Sergey N. Markin

Spatial organization and state-dependent mechanisms for respiratory rhythm and pattern generation

The brainstem respiratory network can operate in multiple functional states engaging different state-dependent neural mechanisms. These mechanisms were studied in the in situ perfused rat brainstem-spinal cord preparation using sequential brainstem transections and administration of riluzole, a pharmacological blocker of persistent sodium current (INaP). Dramatic transformations in the rhythmogenic mechanisms and respiratory motor pattern were observed after removal of the pons and subsequent medullary transactions down to the rostral end of pre-Bötzinger complex (pre-BötC). A computational model of the brainstem respiratory network was developed to reproduce and explain these experimental findings. The model incorporates several interacting neuronal compartments, including the ventral respiratory group (VRG), pre-BötC, Bötzinger complex (BötC), and pons. Simulations mimicking the removal of circuit components following transections closely reproduce the respiratory motor output patterns recorded from the intact and sequentially reduced brainstem preparations. The model suggests that both the operating rhythmogenic mechanism (i.e., network-based or pacemaker-driven) and the respiratory pattern generated (e.g., three-phase, two-phase, or one-phase) depend on the state of the pre-BötC (expression of INaP-dependent intrinsic rhythmogenic mechanisms) and the BötC (providing expiratory inhibition in the network). At the same time, tonic drives from pons and multiple medullary chemoreceptive sites appear to control the state of these compartments and hence the operating rhythmogenic mechanism and motor pattern. Our results suggest that the brainstem respiratory network has a spatial (rostral-to-caudal) organization extending from the rostral pons to the VRG, in which each functional compartment is controlled by more rostral compartments. The model predicts a continuum of respiratory network states relying on different contributions of intrinsic cellular properties versus synaptic interactions for the generation and control of the respiratory rhythm and pattern.

Modeling the spinal cord neural circuitry controlling cat hindlimb movement during locomotion

We have developed a computational model of the spinal cord neural circuitry that controls locomotor movements of simulated cat hindlimbs. The neural circuitry includes two central pattern generators integratedwith re4ex circuits. All neurons were mod eledin the Hod gkin– Huxley style. The musculoskeletal system includes two three-joint hindlimbs and the trunk. Each hind limb is actuatedby nine one- andtwo-joint muscles (a Hill-type mod el). Our simulations allow us to suggest a speci;c network architecture in the spinal cordanda pattern of feed back connectivities (from Ia andIb ;bers andtouch sensors) that provid e stable locomotion and realistic patterns of muscle activation andkinematics of limb movements. c � 2002 Elsevier Science B.V. All rights reserved.

Afferent control of locomotor CPG: insights from a simple neuromechanical model

A simple neuromechanical model has been developed that describes a spinal central pattern generator (CPG) controlling the locomotor movement of a single‐joint limb via activation of two antagonist (flexor and extensor) muscles. The limb performs rhythmic movements under control of the muscular, gravitational and ground reaction forces. Muscle afferents provide length‐dependent (types Ia and II) and force‐dependent (type Ib from the extensor) feedback to the CPG. We show that afferent feedback adjusts CPG operation to the kinematics and dynamics of the limb providing stable “locomotion.” Increasing the supraspinal drive to the CPG increases locomotion speed by reducing the duration of stance phase. We show that such asymmetric, extensor‐dominated control of locomotor speed (with relatively constant swing duration) is provided by afferent feedback independent of the asymmetric rhythmic pattern generated by the CPG alone (in “fictive locomotion” conditions). Finally, we demonstrate the possibility of reestablishing stable locomotion after removal of the supraspinal drive (associated with spinal cord injury) by increasing the weights of afferent inputs to the CPG, which is thought to occur following locomotor training.

Motoneuronal and muscle synergies involved in cat hindlimb control during fictive and real locomotion: a comparison study

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.

A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: I. Rhythm generation

Locomotion in mammals is controlled by a spinal central pattern generator (CPG) coupled to a biomechanical limb system, with afferent feedback to the spinal circuits and CPG closing the control loop. We have considered a simplified model of this system, in which the CPG establishes a rhythm when a supra-spinal activating drive is present and afferent signals from a single-joint limb feed back to affect CPG operation. Using dynamical system methods, in a series of two papers we analyze the mechanisms by which this model produces oscillations, and the characteristics of these oscillations, in the closed- and open-loop regimes. In this first paper, we analyze the phase transition mechanisms operating within the CPG and use the results to explain how afferent feedback allows oscillations to occur at a wider range of drive values to the CPG than the range over which oscillations occur in the CPG without feedback, and then to comment on why stronger feedback leads to faster oscillations. Linking these transitions to structures in the phase plane associated with the limb segment clarifies how increased weights of afferent feedback to the CPG can restore locomotion after removal of supra-spinal drive to simulate spinal cord injury.

