Workshop 4: Neuromechanics of Locomotion

(March 31,2008 - April 4,2008 )

Organizers


Ansgar Bueschges
Zoological Institute, University of Cologne
Robert Full
Department of Integrative Biology, University of California, Berkeley

Workshop 4 focuses on the question of how animals are deceptively simple. They push against the world, with legs, fins, tails, wings, or their whole bodies, and the rest is Newton's third and second laws. But of course locomotion emerges from complex interactions among animals' neural, sensory and motor systems, their muscle-body dynamics, and their environments. Three broad approaches reflect this:

  1. Neurobiology has successfully studied the role of central pattern generators (CPGs) in the control of locomotion. CPGs are networks of neurons that can generate muscular activity in the absense of sensory feedback. By its action, the nervous system can generate a basic neural output that can signal the muscles when to contract. In this mode, the nervous system tells the muscles what to do and muscles pass the message on to limbs, which move the body.
  2. A closely related approach concentrates on proprioceptive feedback in intralimb and interlimb coordination for shaping locomotory patterns. Thus, what the limbs are doing now, tells them what to do next.
  3. Biomechanical studies focus on body-limb-environment dynamics and often ignore neural detail. Thus, Newtonian mechanics, with (mostly) passively-generated forces, tell the body what it must do.

 

All three approaches have generated rich mathematical models of individual neurons and circuits, sensory pathways and state estimators, and body-limb mechanics. Further mathematical modeling, at various spatial and temporal scales, can play a central role in synthesizing these approaches into neuromechanical descriptions of locomotion. Thus, Hodgkin-Huxley meets Newton with A.V. Hill as matchmaker.

This workshop, and the closely-related ones on muscle biomechanics (Workshop 2) and neuroengineering (Workshop 5) will emphasize the development of integrative models. The major mathematical tools will include dynamical systems, stochastic ODE, control theory, and (non-)classical mechanics with intermittent contacts and impacts in running and walking, and unsteady fluid mechanics in swimming and flight.

Accepted Speakers

Andrew Biewener
Department of Organismic and Evolutionary Biology, Harvard University
Reinhard Blickhan
Institute for Sports Science, Friedrich-Schiller-Universit""at
Marcus Bluemel
Zoological Institute, University of Cologne
Anke Borgmann
Zoological Institute, University of Cologne
Jonas Buchli
Computer Science and Neuroscience, University of Southern California
Ansgar Bueschges
Zoological Institute, University of Cologne
Jean-Marie Cabelguen
Neurocentre INSERM, Institut F. Magendie
Avis Cohen
Department of Biology, Program in Neurosciences and Cognitive Science and ISR, College of Business and Management
Noah Cowan
Department of Mechanical Engineering, Johns Hopkins University
Tom Daniel
Department of Biology, University of Washington
Volker Dürr
Zoological Institute, University of Cologne
Orjan Ekeberg
Dept. of Computational Biology, KTH Computer Science and Communication
Lisa Fauci
Mathematics, Tulane University
Bob Full
Department of Integrative Biology, University of California, Berkeley
Sten Grillner
Department of Neuroscience, Nobel Institute for Neurophysiology
Matthias Gruhn
Zoological Institute, University of Cologne
John Guckenheimer
Department of Mathematics, Cornell University
Phil Holmes
Mechanical and Aerospace Engineering, Princeton University
Scott Hooper
Department of Biological Sciences, Ohio University
Auke Ijspeert
School of Computer and Communication Sciences, EPFL, Swiss Federal Institute of Technology
Tetsuya Iwasaki
Mechanical & Aerospace Engineering, University of Virginia
Daniel Koditschek
Electrical & Systems Engineering, University of Pennsylvania
Raghavendra Kukillaya
Mechanical and Aerospace Engineering, Princeton University
Tyler McMillen
Mathematics, California State University, Fullerton
John Miller
INCA (Institute for Numerical Computation & Analysis, Royal College of Surgeons in Ireland Research Inst.
Kiisa Nishikawa
Department of Biological Sciences, Northern Arizona University
Keir Pearson
Department of Physiology, University of Alberta
Shai Revzen
Department of Integrative Biology, University of California, Berkeley
Roy Ritzmann
Department of Biology, Case Western Reserve University
Andy Ruina
Theoretical and Applied Mechanics, Cornell University
Josef Schmitz
Dep. of Biological Cybernetics, Universit""at Bielefeld
Andre Seyfarth
Locomotion Lab, Jena University
Keith Sillar
School of Biology; Division of Biomedical Sciences, University of St. Andrews
Manoj Srinivasan
Mechanical and Aerospace Engineering, Princeton University
Lena Ting
Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology
Arndt Twickel
Institut für Kognitionswissenschaft, Universität Osnabrück
Francisco Valero-Cuevas
Department of Biomedical Engineering, University of Southern California
Jane Wang
Theoretical and Applied Mathematics, Cornell University
Thelma Williams
St. George's Medical School, University of London
Sasha Zill
Anatomy and Pathology, Marshall University
Monday, March 31, 2008
Time Session
09:00 AM
10:30 AM
Ansgar Bueschges - Architecture and operation of neural controllers governing insect leg walking movements

In walking each leg movement results from a contribution of descending signals from the brain, central pattern generating networks (CPG), local feedback from sensory neurons about movements and forces generated in the legs, coordinating signals from neighboring limbs, and finally, the neuromuscular transform at the output stage of the walking system, the leg muscles. We have in recent years made significant advances in understanding the neural basis of insect walking. My talk will summarize the current knowledge of the organization and operation of neural networks in the thoracic ganglia generating single leg stepping. I will also outline our current knowledge on (i) how the leg muscle control system changes speed and walking direction and (ii) the neural mechanisms contributing to intersegmental activation and coordination. In doing so, I will highlight those areas, in which information is presently still too sparse to generate sufficient concepts on neural control mechanisms and in which simulation studies will be most useful. I will place current knowledge from the stick insect into the broader context of locomotor behaviors in other organisms.



 
09:00 AM
10:30 AM
Keir Pearson - Modelling walking in mammals: what we need to know

Computer simulations are being used increasingly to gain insight into the neurobiology and biomechanics of walking in humans and quadrupeds. In general, these simulations are based on very limited knowledge of the neural systems generating the motor patterns for walking, the properties of muscle producing the movements, and the mechanics of muscle action. Nevertheless, these simulations have yielded valuable insights into some low-level features of mammalian locomotion, especially the biomechanical functions of specific muscles and the role of afferent signals in regulating phase transitions of the step cycle. The most obvious shortcoming in developing more versatile and complete simulations of walking is a serious lack of knowledge of the underlying neurobiological mechanisms. Despite enormous effort, we still know little about the cellular and network properties of pattern generating networks in the mammalian spinal cord, and even less about how these networks are controlled by descending signals from the brain during walking. In this presentation I will review the limited data we currently possess, and attempt to identify areas in which additional data would facilitate the development of useful simulations.



 
02:00 PM
03:30 PM
Phil Holmes - Towards an integrated model for insect locomotion

I will review our attempts to build an analytically-tractable, yet biophysically-grounded, neuromechanical model of a running animal, with particular reference to the cockroach Blaberus discoidalis. Building on a sequence of simple mechanical models, we have successively added actuated, axially-sprung legs, jointed legs, and muscles. In doing so we have confirmed the 'preflexive' hypothesis: that feedforward control, coupled with passive dynamics, can yield robustly stable gaits. In parallel work we have modeled the insect central pattern generator and motoneurons. It remains to integrate neurobiology and biomechanics by incorporating models of proprioceptive and exteroceptive sensing. I hope to stimulate a debate on appropriate levels of detail in such integrated models, and, more generally, on their role in the biological sciences.


This is joint worth with J. Schmitt, R. Ghigliazza, J. Seipel, R. Kukillaya, J. Proctor, M. Srinivasan, R. Altendorfer, R.J. Full and D. Koditschek.

04:00 PM
05:30 PM
Andy Ruina - Thoughts on generating control from first principles

One general class of goals is the prediction of human or animal coordination choices from a given physical architecture. This would be useful for the diagnosing and fixing of health problems as well as for the generation of animal like robots (which, to be animal-like, must be robust, smooth, and low in energy use). Candidate principles for generating such a prediction include A. Wiring/evolutionary constraints: animals do what they do because their electrical hardware has evolved a certain way. B. Stability: coordination choices are based on the robust insensitivity to perturbations (of the model, of the sensors and actuators, or of environmental disturbances). C. Energetics: given the body layout and the motion goals the motions minimize some measure of effort. D. Passive mechanisms: bodies do what they do naturally.


