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.

A geometry- and muscle-based control architecture for synthesising biological movement.

A key problem for biological motor control is to establish a link between an idea of a movement and the generation of a set of muscle-stimulating signals that lead to the movement execution. The number of signals to generate is thereby larger than the body's mechanical degrees of freedom in which the idea of the movement may be easily expressed, as the movement is actually executed in this space. A mathematical formulation that provides a solving link is presented in this paper in the form of a layered, hierarchical control architecture. It is meant to synthesise a wide range of complex three-dimensional muscle-driven movements. The control architecture consists of a 'conceptional layer', where the movement is planned, a 'structural layer', where the muscles are stimulated, and between both an additional 'transformational layer', where the muscle-joint redundancy is resolved. We demonstrate the operativeness by simulating human stance and squatting in a three-dimensional digital human model (DHM). The DHM considers 20 angular DoFs and 36 Hill-type muscle-tendon units (MTUs) and is exposed to gravity, while its feet contact the ground via reversible stick-slip interactions. The control architecture continuously stimulates all MTUs ('structural layer') based on a high-level, torque-based task formulation within its 'conceptional layer'. Desired states of joint angles (postural plan) are fed to two mid-level joint controllers in the 'transformational layer'. The 'transformational layer' communicates with the biophysical structures in the 'structural layer' by providing direct MTU stimulation contributions and further input signals for low-level MTU controllers. Thereby, the redundancy of the MTU stimulations with respect to the joint angles is resolved, i.e. a link between plan and execution is established, by exploiting some properties of the biophysical structures modelled. The resulting joint torques generated by the MTUs via their moment arms are fed back to the conceptional layer, closing the high-level control loop. Within our mathematical formulations of the Jacobian matrix-based layer transformations, we identify the crucial information for the redundancy solution to be the muscle moment arms, the stiffness relations of muscle and tendon tissue within the muscle model, and the length-stimulation relation of the muscle activation dynamics. The present control architecture allows the straightforward feeding of conceptional movement task formulations to MTUs. With this approach, the problem of movement planning is eased, as solely the mechanical system has to be considered in the conceptional plan.

Comparative Study of a Biomechanical Model-based and Black-box Approach for Subject-Specific Movement Prediction.

The performance and safety of human robot interaction (HRI) can be improved by using subject-specific movement prediction. Typical models include biomechanical (parametric) or black-box (non-parametric) models. The current work aims to investigate the benefits and drawbacks of these approaches by comparing elbow-joint torque predictions based on electromyography signals of the elbow flexors and extensors. To this end, a parameterized biomechanical model is compared to a non-parametric (Gaussian-process) approach. Both models showed adequate results in predicting the elbow-joint torques. While the non-parametric model requires minimal modeling effort, the parameterized biomechanical model can lead to deeper insight of the underlying subject specific musculoskeletal system.