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Fietkiewicz C, McDougal RA, Corrales Marco D, Chiel HJ, Thomas PJ. Tutorial: using NEURON for neuromechanical simulations. Front Comput Neurosci 2023; 17:1143323. [PMID: 37583894 PMCID: PMC10424731 DOI: 10.3389/fncom.2023.1143323] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Accepted: 06/20/2023] [Indexed: 08/17/2023] Open
Abstract
The dynamical properties of the brain and the dynamics of the body strongly influence one another. Their interaction generates complex adaptive behavior. While a wide variety of simulation tools exist for neural dynamics or biomechanics separately, there are few options for integrated brain-body modeling. Here, we provide a tutorial to demonstrate how the widely-used NEURON simulation platform can support integrated neuromechanical modeling. As a first step toward incorporating biomechanics into a NEURON simulation, we provide a framework for integrating inputs from a "periphery" and outputs to that periphery. In other words, "body" dynamics are driven in part by "brain" variables, such as voltages or firing rates, and "brain" dynamics are influenced by "body" variables through sensory feedback. To couple the "brain" and "body" components, we use NEURON's pointer construct to share information between "brain" and "body" modules. This approach allows separate specification of brain and body dynamics and code reuse. Though simple in concept, the use of pointers can be challenging due to a complicated syntax and several different programming options. In this paper, we present five different computational models, with increasing levels of complexity, to demonstrate the concepts of code modularity using pointers and the integration of neural and biomechanical modeling within NEURON. The models include: (1) a neuromuscular model of calcium dynamics and muscle force, (2) a neuromechanical, closed-loop model of a half-center oscillator coupled to a rudimentary motor system, (3) a closed-loop model of neural control for respiration, (4) a pedagogical model of a non-smooth "brain/body" system, and (5) a closed-loop model of feeding behavior in the sea hare Aplysia californica that incorporates biologically-motivated non-smooth dynamics. This tutorial illustrates how NEURON can be integrated with a broad range of neuromechanical models. Code available at https://github.com/fietkiewicz/PointerBuilder.
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Affiliation(s)
- Chris Fietkiewicz
- Department of Mathematics and Computer Science, Hobart and William Smith Colleges, Geneva, NY, United States
| | - Robert A. McDougal
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, United States
- Wu Tsai Institute, Yale University, New Haven, CT, United States
- Program in Computational Biology and Bioinformatics, Yale University, New Haven, CT, United States
- Section for Biomedical Informatics, Yale School of Medicine, New Haven, CT, United States
| | - David Corrales Marco
- Department of Mathematics and Computer Science, Hobart and William Smith Colleges, Geneva, NY, United States
| | - Hillel J. Chiel
- Department of Biology, Case Western Reserve University, Cleveland, OH, United States
- Department of Neurosciences, Case Western Reserve University, Cleveland, OH, United States
- Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH, United States
| | - Peter J. Thomas
- Department of Biology, Case Western Reserve University, Cleveland, OH, United States
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH, United States
- Department of Cognitive Science, Case Western Reserve University, Cleveland, OH, United States
- Department of Electrical, Control, and Systems Engineering, Case Western Reserve University, Cleveland, OH, United States
- Department of Data and Computer Science, Case Western Reserve University, Cleveland, OH, United States
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Biomechanical and Sensory Feedback Regularize the Behavior of Different Locomotor Central Pattern Generators. Biomimetics (Basel) 2022; 7:biomimetics7040226. [PMID: 36546926 PMCID: PMC9776051 DOI: 10.3390/biomimetics7040226] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 11/30/2022] [Accepted: 12/01/2022] [Indexed: 12/12/2022] Open
Abstract
This work presents an in-depth numerical investigation into a hypothesized two-layer central pattern generator (CPG) that controls mammalian walking and how different parameter choices might affect the stepping of a simulated neuromechanical model. Particular attention is paid to the functional role of features that have not received a great deal of attention in previous work: the weak cross-excitatory connectivity within the rhythm generator and the synapse strength between the two layers. Sensitivity evaluations of deafferented CPG models and the combined neuromechanical model are performed. Locomotion frequency is increased in two different ways for both models to investigate whether the model's stability can be predicted by trends in the CPG's phase response curves (PRCs). Our results show that the weak cross-excitatory connection can make the CPG more sensitive to perturbations and that increasing the synaptic strength between the two layers results in a trade-off between forced phase locking and the amount of phase delay that can exist between the two layers. Additionally, although the models exhibit these differences in behavior when disconnected from the biomechanical model, these differences seem to disappear with the full neuromechanical model and result in similar behavior despite a variety of parameter combinations. This indicates that the neural variables do not have to be fixed precisely for stable walking; the biomechanical entrainment and sensory feedback may cancel out the strengths of excitatory connectivity in the neural circuit and play a critical role in shaping locomotor behavior. Our results support the importance of including biomechanical models in the development of computational neuroscience models that control mammalian locomotion.