I will review some general thoughts about these approaches based on a few robotics-like examples including examples from walking simulations and robots, hopping simulations and robots, bicycles and primitive control theory. Some observations: 1) passive strategies and energy minimizing strategies have some overlap, 2) Given reasonable sensory feedback, short reaction times, and low noise both stability and robustness seem easy to achieve and thus are not useful for making predictions. 3) Given the huge range of possible complex behaviors of neural systems, even small systems, evolutionary constraints do not seem promising for making general predictions. Thus the only reasonable candidate class of predictive theories seem to be those based on some kind of effort minimization and performance optimization. On the other hand, full blown optimal feedback control (e.g., value functions etc) seems to demand too much information management. Rather, optimal trajectories with simple feedback seems to have both predictive ability and a way to make functional control designs.

Tuesday, April 1, 2008
Time Session
09:00 AM
10:00 AM
Sten Grillner - The neural control of lamprey swimming - propulsion, steering and posture

The neural control system underlying the control of locomotion will be presented, including the intrinsic function of the spinal networks coordinating locomotion, the supraspinal command systems that initiate locomotion and the neural mechanisms underlying selection of behavior at the level of the basal ganglia. In addition, the control of body orientation, orienting reflexes and steering will be discussed.


References:



  1. Grillner, S, Kozlov, A, Dario, P, Stefanini C, Menciassi, A, Lansner, A, Hellgren Kotaleski, J. (2007) Modeling a vertebrate motor system: pattern generation, steering and control of body orientation. Prog Brain Res. 2007;165:221-34.

  2. Grillner, S. (2003) The motor infrastructure: From ion channels to neuronal networks. Nature Reviews Neuroscience, 4: 573-586.

  3. Grillner, S. (2006) Biological Pattern Generation: The Cellular and Computational Logic of Networks in Motion. Neuron 52; 751-766.

  4. Saitoh, K., A. Menard, S. Grillner (2007) Tectal Control of Locomotion, Steering, and Eye Movements in Lamprey. J. Neurophysiol. 97:3093-3108.

09:00 AM
10:30 AM
Tyler McMillen, Thelma Williams - Phase coupling between activation and curvature in lamprey swimming

Fish swim by generating waves of muscle activation which travel toward the tail, which in turn generate waves of body curvature. The body curvature waves travel more slowly than the activation waves, and this leads to an increasing delay between muscle activation and muscle shortening. In consequence, near the tail muscle is active partially while lengthening. In this study we have investigated the features responsible for this changing phase lag, by incorporating a physiological model of muscle within a model of passive body and fluid mechanics, and studying the consequences of altering various features of the combined model. We have found that the difference in wave speeds requires the viscoelastic properties of the body, body taper, and the dependence of generated force on muscle length and rate of change of length.


Work done in collaboration with Philip Holmes.

11:00 AM
12:30 PM
Lisa Fauci - Integrative CFD models of undulating lamprey and sperm

Swimming due to sinusoidal body undulations is observed across the spectrum of swimming organisms (and Reynolds numbers) from microscopic flagella to fish. The internal force generating mechanisms range from the action of dynein molecular motors within a flagellar axoneme, to muscle activation in lamprey. These active forces are also mediated by passive structural forces in each system. We will present recent progress in building computational models, based upon an immersed boundary framework, that reflect the full coupling of internal force mechanisms with external fluid mechanics in each of these systems.

11:00 AM
12:30 PM
Keith Sillar - Development of swimming in anuran frog, Xenopus laevis

Swimming in the anuran frog, Xenopus laevis, changes dramatically during the organism's life. A tail-based undulatory strategy, established early in development around the time of hatching, undergoes a period of maturation when the flexibility of the larval swimming pattern increases. Later, a limb-based system appears, initially assisting the tail in generating propulsion before superseding the tail system at metamorphosis.


I will review the nature of the central pattern generating (CPG) networks responsible for generating swimming and how they are modified during development to accommodate the behavioural requirements of the organism. The basic network assembled in ovo produces a motor rhythm in which myotomal motor neurons discharge a single impulse per cycle. I will present recent evidence that electrical coupling between motor neurons is responsible synchronization of motor activity. After hatching the larval swimming rhythm become more burst-like and flexible. The role of a range of neuromodulators which are important in conferring this flexibility including serotonin, noradrenaline and nitric oxide (NO) will be reviewed. NO functions as a metamodulator, governing how brainstem nuclei modify the spinal locomotor circuitry.


The metamorphic period is characterized by a gradual switch from tail- to limb-based swimming. The emerging limb network is initially co-opted into the existing tail circuit before adopting its own cadence and independence. New populations of NO generating neurons appear in the spinal cord, by which time NO's role in modulating swimming switches from inhibitory to excitatory.


Supported by the BBSRC and the Wellcome Trust.

02:00 PM
03:30 PM
Tetsuya Iwasaki - Feedback Control Principles underlying Animal Locomotion

Rhythmic body movements observed in animal locomotion result from interactions of various dynamical elements, including the neuronal circuits called central pattern generators (CPGs), muscle activation by motoneurons, sensory feedback from receptor neurons, body biomechanics, and dynamics of the surrounding environment (e.g. air, water, ground). Feedback control theory provides an integrated view of dynamic interactions and a systems-level framework for understanding the animal locomotion mechanism. Our research has focused on feedback control principles underlying undulatory swimming of leeches. This talk proposes the following hypotheses on the mechanism of animal locomotion: (i) the frequency of body undulation during swimming is chosen close to a resonance mode of the body dynamics, and (ii) the gait (i.e., phase pattern) is chosen to optimize a criterion under the dynamical constraint of the body-fluid interaction. These hypotheses are motivated by observations of leeches "swimming in air" where a body hanged in air by threads oscillates at a frequency near that of normal swimming in water, but exhibits almost no traveling wave. We will provide evidence supporting the hypotheses, by performing theoretical analyses of a mathematical model of leech swimming developed through combinations of physiological experiments and first principles in physics.

02:00 PM
03:30 PM
Eric Tytell - Sensory feedback loops in lamprey swimming

In fishes, undulatory swimming is produced by sets of spinal interneurons constituting a central pattern generator (CPG). The CPG can produce the basic pattern for locomotion in the absence of sensory information, but is strongly affected by sensory input. For instance, proprioceptive feedback from mechanosensory "edge cells" on the margin of the lamprey spinal cord can reset the CPG's rhythm or entrain it to a different frequency. The CPG's output, in turn, activates the muscles, bending the body, and providing proprioceptive input back to the CPG itself. This feedback loop was studied in two ways. First, the input-output relationship between sensory information and the CPG rhythm was investigated during fictive swimming in the isolated spinal cord. The cord was bent sinusoidally back and forth at several points along its length. Bending at caudal segments entrains the CPG so that each side starts a burst just before it is maximally stretched, which is approximately the same phase relationship observed between muscle activity and bending in freely swimming lampreys. Bending at rostral segments, in contrast, results in bursts on each side just after that side is maximally shortened and is beginning to stretch, nearly 50% out of phase with the pattern observed in free swimming. Second, the closed-loop behavior of the spinal cord was investigated by filtering the CPG bursts (its output) in real time with a computer and using the filtered bursts to determine the bending applied to the spinal cord (the CPG input). Filtering was done with a variable phase lag linear filter to test the CPG's stability with different phase relationships between motor output and movement. Additionally, the resonant properties of the lamprey body were simulated in the computer to determine if the CPG frequency would converge to the body's resonant frequency, which would be useful for efficient swimming.


Work done in collaboration with A.H. Cohen.

04:00 PM
04:45 PM
Avis Cohen - Some general organizational principles for motor systems: Feedback loops and their impact

In this presentation, I will describe a range of experiments by many people in many preparations that demonstrate the general organization of motor (and sensory) systems. These studies show that across invertebrates and vertebrates and across the nervous system there is massive feedback among the parts. Within motor systems, there are the well known feedback loops of sensors back to the motor neurons and their interneuron's, but there is also feedforward from the interneurons to the sensors. Furthermore, there is the well known feedforward of the descending systems to the spinal cord, but there is also feedback from the spinal cord to the same descending systems. In both of these loops there is considerable evidence for a positive feedback. In some cases the gain on that feedback loop has been estimated to be less than 1, but in others it clearly is not. This kind of organization is also seen in sensory systems in the brain. In these systems, as well, there is little understanding of the role played by the mutual interactions. The mathematics of all the various interactions is not well developed for a variety of reasons, not the least of which being that the biological details are under determined. With more evidence of the input-output mappings connecting the two systems it will be easier to model the control played by the respective loops. There are likely to be mathematical challenges, as these models will by necessity be non-linear, but they are unlikely to be insurmountable.



