scholarly journals Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion

2018 ◽  
Vol 119 (3) ◽  
pp. 1071-1083 ◽  
Author(s):  
Anton Sobinov ◽  
Sergiy Yakovenko
Keyword(s):  
Analytical Solution ◽  
Central Pattern Generators ◽  
Analytical Description ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Neural Element ◽  
Steering Control ◽  
Velocity Signal ◽  
Robust Model ◽  
Order Of Magnitude

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.

scholarly journals Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion

2017 ◽  
Author(s):  
Anton Sobinov ◽  
Sergiy Yakovenko
Keyword(s):  
Analytical Solution ◽  
Central Pattern Generators ◽  
Analytical Description ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Neural Element ◽  
Steering Control ◽  
Velocity Signal ◽  
Robust Model ◽  
Order Of Magnitude

AbstractThe 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. While 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 computational load of the analytical solution was decreased by order of magnitude when compared to 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 & NoteworthyUsing 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.

Rhythmic Pattern Generation in Invertebrates

2018 ◽  
pp. 390-400
Author(s):  
Astrid A. Prinz
Keyword(s):  
Central Pattern Generators ◽  
Pattern Generation ◽  
Rhythmic Pattern ◽  
Neuronal Circuit ◽  
Neuronal Circuits ◽  
Timing Circuit ◽  
Core Components ◽  
Pattern Generators

This chapter begins by defining central pattern generators (CPGs) and proceeds to focus on one of their core components, the timing circuit. After arguing why invertebrate CPGs are particularly useful for the study of neuronal circuit operation in general, the bulk of the chapter then describes basic mechanisms of CPG operation at the cellular, synaptic, and network levels, and how different CPGs combine these mechanisms in various ways. Finally, the chapter takes a semihistorical perspective to discuss whether or not the study of invertebrate CPGs has seen its prime and what it has contributed—and may continue to offer—to a wider understanding of neuronal circuits in general.

scholarly journals Analytical description of nanowires. I. Regular cross sections for zincblende and diamond structures. Corrigendum

2021 ◽  
Vol 77 (5) ◽  
pp. 861-861
Author(s):  
Dirk König ◽  
Sean C. Smith
Keyword(s):  
Analytical Solution ◽  
Cross Sections ◽  
Exact Analytical Solution ◽  
Analytical Description ◽  
Acta Cryst ◽  
Zinc Blende ◽  
Corrected Version

In the paper by König & Smith [Acta Cryst. (2019), B75, 788–802], several equations had minor errors in their coefficients defining characteristic lengths and area of zinc-blende nanowire cross sections, thereby deviating from the exact analytical solution by 1.4 ± 0.8 %. A fully corrected version of the paper is provided.

RUNNING PATTERN GENERATION OF HUMANOID BIPED WITH A FIXED POINT AND ITS REALIZATION

2009 ◽  
Vol 06 (04) ◽  
pp. 631-656 ◽  
Author(s):  
BAEK-KYU CHO ◽  
ILL-WOO PARK ◽  
JUN-HO OH
Keyword(s):  
Fixed Point ◽  
Angular Momentum ◽  
Sagittal Plane ◽  
Center Of Mass ◽  
Maximum Velocity ◽  
Frontal Plane ◽  
Numerical Approach ◽  
Pattern Generation ◽  
Upper Body ◽  
Running Pattern

This paper discusses the generation of a running pattern for a humanoid biped and verifies the validity of the proposed method of running pattern generation via experiments. Two running patterns are generated independently in the sagittal plane and in the frontal plane and the two patterns are then combined. When a running pattern is created with resolved momentum control in the sagittal plane, the angular momentum of the robot about the Center of Mass (COM) is set to zero, as the angular momentum causes the robot to rotate. However, this also induces unnatural motion of the upper body of the robot. To solve this problem, the biped was set as a virtual under-actuated robot with a free joint at its support ankle, and a fixed point for a virtual under-actuated system was determined. Following this, a periodic running pattern in the sagittal plane was formulated using the fixed point. The fixed point is easily determined in a numerical approach. In this way, a running pattern in the frontal plane was also generated. In an experiment, a humanoid biped known as KHR-2 ran forward using the proposed running pattern generation method. Its maximum velocity was 2.88 km/h.