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Wang Y, Gill JP, Chiel HJ, Thomas PJ. Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems. BIOLOGICAL CYBERNETICS 2022; 116:687-710. [PMID: 36396795 PMCID: PMC9691512 DOI: 10.1007/s00422-022-00951-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 10/17/2022] [Indexed: 06/16/2023]
Abstract
Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25-51, 2015; Lyttle et al. in Biol Cybern 111(1):25-47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701-744, 2021. https://doi.org/10.1137/20M1344974 ) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates' hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties.
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Affiliation(s)
- Yangyang Wang
- Department of Mathematics, The University of Iowa, Iowa City, IA 52242 USA
| | - Jeffrey P. Gill
- Department of Biology, Case Western Reserve University, Cleveland, OH 44106 USA
| | - Hillel J. Chiel
- Department of Biology, Case Western Reserve University, Cleveland, OH 44106 USA
- Department of Neurosciences, Case Western Reserve University, Cleveland, OH 44106 USA
- Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44106 USA
| | - Peter J. Thomas
- Departments of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH 44106 USA
- Department of Biology, Case Western Reserve University, Cleveland, OH 44106 USA
- Department of Cognitive Science, Case Western Reserve University, Cleveland, OH 44106 USA
- Department of Data and Computer Science, Case Western Reserve University, Cleveland, OH 44106 USA
- Department of Electrical, Control and Systems Engineering, Case Western Reserve University, Cleveland, OH 44106 USA
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Kim Y, Aoi S, Fujiki S, Danner SM, Markin SN, Ausborn J, Rybak IA, Yanagihara D, Senda K, Tsuchiya K. Contribution of Afferent Feedback to Adaptive Hindlimb Walking in Cats: A Neuromusculoskeletal Modeling Study. Front Bioeng Biotechnol 2022; 10:825149. [PMID: 35464733 PMCID: PMC9023865 DOI: 10.3389/fbioe.2022.825149] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 02/04/2022] [Indexed: 11/26/2022] Open
Abstract
Mammalian locomotion is generated by central pattern generators (CPGs) in the spinal cord, which produce alternating flexor and extensor activities controlling the locomotor movements of each limb. Afferent feedback signals from the limbs are integrated by the CPGs to provide adaptive control of locomotion. Responses of CPG-generated neural activity to afferent feedback stimulation have been previously studied during fictive locomotion in immobilized cats. Yet, locomotion in awake, behaving animals involves dynamic interactions between central neuronal circuits, afferent feedback, musculoskeletal system, and environment. To study these complex interactions, we developed a model simulating interactions between a half-center CPG and the musculoskeletal system of a cat hindlimb. Then, we analyzed the role of afferent feedback in the locomotor adaptation from a dynamic viewpoint using the methods of dynamical systems theory and nullcline analysis. Our model reproduced limb movements during regular cat walking as well as adaptive changes of these movements when the foot steps into a hole. The model generates important insights into the mechanism for adaptive locomotion resulting from dynamic interactions between the CPG-based neural circuits, the musculoskeletal system, and the environment.
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Affiliation(s)
- Yongi Kim
- Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto Daigaku-Katsura, Kyoto, Japan
| | - Shinya Aoi
- Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto Daigaku-Katsura, Kyoto, Japan
- *Correspondence: Shinya Aoi,
| | - Soichiro Fujiki
- Department of Physiology, School of Medicine, Dokkyo Medical University, Tochigi, Japan
| | - Simon M. Danner
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, United States
| | - Sergey N. Markin
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, United States
| | - Jessica Ausborn
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, United States
| | - Ilya A. Rybak
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, United States
| | - Dai Yanagihara
- Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
| | - Kei Senda
- Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto Daigaku-Katsura, Kyoto, Japan
| | - Kazuo Tsuchiya
- Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto Daigaku-Katsura, Kyoto, Japan
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Yu Z, Thomas PJ. Dynamical consequences of sensory feedback in a half-center oscillator coupled to a simple motor system. BIOLOGICAL CYBERNETICS 2021; 115:135-160. [PMID: 33656573 PMCID: PMC8510507 DOI: 10.1007/s00422-021-00864-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 01/27/2021] [Indexed: 06/12/2023]
Abstract
We investigate a simple model for motor pattern generation that combines central pattern generator (CPG) dynamics with a sensory feedback (FB) mechanism. Our CPG comprises a half-center oscillator with conductance-based Morris-Lecar model neurons. Output from the CPG drives a push-pull motor system with biomechanics based on experimental data. A sensory feedback conductance from the muscles allows modulation of the CPG activity. We consider parameters under which the isolated CPG system has either "escape" or "release" dynamics, and we study both inhibitory and excitatory feedback conductances. We find that increasing the FB conductance relative to the CPG conductance makes the system more robust against external perturbations, but more susceptible to internal noise. Conversely, increasing the CPG conductance relative to the FB conductance has the opposite effects. We find that the "closed-loop" system, with sensory feedback in place, exhibits a richer repertoire of behaviors than the "open-loop" system, with motion determined entirely by the CPG dynamics. Moreover, we find that purely feedback-driven motor patterns, analogous to a chain reflex, occur only in the inhibition-mediated system. Finally, for pattern generation systems with inhibition-mediated sensory feedback, we find that the distinction between escape- and release-mediated CPG mechanisms is diminished in the presence of internal noise. Our observations support an anti-reductionist view of neuromotor physiology: Understanding mechanisms of robust motor control requires studying not only the central pattern generator circuit in isolation, but the intact closed-loop system as a whole.