 
05:30 PM
06:30 PM
Bob Full - Bipedal Bugs, Galloping Ghosts and Gripping Geckos: Bioinspired Computer Animation, Robotics, Artificial Muscles and Adhesives

Integrative biology is providing inspiration to disciplines such as animatronics, animation, mathematics, medicine, robotics and space exploration. In return, these disciplines supply biologists with novel design hypotheses, algorithms and measurement devices. One example is in the area of BioMotion. Comparing the remarkable diversity in nature has lead to the discovery of general principles. Animals are amazing at legged locomotion because they have simple control systems, multifunction actuators and feet that allow no surface to be an obstacle. Extraordinarily diverse animals show the same dynamics - legged animals appear to bounce like people on pogo sticks. Force patterns produced by six-legged insects are the same as those produced by trotting eight-legged crabs, four-legged dogs and even running humans. Rapid running cockroaches can become bipedal as they take 50 steps in a single second and ghost crabs seem to glide with aerial phases. Yet, the advantage of many legs and a sprawled posture appears to be in stability. Mathematical models show that these designs self-stabilize to perturbations without the equivalent of a brain. Control algorithms appear embedded in the form of the animal itself. Muscles tune the system by acting as motors, springs, struts and shocks all in one. Amazing feet permit creatures such as geckos to climb up walls at over meter per second without using claws, glue or suction - just molecular forces. These fundamental principles of animal locomotion have inspired the design of creations in computer animation (A Bug's Life, Pixar), new control circuits, artificial muscles, self-clearing dry adhesives, and autonomous legged robots such as Ariel, Sprawl, Sitckybot and RHex will spawn the next generation of search-and-rescue robots.



 
Wednesday, April 2, 2008
Time Session
09:00 AM
10:30 AM
Roy Ritzmann - How do Insects Re-direct Leg Movements to Deal with Barriers?

The ability of animals to negotiate unpredicted barriers in natural terrain makes them attractive models for robotic design. Animals evaluate objects in their path using sensors on their head, then use that information to formulate commands that ultimately re-direct leg movements. In order to understand this process in insects, we employ a range of behavioral and neurobiological studies directed at both thoracic local control circuits and brain centers. These studies are augmented by robotic hardware models that allow us to test and refine biological hypotheses and examine implementation under real physical conditions.


Our research begins with behavioral observations. Cockroaches deal with blocks in their path by first evaluating the object with antennae and other sensors, then rearing up to an appropriate height for climbing. If the block is replaced with a shelf the insect now has a choice. If the antennae contact the shelf from above, the insect will climb over, while contact from below will cause it to tunnel under the barrier. Antennal contact of a wall may generate turning movements. Other sensors such as vision also affect decisions and all these data must be processed within the insect's brain. Insects that have experienced bilateral lesion of circumoesophageal connectives, that disconnect the brain from the thoracic ganglia, deal with barriers in a less controlled manner. These animals crash into walls, then force themselves around or over them by brute force. Lesions within the brain also generate abnormal behaviors if they involve a region designated as the Central Complex (CC).


We then examine both motor and leg joint kinematics associated with turning by studying cockroaches that are tethered over a lightly oiled plate. In turning, leg joints shift from symmetrical (left-right) movements to asymmetrical actions. Although these are profound changes, our observations suggest that they may arise through a process in which descending commands alter a few critical feedback circuits then allow local reflexes to push the leg toward a new stable state through a cascade of changes.


Our behavioral observations indicate that mechanical stimulation of antennae provide much of the necessary information for evaluating barriers, and lesion studies implement the Central Complex (CC). We, therefore, investigated responses of CC units to mechanical stimulation of antennae. We inserted 16-channel extracellular probes into the CC of restrained cockroaches. In these recordings, we isolated 5-20 units in most experiments. In all, we examined over 250 units and about half of them responded to stimulation of either antenna, with about one-third being biased to one side. Most of these units also responded to visual stimuli. Thus, we found a large multi-sensory population of neurons associated with the CC that could be used to generate the descending activity necessary to alter local circuits and re-direct leg movements. Finally, in tethered insects, we can observer brain activity in relation to actual leg movement. Neurons recorded in the CC show activity associated with step patterns. Furthermore, stimulation in these regions can alter movement. We are currently developing a robotic leg that simulates joint movements of a tethered cockroach and is controlled by feedback circuits that have been documented in insect preparations. This "hardware model" will help us to formulate and test hypotheses of the mechanisms by which brain circuits re-direct leg movements to deal with barriers.

Thursday, April 3, 2008
Time Session
09:00 AM
10:30 AM
Sasha Zill - Force sensing in insect legs: Specificity in load detection and tuning to body structure

Many animals have sensory receptors that detect forces in the legs and use this information to generate and adapt posture and locomotion. Recent studies of campaniform sensilla, sense organs that detect forces as strains in the exoskeleton of insects, have demonstrated that individual receptors show considerable specificity in the parameters of load that are signaled. Neurophysiological recordings in freely moving animals and modeling studies have demonstrated: 1) the presence of signals of unloading as well as loading, both of which are temporally linked with movement velocity during postural perturbations; 2) the signaling of body load as a continuum which changes from modulation of excitatory inputs during normal load variations to the elicitation of inhibition during large or rapid load decreases; 3) the dependence of force feedback upon leg position in walking, as supported by studies using finite element analysis to model receptor discharges in walking. These studies suggest that the specificity of sensory discharges reflects both the morphology and behavioral use of the leg. Comparable tuning of sensory signals to leg and body structure may be advantageous in both animals and walking machines.


 

11:00 AM
12:30 PM
Kiisa Nishikawa - Department of Biological Sciences, Northern Arizona University

Muscle physiologists typically study the behavior of muscle under a limited set of conditions, such as isometric tetanus or isotonic shortening, which rarely apply to movements of freely behaving animals. While investigating ballistic prey capture behavior in toads, we re-discovered the usefulness of an old technique, the load-clamp, for quantifying contractile and elastic properties of muscles and their connective tissues under physiologically relevant conditions. This technique allows muscle properties to be studied under a wide range of conditions, particularly those in which muscles develop force against a resisting force, and shorten when the resisting force is reduced. Using this technique, we developed an elastic recoil model of muscles and connective tissues during ballistic movements. The model accurately predicts the observed amplitude and velocity of movements given only the duration of muscle activation prior to unloading and the external load. It predicts elastic behavior during active shortening for several muscles (depressor mandibulae, sartorius, extensor digitorum longus, soleus) in different species (frog, mouse). In addition, it predicts the elastic behavior of muscle under isometric and isotonic conditions. At the level of the whole organism, the model predicts that appendages of smaller animals will operate at higher stiffness, and hence at greater frequencies, than those of larger animals. The model demonstrates that actively shortening muscles exhibit dynamic stabilization to perturbations in load without requiring neural input. It also suggests that control of rapid movements may require specification of relatively few variables.


Work done in collaboration with Jenna Monroy, Leslie Gilmore, Theodore Uyeno, and A. Kristopher Lappin.

02:00 PM
03:30 PM
Matthias Gruhn - Straight walking and turning on a slippery surface

In stick insects, walking is the result of the co-action of different pattern generators for the single legs and coordinating inter-leg influences. The pattern generator for each leg consists of central pattern generators (CPGs) for each leg joint.


We have used a slippery surface setup to study the coordination of single insect legs in the intact stick insect without the effect of substrate coupling. We analyzed the walking pattern of the front middle and hind legs of animals walking on the slippery surface and compared the kinematics of the straight walking legs with those of the curve walking inside and outside legs. The walking pattern was monitored electrically through tarsal contact measurement, and optically by using synchronized high-speed video. The vectors of leg movement are presented for the intact and the reduced preparation. Animals showed the ability to walk in a coordinated fashion on the slippery surface. Upon change from straight to curve walking, the stride length for the inside legs shortens and the vector of movement of the inner legs changes to pull the animal into the curve, while the outer legs act to pull or push it into the turn. In the reduced two-leg and in the single-leg preparation the behavior of the legs remained largely unchanged in the behavioral contexts of straight walking or turning with only small changes in the extreme positions. This suggests that the stepping behavior of the single leg in a given motor program is highly independent not only of mechanical coupling between, but also of the presence of the other legs.

