The Simultaneous Model-Based Estimation of Joint, Muscle, and Tendon Stiffness is Highly Sensitive to the Tendon Force-Strain Relationship.

OBJECTIVE: Accurate estimation of stiffness across anatomical levels (i.e., joint, muscle, and tendon) in vivo has long been a challenge in biomechanics. Recent advances in electromyography (EMG)-driven musculoskeletal modeling have allowed the non-invasive estimation of stiffness during dynamic joint rotations. Nevertheless, validation has been limited to the joint level due to a lack of simultaneous in vivo experimental measurements of muscle and tendon stiffness. METHODS: With a focus on the triceps surae, we employed a novel perturbation-based experimental technique informed by dynamometry and ultrasonography to derive reference stiffness at the joint, muscle, and tendon levels simultaneously. Here, we propose a new EMG-driven model-based approach that does not require external joint perturbation, nor ultrasonography, to estimate multi-level stiffness. We present a novel set of closed-form equations that enables the person-specific tuning of musculoskeletal parameters dictating biological stiffness, including passive force-length relationships in modeled muscles and tendons. RESULTS: Calibrated EMG-driven musculoskeletal models estimated the reference data with average normalized root-mean-square error ≈ 20%. Moreover, only when calibrated tendons were approximately four times more compliant than typically modeled, our approach could estimate multi-level reference stiffness. CONCLUSION: EMG-driven musculoskeletal models can be calibrated on a larger set of reference data to provide more realistic values for the biomechanical variables across multiple anatomical levels. Moreover, the tendon models that are typically used in musculoskeletal modeling are too stiff. SIGNIFICANCE: Calibrated musculoskeletal models informed by experimental measurements give access to an augmented range of biomechanical variables that might not be easily measured with sensors alone.

Electromyography-driven model-based estimation of ankle torque and stiffness during dynamic joint rotations in perturbed and unperturbed conditions.

The simultaneous modulation of joint torque and stiffness enables humans to perform large repertoires of movements, while versatilely adapting to external mechanical demands. Multi-muscle force control is key for joint torque and stiffness modulation. However, the inability to directly measure muscle force in the intact moving human prevents understanding how muscle force causally links to joint torque and stiffness. Joint stiffness is predominantly estimated via joint perturbation-based experiments in combination with system identification techniques. However, these techniques provide joint-level stiffness estimations with no causal link to the underlying muscle forces. Moreover, the need for joint perturbations limits the generalizability and applicability to study natural movements. Here, we present an electromyography (EMG)-driven musculoskeletal modeling framework that can be calibrated to match reference joint torque and stiffness profiles simultaneously via a multi-term objective function. EMG-driven models calibrated on <2 s of reference torque and stiffness data could blindly estimate reference profiles across 100 s of data not used for calibration. Model calibrations using an objective function comprising torque and stiffness terms always provided less feasible solutions than an objective function comprising solely a torque term, thereby reducing the space of feasible muscle-tendon parameters. Results also showed the proposed framework's ability to estimate joint stiffness in unperturbed conditions, while capturing differences against stiffness profiles derived during perturbed conditions. The proposed framework may provide new ways for studying causal relationships between muscle force and joint torque and stiffness during movements in interaction with the environment, with broad implications across biomechanics, rehabilitation and robotics.

Estimation of Time-Varying Ankle Joint Stiffness Under Dynamic Conditions via System Identification Techniques.

An important goal in the design of next-generation exoskeletons and limb prostheses is to replicate human limb dynamics. Joint impedance determines the dynamic relation between joint displacement and torque. Joint stiffness is the position-dependent component of joint impedance and is key in postural control and movement. However, the mechanisms to modulate joint stiffness are not fully understood yet. The goal of this study is to conduct a systematic analysis on how humans modulate ankle stiffness. Time-varying stiffness was estimated for six healthy subjects under isometric, as well as quick and slow dynamic conditions via system identification techniques; specifically, an ensemble-based algorithm using short segments of ankle torque and position recordings. Our results show that stiffness had the lowest magnitude under quick dynamic conditions. Under isometric conditions, with fixed position and varying muscle activity, stiffness exhibited a higher magnitude. Finally, under slow dynamic conditions, stiffness was found to be the highest. Our results highlight, for the first time, the variability in stiffness modulation strategies across conditions, especially across movement velocity.

Model-Based Estimation of Ankle Joint Stiffness During Dynamic Tasks: a Validation-Based Approach.

Joint stiffness estimation under dynamic conditions still remains a challenge. Current stiffness estimation methods often rely on the external perturbation of the joint. In this study, a novel 'perturbation-free' stiffness estimation method via electromyography (EMG)-driven musculoskeletal modeling was validated for the first time against system identification techniques. EMG signals, motion capture, and dynamic data of the ankle joint were collected in an experimental setup to study the ankle joint stiffness in a controlled way, i.e. at a movement frequency of 0.6 Hz as well as in the presence and absence of external perturbations. The model-based joint stiffness estimates were comparable to system identification techniques. The ability to estimate joint stiffness at any instant of time, with no need to apply joint perturbations, might help to fill the gap of knowledge between the neural and the muscular systems and enable the subsequent development of tailored neurorehabilitation therapies and biomimetic prostheses and orthoses.