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Affiliation(s)
- Zhuojun Yu
- Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH, 44106, USA.
| | - Peter J Thomas
- Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, OH, 44106, USA
- Department of Biology, Case Western Reserve University, Cleveland, OH, 44106, USA
- Department of Cognitive Science, Case Western Reserve University, Cleveland, OH, 44106, USA
- Department of Computer and Data Science, Case Western Reserve University, Cleveland, OH, 44106, USA
- Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, 44106, USA
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Wang Y, Gill JP, Chiel HJ, Thomas PJ. Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 2021; 20:701-744. [PMID: 37207037 PMCID: PMC10194846 DOI: 10.1137/20m1344974] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface. Examples include heel-ground interaction in locomotion, firing rate rectification in neural networks, and stick-slip oscillators. In many rhythmic systems, robustness against external perturbations involves response of both the shape and the timing of the limit cycle trajectory. The existing methods of infinitesimal phase response curve (iPRC) and variational analysis are well established for quantifying changes in timing and shape, respectively, for smooth systems. These tools have recently been extended to nonsmooth dynamics with transversal crossing boundaries. In this work, we further extend the iPRC method to nonsmooth systems with sliding components, which enables us to make predictions about the synchronization properties of weakly coupled stick-slip oscillators. We observe a new feature of the isochrons in a planar limit cycle with hard sliding boundaries: a nonsmooth kink in the asymptotic phase function, originating from the point at which the limit cycle smoothly departs the constraint surface, and propagating away from the hard boundary into the interior of the domain. Moreover, the classical variational analysis neglects timing information and is restricted to instantaneous perturbations. By defining the "infinitesimal shape response curve" (iSRC), we incorporate timing sensitivity of an oscillator to describe the shape response of this oscillator to parametric perturbations. In order to extract timing information, we also develop a "local timing response curve" (lTRC) that measures the timing sensitivity of a limit cycle within any given region. We demonstrate in a specific example that taking into account local timing sensitivity in a nonsmooth system greatly improves the accuracy of the iSRC over global timing analysis given by the iPRC.
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Affiliation(s)
- Yangyang Wang
- Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
| | - Jeffrey P Gill
- Department of Biology, Case Western Reserve University, Cleveland, OH 44106, USA
| | - Hillel J Chiel
- Departments of Biology, Neurosciences and Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44106, USA
| | - Peter J Thomas
- Departments of Biology, Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH 44106, USA
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Lu Q. Dynamics and coupling of fractional-order models of the motor cortex and central pattern generators. J Neural Eng 2020; 17:036021. [PMID: 32344390 DOI: 10.1088/1741-2552/ab8dd6] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
OBJECTIVE Fractional calculus plays a key role in the analysis of neural dynamics. In particular, fractional calculus has been recently exploited for analyzing complex biological systems and capturing intrinsic phenomena. Also, artificial neural networks have been shown to have complex neuronal dynamics and characteristics that can be modeled by fractional calculus. Moreover, for a neural microcircuit placed on the spinal cord, fractional calculus can be employed to model the central pattern generator (CPG). However, the relation between the CPG and the motor cortex is still unclear. APPROACH In this paper, fractional-order models of the CPG and the motor cortex are built on the Van der Pol oscillator and the neural mass model (NMM), respectively. A self-consistent mean field approximation is used to construct the potential landscape of the Van der Pol oscillator. This landscape provides a useful tool to observe the 3D dynamics of the oscillator. To infer the relation of the motor cortex and CPG, the coupling model between the fractional-order Van der Pol oscillator and the NMM is built. As well, the influence of the coupling parameters on the CPG and the motor cortex is assessed. MAIN RESULTS Fractional-order NMM and coupling model of the motor cortex and the CPG are first established. The potential landscape is used to show 3D probabilistic evolution of the Van der Pol oscillator states. Detailed observations of the evolution of the system states can be made with fractional calculus. In particular, fractional calculus enables the observation of the creation of stable modes and switching between them. SIGNIFICANCE The results confirm that the motor cortex and CPG have associated modes or states that can be switched based on changes in the fractional order and the time delay. Fractional calculus and the potential landscape are helpful methods for better understanding of the working principles of locomotion systems.