scholarly journals The initial evolution of millisecond magnetars: an analytical solution

2020 ◽  
Vol 496 (2) ◽  
pp. 2183-2190
Author(s):  
S Çıkıntoğlu ◽  
S Şaşmaz Muş ◽  
K Yavuz Ekşi
Keyword(s):  
Dipole Moment ◽  
Analytical Solution ◽  
Magnetic Dipole ◽  
Inclination Angle ◽  
Magnetic Dipole Moment ◽  
Gamma Ray ◽  
Plateau Phase ◽  
Central Engine ◽  
Initial Evolution ◽  
Order Of Magnitude

ABSTRACT Millisecond magnetars are often invoked as the central engine of some gamma-ray bursts (GRBs), specifically the ones showing a plateau phase. We argue that an apparent plateau phase may not be realized if the magnetic field of the nascent magnetar is in a transient rapid decay stage. Some GRBs that lack a clear plateau phase may also be hosting millisecond magnetars. We present an approximate analytical solution of the coupled set of equations describing the evolution of the angular velocity and the inclination angle between rotation and magnetic axes of a neutron star in the presence of a corotating plasma. We also show how the solution can be generalized to the case of evolving magnetic fields. We determine the evolution of the spin period, inclination angle, magnetic dipole moment, and braking index of six putative magnetars associated with GRB 091018, GRB 070318, GRB 080430, GRB 090618, GRB 110715A, and GRB 140206A through fitting, via Bayesian analysis, the X-ray afterglow light curves by using our recent model. We find that within the first day following the formation of the millisecond magnetar, the inclination angle aligns rapidly, the magnetic dipole moment may decay by a few times, and the braking index varies by an order of magnitude.

scholarly journals From Spinal Central Pattern Generators to Cortical Network: Integrated BCI for Walking Rehabilitation

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
G. Cheron ◽  
M. Duvinage ◽  
C. De Saedeleer ◽  
T. Castermans ◽  
A. Bengoetxea ◽  
...  
Keyword(s):  
Brain Plasticity ◽  
Central Pattern Generators ◽  
Pattern Generation ◽  
Lower Limbs ◽  
Plantar Surface ◽  
Rehabilitation Programs ◽  
Walking Rehabilitation ◽  
Locomotor Patterns ◽  
Pattern Generators ◽  
Clinical Conditions

Success in locomotor rehabilitation programs can be improved with the use of brain-computer interfaces (BCIs). Although a wealth of research has demonstrated that locomotion is largely controlled by spinal mechanisms, the brain is of utmost importance in monitoring locomotor patterns and therefore contains information regarding central pattern generation functioning. In addition, there is also a tight coordination between the upper and lower limbs, which can also be useful in controlling locomotion. The current paper critically investigates different approaches that are applicable to this field: the use of electroencephalogram (EEG), upper limb electromyogram (EMG), or a hybrid of the two neurophysiological signals to control assistive exoskeletons used in locomotion based on programmable central pattern generators (PCPGs) or dynamic recurrent neural networks (DRNNs). Plantar surface tactile stimulation devices combined with virtual reality may provide the sensation of walking while in a supine position for use of training brain signals generated during locomotion. These methods may exploit mechanisms of brain plasticity and assist in the neurorehabilitation of gait in a variety of clinical conditions, including stroke, spinal trauma, multiple sclerosis, and cerebral palsy.

scholarly journals Subperiodic trigonometric subsampling: A numerical approach

2017 ◽  
Vol 11 (2) ◽  
pp. 470-483
Author(s):  
Alvise Sommariva ◽  
Marco Vianello
Keyword(s):  
Regional Scale ◽  
Gaussian Quadrature ◽  
Numerical Approach ◽  
Trigonometric Polynomials ◽  
Earth Surface ◽  
The Earth ◽  
Scale Models ◽  
Order Of Magnitude ◽  
Legendre Quadrature

We show that Gauss-Legendre quadrature applied to trigonometric polynomials on subintervals of the period can be competitive with subperiodic trigonometric Gaussian quadrature. For example with intervals corresponding to few angular degrees, relevant for regional scale models on the earth surface, we see a subsampling ratio of one order of magnitude already at moderate trigonometric degrees.