02:00 PM
03:30 PM
Francisco Valero-Cuevas - Neuromechanics of dynamic manipulation in humans

A theme of my work is related to the questions: How does the neuromechanical system meet the necessary and sufficient conditions for complex function? and What specific contributions come from passive (e.g., tissue) and active (e.g., muscles & neurons) components of dexterous manipulation as a sample complex neuromuscular system? In this presentation I explore those questions in the context of a simple and fundamental aspect of manipulation: making abrupt contact with surfaces to produce fingertip force (as in grasping objects), and producing both motion along a surface and force against it. These two tasks reveal a surprisingly complex and time-critical control strategy, and emphasize that these fundamental aspects of manipulation require cortical involvement. I conclude by underscoring other instances where the complexity of the tendons of the fingers collaborates actively to enhancing the mechanical ability of the fingers, thus providing a clear example of brain-body co-evolution.



 
04:00 PM
04:45 PM
Reinhard Blickhan - Straight walking and turning on a slippery surface

In stick insects, walking is the result of the co-action of different pattern generators for the single legs and coordinating inter-leg influences. The pattern generator for each leg consists of central pattern generators (CPGs) for each leg joint.


We have used a slippery surface setup to study the coordination of single insect legs in the intact stick insect without the effect of substrate coupling. We analyzed the walking pattern of the front middle and hind legs of animals walking on the slippery surface and compared the kinematics of the straight walking legs with those of the curve walking inside and outside legs. The walking pattern was monitored electrically through tarsal contact measurement, and optically by using synchronized high-speed video. The vectors of leg movement are presented for the intact and the reduced preparation. Animals showed the ability to walk in a coordinated fashion on the slippery surface. Upon change from straight to curve walking, the stride length for the inside legs shortens and the vector of movement of the inner legs changes to pull the animal into the curve, while the outer legs act to pull or push it into the turn. In the reduced two-leg and in the single-leg preparation the behavior of the legs remained largely unchanged in the behavioral contexts of straight walking or turning with only small changes in the extreme positions. This suggests that the stepping behavior of the single leg in a given motor program is highly independent not only of mechanical coupling between, but also of the presence of the other legs.

Friday, April 4, 2008
Time Session
09:00 AM
10:00 AM
Jane Wang - Efficient flapping flight

N/A

09:00 AM
10:30 AM
John Guckenheimer, Shai Revzen - A Dynamical Systems Analysis of Running Cockroaches

We use methods from dynamical systems theory to analyze movement of /Blaberus discoidalis/ cockroaches. One of our key objectives is to derive dimensionally reduced models that describe the biomechanical synergies used by an animal steadily running on flat ground. By modeling the motion as a stable periodic orbit in a body centered frame of reference, we may apply Floquet theory to the problem. In the absence of noise, the theory predicts a change of coordinates which rectifies the motion transverse to the orbit to a time invariant linear system with modes that decay exponentially. These Floquet modes can be divided into those that are highly damped and those that are weakly damped. Preliminary results give evidence for few weakly damped modes, and for many highly damped modes that decay in less than a stride. We hypothesize that the weakly damped modes form a template for the neuromechanical control of locomotion.


We describe our use of diverse tools from motion tracking, numerical analysis, visualization and geometric statistics to fit these periodic orbit models to video recordings of running cockroaches. Our focus is on the numerical estimation of a phase variable and of the linearized first return map, with quantified levels of statistical confidence in the presence of noisy data.

11:00 AM
12:30 AM
Lena Ting - Neuromechanical redundancy and hierarchy in posture and movement

Standing balance control is a complex sensorimotor task that is fundamental to the performance of other motor behaviors. Neuromechancial principles for control of posture and balance are little understood, as they involve integration of multiple channels of sensory input and motor output. Descending control of postural response appears to be rather low-dimensional, as muscle activity and biomechanical outputs can be described using just a few parameters related to task-level variables. These data might suggest that the control of balance is simple, as they are aptly described by simple, conceptual, "template" models. However, there are no complex, anatomical, or "anchor" models that can actually stand up using physiological elements - including our own. Moreover, experimentally we observe a wide degree of variability in postural responses across trials and individuals, suggesting that the biological systems are quite robust to variations, whereas our musculoskeletal models are not. What are they missing?


We hypothesize that postural stability requires precise coordination among hierarchal, redundant neuromechanical elements, and that the contributions of each are flexibly adjusted by the nervous system as appropriate to a particular situation. That is, the "simple" task-level commands are only functional if appropriately subserved by neurally-modifiable spinal and peripheral mechanisms for quiet standing. Therefore, we predict that the nervous system modulates interactions between hierarchically organized neuromechanical elements that contribute to feedback neural processes required for reacting to postural perturbations and feedforward neural processes that adjust the intrinsic mechanical stability of the musculoskeletal system. We have evidence in both normal and impaired balance control, of shifts along this continuum between neural and mechanical computations for mitigating disturbances to balance. Our neuromechanical modeling efforts also demonstrate that task-level feedback, postural tone, and postural configuration cannot be independently modulated to produce stable posture. These ideas extend to all motor tasks. I propose that motor control principles adequate for allowing us to reproduce real functions will only be revealed if all levels of the neuromechanical hierarchy, and their interactions, are understood.

11:00 AM
12:30 PM
John Miller - Robust Numerical Methods for Dynamical Systems

New numerical methods are described for the approximate solution of systems of equations arising in mathematical models of the neurodynamics of various modes of animal locomotion. The mathematical models usually involve dynamical systems, which are sometimes large scale. Moreover, feedback of some kind is also normally present, so that the corresponding control problems have to be solved. The relevant systems are described mathematically in terms of differential or differential-algebraic equations, which are frequently stiff systems involving different time-scales. Consequently, severe numerical difficulties in the computations are likely to be encountered, which means that standard finite difference or finite element methods are not effective. We describe recent advances in the construction of robust numerical methods for large-scale dynamical systems with controls. These are robust in the sense that the numerical approximations behave uniformly well regardless of the range of scales present, which is not the case with the numerical approximations generated by standard numerical methods.



 
02:00 PM
02:45 PM
Manoj Srinivasan - Some simple observations about walking and running