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Affiliation(s)
- Qiang Lu
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian 271000, People's Republic of China
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Fujiki S, Aoi S, Tsuchiya K, Danner SM, Rybak IA, Yanagihara D. Phase-Dependent Response to Afferent Stimulation During Fictive Locomotion: A Computational Modeling Study. Front Neurosci 2019; 13:1288. [PMID: 31849596 PMCID: PMC6896512 DOI: 10.3389/fnins.2019.01288] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Accepted: 11/14/2019] [Indexed: 11/13/2022] Open
Abstract
Central pattern generators (CPGs) in the spinal cord generate rhythmic neural activity and control locomotion in vertebrates. These CPGs operate under the control of sensory feedback that affects the generated locomotor pattern and adapt it to the animal's biomechanics and environment. Studies of the effects of afferent stimulation on fictive locomotion in immobilized cats have shown that brief stimulation of peripheral nerves can reset the ongoing locomotor rhythm. Depending on the phase of stimulation and the stimulated nerve, the applied stimulation can either shorten or prolong the current locomotor phase and the locomotor cycle. Here, we used a mathematical model of a half-center CPG to investigate the phase-dependent effects of brief stimulation applied to CPG on the CPG-generated locomotor oscillations. The CPG in the model consisted of two half-centers mutually inhibiting each other. The rhythmic activity in each half-center was based on a slowly inactivating, persistent sodium current. Brief stimulation was applied to CPG half-centers in different phases of the locomotor cycle to produce phase-dependent changes in CPG activity. The model reproduced several results from experiments on the effect of afferent stimulation of fictive locomotion in cats. The mechanisms of locomotor rhythm resetting under different conditions were analyzed using dynamic systems theory methods.
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Affiliation(s)
- Soichiro Fujiki
- Department of Physiology and Biological Information, Dokkyo Medical University School of Medicine, Mibu, Japan
| | - Shinya Aoi
- Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, Japan
| | - Kazuo Tsuchiya
- Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, Japan
| | - Simon M Danner
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, United States
| | - Ilya A Rybak
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, United States
| | - Dai Yanagihara
- Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
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Sobinov A, Yakovenko S. Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion. J Neurophysiol 2018; 119:1071-1083. [PMID: 29187551 PMCID: PMC5899308 DOI: 10.1152/jn.00443.2017] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Revised: 11/22/2017] [Accepted: 11/23/2017] [Indexed: 11/22/2022] Open
Abstract
The coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits, termed central pattern generators (CPGs). A classical CPG model is a system of coupled oscillators that transform locomotor drive into coordinated and gait-specific patterns of muscle recruitment. The network properties of this conceptual model can be simulated by a system of ordinary differential equations with a physiologically inspired coupling locus of interactions capturing the timing relationship for bilateral coordination of limbs in locomotion. Whereas most similar models are solved numerically, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure and to expand it to include steering control. Here, we provided a closed-form analytical solution contrasted against the previous numerical method. The evaluation time of the analytical solution was decreased by an order of magnitude when compared with the numerical approach (relative errors, <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in units of the desired limb locomotor speed. Furthermore, we performed parametric sensitivity analysis in the context of controlling steering and documented two possible mechanisms associated with either an external drive or intrinsic CPG parameters. The results identify specific propriospinal pathways that may be associated with adaptations within the CPG structure. The model offered several network configurations that may generate the same behavioral outcomes. NEW & NOTEWORTHY Using a simple process of leaky integration, we developed an analytical solution to a robust model of spinal pattern generation. We analyzed the ability of this neural element to exert locomotor control of the signal associated with limb speeds and tested the ability of this simple structure to embed steering control using the velocity signal in the model's inputs or within the internal connectivity of its elements.
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Affiliation(s)
- Anton Sobinov
- Centers for Neuroscience, School of Medicine, West Virginia University , Morgantown, West Virginia
| | - Sergiy Yakovenko
- Centers for Neuroscience, School of Medicine, West Virginia University , Morgantown, West Virginia
- Division of Exercise Physiology, Department of Human Performance, School of Medicine, West Virginia University , Morgantown, West Virginia
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Rotstein HG, Schneider E, Szczupak L. Feedback Signal from Motoneurons Influences a Rhythmic Pattern Generator. J Neurosci 2017; 37:9149-9159. [PMID: 28821650 PMCID: PMC6596741 DOI: 10.1523/jneurosci.0756-17.2017] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2017] [Revised: 08/01/2017] [Accepted: 08/09/2017] [Indexed: 12/24/2022] Open
Abstract
Motoneurons are not mere output units of neuronal circuits that control motor behavior but participate in pattern generation. Research on the circuit that controls the crawling motor behavior in leeches indicated that motoneurons participate as modulators of this rhythmic motor pattern. Crawling results from successive bouts of elongation and contraction of the whole leech body. In the isolated segmental ganglia, dopamine can induce a rhythmic antiphasic activity of the motoneurons that control contraction (DE-3 motoneurons) and elongation (CV motoneurons). The study was performed in isolated ganglia where manipulation of the activity of specific motoneurons was performed in the course of fictive crawling (crawling). In this study, the membrane potential of CV was manipulated while crawling was monitored through the rhythmic activity of DE-3. Matching behavioral observations that show that elongation dominates the rhythmic pattern, the electrophysiological activity of CV motoneurons dominates the cycle. Brief excitation of CV motoneurons during crawling episodes resets the rhythmic activity of DE-3, indicating that CV feeds back to the rhythmic pattern generator. CV hyperpolarization accelerated the rhythm to an extent that depended on the magnitude of the cycle period, suggesting that CV exerted a positive feedback on the unit(s) of the pattern generator that controls the elongation phase. A simple computational model was implemented to test the consequences of such feedback. The simulations indicate that the duty cycle of CV depended on the strength of the positive feedback between CV and the pattern generator circuit.SIGNIFICANCE STATEMENT Rhythmic movements of animals are controlled by neuronal networks that have been conceived as hierarchical structures. At the basis of this hierarchy, we find the motoneurons, few neurons at the top control global aspects of the behavior (e.g., onset, duration); and within these two ends, specific neuronal circuits control the actual rhythmic pattern of movements. We have investigated whether motoneurons are limited to function as output units. Analysis of the network that controls crawling behavior in the leech has clearly indicated that motoneurons, in addition to controlling muscle activity, send signals to the pattern generator. Physiological and modeling studies on the role of specific motoneurons suggest that these feedback signals modulate the phase relationship of the rhythmic activity.
