Spindle model responsive to mixed fusimotor inputs and testable predictions of beta feedback effects

A physiologically enhanced muscle spindle model: using a Hill-type model for extrafusal fibers as template for intrafusal fibers

The muscle spindle is an essential proprioceptor, significantly involved in sensing limb position and movement. Although biological spindle models exist for years, the gold-standard for motor control in biomechanics are still sensors built of homogenized spindle output models due to their simpler combination with neuro-musculoskeletal models. Aiming to improve biomechanical simulations, this work establishes a more physiological model of the muscle spindle, aligned to the advantage of easy integration into large-scale musculoskeletal models. We implemented four variations of a spindle model in Matlab/Simulink®: the Mileusnic et al. (2006) model, Mileusnic model without mass, our enhanced Hill-type model, and our enhanced Hill-type model with parallel damping element (PDE). Different stretches in the intrafusal fibers were simulated in all model variations following the spindle afferent recorded in previous experiments in feline soleus muscle. Additionally, the enhanced Hill-type models had their parameters extensively optimized to match the experimental conditions, and the resulting model was validated against data from rats' triceps surae muscle. As result, the Mileusnic models present a better overall performance generating the afferent firings compared to the common data evaluated. However, the enhanced Hill-type model with PDE exhibits a more stable performance than the original Mileusnic model, at the same time that presents a well-tuned Hill-type model as muscle spindle fibers, and also accounts for real sarcomere force-length and force-velocity aspects. Finally, our activation dynamics is similar to the one applied to Hill-type model for extrafusal fibers, making our proposed model more easily integrated in multi-body simulations.

Calcium-binding protein parvalbumin in the spinal cord and dorsal root ganglia

Parvalbumin is one of the calcium-binding proteins. In the spinal cord, it is mainly expressed in inhibitory neurons; in the dorsal root ganglia, it is expressed in proprioceptive neurons. In contrast to in the brain, weak systematization of parvalbumin-expressing neurons occurs in the spinal cord. The aim of this paper is to provide a systematic review of parvalbumin-expressing neuronal populations throughout the spinal cord and the dorsal root ganglia of mammals, regarding their mapping, co-expression with some functional markers. The data reviewed are mostly concerning rodentia species because they are predominantly presented in literature.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

Control of Mammalian Locomotion by Somatosensory Feedback

When animals walk overground, mechanical stimuli activate various receptors located in muscles, joints, and skin. Afferents from these mechanoreceptors project to neuronal networks controlling locomotion in the spinal cord and brain. The dynamic interactions between the control systems at different levels of the neuraxis ensure that locomotion adjusts to its environment and meets task demands. In this article, we describe and discuss the essential contribution of somatosensory feedback to locomotion. We start with a discussion of how biomechanical properties of the body affect somatosensory feedback. We follow with the different types of mechanoreceptors and somatosensory afferents and their activity during locomotion. We then describe central projections to locomotor networks and the modulation of somatosensory feedback during locomotion and its mechanisms. We then discuss experimental approaches and animal models used to investigate the control of locomotion by somatosensory feedback before providing an overview of the different functional roles of somatosensory feedback for locomotion. Lastly, we briefly describe the role of somatosensory feedback in the recovery of locomotion after neurological injury. We highlight the fact that somatosensory feedback is an essential component of a highly integrated system for locomotor control. © 2021 American Physiological Society. Compr Physiol 11:1-71, 2021.

A leg to stand on: computational models of proprioception

Dexterous motor control requires feedback from proprioceptors, internal mechanosensory neurons that sense the body's position and movement. An outstanding question in neuroscience is how diverse proprioceptive feedback signals contribute to flexible motor control. Genetic tools now enable targeted recording and perturbation of proprioceptive neurons in behaving animals; however, these experiments can be challenging to interpret, due to the tight coupling of proprioception and motor control. Here, we argue that understanding the role of proprioceptive feedback in controlling behavior will be aided by the development of multiscale models of sensorimotor loops. We review current phenomenological and structural models for proprioceptor encoding and discuss how they may be integrated with existing models of posture, movement, and body state estimation.