N/A

Name Affiliation
Aguda, Baltazar bdaguda@gmail.com Mathematical Biosciences Institute, The Ohio State University
Apaydin, Elif apaydin.2@osu.edu Biomedical Engineering, The Ohio State University
Baker, Greg baker.27@osu.edu Department of Mathematics, The Ohio State University
Banerjee, Sayanti banerjee.35@osu.edu Mathematics, The Ohio State University
Basso, Michele basso.2@osu.edu Division of Physical Therapy, The Ohio State University
Best, Janet jbest@mbi.osu.edu
Biewener, Andrew abiewener@oeb.harvard.edu Department of Organismic and Evolutionary Biology, Harvard University
Blickhan, Reinhard reinhard.blickhan@rz.uni-jena.de Institute for Sports Science, Friedrich-Schiller-Universit""at
Bluemel, Marcus bluemelm@uni-koeln.de Zoological Institute, University of Cologne
Borgmann, Anke Anke.borgmann@smail.uni-koeln.de Zoological Institute, University of Cologne
Buchli, Jonas jonas@buchli.org Computer Science and Neuroscience, University of Southern California
Bueschges, Ansgar ansgar.bueschges@uni-koeln.de Zoological Institute, University of Cologne
Buford, John buford.5@osu.edu Physiology and Cell Biology, The Ohio State University
Bunderson, Nate nbunderson@gatech.edu Biomedical Engineering, Georgia Institute of Technology
Cabelguen, Jean-Marie cabelguen@bordeaux.inserm.fr Neurocentre INSERM, Institut F. Magendie
Chaudhari, Ajit chaudhari.2@osu.edu Orthopaedics, The Ohio State University
Chen, Linda chen.151@osu.edu Department of Mathematics, The Ohio State University
Cohen, Avis avis@umd.edu Department of Biology, Program in Neurosciences and Cognitive Science and ISR, College of Business and Management
Coskun, Huseyin hcusckun@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Cowan, Noah ncowan@jhu.edu Department of Mechanical Engineering, Johns Hopkins University
Daniel, Tom danielt@u.washington.edu Department of Biology, University of Washington
Daun, Silvia dauns@upmc.edu Mathematics Department, University of Pittsburgh
Day, Judy jday@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Detloff, Megan detloff.1@osu.edu Neuroscience, The Ohio State University
DiCaprio, Ralph rdicaprio1@ohiou.edu Biological Sciences, Ohio University
Djordjevic, Marko mdjordjevic@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Drr, Volker volker.duerr@uni-koeln.de Zoological Institute, University of Cologne
Ekeberg, Orjan orjan@nada.kth.se Dept. of Computational Biology, KTH Computer Science and Communication
Enciso, German German_Enciso@hms.harvard.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Fauci, Lisa fauci@tulane.edu Mathematics, Tulane University
Fuchs, Einat fuchsein@post.tau.ac.il Dept. of Zoology, Life Science, Tel-Aviv University
Full, Robert rjfull@berkeley.edu Department of Integrative Biology, University of California, Berkeley
Gooch, Keith gooch.20@osu.edu Biomedical Engineering, The Ohio State University
Grajdeanu, Paula pgrajdeanu@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Green, Edward egreen@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Grillner, Sten sten.grillner@neuro.ki.se Department of Neuroscience, Nobel Institute for Neurophysiology
Grotewold, Erich grotewold.1@osu.edu MBI-Long Term Visitor, The Ohio State University
Gruhn, Matthias mgruhn@uni-koeln.de Zoological Institute, University of Cologne
Guckenheimer, John gucken@cam.cornell.edu; Department of Mathematics, Cornell University
Hamilton, Ian hamilton.598@osu.edu EEOB, The Ohio State University
Hemkin, Sheryl hemkins@kenyon.edu Chemistry, Kenyon College
Herrera, Marco herrera@math.arizona.edu Physiology, University of Arizona
Hillen, Brian K. brian.hillen@asu.edu Bioengineering, Arizona State University
Hoffman, Kathleen khoffman@math.umbc.edu Mathematics and Statistics, University of Maryland Baltimore County
Holmes, Phil pholmes@Math.Princeton.EDU Mechanical and Aerospace Engineering, Princeton University
Hooper , Scott hooper@ohio.edu Department of Biological Sciences, Ohio University
Hovmoller, Rasmus rhovmoller@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Hsu, Chia-Yu chsu1@tulane.edu Center for Comp. Science, Math Department, Tulane University
Hsu, Jason hsu.1@osu.edu Department of Statistics, The Ohio State University
Ijspeert, Auke Auke.ijspeert@epfl.ch School of Computer and Communication Sciences, EPFL, Swiss Federal Institute of Technology
Iwasaki, Tetsuya iwasaki@virginia.edu Mechanical & Aerospace Engineering, University of Virginia
Jones, Adam adam.jones@umontana.edu Center for Structural and Functional Neuroscience, University of Montana
Jusufi, Ardian ardianj@berkeley.edu Department of Integrative Biology, University of California, Berkeley
Kaasen, Rune r.kaasen@mat.dtu.dk MBI-Long Term Visitor, The Ohio State University
Kao, Chiu-Yen kao.71@osu.edu MBI - Long Term Visitor, The Ohio State University
Kegelmeyer, Deb kegelmeyer.1@osu.edu Physical Therapy, The Ohio State University
Keller, Bridget holcomb7@marshall.com Dept. of Anatomy and Pathology, Marshall University
Kim, Yangjin ykim@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Koditschek, Daniel kod@seas.upenn.edu Electrical & Systems Engineering, University of Pennsylvania
Kukillaya, Raghavendra rkukilla@Princeton.EDU Mechanical and Aerospace Engineering, Princeton University
Kurse, Manish kurse@usc.edu Biomedical Engineering, University of Southern California
Lathrop, Becky lathrop.16@osu.edu Mechanical Engineering, The Ohio State University
Li, Weiwei weiwei.lili@gmail.com Biomedical Engineering, University of Southern California
Lin, Shili lin.328@osu.edu Department of Statistics, The Ohio State University
Lou, Yuan lou@math.ohio-state.edu MBI - Long Term Visitor, The Ohio State University
Machiraju, Raghu machiraju@math.ohio-state.edu Computer Science and Engineering, The Ohio State University
Mangel, Stuart mangel.1@osu.edu Department of Neuroscience, The Ohio State University
Martinez, Aleix martinez.158@osu.edu Electrical and Computer Engineering, The Ohio State University
Matzavinos, Tasos tasos@math.ohio-state.edu MBI - Long term visitor, The Ohio State University
McMillen, Tyler tmcmillen@fullerton.edu Mathematics, California State University, Fullerton
Miller, John jm@incaireland.org INCA (Institute for Numerical Computation & Analysis, Royal College of Surgeons in Ireland Research Inst.
Montgomery, Lynnette montgomery.703@osu.edu Neuroscience Granduate Studies Program, The Ohio State University
Morin, Brooke morin.20@osu.edu Mechanical Engineering, The Ohio State University
Nevai, Andrew anevai@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Nishikawa, Kiisa Kiisa.Nishikawa@nau.edu Department of Biological Sciences, Northern Arizona University
Oster, Andrew aoester@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Passino, Kevin passino.1@osu.edu EEOB, The Ohio State University
Pearson, Keir keir.pearson@ualberta.ca Department of Physiology, University of Alberta
Potter, Dustin potter.153@osu.edu Comprehensive Cancer Center, The Ohio State University
Proctor, Joshua jproctor@Princeton.EDU Mechanical and Aerospace Engineering, Princeton University
Rempe, Michael mrempe@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Revzen, Shai shrevz@berkeley.edu Department of Integrative Biology, University of California, Berkeley
Ritzmann, Roy rer3@po.cwru.edu Department of Biology, Case Western Reserve University
Roth, Eatai ncowan@jhu.edu Department of Mechanical Engineering, Johns Hopkins University
Ruina, Andy ruina@cornell.edu Theoretical and Applied Mechanics, Cornell University
Santner, Tom santner.1@osu.edu Department of Statistics, The Ohio State University
Schmiedeler, Jim schmiedeler.2@osu.edu Mechanical Engineering, The Ohio State University
Schmitz, Josef josef.schmitz@uni-bielefeld.de Dep. of Biological Cybernetics, Universit""at Bielefeld
Schugart, Richard richard.schugart@wku.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Seipel, Justin jseipel@berkeley.edu Integrative Biology, University of California, Berkeley
Seyfarth, Andre oas@uni-jena.de Locomotion Lab, Jena University
Shih, Chih-Wen shih@math.ohio-state.edu MBI - Long term visitor, The Ohio State University
Sillar, Keith kts1@st-andrews.ac.uk School of Biology; Division of Biomedical Sciences, University of St. Andrews
Siston, Robert siston.1@osu.edu Mechanical Engineering, The Ohio State University
Smith, Greg greg@as.wm.edu MBI - Long term visitor, The Ohio State University
Sponberg, Simon sponberg@calmail.berkeley.edu Department of Integrative Biology, University of California, Berkeley
Srinivasan, Manoj msriniva@princeton.edu Mechanical and Aerospace Engineering, Princeton University
Srinivasan, Partha p.srinivasan35@csuohio.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Stigler, Brandy bstigler@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Sun, Shuying ssun@mbi.osu.edu Mathematical Biosciences Institute (MBI), The Ohio State University
Szomolay, Barbara b.szomolay@imperial.ac.uk Mathematical Biosciences Institute (MBI), The Ohio State University
Talaty, Mukul mctalaty@einstein.edu Physical Medicine & Rehabilitation, Moss Rehab
Ting, Lena lting@emory.edu Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology
Twickel, Arndt Institut für Kognitionswissenschaft, Universität Osnabrück
Tytell, Eric tytell@umd.edu Laboratory for Neural Control of Locomotion, College of Business and Management
Valero-Cuevas, Francisco valero@USC.edu Department of Biomedical Engineering, University of Southern California
Venkadesan, Madhusudhan mv72@cornell.edu Department of Mathematics, Cornell University
Verducci, Tom verducci.1@osu.edu Department of Statistics, The Ohio State University
Wang, Jane zw24@cornell.edu Theoretical and Applied Mathematics, Cornell University
Williams, Thelma twilli@blueyonder.co.uk St. George's Medical School, University of London
Worthen-Chaudhari, Lise worthen-chaudhari.1@osu.edu PM&R, The Ohio State University
Xu, Ronald xu.202@osu.edu Biomedical Engineering, The Ohio State University
Zhao, Yi zhao.178@osu.edu Biomedical Engineering, The Ohio State University
Zill, Sasha sensillum@aol.com Anatomy and Pathology, Marshall University
Straight walking and turning on a slippery surface

In stick insects, walking is the result of the co-action of different pattern generators for the single legs and coordinating inter-leg influences. The pattern generator for each leg consists of central pattern generators (CPGs) for each leg joint.


We have used a slippery surface setup to study the coordination of single insect legs in the intact stick insect without the effect of substrate coupling. We analyzed the walking pattern of the front middle and hind legs of animals walking on the slippery surface and compared the kinematics of the straight walking legs with those of the curve walking inside and outside legs. The walking pattern was monitored electrically through tarsal contact measurement, and optically by using synchronized high-speed video. The vectors of leg movement are presented for the intact and the reduced preparation. Animals showed the ability to walk in a coordinated fashion on the slippery surface. Upon change from straight to curve walking, the stride length for the inside legs shortens and the vector of movement of the inner legs changes to pull the animal into the curve, while the outer legs act to pull or push it into the turn. In the reduced two-leg and in the single-leg preparation the behavior of the legs remained largely unchanged in the behavioral contexts of straight walking or turning with only small changes in the extreme positions. This suggests that the stepping behavior of the single leg in a given motor program is highly independent not only of mechanical coupling between, but also of the presence of the other legs.