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Affiliation(s)
- Horacio G Rotstein
- Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, New Jersey 07102
| | - Elisa Schneider
- Departamento de Fisiología, Biología Molecular y Celular Dr. Héctor Maldonado, Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, and
- Instituto de Fisiología, Biología Molecular y Neurociencias, CONICET-Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
| | - Lidia Szczupak
- Departamento de Fisiología, Biología Molecular y Celular Dr. Héctor Maldonado, Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, and
- Instituto de Fisiología, Biología Molecular y Neurociencias, CONICET-Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
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Prochazka A. Neurophysiology and neural engineering: a review. J Neurophysiol 2017; 118:1292-1309. [PMID: 28566462 PMCID: PMC5558026 DOI: 10.1152/jn.00149.2017] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Revised: 05/30/2017] [Accepted: 05/30/2017] [Indexed: 12/19/2022] Open
Abstract
Neurophysiology is the branch of physiology concerned with understanding the function of neural systems. Neural engineering (also known as neuroengineering) is a discipline within biomedical engineering that uses engineering techniques to understand, repair, replace, enhance, or otherwise exploit the properties and functions of neural systems. In most cases neural engineering involves the development of an interface between electronic devices and living neural tissue. This review describes the origins of neural engineering, the explosive development of methods and devices commencing in the late 1950s, and the present-day devices that have resulted. The barriers to interfacing electronic devices with living neural tissues are many and varied, and consequently there have been numerous stops and starts along the way. Representative examples are discussed. None of this could have happened without a basic understanding of the relevant neurophysiology. I also consider examples of how neural engineering is repaying the debt to basic neurophysiology with new knowledge and insight.
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Affiliation(s)
- Arthur Prochazka
- Department of Physiology, University of Alberta, Edmonton, Alberta, Canada
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Danner SM, Wilshin SD, Shevtsova NA, Rybak IA. Central control of interlimb coordination and speed-dependent gait expression in quadrupeds. J Physiol 2016; 594:6947-6967. [PMID: 27633893 DOI: 10.1113/jp272787] [Citation(s) in RCA: 68] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2016] [Accepted: 09/13/2016] [Indexed: 12/29/2022] Open
Abstract
KEY POINTS Quadrupeds express different gaits depending on speed of locomotion. Central pattern generators (one per limb) within the spinal cord generate locomotor oscillations and control limb movements. Neural interactions between these generators define interlimb coordination and gait. We present a computational model of spinal circuits representing four rhythm generators with left-right excitatory and inhibitory commissural and fore-hind inhibitory interactions within the cord. Increasing brainstem drive to all rhythm generators and excitatory commissural interneurons induces an increasing frequency of locomotor oscillations accompanied by speed-dependent gait changes from walk to trot and to gallop and bound. The model closely reproduces and suggests explanations for multiple experimental data, including speed-dependent gait transitions in intact mice and changes in gait expression in mutants lacking certain types of commissural interneurons. The model suggests the possible circuit organization in the spinal cord and proposes predictions that can be tested experimentally. ABSTRACT As speed of locomotion is increasing, most quadrupeds, including mice, demonstrate sequential gait transitions from walk to trot and to gallop and bound. The neural mechanisms underlying these transitions are poorly understood. We propose that the speed-dependent expression of different gaits results from speed-dependent changes in the interactions between spinal circuits controlling different limbs and interlimb coordination. As a result, the expression of each gait depends on (1) left-right interactions within the spinal cord mediated by different commissural interneurons (CINs), (2) fore-hind interactions on each side of the spinal cord and (3) brainstem drives to rhythm-generating circuits and CIN pathways. We developed a computational model of spinal circuits consisting of four rhythm generators (RGs) with bilateral left-right interactions mediated by V0 CINs (V0D and V0V sub-types) providing left-right alternation, and conditional V3 CINs promoting left-right synchronization. Fore and hind RGs mutually inhibited each other. We demonstrate that linearly increasing excitatory drives to the RGs and V3 CINs can produce a progressive increase in the locomotor speed accompanied by sequential changes of gaits from walk to trot and to gallop and bound. The model closely reproduces and suggests explanations for the speed-dependent gait expression observed in vivo in intact mice and in mutants lacking V0V or all V0 CINs. Specifically, trot is not expressed after removal of V0V CINs, and only bound is expressed after removal of all V0 CINs. The model provides important insights into the organization of spinal circuits and neural control of locomotion.
