Biological dynamical systems are typically multidimensional, nonlinear, hierarchical, and noisy. Problems of control are ubiquitous; examples include fixed-point control (maintenance of posture, homeostatic control), control of rhythmic movements (locomotion, respiratory control), control of rhythmic processes (circadian activation, oscillatory neural activity). Nearly all areas of control theory have potential application to biological neural and motor systems, including feedback control; estimation and control of nonlinear systems; geometric control; optimization-based control; stability analysis; model identification and parameter estimation; model predictive control; observability and controllability in coupled networks; and stochastic control. At the same time, biological control problems can stretch control theory in new directions. For example, control theory has focused on negative feedback control (i.e. homeostasis) while neuromodulation may involve the interaction of multiple positive and negative feedback components. Moreover, neural and motor systems may prioritize robustness over optimality. Nonlinear control theory for limit cycle or other rhythmic dynamics is also much less developed than for linear systems and other forms of dynamics. The workshop will bring together experimental biologists, control theorists, mathematical biologists, and clinicians to forge new interdisciplinary connections to understand control of biological neuronal and motor systems.
One area of focus will be the rhythmic activity patterns that some brain areas produce through intrinsic dynamics, perhaps activated by tonic (sustained or transient) input signals. In some cases, these activity patterns drive repetitive behaviors such as various forms of locomotion, respiration, and mastication; similar dynamics may arise in circadian and sleep rhythms. An organism interacts with some aspect of its environment through these behaviors, and these interactions result in feedback signals that can alter the ongoing intrinsic dynamics to maintain homeostasis, meet metabolic demands, or optimize reward. Problems in this area include modeling the closed loop circuits involved, determining the control principles that modulate neural activity and behavior, and applying external (i.e., man-made) controls to remedy related disorders or otherwise improve performance.
A second major theme will be non-oscillatory motor behaviors that include stationary control problems (maintenance of posture, balancing a vertical rod) as well as nonstationary problems (maintaining one's gaze on a moving target) and single movement control problems (reaching and grasping; hitting a golf ball). Some aspects of these problems are classical, such as the mathematics of stabilizing an inverted pendulum. There is a rich body of relevant theory: state estimation and feedforward control, stabilization and negative feedback control, and internal and inverse models. But the relationship between such idealized systems and the noisy, overcomplete space of near-optimal solutions used by biological motor systems for such tasks is still poorly understood.
The workshop topics will also include the use of control to modulate pathological brain states, such as synchronization arising in epilepsy and oscillations arising in parkinsonism. Closed loop control of a distributed neuronal circuit based on sparse data represents an important frontier that arises in these clinical applications.
Organizers
Jonathan Rubin
Department of Mathematics
University of Pittsburgh
rubin@math.pitt.edu
Terence Sanger
Department of Biomedical Engineering
University of Southern California
terry@sangerlab.net
Rodolphe Sepulchre
Department of Engineering
University of Cambridge
r.sepulchre@eng.cam.ac.uk
Peter Thomas
Mathematics, Applied Mathematics, and Statistics
Case Western Reserve University
pjthomas@case.edu
Participants and Talks
| Name | Affiliation | |
|---|---|---|
| Satyajit Ambike | sambike@purdue.edu | Health and Kinesiology, Purdue University |
| Max Berniker | mbernike@uic.edu | Mechanical Engineering, University of Illinois at Chicago |
| Sayak Bhattacharya | sbhatt11@jhu.edu | Electrical and Computer Engineering, Johns Hopkins University |
| Ansgar Bueschges | ansgar.bueschges@uni-koeln.de | Animal Physiology, Institute for Zoology |
| Jacob Carroll | jac21934@vt.edu | Physics, Virginia Tech |
| Joshua Chang | joshuac@gmail.com | Department of Neurology, Dell Medical School, University of Texas |
| ShiNung Ching | shinung@ese.wustl.edu | Electrical and Systems Engineering, Washington University |
| Casey Diekman | casey.o.diekman@njit.edu | Mathematical Sciences, New Jersey Institute of Technology |
| Guillaume Drion | gdrion@ulg.ac.be | Electrical Engineering and Computer Science, University of Liege |
| Amanda Edwards | aedwar41@jhmi.edu | School of Medicine, Johns Hopkins University |
| Ahmed El Hady | ahady@princeton.edu | Neuroscience, Princeton Neuroscience Institute |
| AmirAli Farokhniaee | axf313@case.edu | Biomedical Engineering, Case Western Reserve University |
| Alessio Franci | afranci@ciencias.unam.mx | Mathematics, National Autonomous University of Mexico (UNAM) |
| John Guckenheimer | jmg16@cornell.edu | Mathematics Department, Cornell University |
| Kathleen Hoffman | khoffman@math.umbc.edu | Mathematics and Statistics, University of Maryland Baltimore County |
