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.

'Falling heads': investigating reflexive responses to head-neck perturbations.

BACKGROUND: Reflexive responses to head-neck perturbations affect the injury risk in many different situations ranging from sports-related impact to car accident scenarios. Although several experiments have been conducted to investigate these head-neck responses to various perturbations, it is still unclear why and how individuals react differently and what the implications of these different responses across subjects on the potential injuries might be. Therefore, we see a need for both experimental data and biophysically valid computational Human Body Models with bio-inspired muscle control strategies to understand individual reflex responses better. METHODS: To address this issue, we conducted perturbation experiments of the head-neck complex and used this data to examine control strategies in a simulation model. In the experiments, which we call 'falling heads' experiments, volunteers were placed in a supine and a prone position on a table with an additional trapdoor supporting the head. This trapdoor was suddenly released, leading to a free-fall movement of the head until reflexive responses of muscles stopped the downwards movement. RESULTS: We analysed the kinematic, neuronal and dynamic responses for all individuals and show their differences for separate age and sex groups. We show that these results can be used to validate two simple reflex controllers which are able to predict human biophysical movement and modulate the response necessary to represent a large variability of participants. CONCLUSIONS: We present characteristic parameters such as joint stiffness, peak accelerations and latency times. Based on this data, we show that there is a large difference in the individual reflexive responses between participants. Furthermore, we show that the perturbation direction (supine vs. prone) significantly influences the measured kinematic quantities. Finally, 'falling heads' experiments data are provided open-source to be used as a benchmark test to compare different muscle control strategies and to validate existing active Human Body Models directly.

Optimality Principles in Human Point-to-Manifold Reaching Accounting for Muscle Dynamics.

Human arm movements are highly stereotypical under a large variety of experimental conditions. This is striking due to the high redundancy of the human musculoskeletal system, which in principle allows many possible trajectories toward a goal. Many researchers hypothesize that through evolution, learning, and adaption, the human system has developed optimal control strategies to select between these possibilities. Various optimality principles were proposed in the literature that reproduce human-like trajectories in certain conditions. However, these studies often focus on a single cost function and use simple torque-driven models of motion generation, which are not consistent with human muscle-actuated motion. The underlying structure of our human system, with the use of muscle dynamics in interaction with the control principles, might have a significant influence on what optimality principles best model human motion. To investigate this hypothesis, we consider a point-to-manifold reaching task that leaves the target underdetermined. Given hypothesized motion objectives, the control input is generated using Bayesian optimization, which is a machine learning based method that trades-off exploitation and exploration. Using numerical simulations with Hill-type muscles, we show that a combination of optimality principles best predicts human point-to-manifold reaching when accounting for the muscle dynamics.

Muscles Reduce Neuronal Information Load: Quantification of Control Effort in Biological vs. Robotic Pointing and Walking.

It is hypothesized that the nonlinear muscle characteristic of biomechanical systems simplify control in the sense that the information the nervous system has to process is reduced through off-loading computation to the morphological structure. It has been proposed to quantify the required information with an information-entropy based approach, which evaluates the minimally required information to control a desired movement, i.e., control effort. The key idea is to compare the same movement but generated by different actuators, e.g., muscles and torque actuators, and determine which of the two morphologies requires less information to generate the same movement. In this work, for the first time, we apply this measure to numerical simulations of more complex human movements: point-to-point arm movements and walking. These models consider up to 24 control signals rendering the brute force approach of the previous implementation to search for the minimally required information futile. We therefore propose a novel algorithm based on the pattern search approach specifically designed to solve this constraint optimization problem. We apply this algorithm to numerical models, which include Hill-type muscle-tendon actuation as well as ideal torque sources acting directly on the joints. The controller for the point-to-point movements was obtained by deep reinforcement learning for muscle and torque actuators. Walking was controlled by proprioceptive neural feedback in the muscular system and a PD controller in the torque model. Results show that the neuromuscular models consistently require less information to successfully generate the movement than the torque-driven counterparts. These findings were consistent for all investigated controllers in our experiments, implying that this is a system property, not a controller property. The proposed algorithm to determine the control effort is more efficient than other standard optimization techniques and provided as open source.