From muscle spindle to spinal cord : a modelling approach of the hierarchical organization in sensorimotor control

Abstract

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. The performance of new studies that consider different structures of the hierarchical sensorimotor control system, implementing physiologically-motivated neuromechanical models aligned to proprioception, is essential to enable a more holistic understanding about movement. The incorporation of more biological proprioceptive and neuronal circuit models to muscles can make neuro-musculoskeletal systems more appropriate to investigate and elucidate motor control. Therefore, initially, this doctoral dissertation presents a more physiological model of the muscle spindle that considers the individual characteristics of involved tissue compartments, aligned to the advantage of easy integration into large-scale musculoskeletal models. Different stretches in the intrafusal fibers were simulated in the model's variations following the spindle afferent recorded in previous experiments in feline soleus muscle. Additionally, the proposed enhanced Hill-type spindle 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 model exhibits a stable and valid prediction of experimentally observed muscle spindle responses. At the same time, it presents a well-tuned Hill-type model as muscle spindle fibers – accounting for real sarcomere force-length and force-velocity aspects - and its activation dynamics is similar to the one applied to Hill-type model for extrafusal fibers, making it more easily integrated in multi-body simulations. Furthermore, this dissertation aims to demonstrate that the afferent firings from the muscle spindle model can be processed by neuronal networks and are important for motor control. Hence, the spindle model was integrated to a previous implemented extrafusal fiber model, inside of the demoa multi-body simulation framework. This structure composed by extrafusal (muscle) and intrafusal (spindle) fibers replaced the muscle-tendon units (MTUs) of a prior developed arm model composed by two degrees of freedom and six MTUs, into the same simulation framework. Additionally, a spinal cord model, based on literature, was implemented in the Nest spiking neural network simulator. The spinal network has 6 neurons per muscle - alpha, dynamic gamma and static gamma motoneurons, together with Ia, propriospinal and Renshaw interneurons – and their respective physiological connections. The coupling between demoa and Nest simulators was implemented using a Cython interface. The spinal cord network - in its two variations of complete and simpler circuitry (including only Renshaw pathway, without spindle proprioception) - had its synaptic weights optimized to perform a center-out reaching task using the musculoskeletal model, without and with perturbation (increment of lower arm segment in 1 kg). As result, the complete spinal cord circuitry learned how to successfully reach all the evaluated targets without and with perturbation, demonstrating the sensorimotor control learning in the environment formed from muscle spindle to spinal circuitry, encompassing the two simulators. On the other hand, the simpler spinal cord circuitry did not succeed in the task of reach all the targets, also demonstrating reduced performance with perturbation. Moreover, the spindle afferent synapses in the complete circuitry were intensified for the higher targets (considered more difficult under gravity) when comparing the scenarios without and with perturbation. Therefore, the muscle spindle connections were strengthened for difficult targets under perturbation, highlighting the importance of spindle proprioception in these more difficult scenarios, as well as indicated by the circuitry that does not consider proprioception and did not show a similar successful performance. Finally, this dissertation offers a novel possibility of neuro-musculoskeletal modelling environment formed with demoa and Nest simulators. Future outlook includes the integration of the musculoskeletal and spinal cord models with higher-level models of Central Nervous System, aligned to further sophisticated details of the current modelling, to allow a more comprehensive understanding of sensorimotor behavior.