Alexander N. Klishko

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.

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.

Paw-shake response and locomotion: can one CPG generate two different rhythmic behaviors?

Rhythmic limb movements like locomotion or paw-shake response are controlled by network of spinal circuits, known as central pattern generators (CPGs), as evidenced from locomotor-like and paw-shake like activity in limb peripheral nerves elicited in decerebrate or spinal animals with blocked neuromuscular transmission [4]. Unlike fictive locomotion and scratch, that are likely controlled by distinct CPGs [3], fictive paw-shake response has not been systematically investigated and it is not known whether it is controlled by a specialized CPG or by the CPG that also controls locomotion. In-vivo recordings of paw-shake motor patterns elicited by stimulation of paw skin afferents [7] have revealed high frequency hindlimb oscillations (~10 Hz) with atypical muscle synergies – reciprocal activation of anterior and posterior hindlimb muscles in each half of the paw-shake cycle; both anterior and posterior muscle groups include flexor and extensor muscles. We asked whether a paw-shake response with the atypical muscle synergies can be generated by a typical half-center locomotor CPG reciprocally activating flexor and extensor muscles. Using software AnimatLab [2] we developed a 5-segment cat hindlimb model with 12 Hill-type muscle actuators controlled by (1) a half-center CPG activating flexor and extensor muscles (two-joint muscles received both flexion- and extension-related signals [5,6]) and (2) proprioceptive input originated from the muscle spindle and Golgi tendon organ afferents. The CPG was modeled by two single-compartment spiking neurons in a half-center configuration. Other neurons (Ia-afferents, alpha-motor neurons, Ia-interneurons, and interneurons mediating autogenic and heterogenic reflex pathways) were modeled as non-spiking neurons (firing rate model based on work by [1]). Model parameters were adjusted such that computer simulations reproduced the recorded paw-shake mechanics and the anterior-posterior muscle activation patterns. The obtained results demonstrated that a half-center locomotor CPG can produce movement mechanics and muscle activity patterns typical for paw-shake responses if (1) the locomotor CPG is capable to operate at frequencies 3 to10 times higher than during locomotion and (2) synaptic weights in spinal circuits can be modified during paw-shake response. We speculate that the two conditions can be realized by sensory input from paw skin afferents.

Control of Cat Walking and Paw-Shake by a Multifunctional Central Pattern Generator

Central pattern generators (CPGs) are oscillatory neuronal networks controlling rhythmic motor behaviors such as swimming, walking, and breathing. Multifunctional CPGs are capable of producing multiple patterns of rhythmic activity with different periods. Here, we investigate whether two cat rhythmic motor behaviors, walking and paw-shaking, could be controlled by a single multifunctional CPG. To do this, we have created a parsimonious model of a half-center oscillator composed of two mutually inhibitory neurons. Two basic activity regimes coexist in this model: fast 10 Hz paw-shake regime and a slow 2 Hz walking regime. It is possible to switch from paw-shaking to walking with a short pulse of conductance in one neuron, and it is possible to switch from walking to paw-shaking with a longer pulse of excitatory conductance in both neurons. The paw-shake and walking rhythms generated by the CPG model were used as input to a neuromechanical model of the cat hindlimbs to simulate the corresponding rhythmic behaviors. Simulation results demonstrated that the multifunctional half-center locomotor CPG could produce movement mechanics and muscle activity patterns typical for cat walking or paw-shake responses if synaptic weights in selected spinal circuits were altered during each behavior. We propose that the selection of CPG regimes and spinal circuitry is triggered by sensory input from paw skin afferents.

Multifunctional central pattern generator controlling walking and paw shaking

Central pattern generators (CPGs) are oscillatory neuronal networks controlling rhythmic motor tasks such as breathing and walking. A multifunctional CPG can produce multiple patterns, e.g. patterns with different periods [1-5]. Here, we investigate whether a pair of cat behaviors -- walking and paw shaking -- could be controlled by a single multifunctional CPG exhibiting multistability of oscillatory regimes. In experiments, both behaviors can be elicited in a spinalized cat, and there is evidence that the same circuitry is used for both rhythms [2,3]. We present a parsimonious model of a half-center oscillator composed of two mutually inhibitory neurons. These cells contains two slowly inactivating inward currents, a persistent Na+ current (INaP) and a low voltage activated Ca++ current (ICaLVA). The dynamics of the multifunctional CPG is based on that the ICaLVA inactivates much slower than INaP and at the more hyperpolarized membrane potentials. Here, we demonstrate the co-existence of two rhythms (Figure ​(Figure1).1). At first, the model demonstrates walking pattern. A switch from a slow, 1-2 Hz walking rhythm to fast, 7-10 Hz paw shake rhythm was elicited by a pulse of conductance of excitatory current delivered to extensor and flexor neurons. Then, a switch back to walking was triggered by a shorter pulse of conductance of inhibitory current delivered to the extensor neuron. Figure 1 Two mutually inhibitory interneurons, IntE (Extensor Interneuron) and IntF (Flexor Interneuron) produce alternating bursting activity at approximately 1.6 Hz representing walking pattern. A switch to paw shaking is executed by a pulse of excitatory conductance ... The CPG model was also incorporated into a neuromechanical model of a cat hindlimb in the AnimatLab environment [6]. The model provides a cellular mechanism of multifunctional CPG operation.