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state-of-the-art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub-models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Focal Vibration Stretches Muscle Fibers by Producing Muscle Waves

Focal vibration is an effective intervention for the management of spasticity. However, its neuromechanical effects, particularly how tonic vibration reflex is induced explicitly, remain implicit. In this paper, we utilize a high-speed camera and a method of image processing to quantify the muscle vibration rigorously and disclose the neuromechanical mechanism of focal vibration. The vibration of 75 Hz is applied on the muscle belly of the biceps brachii and muscle responses are captured by a high-speed camera in profile. The muscle silhouettes are identified by the Canny edge detector to represent the stretch of muscle fibers, and the consistency between the muscle stretch and profile deformation has been confirmed by the magnetic resonance imaging in advance. Oscillations of muscle points discretized by pixels are identified by the fast Fourier transformation, respectively, and results demonstrate that focal vibration stretches muscle by producing muscle waves. Specifically, each point vibrates harmonically, and, given the linear phase modulation with transverse position, the muscle vibration propagates as traveling waves. The propagation of muscle waves is associated with muscle stretch, whose frequency is the same with the vibrator due to the curved baseline, and thus induces the tonic vibration reflex via spinal circuits.

Microneurography as a tool to develop decoding algorithms for peripheral neuro-controlled hand prostheses

BACKGROUND

The usability of dexterous hand prostheses is still hampered by the lack of natural and effective control strategies. A decoding strategy based on the processing of descending efferent neural signals recorded using peripheral neural interfaces could be a solution to such limitation. Unfortunately, this choice is still restrained by the reduced knowledge of the dynamics of human efferent signals recorded from the nerves and associated to hand movements.

FINDINGS

To address this issue, in this work we acquired neural efferent activities from healthy subjects performing hand-related tasks using ultrasound-guided microneurography, a minimally invasive technique, which employs needles, inserted percutaneously, to record from nerve fibers. These signals allowed us to identify neural features correlated with force and velocity of finger movements that were used to decode motor intentions. We developed computational models, which confirmed the potential translatability of these results showing how these neural features hold in absence of feedback and when implantable intrafascicular recording, rather than microneurography, is performed.

CONCLUSIONS

Our results are a proof of principle that microneurography could be used as a useful tool to assist the development of more effective hand prostheses.

Proprioceptive Recognition with Artificial Neural Networks Based on Organizations of Spinocerebellar Tract and Cerebellum

Muscle kinematics and kinetics are nonlinearly encoded by proprioceptors, and the changes in muscle length and velocity are integrated into Ia afferent. Besides, proprioceptive signals from multiple muscles are probably mixed in afferent pathways, which all lead to difficulties in proprioceptive recognition for the cerebellum. In this study, the artificial neural networks, whose organizations are biologically based on the spinocerebellar tract and cerebellum, are utilized to decode the proprioceptive signals. Consistent with the controversy of the proprioceptive division in the dorsal spinocerebellar tract, the spinocerebellar tract networks incorporated two distinct inferences, (1) the centralized networks, which mixed Ia, II, and Ib and processed them together; (2) the decentralized networks, which processed Ia, II, and Ib afferents separately. The cerebellar networks were based on the Marr-Albus model to recognize the kinematic states. The networks were trained by a specific movement, and the trained networks were subsequently required to predict kinematic states of six movements. The results demonstrated that the centralized networks, which were more consistent with the physiological findings in recent years, had better recognition accuracy than the decentralized networks, and the networks were still effective even when proprioceptive afferents from multiple muscles were integrated.