Architecture and operation of neural controllers governing insect leg walking movements

In walking each leg movement results from a contribution of descending signals from the brain, central pattern generating networks (CPG), local feedback from sensory neurons about movements and forces generated in the legs, coordinating signals from neighboring limbs, and finally, the neuromuscular transform at the output stage of the walking system, the leg muscles. We have in recent years made significant advances in understanding the neural basis of insect walking. My talk will summarize the current knowledge of the organization and operation of neural networks in the thoracic ganglia generating single leg stepping. I will also outline our current knowledge on (i) how the leg muscle control system changes speed and walking direction and (ii) the neural mechanisms contributing to intersegmental activation and coordination. In doing so, I will highlight those areas, in which information is presently still too sparse to generate sufficient concepts on neural control mechanisms and in which simulation studies will be most useful. I will place current knowledge from the stick insect into the broader context of locomotor behaviors in other organisms.



 
Some general organizational principles for motor systems: Feedback loops and their impact

In this presentation, I will describe a range of experiments by many people in many preparations that demonstrate the general organization of motor (and sensory) systems. These studies show that across invertebrates and vertebrates and across the nervous system there is massive feedback among the parts. Within motor systems, there are the well known feedback loops of sensors back to the motor neurons and their interneuron's, but there is also feedforward from the interneurons to the sensors. Furthermore, there is the well known feedforward of the descending systems to the spinal cord, but there is also feedback from the spinal cord to the same descending systems. In both of these loops there is considerable evidence for a positive feedback. In some cases the gain on that feedback loop has been estimated to be less than 1, but in others it clearly is not. This kind of organization is also seen in sensory systems in the brain. In these systems, as well, there is little understanding of the role played by the mutual interactions. The mathematics of all the various interactions is not well developed for a variety of reasons, not the least of which being that the biological details are under determined. With more evidence of the input-output mappings connecting the two systems it will be easier to model the control played by the respective loops. There are likely to be mathematical challenges, as these models will by necessity be non-linear, but they are unlikely to be insurmountable.



 
Integrative CFD models of undulating lamprey and sperm

Swimming due to sinusoidal body undulations is observed across the spectrum of swimming organisms (and Reynolds numbers) from microscopic flagella to fish. The internal force generating mechanisms range from the action of dynein molecular motors within a flagellar axoneme, to muscle activation in lamprey. These active forces are also mediated by passive structural forces in each system. We will present recent progress in building computational models, based upon an immersed boundary framework, that reflect the full coupling of internal force mechanisms with external fluid mechanics in each of these systems.

Bipedal Bugs, Galloping Ghosts and Gripping Geckos: Bioinspired Computer Animation, Robotics, Artificial Muscles and Adhesives

Integrative biology is providing inspiration to disciplines such as animatronics, animation, mathematics, medicine, robotics and space exploration. In return, these disciplines supply biologists with novel design hypotheses, algorithms and measurement devices. One example is in the area of BioMotion. Comparing the remarkable diversity in nature has lead to the discovery of general principles. Animals are amazing at legged locomotion because they have simple control systems, multifunction actuators and feet that allow no surface to be an obstacle. Extraordinarily diverse animals show the same dynamics - legged animals appear to bounce like people on pogo sticks. Force patterns produced by six-legged insects are the same as those produced by trotting eight-legged crabs, four-legged dogs and even running humans. Rapid running cockroaches can become bipedal as they take 50 steps in a single second and ghost crabs seem to glide with aerial phases. Yet, the advantage of many legs and a sprawled posture appears to be in stability. Mathematical models show that these designs self-stabilize to perturbations without the equivalent of a brain. Control algorithms appear embedded in the form of the animal itself. Muscles tune the system by acting as motors, springs, struts and shocks all in one. Amazing feet permit creatures such as geckos to climb up walls at over meter per second without using claws, glue or suction - just molecular forces. These fundamental principles of animal locomotion have inspired the design of creations in computer animation (A Bug's Life, Pixar), new control circuits, artificial muscles, self-clearing dry adhesives, and autonomous legged robots such as Ariel, Sprawl, Sitckybot and RHex will spawn the next generation of search-and-rescue robots.



 
The neural control of lamprey swimming - propulsion, steering and posture

The neural control system underlying the control of locomotion will be presented, including the intrinsic function of the spinal networks coordinating locomotion, the supraspinal command systems that initiate locomotion and the neural mechanisms underlying selection of behavior at the level of the basal ganglia. In addition, the control of body orientation, orienting reflexes and steering will be discussed.


References:



  1. Grillner, S, Kozlov, A, Dario, P, Stefanini C, Menciassi, A, Lansner, A, Hellgren Kotaleski, J. (2007) Modeling a vertebrate motor system: pattern generation, steering and control of body orientation. Prog Brain Res. 2007;165:221-34.

  2. Grillner, S. (2003) The motor infrastructure: From ion channels to neuronal networks. Nature Reviews Neuroscience, 4: 573-586.

  3. Grillner, S. (2006) Biological Pattern Generation: The Cellular and Computational Logic of Networks in Motion. Neuron 52; 751-766.

  4. Saitoh, K., A. Menard, S. Grillner (2007) Tectal Control of Locomotion, Steering, and Eye Movements in Lamprey. J. Neurophysiol. 97:3093-3108.

Straight walking and turning on a slippery surface

In stick insects, walking is the result of the co-action of different pattern generators for the single legs and coordinating inter-leg influences. The pattern generator for each leg consists of central pattern generators (CPGs) for each leg joint.


We have used a slippery surface setup to study the coordination of single insect legs in the intact stick insect without the effect of substrate coupling. We analyzed the walking pattern of the front middle and hind legs of animals walking on the slippery surface and compared the kinematics of the straight walking legs with those of the curve walking inside and outside legs. The walking pattern was monitored electrically through tarsal contact measurement, and optically by using synchronized high-speed video. The vectors of leg movement are presented for the intact and the reduced preparation. Animals showed the ability to walk in a coordinated fashion on the slippery surface. Upon change from straight to curve walking, the stride length for the inside legs shortens and the vector of movement of the inner legs changes to pull the animal into the curve, while the outer legs act to pull or push it into the turn. In the reduced two-leg and in the single-leg preparation the behavior of the legs remained largely unchanged in the behavioral contexts of straight walking or turning with only small changes in the extreme positions. This suggests that the stepping behavior of the single leg in a given motor program is highly independent not only of mechanical coupling between, but also of the presence of the other legs.

A Dynamical Systems Analysis of Running Cockroaches

We use methods from dynamical systems theory to analyze movement of /Blaberus discoidalis/ cockroaches. One of our key objectives is to derive dimensionally reduced models that describe the biomechanical synergies used by an animal steadily running on flat ground. By modeling the motion as a stable periodic orbit in a body centered frame of reference, we may apply Floquet theory to the problem. In the absence of noise, the theory predicts a change of coordinates which rectifies the motion transverse to the orbit to a time invariant linear system with modes that decay exponentially. These Floquet modes can be divided into those that are highly damped and those that are weakly damped. Preliminary results give evidence for few weakly damped modes, and for many highly damped modes that decay in less than a stride. We hypothesize that the weakly damped modes form a template for the neuromechanical control of locomotion.


We describe our use of diverse tools from motion tracking, numerical analysis, visualization and geometric statistics to fit these periodic orbit models to video recordings of running cockroaches. Our focus is on the numerical estimation of a phase variable and of the linearized first return map, with quantified levels of statistical confidence in the presence of noisy data.

Towards an integrated model for insect locomotion

I will review our attempts to build an analytically-tractable, yet biophysically-grounded, neuromechanical model of a running animal, with particular reference to the cockroach Blaberus discoidalis. Building on a sequence of simple mechanical models, we have successively added actuated, axially-sprung legs, jointed legs, and muscles. In doing so we have confirmed the 'preflexive' hypothesis: that feedforward control, coupled with passive dynamics, can yield robustly stable gaits. In parallel work we have modeled the insect central pattern generator and motoneurons. It remains to integrate neurobiology and biomechanics by incorporating models of proprioceptive and exteroceptive sensing. I hope to stimulate a debate on appropriate levels of detail in such integrated models, and, more generally, on their role in the biological sciences.


This is joint worth with J. Schmitt, R. Ghigliazza, J. Seipel, R. Kukillaya, J. Proctor, M. Srinivasan, R. Altendorfer, R.J. Full and D. Koditschek.