Pattern Generation in the Buccal System of Freely BehavingLymnaea stagnalis

1999 ◽  
Vol 82 (6) ◽  
pp. 3378-3391 ◽  
Author(s):  
Rene F. Jansen ◽  
Anton W. Pieneman ◽  
Andries ter Maat
Keyword(s):  
Electrical Activity ◽  
Lymnaea Stagnalis ◽  
Central Pattern Generators ◽  
Phase Relationship ◽  
Pattern Generation ◽  
Egg Laying ◽  
Motor Patterns ◽  
Freely Behaving ◽  
Behavioral Requirements

Central pattern generators (CPGs) are neuronal circuits that drive active repeated movements such as walking or swimming. Although CPGs are, by definition, active in isolated central nervous systems, sensory input is thought play an important role in adjusting the output of the CPGs to meet specific behavioral requirements of intact animals. We investigated, in freely behaving snails ( Lymnaea stagnalis), how the buccal CPG is used during two different behaviors, feeding and egg laying. Analysis of the relationship between unit activity recorded from buccal nerves and the movements of the buccal mass showed that electrical activity in laterobuccal/ventrobuccal (LB/VB) nerves was as predicted from in vitro data, but electrical activity in the posterior jugalis nerve was not. Autodensity and interval histograms showed that during feeding the CPG produces a much stronger rhythm than during egg laying. The phase relationship between electrical activity and buccal movement changed little between the two behaviors. Fitting the spike trains recorded during the two behaviors with a simple model revealed differences in the patterns of electrical activity produced by the buccal system during the two behaviors investigated. During egg laying the bursts contained less spikes, and the number of spikes per burst was significantly more variable than during feeding. The time between two bursts of in a spike train was longer during egg laying than during feeding. The data show what the qualitative and quantitative differences are between two motor patterns produced by the buccal system of freely behaving Lymnaea stagnalis.

Correlated and uncorrelated high-frequency oscillations in phrenic and recurrent laryngeal neurograms

1988 ◽  
Vol 59 (4) ◽  
pp. 1188-1203 ◽  
Author(s):  
E. N. Bruce
Keyword(s):  
Central Pattern Generators ◽  
Power Spectra ◽  
Power Spectral Analysis ◽  
Pattern Generation ◽  
Common Source ◽  
Power Spectral ◽  
Left And Right ◽  
Motor Outputs ◽  
Pattern Generators ◽  
40 Hz

1. Power spectral analysis of phrenic and recurrent laryngeal (or efferent vagal) inspiratory discharge activity from anesthetized cats revealed a peak within the 60- to 110-Hz range in all spectra, plus a peak within the 40- to 60-Hz range in the laryngeal (and efferent vagal) spectra, and a peak less than 40 Hz in the phrenic spectra. 2. A 60- to 110-Hz peak was present in coherence spectra between the left and right phrenic neurograms, the left and right recurrent laryngeal (and efferent vagal) neurograms, and all combinations of phrenic-laryngeal (and phrenic-efferent vagal) pairs. It is concluded that the nearly-periodic oscillations represented by these peaks arise from a single source that projects functionally in parallel to many respiratory motor outputs. This source may be part of, or interact with, respiratory central pattern generation. 3. The 40- to 60-Hz oscillations in left and right recurrent laryngeal (and efferent vagal) neurograms were uncorrelated or occasionally were very weakly correlated. Thus it is unlikely that these oscillations arise from a common source such as a second respiratory central pattern generator. 4. The oscillations less than 40 Hz were weakly correlated between left and right phrenic neurograms. This correlation may be due substantially to spinal crossed-phrenic pathways. 5. It is proposed that both the 40- to 60-Hz oscillations in recurrent laryngeal neurograms and the oscillations below 40 Hz in phrenic neurograms originate in neural circuits associated with individual left or right recurrent laryngeal or phrenic motor outputs. 6. Our results do not support the interpretation that multiple peaks in phrenic and recurrent laryngeal power spectra are due to two respiratory central pattern generators whose outputs have parallel pathways to respiratory motoneurons.

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