Proprioceptive Feedback through a Neuromorphic Muscle Spindle Model

Connecting biologically inspired neural simulations to physical or simulated embodiments can be useful both in robotics, for the development of a new kind of bio-inspired controllers, and in neuroscience, to test detailed brain models in complete action-perception loops. The aim of this work is to develop a fully spike-based, biologically inspired mechanism for the translation of proprioceptive feedback. The translation is achieved by implementing a computational model of neural activity of type Ia and type II afferent fibers of muscle spindles, the primary source of proprioceptive information, which, in mammals is regulated through fusimotor activation and provides necessary adjustments during voluntary muscle contractions. As such, both static and dynamic γ-motoneurons activities are taken into account in the proposed model. Information from the actual proprioceptive sensors (i.e., motor encoders) is then used to simulate the spindle contraction and relaxation, and therefore drive the neural activity. To assess the feasibility of this approach, the model is implemented on the NEST spiking neural network simulator and on the SpiNNaker neuromorphic hardware platform and tested on simulated and physical robotic platforms. The results demonstrate that the model can be used in both simulated and real-time robotic applications to translate encoder values into a biologically plausible neural activity. Thus, this model provides a completely spike-based building block, suitable for neuromorphic platforms, that will enable the development of sensory-motor closed loops which could include neural simulations of areas of the central nervous system or of low-level reflexes.

A review of human sensory dynamics for application to models of driver steering and speed control

In comparison with the high level of knowledge about vehicle dynamics which exists nowadays, the role of the driver in the driver-vehicle system is still relatively poorly understood. A large variety of driver models exist for various applications; however, few of them take account of the driver's sensory dynamics, and those that do are limited in their scope and accuracy. A review of the literature has been carried out to consolidate information from previous studies which may be useful when incorporating human sensory systems into the design of a driver model. This includes information on sensory dynamics, delays, thresholds and integration of multiple sensory stimuli. This review should provide a basis for further study into sensory perception during driving.

The consequences of short-range stiffness and fluctuating muscle activity for proprioception of postural joint rotations: the relevance to human standing

Proprioception comes from muscles and tendons. Tendon compliance, muscle stiffness, and fluctuating activity complicate transduction of joint rotation to a proprioceptive signal. These problems are acute in postural regulation because of tiny joint rotations and substantial short-range muscle stiffness. When studying locomotion or perturbed balance these problems are less applicable. We recently measured short-range stiffness in standing and considered the implications for load stability. Here, using an appropriately simplified model we analyze the conversion of joint rotation to spindle input and tendon tension while considering the effect of short-range stiffness, tendon compliance, fluctuating muscle activity, and fusimotor activity. Basic principles determine that when muscle stiffness and tendon compliance are high, fluctuating muscle activity is the greatest factor confounding registration of postural movements, such as ankle rotations during standing. Passive and isoactive muscle, uncomplicated by active length fluctuations, enable much better registration of joint rotation and require fewer spindles. Short-range muscle stiffness is a degrading factor for spindle input and enhancing factor for Golgi input. Constant fusimotor activity does not enhance spindle registration of postural joint rotations in actively modulated muscle: spindle input remains more strongly associated with muscle activity than joint rotation. A hypothesized rigid alpha-gamma linkage could remove this association with activity but would require large numbers of spindles in active postural muscles. Using microneurography, the existence of a rigid alpha-gamma linkage could be identified from the correlation between spindle output and muscle activity. Basic principles predict a proprioceptive "dead zone" in the active agonist muscle that is related to the short-range muscle stiffness.

A comparison of resonance tuning with positive versus negative sensory feedback

We used a computational model of rhythmic movement to analyze how the connectivity of sensory feedback affects the tuning of a closed-loop neuromechanical system to the mechanical resonant frequency (omega(r)). Our model includes a Matsuoka half-center oscillator for a central pattern generator (CPG) and a linear, one-degree-of-freedom system for a mechanical component. Using both an open-loop frequency response analysis and closed-loop simulations, we compared resonance tuning with four different feedback configurations as the mechanical resonant frequency, feedback gain, and mechanical damping varied. The feedback configurations consisted of two negative and two positive feedback connectivity schemes. We found that with negative feedback, resonance tuning predominantly occurred when omega(r) was higher than the CPG's endogenous frequency (omega(CPG)). In contrast, with the two positive feedback configurations, resonance tuning only occurred if omega(r) was lower than omega(CPG). Moreover, the differences in resonance tuning between the two positive (negative) feedback configurations increased with increasing feedback gain and with decreasing mechanical damping. Our results indicate that resonance tuning can be achieved with positive feedback. Furthermore, we have shown that the feedback configuration affects the parameter space over which the endogenous frequency of the CPG or resonant frequency the mechanical dynamics dominates the frequency of a rhythmic movement.