A neuromechanical computational model of spinal control of locomotion

We developed a neuromechanical computational model of cat locomotion that simulated the locomotor movements of cat hindlimbs controlled by spinal locomotor central pattern generators (CPGs, one per limb). In the closed-loop model, CPG operation was adjusted by afferent feedback from the hindlimbs. The CPG model was based on the previous two-level model [4] and included a half-center rhythm generator (RG), producing alternating flexor and extensor activities, and a pattern formation (PF) network operating under control of RG and controlling the synergetic activities of different hindlimb motoneuron pools. This basic model [4] was extended by incorporating additional neural circuits at the PF level allowing the CPG to generate the complex activity patterns of motoneurons controlling two-joint muscles. The model included reflex circuits, mediating reciprocal inhibition between antagonistic motoneurons, recurrent inhibition of motoneurons via Renshaw cells, and di-synaptic excitation of extensors by extensor afferents during stance phase of locomotion. The hindlimbs with the pelvis and trunk were modeled as a 10 degree-of-freedom sagittal plane system of rigid segments interconnected by frictionless revolute joints. The hindlimb interactions with the ground and other body segments were modeled as linear springs and dampers [1,2]. The two hindlimbs were driven by 18 muscle actuators representing major hindlimb muscles in the cat. The dynamics of each muscle-tendon unit was described by a Hill-type model extended to account for muscle mass, pennation angle, and force-length-velocity properties of muscle and tendon [1,2]. All muscles generated motion-dependent afferent signals which were calculated as functions of muscle length, velocity and force using modified regression equations from [3]. Parameters of the musculoskeletal model were identified by minimizing a mismatch between the computed (based on the recorded hindlimb muscle activity) and experimentally recorded changes in the joint angles, joint moments and ground reaction forces using the simulated annealing optimization algorithm [1,2]. The developed neuromechanical model demonstrated stable locomotion and exhibited realistic patterns of muscle activation, limb kinematics, and ground reaction force dynamics. The model was used for investigation of the role of afferent feedback and the CPG in control of locomotion under different conditions.

A Prototype of a Neural, Powered, Transtibial Prosthesis for the Cat: Benchtop Characterization

We developed a prototype of a neural, powered, transtibial prosthesis for the use in a feline model of prosthetic gait. The prosthesis was designed for attachment to a percutaneous porous titanium implant integrated with bone, skin, and residual nerves and muscles. In the benchtop testing, the prosthesis was fixed in a testing rig and subjected to rhythmic vertical displacements and interactions with the ground at a cadence corresponding to cat walking. Several prosthesis functions were evaluated. They included sensing ground contact, control of transitions between the finite states of prosthesis loading, and a closed-loop modulation of the linear actuator gain in each loading cycle. The prosthetic design parameters (prosthesis length = 55 mm, mass = 63 g, peak extension moment = 1 Nm) corresponded closely to those of the cat foot-ankle with distal shank and the peak ankle extension moment during level walking. The linear actuator operated the prosthetic ankle joint using inputs emulating myoelectric activity of residual muscles. The linear actuator gain was modulated in each cycle to minimize the difference between the peak of ground reaction forces (GRF) recorded by a ground force sensor and a target force value. The benchtop test results demonstrated a close agreement between the GRF peaks and patterns produced by the prosthesis and by cats during level walking.

Computing Motion Dependent Afferent Activity During Cat Locomotion Using a Forward Dynamics Musculoskeletal Model

The structure and function of mammalian locomotor central pattern generators (CPGs) and their control by afferent feedback in vivo are not completely understood. The aim of this study was to develop a forward dynamics model of cat hindlimbs that using neural or muscle activity as input generates realistic locomotion mechanics and motion-dependent afferent activity. This model can be combined with CPG models to study the spinal control of locomotion using a comprehensive closed-loop neuromechanical model. The developed planar, 10-DOF model of two cat hindlimbs with 18 Hill-type muscle actuators generated realistic walking mechanics and firing rates of muscle type Ia, Ib, II and paw pad cutaneous afferents matching experimental results. The afferent activities were obtained from computed muscle fiber length and velocity, tendon force and simplified relationships transforming these mechanical variables to the afferent firing rates. The computed afferent signals were consistent with their suggested role in triggering locomotor phase transitions.