| Neville Hogan | neville@mit.edu | Mechanical Engineering, Massachusetts Institute of Technology |
| Mary Ann Horn | mary.ann.horn@vanderbilt.edu | Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University |
| Auke Ijspeert | Auke.ijspeert@epfl.ch | Bioengineering, EPFL |
| Varun Joshi | joshi.142@osu.edu | Mechanical and Aerospace Engineering, The Ohio State University |
| Ali Khaledi Nasab | ak705714@ohio.edu | Physics and Astronomy, Ohio University |
| Ruby Kim | rubyshkim@gmail.com | Math, Duke University |
| Andre Longtin | alongtin@uottawa.ca | Physics, |
| Kenneth Loparo | kal4@case.edu | EECS, |
| Cameron McIntyre | ccm4@case.edu | Department of Biomedical Engineering, Case Western Reserve University |
| Paul Miller | pmiller@brandeis.edu | Volen Center, Brandeis University |
| Jeff Moehlis | moehlis@engineering.ucsb.edu | Mechanical Engineering, University of California, Santa Barbara |
| Choongseok Park | cpark@ncat.edu | Mathematics, North Carolina Agricultural and Technical State University |
| Robert Parker | rparker@pitt.edu | Chemical and Petroleum Engineering, University of Pittsburgh |
| David Paydarfar | David.Paydarfar@austin.utexas.edu | Neurology, University of Texas |
| Hugh Piggins | hugh.d.piggins@manchester.ac.uk | Neuroscience, The University of Manchester |
| Jason Ritt | jritt@bu.edu | Biomedical Engineering, Boston University |
| Renaud Ronsse | renaud.ronsse@uclouvain.be | iMMC, Universit'e Catholique de Louvain |
| Leonid Rubchinsky | lrubchin@iupui.edu | Department of Mathematical Sciences, Indiana University--Purdue University |
| Jonathan Rubin | rubin@math.pitt.edu | Department of Mathematics, University of Pittsburgh |
| Terence Sanger | terry@sangerlab.net | Department of Biomedical Engineering, University of Southern California |
| Stefan Schaal | sschaal@usc.edu | Computer Science and Neuroscience, University of Southern California |
| Nidhi Seethapathi | seethapathi.1@osu.edu | Mechanical Engineering, |
| Rodolphe Sepulchre | r.sepulchre@eng.cam.ac.uk | Department of Engineering, University of Cambridge |
| Vrutangkumar Shah | shah_vrutangkumar@iitgn.ac.in | Mechanical Engineering, Indian Institute of Technology Gandhinagar |
| Ivan Soltesz | isoltesz@stanford.edu | Neurosurgery, Stanford University |
| Manoj Srinivasan | srinivasan.88@osu.edu | Mechanical and Aerospace Engineering, The Ohio State University |
| Dagmar Sternad | dagmar@neu.edu | Biology, Electrical and Computer Engineering, Physics, Northeastern University |
| Peter Thomas | pjthomas@case.edu | Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University |
| Lena Ting | lting@emory.edu | Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology |
| Matthew Tresch | m-tresch@northwestern.edu | Biomedical Engineering, Northwestern University |
| Tom Van Wouwe | tom_van_wouwe@hotmail.com | Movement Sciences, Katholieke Universiteit Leuven |
| Pablo Varona | pablo.varona@uam.es | Ingenieria Informatica, Universidad Autonoma de Madrid |
| Martin Wechselberger | wm@maths.usyd.edu.au | Mathematics & Statistics, University of Sydney |
| Dan Wilson | dan.d.wilson8@gmail.com | Mathematics, University of Pittsburgh |
A normative approach to motor control networks
Max Berniker
One of the biggest obstacles in the study motor control is the large number of unobserved neurons responsible for movement. To alleviate this difficulty the study is broadly broken into two approaches: examining motor behaviors and examining neural activity. Motor behaviors are examined to infer the underlying processes that generate movement; processes computed by the unseen neurons. Neural activity is examined to infer these same processes of motor control, but only a small faction of these neurons can be observed. What is missing is a middle ground to bridge the gap between the neural processes of motor control and the resulting behavior. Here we introduce a normative approach to examine the properties of a spiking network designed to test candidate control processes and generate testable predictions for both neural activity and motor behaviors. The network, whose neurons fire probabilistically, is designed to generate the control signal for point-to-point reaching movements that minimizes a prescribed motor cost. Thus the network computes a known and analyzable control process. After being optimized the network is used to simulate reaching behaviors and neural activity. Using this data we perform typical neural analyses. Peristimulus time histograms are created for each neuron, revealing activity consistent with empirical results (e.g. phasic increases and decreases in spiking activity that vary with reach direction). Cosine tuning curves are also found, revealing that the average activity of many neurons varies with reach direction. Similarly, population vectors created from these tuning curves predict reaching directions. Finally, a dynamical system's analysis that maps the network's average firing rates to a low-dimensional space (jPCA) reveals oscillatory activity for point-to-point reaches. Importantly, these various features of network activity can be analyzed in terms of the known probability distributions of neurons, which can vary with different motor costs. We suggest this approach can be used to analyze candidate hypothesis for the processes that generate movement, linking observed neural behavior with motor behavior.