Mathematical models of proprioceptors. I. Control and transduction in the muscle spindle

We constructed a physiologically realistic model of a lower-limb, mammalian muscle spindle composed of mathematical elements closely related to the anatomical components found in the biological spindle. The spindle model incorporates three nonlinear intrafusal fiber models (bag(1), bag(2), and chain) that contribute variously to action potential generation of primary and secondary afferents. A single set of model parameters was optimized on a number of data sets collected from feline soleus muscle, accounting accurately for afferent activity during a variety of ramp, triangular, and sinusoidal stretches. We also incorporated the different temporal properties of fusimotor activation as observed in the twitchlike chain fibers versus the toniclike bag fibers. The model captures the spindle's behavior both in the absence of fusimotor stimulation and during activation of static or dynamic fusimotor efferents. In the case of simultaneous static and dynamic fusimotor efferent stimulation, we demonstrated the importance of including the experimentally observed effect of partial occlusion. The model was validated against data that originated from the cat's medial gastrocnemius muscle and were different from the data used for the parameter determination purposes. The validation record included recently published experiments in which fusimotor efferent and spindle afferent activities were recorded simultaneously during decerebrate locomotion in the cat. This model will be useful in understanding the role of the muscle spindle and its fusimotor control during both natural and pathological motor behavior.

Active, non-spring-like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced?

In humans, during standing the calf muscles soleus and gastrocnemius actively prevent forward toppling about the ankles. It has been generally assumed that these postural muscles behave like springs with dynamic stiffness reflecting their mechanical properties, reflex gain including higher derivatives, and central control. Here, for the first time, we have used an ultrasound scanner and automated image analysis to record the tiny muscular movements occurring in normal standing. This new, non-invasive technique resolves changes in muscle length as small as 10 mum without disturbing the standing process. This technical achievement has allowed us to test the long-established mechano-reflex, muscle spring hypothesis that muscle length changes in a spring-like way during sway of the body. Our results contradict that hypothesis. Muscle length changes in a non-spring-like manner: on average, shortening during forward sway and lengthening during backwards sway (paradoxical movements). This counter-intuitive result is a consequence of the fact that calf muscles generate tension through a series elastic component (SEC, Achilles tendon and foot) which limits maximal ankle stiffness to 92 +/- 20% of that required to balance the body. Paradoxical movements cannot be generated by stretch reflexes with constant intrafusal drive but might be produced by reflex coupling of extrafusal (alpha) and intrafusal (beta, gamma) drive or by positive force feedback. Standing requires the predictive ability to produce the observed muscle movements preceded (110 +/- 50 ms) by corresponding changes in integrated EMG signal. We suggest higher level anticipatory control is more plausible.

Gamma→Alpha Linkage and Persistent Firing of Ia Fibers by Pudendal Nerve Stimulation in the Decerebrate Cat

The sensory pudendal nerve (SPN) was stimulated in decerebrate female cats. Spikes of single Ia muscle spindle afferents from the medial gastrocnemius (MG) muscle were recorded in dorsal root filaments. Electroneurography (ENG) was recorded in a cut nerve filament to the MG muscle; MG electromyography (EMG) was also recorded. Single shock to SPN induced discharges of small ENG spikes (SS) with similar amplitude to that of gamma spikes elicited by ventral root stimulation. Thus SS were identified as gamma spikes. The latency of the gamma discharge was ∼15 ms. As expected, the onset of the gamma discharge preceded a discharge of Ia spikes; the time difference between both discharges was ∼5 ms. After the initial bursts, the Ia and the gamma activities paused during 20–30 ms but later increased again to last ∼1 s. After the shock, the EMG activity was depressed during ∼50 ms; later, motor-unit spikes may show transient activation. Thus the onset of the gamma activation preceded the activation of motor units (gamma→alpha link). Trains of shocks (1 or 100 Hz) to SPN induced a sustained increase in the frequency of gamma spikes, Ia spikes, and motor units that outlasted the train by 20–120 s. The sustained firing of Ia fibers might trigger or help to trigger and maintain the response of alpha-motoneurons.