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Affiliation(s)
- Simon M Danner
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, USA
| | - Simon D Wilshin
- Structure and Motion Laboratory, The Royal Veterinary College, University of London, London, UK
| | - Natalia A Shevtsova
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, USA
| | - Ilya A Rybak
- Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, USA
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The significance of dynamical architecture for adaptive responses to mechanical loads during rhythmic behavior. J Comput Neurosci 2014; 38:25-51. [PMID: 25182251 PMCID: PMC4544651 DOI: 10.1007/s10827-014-0519-3] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2013] [Revised: 06/25/2014] [Accepted: 07/22/2014] [Indexed: 11/21/2022]
Abstract
Many behaviors require reliably generating sequences of motor activity while adapting the activity to incoming sensory information. This process has often been conceptually explained as either fully dependent on sensory input (a chain reflex) or fully independent of sensory input (an idealized central pattern generator, or CPG), although the consensus of the field is that most neural pattern generators lie somewhere between these two extremes. Many mathematical models of neural pattern generators use limit cycles to generate the sequence of behaviors, but other models, such as a heteroclinic channel (an attracting chain of saddle points), have been suggested. To explore the range of intermediate behaviors between CPGs and chain reflexes, in this paper we describe a nominal model of swallowing in Aplysia californica. Depending upon the value of a single parameter, the model can transition from a generic limit cycle regime to a heteroclinic regime (where the trajectory slows as it passes near saddle points). We then study the behavior of the system in these two regimes and compare the behavior of the models with behavior recorded in the animal in vivo and in vitro. We show that while both pattern generators can generate similar behavior, the stable heteroclinic channel can better respond to changes in sensory input induced by load, and that the response matches the changes seen when a load is added in vivo. We then show that the underlying stable heteroclinic channel architecture exhibits dramatic slowing of activity when sensory and endogenous input is reduced, and show that similar slowing with removal of proprioception is seen in vitro. Finally, we show that the distributions of burst lengths seen in vivo are better matched by the distribution expected from a system operating in the heteroclinic regime than that expected from a generic limit cycle. These observations suggest that generic limit cycle models may fail to capture key aspects of Aplysia feeding behavior, and that alternative architectures such as heteroclinic channels may provide better descriptions.
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14
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Frigon A, D'Angelo G, Thibaudier Y, Hurteau MF, Telonio A, Kuczynski V, Dambreville C. Speed-dependent modulation of phase variations on a step-by-step basis and its impact on the consistency of interlimb coordination during quadrupedal locomotion in intact adult cats. J Neurophysiol 2014; 111:1885-902. [PMID: 24523521 DOI: 10.1152/jn.00524.2013] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
It is well established that stance duration changes more than swing duration for a given change in cycle duration. Small variations in cycle duration are also observed at any given speed on a step-by-step basis. To evaluate the step-by-step effect of speed on phase variations, we measured the slopes of the linear regressions between the phases (i.e., stance, swing) and cycle duration during individual episodes at different treadmill speeds in five adult cats. We also determined the pattern of dominance, defined as the phase that varies most with cycle duration. We found a significant effect of speed on hindlimb phase variations, with significant differences observed between the slowest speed of 0.3 m/s compared with faster speeds. Moreover, although patterns of phase dominance were primarily stance/extensor dominated at the slowest speeds, as speed increased the patterns were increasingly categorized as covarying, whereby both stance/extensor and swing/flexor phases changed in approximately equal proportion with cycle duration. Speed significantly affected the relative duration of support periods as well as interlimb phasing between homolateral and diagonal pairs of limbs but not between homologous pairs of limbs. Speed also significantly affected the consistency of interlimb coordination on a step-by-step basis, being less consistent at the slowest speed of 0.3 m/s compared with faster speeds. We found a strong linear relationship between hindlimb phase variations and the consistency of interlimb coordination. Therefore, results show that phase variations on a step-by-step basis are modulated by speed, which appears to influence the consistency of interlimb coordination.
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Affiliation(s)
- Alain Frigon
- Department of Physiology and Biophysics, Faculty of Medicine and Health Sciences, Centre de recherche Clinique Étienne-Le Bel, Université de Sherbrooke, Sherbrooke, Quebec, Canada
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15
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Phase locking asymmetries at flexor-extensor transitions during fictive locomotion. PLoS One 2013; 8:e64421. [PMID: 23700475 PMCID: PMC3660298 DOI: 10.1371/journal.pone.0064421] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2012] [Accepted: 04/15/2013] [Indexed: 01/12/2023] Open
Abstract
The motor output for walking is produced by a network of neurons termed the spinal central pattern generator (CPG) for locomotion. The basic building block of this CPG is a half-center oscillator composed of two mutually inhibitory sets of interneurons, each controlling one of the two dominant phases of locomotion: flexion and extension. To investigate symmetry between the two components of this oscillator, we analyzed the statistics of natural variation in timing during fictive locomotion induced by stimulation of the midbrain locomotor region in the cat. As a complement to previously published analysis of these data focused on burst and cycle durations, we present a new analysis examining the strength of phase locking at the transitions between flexion and extension. Across our sample of nerve pairs, phase locking at the transition from extension to flexion (E to F) is stronger than at the transition from flexion to extension (F to E). This pattern did not reverse when considering bouts of fictive locomotion that were flexor vs. extensor dominated, demonstrating that asymmetric locking at the transitions between phases is dissociable from which phase dominates cycle duration. We also find that the strength of phase locking is correlated with the mean latency between burst offset and burst onset. These results are interpreted in the context of a hypothesis where network inhibition and intrinsic oscillatory mechanisms make distinct contributions to flexor-extensor alternation in half-center networks.