Adaptive Locomotor Behavior: Neural Mechanisms Underlying Coordination of Motor Activity in a Six-Legged Biological Walking System
Ansgar Büschges (Animal Physiology, Institute for Zoology)
The generation of motor behavior is a main function of all animals’ nervous systems. In the past decades detailed information has become available on the organization and operation of those neuronal networks that generate the motor output needed for locomotion. This encompasses the movement of wings for flying, the trunk and fins for swimming, or legs for walking. Today, a lot is known about the generation of so-called basic or default locomotor patterns, e.g. single leg stepping in walking. In contrast, we are only starting to find out (i) how the networks involved in these behaviors generate flexible motor output allowing for the generation of adaptive locomotor behavior, for instance changes in heading, direction and walking speed, (ii) how these networks interact with each other to generate proper coordination for locomotion, e.g. between the stepping legs of a walking animal, and finally (iii) which aspects of the motor output need to be controlled by the brain and which are under local control in order to allow for the full functional range in locomotion. The talk will present recent findings on these three topics gathered from studies on insect walking, both in the stick insect and the fruit fly.
Model-free approaches to controlling neuronal circuits
ShiNung Ching (Electrical and Systems Engineering, Washington University)
Using stimulation to modulate activity in neuronal circuits has broad applicability in both clinical and basic scientific domains. A pressing need in these applications is the design of principled stimulation inputs that go beyond the ‘square pulse’ type waveforms commonly used in current practice. Such waveforms are likely inefficient and too blunt to achieve neuroscientific goals such as investigations of temporal neural coding. Control theory can help to obviate this issue by optimizing extrinsic inputs for maximizing activity-based objective functions. However, in this regard the complexity and diversity of neural dynamics presents a major analytical challenge for the deployment of classical control methods. Indeed, progress in neurostimulation design and optimization has usually required abstraction of dynamics to low-dimensional canonical models, or assumptions of heterogeneity across a neuronal population. This talk will explore approaches that do not require an explicit mathematical model for the circuit to be controlled. These approaches blend ideas from adaptive control theory, system identification and machine learning, wherein the controller builds a representation of the targeted circuit in an online fashion. The representation is not a biophysical model, but rather a recurrent network construct that approximates the dynamics of the circuit in question. Thus, control can be performed on large, irregularly connected populations of spiking neurons, at the expense of needing sufficient observations to build the representation. Interestingly, for some formulations, the learned control strategy itself produces spiking activity, providing interpretations of how control objectives may manifest intrinsically within neuronal networks.
Eupnea, Tachypnea, and Autoresuscitation in a Closed-Loop Respiratory Control Model
Casey Diekman (Mathematical Sciences, New Jersey Institute of Technology)
The mechanisms underlying oscillations in a central pattern generator (CPG) may differ fundamentally in the intact organism versus an isolated CPG preparation. We investigate this aspect of rhythmogenesis in a computational model of closed-loop respiratory control, incorporating minimal models of the brainstem CPG, lung mechanics, oxygen handling, metabolism, and chemosensation. We analyze the model behavior using fast/slow dynamical systems analysis and open-loop/closed-loop control analysis. We show that eupnea-like bursting oscillations arise from a distinct mechanism in the intact (closed loop) versus isolated (open loop) systems. The closed-loop model exhibits bistability between eupnea-like bursting and tachypnea-like tonic spiking, and we demonstrate that imposed bouts of hypoxia can induce a dramatic transition from eupnea to tachypnea. For moderate bouts of hypoxia, the endogenous properties of the ionic conductances in the Butera-Rinzel-Smith CPG model can lead to spontaneous autoresuscitation and recovery to eupnea. We also find that chemosensory feedback gives the closed-loop control system greater robustness to changes in metabolic demand than the open-loop control system.
Cellular control of network rhythmic activity
Guillaume Drion
Nervous system functions are regulated by fast and localized modulation of neural network rhythmic activity. This feature is conserved amongst very different systems, ranging from invertebrate central pattern generators to mammal midbrain and cortical structures. These systems however strongly differ in their structure, function and physiological properties, and are regulated by a large number of interconnected mechanisms, which makes the extraction of key players in the robust regulation of rhythmic activity an arduous task. This talk will introduce a cellular dynamical property called slow regenerativity from which robust and tunable modulation of rhythmic activity can emerge in many different systems, both at the cellular and network levels. It will discuss the ubiquity of slow regenerativity for the control of nervous system activity and illustrate its significance through several key physiological examples.