Organization of left-right coordination of neuronal activity in the mammalian spinal cord: Insights from computational modelling

Coordination of neuronal activity between left and right sides of the mammalian spinal cord is provided by several sets of commissural interneurons (CINs) whose axons cross the midline. Genetically identified inhibitory V0D and excitatory V0V CINs and ipsilaterally projecting excitatory V2a interneurons were shown to secure left–right alternation at different locomotor speeds. We have developed computational models of neuronal circuits in the spinal cord that include left and right rhythm‐generating centres interacting bilaterally via three parallel pathways mediated by V0D, V2a–V0V and V3 neuron populations. The models reproduce the experimentally observed speed‐dependent left–right coordination in normal mice and the changes in coordination seen in mutants lacking specific neuron classes. The models propose an explanation for several experimental results and provide insights into the organization of the spinal locomotor network and parallel CIN pathways involved in gait control at different locomotor speeds.

A dynamical systems analysis of afferent control in a neuromechanical model of locomotion: II. Phase asymmetry

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.

A Neuromechanical Model of Spinal Control of Locomotion

We have developed a neuromechanical computational model of cat hindlimb locomotion controlled by spinal central pattern generators (CPGs, one per hindlimb) and motion-dependent afferent feedback. Each CPG represents an extension of previously developed two-level model (Rybak et al. J Physiol 577:617–639, 2006a, J Physiol 577:641–658, 2006b) and includes a half-center rhythm generator (RG), generating the locomotor rhythm, and a pattern formation (PF) network operating under control of RG and managing the synergetic activity of different hindlimb motoneuronal pools. The basic two-level CPG model was extended by incorporating additional neural circuits allowing the CPG to generate the complex activity patterns of motoneurons controlling proximal two-joint muscles (Shevtsova et al., Chap. 5, Neuromechanical modeling of posture and locomotion, Springer, New York, 2015). The spinal cord circuitry in the model includes reflex circuits mediating reciprocal inhibition between flexor and extensor motoneurons and disynaptic excitation of extensor motoneurons by load-sensitive afferents. The hindlimbs and trunk were modeled as a 2D system of rigid segments driven by Hill-type muscle actuators with force-length-velocity dependent properties. The musculoskeletal model has been tuned to reproduce the mechanics of locomotion; as a result, the computed motion-dependent activity of muscle group Ia, Ib, and II afferents and the paw-pad cutaneous afferents matched well the cat in vivo afferent recordings reported in the literature (Prilutsky et al., Chap. 10, Neuromechanical modeling of posture and locomotion, Springer, New York, 2015). In the neuromechanical model, the CPG operation is adjusted by afferent feedback from the moving hindlimbs. The model demonstrates stable locomotion with realistic mechanical characteristics and exhibits realistic patterns of muscle activity. The model can be used as a testbed to study spinal control of locomotion in various normal and pathological conditions.

A Real-Time System for Small Animal Neurorobotics at Spinal or Cortical Levels.

We present a real-time system for small animal neurorobotics and neuroprosthetics at spinal or cortical levels. The system combines biomechanics, neural recording and a 3D robotics system including sensable devices phantoms, ATI 6 axis force transducers, cybernetics (bionic technology) cerebus neural recording system, computer boards buffered DAS16s, and an OPTOTRAK and 120 Hz camera system. The system allows real-time combination of neural data, force data and robot interaction at rates of 1 kilohertz, and allows full data recording. Up to 2 robots and 5 force sensors with 128 channels of neural data and 16 channels of EMG form the present core system. The force sensors and robot are controlled from a single machine using a dedicated Venturcom/Phar Lap ETS real time operating system. Elastic, viscous, translational and barrier constraint fields can be combined or recruited by neural activity. The main control loop can also support PID control. Neural data from up to 256 neurons (2 per channel, 128 channels) identified in real-time with multiple threshold windows on the cybernetics are delivered for robot control. Other data collection is synchronized by the main host. The robot(s) connect to rats or frogs through bone implants or with a saddle-harness arrangement

NeuroCAD – the modular simulation environment for effective biologically plausible neuromodeling

Simulation of biologically plausible neural models from a single cell to networks usually requires substantial computational resources for numerical solution of differential equations. Various advanced methods to reduce the computational cost but keep an accuracy and effectiveness of solving differential equations are offered and implemented in several program environments. However efficacy of these methods is often reduced by non effective programming paradigms.