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16
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Hillen BK, Abbas JJ, Jung R. Accelerating locomotor recovery after incomplete spinal injury. Ann N Y Acad Sci 2013; 1279:164-74. [PMID: 23531014 DOI: 10.1111/nyas.12061] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
A traumatic spinal injury can destroy cells, irreparably damage axons, and trigger a cascade of biochemical responses that increase the extent of injury. Although damaged central nervous system axons do not regrow well naturally, the distributed nature of the nervous system and its capacity to adapt provide opportunities for recovery of function. It is apparent that activity-dependent plasticity plays a role in this recovery and that the endogenous response to injury heightens the capacity for recovery for at least several weeks postinjury. To restore locomotor function, researchers have investigated the use of treadmill-based training, robots, and electrical stimulation to tap into adaptive activity-dependent processes. The current challenge is to maximize the degree of functional recovery. This manuscript reviews the endogenous neural system response to injury, and reviews data and presents novel analyses of these from a rat model of contusion injury that demonstrates how a targeted intervention can accelerate recovery, presumably by engaging processes that underlie activity-dependent plasticity.
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Affiliation(s)
- Brian K Hillen
- Department of Biomedical Engineering, Florida International University, Miami, FL 33174, USA
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17
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Dhingra RR, Zhu Y, Jacono FJ, Katz DM, Galán RF, Dick TE. Decreased Hering-Breuer input-output entrainment in a mouse model of Rett syndrome. Front Neural Circuits 2013; 7:42. [PMID: 23565077 PMCID: PMC3615412 DOI: 10.3389/fncir.2013.00042] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2012] [Accepted: 03/01/2013] [Indexed: 11/30/2022] Open
Abstract
Rett syndrome, a severe X-linked neurodevelopmental disorder caused by mutations in the gene encoding methyl-CpG-binding protein 2 (Mecp2), is associated with a highly irregular respiratory pattern including severe upper-airway dysfunction. Recent work suggests that hyperexcitability of the Hering-Breuer reflex (HBR) pathway contributes to respiratory dysrhythmia in Mecp2 mutant mice. To assess how enhanced HBR input impacts respiratory entrainment by sensory afferents in closed-loop in vivo-like conditions, we investigated the input (vagal stimulus trains) - output (phrenic bursting) entrainment via the HBR in wild-type and MeCP2-deficient mice. Using the in situ perfused brainstem preparation, which maintains an intact pontomedullary axis capable of generating an in vivo-like respiratory rhythm in the absence of the HBR, we mimicked the HBR feedback input by stimulating the vagus nerve (at threshold current, 0.5 ms pulse duration, 75 Hz pulse frequency, 100 ms train duration) at an inter-burst frequency matching that of the intrinsic oscillation of the inspiratory motor output of each preparation. Using this approach, we observed significant input-output entrainment in wild-type mice as measured by the maximum of the cross-correlation function, the peak of the instantaneous relative phase distribution, and the mutual information of the instantaneous phases. This entrainment was associated with a reduction in inspiratory duration during feedback stimulation. In contrast, the strength of input-output entrainment was significantly weaker in Mecp2 (-/+) mice. However, Mecp2 (-/+) mice also had a reduced inspiratory duration during stimulation, indicating that reflex behavior in the HBR pathway was intact. Together, these observations suggest that the respiratory network compensates for enhanced sensitivity of HBR inputs by reducing HBR input-output entrainment.