Virtual Reality Alteration of Visual Feedback in Cerebellar Patients Can Improve Reaching
Amanda Edwards
People with damage to their cerebellum often exhibit "reaching ataxia", or misdirected, poorly scaled movement patterns which are reminiscent of a poorly tuned control system. Ataxia affects most all activities of daily living (e.g. eating, cooking, bathing, dressing, working). It is believed that these patients have a static, miscalibrated internal model of their body dynamics; however, it is unknown whether their feedback control is intact. We challenged these participants with visuomotor system identification tasks in order to model their feedback control architecture. Our results suggest that cerebellar patients have intact feedback control, but are forced to rely on time-delayed visual feedback. The key difference is that healthy subjects seem to be able to compensate for their visuomotor delay suggesting that the cerebellum may be serving the role of a Smith predictor for this task. Finally, we were able to leverage the cerebellar patients intact visuomotor feedback control system to improve the scaling of these movements by altering their visual feedback based on their real-time movement in a virtual reality environment.
Neuronal negative conductances in network and circadian rhythms
Alessio Franci (Mathematics, National Autonomous University of Mexico (UNAM))
Fluctuations in neuronal electrical activity span orders of magnitude both in temporal and spatial scales. The fine grain scale of ion channels and single neurons is mathematically captured by nonlinear electrical circuits. The behavior of those circuits is robustly regulated by modulating a few feedback loops that combine the dynamic response of neuronal ionic currents. Positive feedback loops play a key role by creating regions of negative conductance that are responsible for neuronal switching and oscillatory behaviors.
The role of neuronal negative conductance propagates at the medium scale of neuron networks and at the gross scale of whole body circadian rhythms. At the medium scale, it endows networks with rapid and localized switching capabilities that regulate brain information processing (brain states). At the gross scale, it allows robust circadian fluctuations in neuron electrical activity that influence cellular clock oscillations through calcium-dependent signaling pathways, thus closing a feedback loop essential for free-running molecular oscillations.
Using Randomness in Locomotion
John Guckenheimer (Mathematics Department, Cornell University)
Animal locomotion results from interactions of rhythmic movements of the body with the environment.
A biomechanical model for the movements may yield an unstable periodic orbit of a dynamical system. In these circumstances, the animal must exercise active control to maintain stability. This lecture will discuss the problem of estimating the Floquet multipliers which characterize local stability properties of a periodic orbit. The information needed depends upon perturbations from the periodic orbit. Animals can either rely upon fluctuations in the environment (''noise'') or generate excitations that move the organism off the orbit to obtain the required information. We discuss these alternatives in terms of the distribution of residuals between the animal's trajectory and the target periodic orbit for its motion.
Understanding Lamprey Locomotion Using an Interdisciplinary Approach
Kathleen Hoffman (Mathematics and Statistics, University of Maryland Baltimore County)
Lamprey locomotion involves electrical signal in the central nervous system, to the force generation of the muscle, to the interaction between the body and the environment. Proprioceptive feedback from sensory organs, called edge cells, are known to modulate the rhythm of the electrical signal in the spinal cord. Modeling this set of complex systems involves coupled oscillators, representing the central pattern generator (CPG) for locomotion, a Hill-type muscle model for force generation, and a fluid-elastic body interaction that simulates the body in the fluid environment. Understanding this complex system involves an integrated interdisciplinary approach that combines biological experiments, experimental fluid dynamics, and different types of mathematical models for the CPG, muscle, body and fluids. In this talk, I will discuss the work of an interdisciplinary team of researchers that have combined their expertise to further understand this complex problem.
Joint work with: Eric Tytell (Tufts), Tim Kiemel (UMCP), Lisa Fauci (Tulane), Christina Hamlet (Buchnell), Nicole Massarelli (Schoolcraft College), Megan Leftwich (GWU)
How do we manage it? The paradox of human performance
Neville Hogan (Mechanical Engineering, Massachusetts Institute of Technology)
Despite vastly slower ‘hardware’ (e.g. muscles) and ‘wetware’ (e.g. neurons) human dexterity and agility significantly out-perform contemporary robots. How is this possible? Slow actuators and long communication delays require predictive control based on some form of internal model—but what form? One possible answer is based on dynamic primitives; they enable highly dynamic behavior with minimal high-level supervision and intervention. Supporting this proposal, I will review a surprising limitation arising from control via dynamic primitives—moving slowly is hard for humans. Controlling physical interaction requires a special class of dynamic primitives, mechanical impedances. Both motion and interaction primitives may be combined by a nonlinear generalization of the classical equivalent electrical circuit. It reconciles contrasting constraints of information-processing (computation) and energy-processing (physical dynamics). I suggest that nonlinear equivalent networks provide a general basis for the internal models required for high-performance interactive control, and especially physical human-robot interaction.
