in power grids. In this case, the method is customized to different challenging scenarios involving renewable energy sources, resulting in accurate estimations of this parameter

On the intrinsic control properties of muscle and relexes: exploring the interaction between neural and musculoskeletal dynamics in the framework of the equilbrium-point hypothesis

The aim of this thesis is to examine the relationship between the intrinsic dynamics of the body and its neural control. Specifically, it investigates the influence of musculoskeletal properties on the control signals needed for simple goal-directed movements in the framework of the equilibriumpoint (EP) hypothesis. To this end, muscle models of varying complexity are studied in isolation and when coupled to feedback laws derived from the EP hypothesis. It is demonstrated that the dynamical landscape formed by non-linear musculoskeletal models features a stable attractor in joint space whose properties, such as position, stiffness and viscosity, can be controlled through differential- and co-activation of antagonistic muscles. The emergence of this attractor creates a new level of control that reduces the system’s degrees of freedom and thus constitutes a low-level motor synergy. It is described how the properties of this stable equilibrium, as well as transient movement dynamics, depend on the various modelling assumptions underlying the muscle model. The EP hypothesis is then tested on a chosen musculoskeletal model by using an optimal feedback control approach: genetic algorithm optimisation is used to identify feedback gains that produce smooth single- and multijoint movements of varying amplitude and duration. The importance of different feedback components is studied for reproducing invariants observed in natural movement kinematics. The resulting controllers are demonstrated to cope with a plausible range of reflex delays, predict the use of velocity-error feedback for the fastest movements, and suggest that experimentally observed triphasic muscle bursts are an emergent feature rather than centrally planned. Also, control schemes which allow for simultaneous control of movement duration and distance are identified. Lastly, it is shown that the generic formulation of the EP hypothesis fails to account for the interaction torques arising in multijoint movements. Extensions are proposed which address this shortcoming while maintaining its two basic assumptions: control signals in positional rather than force-based frames of reference; and the primacy of control properties intrinsic to the body over internal models. It is concluded that the EP hypothesis cannot be rejected for single- or multijoint reaching movements based on claims that predicted movement kinematics are unrealistic