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Affiliation(s)
- Rishi R. Dhingra
- Division of Pulmonary, Critical Care and Sleep Medicine, Department of Medicine, Case Western Reserve UniversityCleveland, OH, USA
- Department of Neurosciences, Case Western Reserve UniversityCleveland, OH, USA
| | - Yenan Zhu
- Department of Neurosciences, Case Western Reserve UniversityCleveland, OH, USA
- Systems Biology and Bioinformatics Program, Case Western Reserve UniversityCleveland, OH, USA
| | - Frank J. Jacono
- Division of Pulmonary, Critical Care and Sleep Medicine, Department of Medicine, Case Western Reserve UniversityCleveland, OH, USA
- Louis Stokes Veterans Affairs Medical Center, Case Western Reserve UniversityCleveland, OH, USA
| | - David M. Katz
- Department of Neurosciences, Case Western Reserve UniversityCleveland, OH, USA
| | - Roberto F. Galán
- Department of Neurosciences, Case Western Reserve UniversityCleveland, OH, USA
- Systems Biology and Bioinformatics Program, Case Western Reserve UniversityCleveland, OH, USA
| | - Thomas E. Dick
- Division of Pulmonary, Critical Care and Sleep Medicine, Department of Medicine, Case Western Reserve UniversityCleveland, OH, USA
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18
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Clewley R. Hybrid models and biological model reduction with PyDSTool. PLoS Comput Biol 2012; 8:e1002628. [PMID: 22912566 PMCID: PMC3415397 DOI: 10.1371/journal.pcbi.1002628] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2011] [Accepted: 06/08/2012] [Indexed: 12/31/2022] Open
Abstract
The PyDSTool software environment is designed to develop, simulate, and analyze dynamical systems models, particularly for biological applications. Unlike the engineering application focus and graphical specification environments of most general purpose simulation tools, PyDSTool provides a programmatic environment well suited to exploratory data- and hypothesis-driven biological modeling problems. In this work, we show how the environment facilitates the application of hybrid dynamical modeling to the reverse engineering of complex biophysical dynamics; in this case, of an excitable membrane. The example demonstrates how the software provides novel tools that support the inference and validation of mechanistic hypotheses and the inclusion of data constraints in both quantitative and qualitative ways. The biophysical application is broadly relevant to models in the biosciences. The open source and platform-independent PyDSTool package is freely available under the BSD license from http://sourceforge.net/projects/pydstool/. The hosting service provides links to documentation and online forums for user support.
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Affiliation(s)
- Robert Clewley
- Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America.
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Markin SN, Lemay MA, Prilutsky BI, Rybak IA. Motoneuronal and muscle synergies involved in cat hindlimb control during fictive and real locomotion: a comparison study. J Neurophysiol 2011; 107:2057-71. [PMID: 22190626 DOI: 10.1152/jn.00865.2011] [Citation(s) in RCA: 55] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
We compared the activity profiles and synergies of spinal motoneurons recorded during fictive locomotion evoked in immobilized decerebrate cat preparations by midbrain stimulation to the activity profiles and synergies of the corresponding hindlimb muscles obtained during forward level walking in cats. The fictive locomotion data were collected in the Spinal Cord Research Centre, University of Manitoba, and provided by Dr. David McCrea; the real locomotion data were obtained in the laboratories of M. A. Lemay and B. I. Prilutsky. Scatterplot representation and minimum spanning tree clustering algorithm were used to identify the possible motoneuronal and muscle synergies operating during both fictive and real locomotion. We found a close similarity between the activity profiles and synergies of motoneurons innervating one-joint muscles during fictive locomotion and the profiles and synergies of the corresponding muscles during real locomotion. However, the activity patterns of proximal nerves controlling two-joint muscles, such as posterior biceps and semitendinosus (PBSt) and rectus femoris (RF), were not uniform in fictive locomotion preparations and differed from the activity profiles of the corresponding two-joint muscles recorded during forward level walking. Moreover, the activity profiles of these nerves and the corresponding muscles were unique and could not be included in the synergies identified in fictive and real locomotion. We suggest that afferent feedback is involved in the regulation of locomotion via motoneuronal synergies controlled by the spinal central pattern generator (CPG) but may also directly affect the activity of motoneuronal pools serving two-joint muscles (e.g., PBSt and RF). These findings provide important insights into the organization of the spinal CPG in mammals, the motoneuronal and muscle synergies engaged during locomotion, and their afferent control.
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Affiliation(s)
- Sergey N Markin
- Dept. of Neurobiology and Anatomy, Drexel Univ. College of Medicine, Philadelphia, PA 19129, USA
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20
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Spardy LE, Markin SN, Shevtsova NA, Prilutsky BI, Rybak IA, Rubin JE. A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: II. Phase asymmetry. J Neural Eng 2011; 8:065004. [PMID: 22058275 DOI: 10.1088/1741-2560/8/6/065004] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
In this paper we analyze a closed loop neuromechanical model of locomotor rhythm generation. The model is composed of a spinal central pattern generator (CPG) and a single-joint limb, with CPG outputs projecting via motoneurons to muscles that control the limb and afferent signals from the muscles feeding back to the CPG. In a preceding companion paper (Spardy et al 2011 J. Neural Eng. 8 065003), we analyzed how the model generates oscillations in the presence or absence of feedback, identified curves in a phase plane associated with the limb that signify where feedback levels induce phase transitions within the CPG, and explained how increasing feedback strength restores oscillations in a model representation of spinal cord injury; from these steps, we derived insights about features of locomotor rhythms in several scenarios and made predictions about rhythm responses to various perturbations. In this paper, we exploit our analytical observations to construct a reduced model that retains important characteristics from the original system. We prove the existence of an oscillatory solution to the reduced model using a novel version of a Melnikov function, adapted for discontinuous systems, and also comment on the uniqueness and stability of this solution. Our analysis yields a deeper understanding of how the model must be tuned to generate oscillations and how the details of the limb dynamics shape overall model behavior. In particular, we explain how, due to the feedback signals in the model, changes in the strength of a tonic supra-spinal drive to the CPG yield asymmetric alterations in the durations of different locomotor phases, despite symmetry within the CPG itself.
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Affiliation(s)
- Lucy E Spardy
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
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