"Adaptive locomotion control: modeling the interplay between central pattern generators and sensory feedback using mathematical models and robots" - Auke Ijspeert (School of Computer and Communication Sciences, EPFL, Swiss Federal Institute of Technology)
Animal locomotion is amazing in its agility and diversity. Most animals control their movements thanks to a combination of neural oscillatory circuits (central pattern generators, CPGs), reflexes, and descending modulation from higher control centers. Because of the complex nonlinear interactions between different components, the control principles underlying locomotion are not yet completely understood, nor are how they have evolved to adapt to different ecological niches and different modes of locomotion.
In this talk, I will present how robots and mathematical models of the spinal cord can be used to investigate the principles of locomotion control in vertebrate animals, from lamprey to human. In particular, I will focus on the interaction between CPGs and sensory feedback in order to investigate their respective roles in gait generation, and how these roles have possibly changed during evolution from fish to mammals.
Stochastic Optimal Control and Sensory focussing
Andre Longtin (Physics)
Stochastic optimal control is a technique that allows the determination of a control signal to a noise-driven system to achieve a certain goal while minimizing certain costs. This talk will summarize recent efforts at controlling the firing times of a stochastic excitable system using stochastic optimal control. We consider both the cases where only a knowledge of the previous firing time is available, as well as the more information-rich case where one can monitor the ongoing voltage fluctuations. The talk will also consider the design of stimuli that can best reveal information about system parameters through a combination of information theory and stochastic optimal control. Finally we will present recent work on the control of sensory focus, in which the boundary between tonic and bursting activity serves as an optimal position where the Fisher information about an external input is maximized.
Introduction to Linear Systems Theory
Kenneth Loparo (EECS)
This talk will provide an introduction to linear systems theory including (1) dynamical systems terminology and basic concepts (e.g. equilibrium, linearization, stability and control); (2) input/output maps, state space realizations, controllability, observability and stability of linear dynamical systems; (3) estimation and control of linear systems (e.g. observers, linear quadratic regulators, and the separation principle).
Beta Activity and Subthalamic Deep Brain Stimulation
Cameron McIntyre (Department of Biomedical Engineering, Case Western Reserve University)
An electrophysiological hallmark of Parkinson’s disease (PD) is abnormal oscillatory activity, most notably excessive synchronization in the beta band (12-20 Hz). These oscillations are seen throughout the cortical-subcortical motor circuitry, and historically have been thought to arise within the basal ganglia (BG). However, recent theoretical and experimental studies have suggested a cortical origin for the abnormal activity. As such, a substantial scientific effort is currently focused on characterizing cortical activity in the parkinsonian state, as well as its modulation by deep brain stimulation (DBS). Hyperdirect neurons have been identified as key players in this puzzle because of their unique anatomical connections and powerful influence over network activity. Hyperdirect neurons are a special subset (~5%) of layer V pyramidal neurons whose corticofugal axon projects down internal capsule and into the spinal cord, while also sending an axon collateral to the subthalamic nucleus (STN). One prevailing hypothesis is that pathological beta activity arises within cortex and is transmitted into the BG via the hyperdirect pathway. In line with this hypothesis, selective optogenetic stimulation of the hyperdirect pathway is sufficient to alleviate parkinsonian symptoms in rodents and numerous recent clinical DBS studies have come to a similar conclusion in humans. My presentation will provide an overview of experimental work analyzing the hyperdirect pathway, followed by new modeling results on DBS of this pathway and its subsequent effect on cortical network activity.
Stability requirements and benefit of multiple forms of neuronal homeostasis
Paul Miller (Volen Center, Brandeis University)
When more than one homeostatic process is at work in a given system, there is always a chance the two will compete with each other. For example, if two thermostats in a room control different heating/cooling systems, unless their set-points are identical, one could be causing heating and the other cooling while the temperature lies intermediate between the two set-points. In neurons, multiple homeostatic mechanisms appear to be at play. We focus on two categories, synaptic scaling, which impacts connection strengths between neurons, and intrinsic homeostasis, which impacts the excitability of neurons. We find criteria for the two homeostatic mechanisms to cooperate and produce a stable state of time-averaged neural activity. We show that in these conditions the neuron can respond to stimuli more reliably, because the variance as well as the mean of its firing rate can be controlled with two sensors. Finally, we demonstrate that within a recurrent feedback circuit, a useful computational operation--temporal integration of inputs--can be achieved by these dual control mechanisms operating together, i. e., they robustly achieve the fine-tuning of the circuit that is necessary.
Modeling Practices for Control - a Model Predictive Control (MPC) Tutorial
Robert Parker (Chemical and Petroleum Engineering, University of Pittsburgh)
The concept of automated closed-loop feedback control has been used in the chemical industries since the 1950s. While these feedback control methods work well in industrial practice, the challenges of biological systems -- including comparative data sparsity, a lack of full state measurements, challenging dynamics, and nonlinearity -- often lead to undesirable performance using simple feedback controllers. This talk will introduce Model Predictive Control, which serves as the algorithm driving many of the closed-loop insulin pumps in development for insulin-dependent diabetic patients. By developing an accurate model of they physical system, and using that model explicitly in the synthesis and solution of the on-line control problem, performance superior to that offered by feedback control is possible, even for challenging biological systems. This talk will provide an overview of model construction from first-principles knowledge as well as data-driven modeling, as well as the synthesis of the MPC controller to achieve clinically-relevant performance objectives. An example application of these tools will be discussed in the context of glucose control for diabetic and/or critical care patients.