Feedback Control Principles underlying Animal Locomotion

Rhythmic body movements observed in animal locomotion result from interactions of various dynamical elements, including the neuronal circuits called central pattern generators (CPGs), muscle activation by motoneurons, sensory feedback from receptor neurons, body biomechanics, and dynamics of the surrounding environment (e.g. air, water, ground). Feedback control theory provides an integrated view of dynamic interactions and a systems-level framework for understanding the animal locomotion mechanism. Our research has focused on feedback control principles underlying undulatory swimming of leeches. This talk proposes the following hypotheses on the mechanism of animal locomotion: (i) the frequency of body undulation during swimming is chosen close to a resonance mode of the body dynamics, and (ii) the gait (i.e., phase pattern) is chosen to optimize a criterion under the dynamical constraint of the body-fluid interaction. These hypotheses are motivated by observations of leeches "swimming in air" where a body hanged in air by threads oscillates at a frequency near that of normal swimming in water, but exhibits almost no traveling wave. We will provide evidence supporting the hypotheses, by performing theoretical analyses of a mathematical model of leech swimming developed through combinations of physiological experiments and first principles in physics.

Phase coupling between activation and curvature in lamprey swimming

Fish swim by generating waves of muscle activation which travel toward the tail, which in turn generate waves of body curvature. The body curvature waves travel more slowly than the activation waves, and this leads to an increasing delay between muscle activation and muscle shortening. In consequence, near the tail muscle is active partially while lengthening. In this study we have investigated the features responsible for this changing phase lag, by incorporating a physiological model of muscle within a model of passive body and fluid mechanics, and studying the consequences of altering various features of the combined model. We have found that the difference in wave speeds requires the viscoelastic properties of the body, body taper, and the dependence of generated force on muscle length and rate of change of length.


Work done in collaboration with Philip Holmes.

Robust Numerical Methods for Dynamical Systems

New numerical methods are described for the approximate solution of systems of equations arising in mathematical models of the neurodynamics of various modes of animal locomotion. The mathematical models usually involve dynamical systems, which are sometimes large scale. Moreover, feedback of some kind is also normally present, so that the corresponding control problems have to be solved. The relevant systems are described mathematically in terms of differential or differential-algebraic equations, which are frequently stiff systems involving different time-scales. Consequently, severe numerical difficulties in the computations are likely to be encountered, which means that standard finite difference or finite element methods are not effective. We describe recent advances in the construction of robust numerical methods for large-scale dynamical systems with controls. These are robust in the sense that the numerical approximations behave uniformly well regardless of the range of scales present, which is not the case with the numerical approximations generated by standard numerical methods.



 
Department of Biological Sciences, Northern Arizona University

Muscle physiologists typically study the behavior of muscle under a limited set of conditions, such as isometric tetanus or isotonic shortening, which rarely apply to movements of freely behaving animals. While investigating ballistic prey capture behavior in toads, we re-discovered the usefulness of an old technique, the load-clamp, for quantifying contractile and elastic properties of muscles and their connective tissues under physiologically relevant conditions. This technique allows muscle properties to be studied under a wide range of conditions, particularly those in which muscles develop force against a resisting force, and shorten when the resisting force is reduced. Using this technique, we developed an elastic recoil model of muscles and connective tissues during ballistic movements. The model accurately predicts the observed amplitude and velocity of movements given only the duration of muscle activation prior to unloading and the external load. It predicts elastic behavior during active shortening for several muscles (depressor mandibulae, sartorius, extensor digitorum longus, soleus) in different species (frog, mouse). In addition, it predicts the elastic behavior of muscle under isometric and isotonic conditions. At the level of the whole organism, the model predicts that appendages of smaller animals will operate at higher stiffness, and hence at greater frequencies, than those of larger animals. The model demonstrates that actively shortening muscles exhibit dynamic stabilization to perturbations in load without requiring neural input. It also suggests that control of rapid movements may require specification of relatively few variables.


Work done in collaboration with Jenna Monroy, Leslie Gilmore, Theodore Uyeno, and A. Kristopher Lappin.

Modelling walking in mammals: what we need to know

Computer simulations are being used increasingly to gain insight into the neurobiology and biomechanics of walking in humans and quadrupeds. In general, these simulations are based on very limited knowledge of the neural systems generating the motor patterns for walking, the properties of muscle producing the movements, and the mechanics of muscle action. Nevertheless, these simulations have yielded valuable insights into some low-level features of mammalian locomotion, especially the biomechanical functions of specific muscles and the role of afferent signals in regulating phase transitions of the step cycle. The most obvious shortcoming in developing more versatile and complete simulations of walking is a serious lack of knowledge of the underlying neurobiological mechanisms. Despite enormous effort, we still know little about the cellular and network properties of pattern generating networks in the mammalian spinal cord, and even less about how these networks are controlled by descending signals from the brain during walking. In this presentation I will review the limited data we currently possess, and attempt to identify areas in which additional data would facilitate the development of useful simulations.



 
A Dynamical Systems Analysis of Running Cockroaches

We use methods from dynamical systems theory to analyze movement of /Blaberus discoidalis/ cockroaches. One of our key objectives is to derive dimensionally reduced models that describe the biomechanical synergies used by an animal steadily running on flat ground. By modeling the motion as a stable periodic orbit in a body centered frame of reference, we may apply Floquet theory to the problem. In the absence of noise, the theory predicts a change of coordinates which rectifies the motion transverse to the orbit to a time invariant linear system with modes that decay exponentially. These Floquet modes can be divided into those that are highly damped and those that are weakly damped. Preliminary results give evidence for few weakly damped modes, and for many highly damped modes that decay in less than a stride. We hypothesize that the weakly damped modes form a template for the neuromechanical control of locomotion.


We describe our use of diverse tools from motion tracking, numerical analysis, visualization and geometric statistics to fit these periodic orbit models to video recordings of running cockroaches. Our focus is on the numerical estimation of a phase variable and of the linearized first return map, with quantified levels of statistical confidence in the presence of noisy data.

How do Insects Re-direct Leg Movements to Deal with Barriers?

The ability of animals to negotiate unpredicted barriers in natural terrain makes them attractive models for robotic design. Animals evaluate objects in their path using sensors on their head, then use that information to formulate commands that ultimately re-direct leg movements. In order to understand this process in insects, we employ a range of behavioral and neurobiological studies directed at both thoracic local control circuits and brain centers. These studies are augmented by robotic hardware models that allow us to test and refine biological hypotheses and examine implementation under real physical conditions.


Our research begins with behavioral observations. Cockroaches deal with blocks in their path by first evaluating the object with antennae and other sensors, then rearing up to an appropriate height for climbing. If the block is replaced with a shelf the insect now has a choice. If the antennae contact the shelf from above, the insect will climb over, while contact from below will cause it to tunnel under the barrier. Antennal contact of a wall may generate turning movements. Other sensors such as vision also affect decisions and all these data must be processed within the insect's brain. Insects that have experienced bilateral lesion of circumoesophageal connectives, that disconnect the brain from the thoracic ganglia, deal with barriers in a less controlled manner. These animals crash into walls, then force themselves around or over them by brute force. Lesions within the brain also generate abnormal behaviors if they involve a region designated as the Central Complex (CC).


We then examine both motor and leg joint kinematics associated with turning by studying cockroaches that are tethered over a lightly oiled plate. In turning, leg joints shift from symmetrical (left-right) movements to asymmetrical actions. Although these are profound changes, our observations suggest that they may arise through a process in which descending commands alter a few critical feedback circuits then allow local reflexes to push the leg toward a new stable state through a cascade of changes.


Our behavioral observations indicate that mechanical stimulation of antennae provide much of the necessary information for evaluating barriers, and lesion studies implement the Central Complex (CC). We, therefore, investigated responses of CC units to mechanical stimulation of antennae. We inserted 16-channel extracellular probes into the CC of restrained cockroaches. In these recordings, we isolated 5-20 units in most experiments. In all, we examined over 250 units and about half of them responded to stimulation of either antenna, with about one-third being biased to one side. Most of these units also responded to visual stimuli. Thus, we found a large multi-sensory population of neurons associated with the CC that could be used to generate the descending activity necessary to alter local circuits and re-direct leg movements. Finally, in tethered insects, we can observer brain activity in relation to actual leg movement. Neurons recorded in the CC show activity associated with step patterns. Furthermore, stimulation in these regions can alter movement. We are currently developing a robotic leg that simulates joint movements of a tethered cockroach and is controlled by feedback circuits that have been documented in insect preparations. This "hardware model" will help us to formulate and test hypotheses of the mechanisms by which brain circuits re-direct leg movements to deal with barriers.

