The discharge frequencies of primary muscle spindle endings during simultaneous stimulation of two fusimotor filaments

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.

Experiments and models of sensorimotor interactions during locomotion

During locomotion sensory information from cutaneous and muscle receptors is continuously integrated with the locomotor central pattern generator (CPG) to generate an appropriate motor output to meet the demands of the environment. Sensory signals from peripheral receptors can strongly impact the timing and amplitude of locomotor activity. This sensory information is gated centrally depending on the state of the system (i.e., rest vs. locomotion) but is also modulated according to the phase of a given task. Consequently, if one is to devise biologically relevant walking models it is imperative that these sensorimotor interactions at the spinal level be incorporated into the control system.

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

Skeletofusimotor (beta) motoneurons innervate both extrafusal muscle units and muscle fibers within muscle spindle stretch receptors. By receiving excitation from group Ia muscle spindle afferents and driving the muscle spindle afferents that excite them, they form a positive feedback loop of unknown function. To study it, we developed a computationally efficient model of group Ia afferent behavior, capable of responding to multiple fusimotor inputs, that matched experimental data. This spindle model was then incorporated into a simulation of group Ia feedback during ramp/hold and triangular stretches with and without closure of the beta loop, assuming that gamma and beta fusimotor drives of the same type (static or dynamic) have identical effects on spindle afferent firing. The effects of beta feedback were implemented by driving a fusimotor input with a delayed and filtered fraction of the spindle afferent output. During triangular stretches, feedback through static beta motoneurons enhanced Ia afferent firing during shortening of the spindle. In contrast, closure of a dynamic beta loop increased Ia firing during lengthening. The strength of beta feedback, estimated as a "loop gain" was comparable to experimental estimates. The loop gain increased with velocity and amplitude of stretch but decreased with increased superimposed gamma fusimotor rates. The strongest loop gains were seen when the beta loop and the gamma bias were of different types (static vs. dynamic).

Models of ensemble firing of muscle spindle afferents recorded during normal locomotion in cats

1. The aim of this work was to compare the ability of several mathematical models to predict the firing characteristics of muscle spindle primary afferents recorded chronically during normal stepping in cats. 2. Ensemble firing profiles of nine hamstring spindle primary (presumed group Ia) afferents were compiled from stored data from 132 step cycles. Three sets of profiles corresponding to slow, medium and fast steps were generated by averaging groups of step cycles aligned to peak muscle length in each cycle. 3. Five models obtained from the literature were compared. Each of these models was used to predict the spindle firing profiles from the averaged muscle length signals. The models were also used in the reverse direction, namely to predict muscle length from the firing profiles. A sixth model incorporating some key aspects of the other models was also included in the comparisons. 4. Five of the models predicted spindle firing well, with root mean square (r.m.s.) errors lower than 14 % of the modulation depth of the target profiles. The key variable in achieving good predictions was muscle velocity, the best fits being obtained with power-law functions of velocity, with an exponent of 0.5 or 0.6 (i.e. spindle firing rate is approximately proportional to the square root of muscle velocity). The fits were slightly improved by adding small components of EMG signal to mimic fusimotor action linked to muscle activation. The modest relative size of EMG-linked fusimotor action may be related to the fact that hamstring muscles are not strongly recruited in stepping. 5. Length was predicted very accurately from firing profiles with the inverse of the above models, indicating that the nervous system could in principle process spindle firing in a relatively simple way to give accurate information on muscle length. 6. The responses of the models to standard ramp-and-hold displacements at 10 mm s-1 were also studied (i.e. velocities that were an order of magnitude lower than that during stepping). In these cases components of spindle primary response related to length as well as velocity were needed for good fits. Because these length-related components detracted from rather than improved predictions of the step cycle data, an attenuation of length dependence at high muscle velocities emerged as a possibility. 7. We conclude that in this study we have identified models and parameters that may be used to predict spindle afferent firing from the time course of muscle length in the cat step cycle.

Static and dynamic fusimotor controls in various hindlimb muscles during locomotor activity in the decorticate cat

During stereotyped locomotor movements of the acute decorticate (thalamic) cate, the static and dynamic fusimotor actions upon spindles of various hindlimb muscles were studied in relation to extrafusal activities. For this purpose, the rhythmic alterations in the responses of spindle endings to appropriate repetitive stretches were analyzed. Co-activation of alpha motoneurones with static and dynamic fusimotor neurones throughout the locomotor cycle was demonstrated. Quantitative differences were found between the fusimotor influences on spindles of various muscle groups. The static action was stronger than the dynamic one in pure flexor muscles; a predominantly dynamic action occurred in pure extensor ones while both actions were balanced in proximal bifunctional muscles. These results are discussed in relation to the known characteristics of fusimotor innervation and to the control of locomotor movement.

Static and dynamic fusimotor interaction and the possibility of multiple pace-makers operating in the cat muscle spindle

The interaction of static and dynamic fusimotor activation on the firing of primary muscle spindle afferents has been studied in the cat soleus muscle at constant length and during sinusoidal stretching. Cycle histogram analysis revealed summation of static and dynamic action during the peak of the afferent response to sinusoidal stretching, while static action completely occluded the dynamic effect during the trough of the response. Occlusion was complete as long as, for single fusimotor activation, the static-induced trough response exceeded the dynamic-induced one by about 25%. The investigation of inter-spike interval distributions obtained at constant muscle length revealed occlusion of dynamic by static action in 8 out of 13 cases. A model of multiple spike generation in primary spindle afferents is considered which is based on two or more pacemakers arranged in parallel, with a common pacemaker in series.