Oscillopathies: From Squid Axons to Infant Apneas
David Paydarfar (Neurology, University of Texas)
Abnormal neural oscillations are implicated in certain disease states, for example repetitive firing of injured axons evoking painful paresthesia, and rhythmic discharges of cortical neurons in patients with epilepsy. In other clinical conditions, the pathological state manifests as a vulnerability of an oscillator to switch off, for example prolonged pauses in automatic breathing commonly observed in preterm infants. I will present theory and experimental observations on the initiation and termination of neural rhythms at the cellular, tissue and organism levels. The findings suggest how small appropriately tuned noisy inputs could silence a neural oscillator or, conversely, could promote rhythmic activity. Noise-sensitive neurons have intrinsic properties that yield interesting physiological properties on the edge of a bifurcation, affording remarkable adaptive capacities to circuits that require rapid and efficient on-off switching; between multiple modes of activity (e.g., quiescence, repetitive firing, bursting) and between multiple functions (e.g., breathing, swallowing, coughing, and vocalization). I will illustrate the therapeutic potential of stochastic stimulation for promoting stability of breathing and preventing central apnea in preterm infants.
Optogenetic vs. electrical stimulation effects on synchronized oscillations of neural activity
Leonid Rubchinsky (Department of Mathematical Sciences, Indiana University--Purdue University)
Deep brain stimulation (DBS) is used as a therapeutic procedure to treat symptoms of several neurological and neuropsychiatric disorders by controlling electrical activity of neural circuits. In particular it is used to treat motor symptoms of Parkinson’s disease (PD), associated with excessive oscillatory synchronized activity in the beta frequency band. An alternative way to stimulate neural circuits is an emerging technology of optogenetics. It is not clear when/if optogenetics will eventually be possible to implement in clinical practice. However, it is emerging as a widely used experimental tool to control brain networks. Thus, the goal of his study is to explore how effective an optogenetic stimulation in comparison with electrical stimulation in their network effects on elevated synchronized oscillatory activity. We use a computational model of subthalamic and pallidal circuits, which was developed to reproduce experimentally observed beta-band activity patterns. We model electrical stimulation as well as optogenetic stimulation of two types (excitatory via channelrhodopsin and inhibitory via halorodopsin). All three modes of stimulation can decrease beta synchrony. The actions of different stimulation types on the beta activity differ from each other. Electrical DBS and optogenetic excitation have somewhat similar effects on the network. They both cause desynchronization and suppression of the beta-band bursting. As intensity of stimulation is growing, they synchronize the network at higher (non-beta) frequencies in almost tonic dynamics. Optogenetic inhibition effectively reduces spiking and bursting activity of the targeted neurons. We compare the stimulation modes in terms of the minimal effective current delivered to basal ganglia neurons in order to suppress beta activity below a threshold. Optogenetic inhibition usually requires less effective current than electrical DBS to achieve beta suppression. Optogenetic excitation, while as not efficacious as optogenetic inhibition, still usually requires less effective current than electrical DBS to suppress beta activity. Our results suggest that optogenetic stimulation may introduce smaller effective currents than conventional electrical DBS, but still achieve sufficient beta activity suppression. Thus, optogenetic stimulation may be more effective than electrical stimulation in control of synchronized oscillatory neural activity because of the different ways of how stimulations interact with network dynamics.
Risk-Aware Control
Terence Sanger (Department of Biomedical Engineering, University of Southern California)
Stochastic Dynamic Operators
Terence Sanger (Biomedical Engineering, USC)
Nonlinear Filters for the Linearly-inclined
Terence Sanger (Biomedical Engineering, USC)
Perception, Action, Learning, and Associative Skill Memories
Stefan Schaal (Computer Science and Neuroscience, University of Southern California)
Autonomous robot systems have to make perceptual and control decisions at every moment of time, and have to learn and adapt to improve the system’s performance. High dimensional continuous state-action spaces still pose significant scaling problems for learning algorithms to find (approximately) optimal solutions, and appropriate task descriptions or cost functions require a large amount of human guidance. In order to address autonomous skillful movement generation in complex robot and task scenarios, we have been working on a variety of sub problems to facilitate robust task achievement. Among these topics are general representations for movement in form of movement primitives, trajectory-based reinforcement learning with path integral reinforcement learning, and inverse reinforcement learning to extract the “intent” of observed behavior. However, this “action centric” view of skill acquisition needs to be extended with a stronger perceptual component, as in the end the entire perception-action learning loop could be considered the key element to address, rather than isolated components of this loop. In some tentative initial research, we have been exploring Associative Skill Memories, i.e., the simple idea to start memorizing all sensory events and their statistics together with each movement skill. This concepts opens a wide spectrum of adding predictive, corrective, and switching behaviors in motor skills, and may create an interesting foundation to automatically generate the graphs underlying complex sequential motor skills.