Thoughts on generating control from first principles

One general class of goals is the prediction of human or animal coordination choices from a given physical architecture. This would be useful for the diagnosing and fixing of health problems as well as for the generation of animal like robots (which, to be animal-like, must be robust, smooth, and low in energy use). Candidate principles for generating such a prediction include A. Wiring/evolutionary constraints: animals do what they do because their electrical hardware has evolved a certain way. B. Stability: coordination choices are based on the robust insensitivity to perturbations (of the model, of the sensors and actuators, or of environmental disturbances). C. Energetics: given the body layout and the motion goals the motions minimize some measure of effort. D. Passive mechanisms: bodies do what they do naturally.


I will review some general thoughts about these approaches based on a few robotics-like examples including examples from walking simulations and robots, hopping simulations and robots, bicycles and primitive control theory. Some observations: 1) passive strategies and energy minimizing strategies have some overlap, 2) Given reasonable sensory feedback, short reaction times, and low noise both stability and robustness seem easy to achieve and thus are not useful for making predictions. 3) Given the huge range of possible complex behaviors of neural systems, even small systems, evolutionary constraints do not seem promising for making general predictions. Thus the only reasonable candidate class of predictive theories seem to be those based on some kind of effort minimization and performance optimization. On the other hand, full blown optimal feedback control (e.g., value functions etc) seems to demand too much information management. Rather, optimal trajectories with simple feedback seems to have both predictive ability and a way to make functional control designs.

Development of swimming in anuran frog, Xenopus laevis

Swimming in the anuran frog, Xenopus laevis, changes dramatically during the organism's life. A tail-based undulatory strategy, established early in development around the time of hatching, undergoes a period of maturation when the flexibility of the larval swimming pattern increases. Later, a limb-based system appears, initially assisting the tail in generating propulsion before superseding the tail system at metamorphosis.


I will review the nature of the central pattern generating (CPG) networks responsible for generating swimming and how they are modified during development to accommodate the behavioural requirements of the organism. The basic network assembled in ovo produces a motor rhythm in which myotomal motor neurons discharge a single impulse per cycle. I will present recent evidence that electrical coupling between motor neurons is responsible synchronization of motor activity. After hatching the larval swimming rhythm become more burst-like and flexible. The role of a range of neuromodulators which are important in conferring this flexibility including serotonin, noradrenaline and nitric oxide (NO) will be reviewed. NO functions as a metamodulator, governing how brainstem nuclei modify the spinal locomotor circuitry.


The metamorphic period is characterized by a gradual switch from tail- to limb-based swimming. The emerging limb network is initially co-opted into the existing tail circuit before adopting its own cadence and independence. New populations of NO generating neurons appear in the spinal cord, by which time NO's role in modulating swimming switches from inhibitory to excitatory.


Supported by the BBSRC and the Wellcome Trust.

Some simple observations about walking and running

N/A

Neuromechanical redundancy and hierarchy in posture and movement

Standing balance control is a complex sensorimotor task that is fundamental to the performance of other motor behaviors. Neuromechancial principles for control of posture and balance are little understood, as they involve integration of multiple channels of sensory input and motor output. Descending control of postural response appears to be rather low-dimensional, as muscle activity and biomechanical outputs can be described using just a few parameters related to task-level variables. These data might suggest that the control of balance is simple, as they are aptly described by simple, conceptual, "template" models. However, there are no complex, anatomical, or "anchor" models that can actually stand up using physiological elements - including our own. Moreover, experimentally we observe a wide degree of variability in postural responses across trials and individuals, suggesting that the biological systems are quite robust to variations, whereas our musculoskeletal models are not. What are they missing?


We hypothesize that postural stability requires precise coordination among hierarchal, redundant neuromechanical elements, and that the contributions of each are flexibly adjusted by the nervous system as appropriate to a particular situation. That is, the "simple" task-level commands are only functional if appropriately subserved by neurally-modifiable spinal and peripheral mechanisms for quiet standing. Therefore, we predict that the nervous system modulates interactions between hierarchically organized neuromechanical elements that contribute to feedback neural processes required for reacting to postural perturbations and feedforward neural processes that adjust the intrinsic mechanical stability of the musculoskeletal system. We have evidence in both normal and impaired balance control, of shifts along this continuum between neural and mechanical computations for mitigating disturbances to balance. Our neuromechanical modeling efforts also demonstrate that task-level feedback, postural tone, and postural configuration cannot be independently modulated to produce stable posture. These ideas extend to all motor tasks. I propose that motor control principles adequate for allowing us to reproduce real functions will only be revealed if all levels of the neuromechanical hierarchy, and their interactions, are understood.

Sensory feedback loops in lamprey swimming

In fishes, undulatory swimming is produced by sets of spinal interneurons constituting a central pattern generator (CPG). The CPG can produce the basic pattern for locomotion in the absence of sensory information, but is strongly affected by sensory input. For instance, proprioceptive feedback from mechanosensory "edge cells" on the margin of the lamprey spinal cord can reset the CPG's rhythm or entrain it to a different frequency. The CPG's output, in turn, activates the muscles, bending the body, and providing proprioceptive input back to the CPG itself. This feedback loop was studied in two ways. First, the input-output relationship between sensory information and the CPG rhythm was investigated during fictive swimming in the isolated spinal cord. The cord was bent sinusoidally back and forth at several points along its length. Bending at caudal segments entrains the CPG so that each side starts a burst just before it is maximally stretched, which is approximately the same phase relationship observed between muscle activity and bending in freely swimming lampreys. Bending at rostral segments, in contrast, results in bursts on each side just after that side is maximally shortened and is beginning to stretch, nearly 50% out of phase with the pattern observed in free swimming. Second, the closed-loop behavior of the spinal cord was investigated by filtering the CPG bursts (its output) in real time with a computer and using the filtered bursts to determine the bending applied to the spinal cord (the CPG input). Filtering was done with a variable phase lag linear filter to test the CPG's stability with different phase relationships between motor output and movement. Additionally, the resonant properties of the lamprey body were simulated in the computer to determine if the CPG frequency would converge to the body's resonant frequency, which would be useful for efficient swimming.


Work done in collaboration with A.H. Cohen.

Neuromechanics of dynamic manipulation in humans

A theme of my work is related to the questions: How does the neuromechanical system meet the necessary and sufficient conditions for complex function? and What specific contributions come from passive (e.g., tissue) and active (e.g., muscles & neurons) components of dexterous manipulation as a sample complex neuromuscular system? In this presentation I explore those questions in the context of a simple and fundamental aspect of manipulation: making abrupt contact with surfaces to produce fingertip force (as in grasping objects), and producing both motion along a surface and force against it. These two tasks reveal a surprisingly complex and time-critical control strategy, and emphasize that these fundamental aspects of manipulation require cortical involvement. I conclude by underscoring other instances where the complexity of the tendons of the fingers collaborates actively to enhancing the mechanical ability of the fingers, thus providing a clear example of brain-body co-evolution.



 
Efficient flapping flight

N/A

Phase coupling between activation and curvature in lamprey swimming

Fish swim by generating waves of muscle activation which travel toward the tail, which in turn generate waves of body curvature. The body curvature waves travel more slowly than the activation waves, and this leads to an increasing delay between muscle activation and muscle shortening. In consequence, near the tail muscle is active partially while lengthening. In this study we have investigated the features responsible for this changing phase lag, by incorporating a physiological model of muscle within a model of passive body and fluid mechanics, and studying the consequences of altering various features of the combined model. We have found that the difference in wave speeds requires the viscoelastic properties of the body, body taper, and the dependence of generated force on muscle length and rate of change of length.


Work done in collaboration with Philip Holmes.

Force sensing in insect legs: Specificity in load detection and tuning to body structure

Many animals have sensory receptors that detect forces in the legs and use this information to generate and adapt posture and locomotion. Recent studies of campaniform sensilla, sense organs that detect forces as strains in the exoskeleton of insects, have demonstrated that individual receptors show considerable specificity in the parameters of load that are signaled. Neurophysiological recordings in freely moving animals and modeling studies have demonstrated: 1) the presence of signals of unloading as well as loading, both of which are temporally linked with movement velocity during postural perturbations; 2) the signaling of body load as a continuum which changes from modulation of excitatory inputs during normal load variations to the elicitation of inhibition during large or rapid load decreases; 3) the dependence of force feedback upon leg position in walking, as supported by studies using finite element analysis to model receptor discharges in walking. These studies suggest that the specificity of sensory discharges reflects both the morphology and behavioral use of the leg. Comparable tuning of sensory signals to leg and body structure may be advantageous in both animals and walking machines.