Feedback, sensitivity, and excitability.
Rodolphe Sepulchre (Department of Engineering, University of Cambridge)
Feedback and sensitivity are core concepts of control theory, but the theory is grounded in the frequency-domain analysis of open dynamical systems and mature only for linear time-invariant (LTI) systems. Excitability is a core concept of mathematical physiology, but the theory is grounded in the state-space analysis of closed dynamical systems, with little contact to control theory.
This tutorial will review the three concepts, with the aim of connecting them to address the control and modulation of rhythmic behaviors encountered in biology.
The emphasis will be on experimental questions of neurophysiology. This discipline benefits from a matured modeling framework grounded in circuit theory, a key historical bridge between input-output and state-space modeling.
Organization and Control of Hippocampal Circuits
Ivan Soltesz (Neurosurgery, Stanford University)
Throughout the cortical mantle, distinct inhibitory cell types deliver GABA to specific spatial domains of principal cells at particular times during behaviorally relevant network oscillations. Recent results from the hippocampus of awake mice have revealed emerging principles of the temporal ordering of interneuronal discharges during network oscillations. We will discuss new evidence showing the highly non-homogeneous organization of inhibitory-excitatory microcircuits in the hippocampus is highly selective with respect to the long-distance projection patterns of the heterogeneous pyramidal cell populations. Next, the question of closed-loop optogenetic control of hippocampal pathological activity will be addressed. Finally, we will discuss results from data-driven, full-scale (1:1) computational models of the hippocampus that give us quantitative insights into the roles of the various constituent cell types in ensemble network activities.
Control of Discrete and Rhythmic Motor Skills - A Task-Dynamic Approach
Dagmar Sternad (Biology, Electrical and Computer Engineering, Physics, Northeastern University)
While everyday actions flexibly combine rhythmic and discrete movement elements, motor neuroscience research has largely studied these movement types in isolation, developing separate accounts for these two movement forms. Supported by a series of brain-imaging, behavioral and modeling studies, our premise is that rhythmic and discrete behaviors are two dynamic primitives constituting more complex actions. Our research analyzes how task dynamics constrain and enable actions and their improvement with practice. We start with a mechanical model of the task and render it in a virtual environment with a fully known solution space. Based on mathematical analyses of the modeled task, we study how humans develop solutions to meet complex task demands. Key concepts in our analysis are variability, stability, and predictability. Using three model tasks, throwing a ball, rhythmic bouncing of a ball, and transporting a cup of coffee, we show that humans develop skill by: 1) finding error-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, 3) optimizing predictability of object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, modules that overcome substantial delays and noise in the neuro-mechanical system. Extending from these experimental platforms we have developed interventions that assess or help restore functional behavior in neurological patients.
Force encoding in muscle spindles - implications for sensorimotor control of balance
Lena Ting (Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology)
Proprioceptive sensory information is essential to movement, particularly in sensorimotor responses to external perturbations to the body. Our data show that rapid increase in resistive force of a passive muscle when stretched, i.e. short-range stiffness may cause enhanced sensory signals that facilitate the detection and predictive response to sudden mechanical perturbations to the body. Importantly, this history-dependent property of muscle spindle firing rates does not have a unique relationship to muscle length or velocity, but rather can be predicted in fine detail based on a unique pseudo-linear transformation between muscle force and the first time derivative of force, dF/dt and muscle spindle afferent firing rate. Several history-dependent features of muscle spindle firing rates can be predicted based on muscle force and dF/dt and are likely due to cross-bridge cycling kinetics in muscle fibers. Such history-dependence is lacking in current models of muscle spindles, but could be necessary to explain a number of phenomena from postural response to perturbation, spasticity, and perception of limb position. Moreover, the encoding of force as a proxy for length in muscle spindles has many implications for normal and impaired control of movement.
Transient neural dynamics: integrating models and novel experimental paradigms
Pablo Varona (Ingenieria Informatica, Universidad Autonoma de Madrid)
Many brain functions, from motor control to cognitive activity can be seen as built from transient sequential dynamics. This sequential switching dynamics may have as an origin a winnerless competition among different brain elements. A novel theoretical formalism based on heteroclinic networks describes such dynamics and provides insight for the interpretation of many experimental results. On the other hand, closed-loop technologies have an enormous potential to precisely control the spatio-temporal aspects of a stimulus and to build activity-dependent stimulus-response loops to interact with neural systems and control them in a millisecond time scale. Establishing these loops is an essential step towards understanding the dynamics of transient neural processes and bridges between traditionally disparate levels of analysis. In this talk I will argue that heteroclinic networks and closed-loop technologies largely contribute to the study of brain sequential dynamics.
Two-stroke relaxation oscillators
Martin Wechselberger (Mathematics & Statistics, University of Sydney)
Control of Weakly (and Not So Weakly) Perturbed Neural Oscillatory
Dan Wilson (Mathematics, University of Pittsburgh)
While high-frequency deep brain stimulation (DBS) is a decades old treatment for alleviating the motor symptoms of Parkinson’s disease, its mechanisms are not well understood. Some experimental evidence suggest that DBS works by making neurons fire more regularly, while other seemingly contradictory evidence suggests that DBS works by making neural firing patterns less synchronized. Here, we present theoretical and numerical results that suggest that these two mechanisms are not mutually exclusive. Specifically, in a noisy group of phase oscillators, high frequency perturbations can separate the population into multiple clusters, each with a nearly identical proportion of the overall population. Exploitation of this phenomenon could lead to better DBS protocols.
Deep brain stimulation induced synaptic depletion is a robust phenomenon independent of synapse type
AmirAli Farokhniaee (Biomedical Engineering, Case Western Reserve University)
Deep brain stimulation (DBS) is a successful clinical therapy for a wide range of neurological disorders; however, the physiological mechanisms of DBS remain unresolved. Computational models of DBS commonly suggest robust generation of DBS-induced action potentials (APs) in neural pathways that course by the electrode and that those APs propagate to their axon terminals. From a network activity perspective, the fundamental effect of AP invasion into a synaptic terminal is transmitter release. However, little attention is typically paid to quantifying the actual synaptic effect of the DBS-activated pathways on their post-synaptic targets. We propose that one hypothesis that can help explain the mechanisms of DBS is the exhaustion of synaptic transmitter release in directly stimulated pathways. Synapses typically have a readily releasable pool of neurotransmitters packaged in vesicles and machinery to replenish that pool once they are released. However, high frequency (~130 Hz) driving of a synapse quickly exhausts the readily releasable pool and overwhelms the recycling machinery. In turn, postsynaptic currents (PSC) during DBS can be dramatically reduced, effectively eliminating the ability of the synapse to modulate the post-synaptic neuron or transmit any information. This basic phenomenon can be most easily studied at glutamatergic synapses where a wealth of experimental data is available to parameterize the model. However, multiple glutamatergic synapse types are known to exist, including Depressing (D), Facilitating (F), and Pseudo-Linear (PL). Therefore, we set out to quantify how these different synapse types would respond to DBS. We used a leaky integrate and fire (LIF) neuron model to evaluate the post-synaptic response to DBS-driven synaptic inputs. Our theoretical results suggest that the synaptic depletion is a robust effect in DBS activated glutamatergic pathways, independent of the synapse type. In turn, DBS effectively creates a “synaptic lesion” in directly stimulated pathways and this mechanism is especially relevant to DBS of the hyperdirect pathway for the treatment of Parkinson’s disease.
Does the nervous system regulate internal joint state?
Matthew Tresch (Biomedical Engineering, Physical Medicine and Rehab, and Physiology, J. L. Kellogg Graduate School of Management)
Although the neural control of movement is usually considered in terms of the control of variables affecting task performance, neural systems might also control the state of other variables that have a less visible impact upon behavior. We are examining the hypothesis that the nervous system actively monitors and regulates the state of internal joint variables in order to minimize excessive stresses and strains on joint cartilage and ligaments. We are studying these issues in the rat knee joint, evaluating the neural control of task and joint variables by quadriceps muscles using a combination of biomechanical and behavioral studies. We first measured the task relevant actions of quadriceps muscles, measuring the isometric forces and moments produced at the ankle from stimulating each muscle in situ. We found that vastus lateralis (VL) and vastus medialis (VM) produced very similar forces and moments to one another across the hindlimb workspace. Thus, these two muscles have redundant contributions to task performance. When we measured the forces that these muscles exert on the patella, however, we found that they produced opposing mediolateral patellar forces, suggesting that these muscles have antagonistic actions on internal joint variables. Unbalanced mediolateral forces on the patella would result in excessive stresses between the patella and the femoral groove, potentially leading to cartilage degradation and osteoarthritis. We therefore evaluated whether the nervous system balances activation of VM and VL to minimize net mediolateral patellar forces, paralyzing VL and then observing adaptations in muscle activations. After VL paralysis task performance could easily be restored by activation of VM, since VM and VL have redundant task contributions. However, we observed that animals preferentially compensated for the loss of VL by increasing activation of rectus femoris, which produces minimal mediolateral forces on the patella. This adaptation pattern is consistent with the hypothesis that the nervous system chooses muscle activations not only to maintain task performance but also to maintain internal joint integrity. We are currently performing experiments to evaluate this hypothesis further, using additional perturbations of limb mechanics and of sensory pathways involved in the neural control of joint variables.
